text: The rainbow darter Etheostoma caeruleum is a small fish in the perch family (Percidae) that is adapted to fast-flowing streams in eastern North America. It is relatively sensitive to habitat degradation and is widely used as a sentinel of stream condition. To provide a complementary tool for assessing the integrity of stream ecosystems, 16 highly polymorphic tetranucleotide microsatellite markers were identified for these darters. Between four and 16 loci were found to be useful in five congeneric species. These markers will be useful for characterizing population genetic structure and diversity of rainbow darters and related fishes.


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Published: 27 April 2010
A total of 2.3 million tonnes (57,000 TJ) of hard coal were consumed as fuel in the generation of electricity and heat in the January to March period of 2010. The consumption increased by 31 per cent from the previous year. Use of hard coal went up especially in separate production of electricity. The growth in the consumption was due to diminished production of hydro power from the year before.
Consumption of Hard Coal, million tonnes
In the first quarter of the year, the consumption of hard coal was a third up on the average for the 2000s. The consumption of hard coal was last this high in 2004.
The consumption of electricity increased by 7 per cent from the previous year. The consumption of electricity in industry, which was brought down by the economic downturn, began to rise again in the latter half of 2009 and the growth continued through the January-March period. The weather was also colder than in the year before, and this put electricity consumption up. At the same time the worse than average water situation lowered the production of hydro power in Finland in the first quarter.
Source: Since 2005 Statistics Finland, _PHONE_ Coal User's Committee/Finergy, Statistics Finland
Inquiries: Anssi Vuorio 09 _PHONE_, _EMAIL_
Director in charge: Leena Storgårds
Publication in pdf-format (191.9 kB)
Tables in databases

source: HuggingFaceFW/fineweb-edu


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There are 7+ studies on pubmed
- Associated with genital-tract disease in cattle.
- "In pure culture, strain CelloT could only grow on a variety of sugars. Glucose was converted to acetate, ethanol and H2. "
- common antibiotics appear to increase it
- " The antibiotics streptomycin and polymyxin B may be used to inhibit growth of contaminants."[Bergey's manual of Systematic Bacteriology, Volume 4] i.e. This genus is resistant to these antibiotics.
Note: This bacteria is hard to culture, which means testing of antibiotics to find an effective one very challenging.
- Polymyxin B

source: openbmb/Ultra-FineWeb


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Concerto for Orchestra
Although a concerto
is usually a piece of music
for one or more solo instruments
pitted against an orchestra
, several composers
have written works with the apparently contradictory title Concerto for Orchestra
. This title is usually chosen to emphasise soloistic and virtuosic treatment of the instruments of the orchestra.
The best known Concerto for Orchestra is the one by Béla Bartók (1943), although the title had been used several times before.
Concertos for Orchestra (in chronological order)
Goffredo Petrassi made the concerto for orchestra something of a speciality, writing eight of them since the 1930s.


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Mining the GEO database for perturbation data sets
Suitable for small one off analyses of less than 10 GSE.
Suitable for large and repeated analyses including many GSEs.
See and contribute to the source code.
What is GEOracle?
GEOracle is a R Shiny app that greatly speeds up the identification and processing of large numbers of perturbation microarray gene expression data sets from GEO. It uses text mining of the GEO metadata along with machine learning techniques to automatically:
- Identify perturbation GSEs
- Cluster GSM samples
- Label clusters as control or perturbation
- Pair each perturbation cluster with it's control.
- Identify the molecule that is being perturbed and the direction of perturbation.
It provides this information via an interactive interface that allows the user to verify and change the details of the perturbation experiments. The work flow is described below.
- Make sure you have an up to date version of R (3.3+) and the Shiny package installed.
- Download GEOracle and then unzip it somewhere permanent
- Open server.R or ui.R in RStudio
- Click 'Run App' in the top right corner of the screen
GEOracle will then attempt to install all neccessary packages and download the full database of metadata from GEO (~5GB of space required). Once complete GEOracle will open as a Shiny app in a web browser or as a new R studio window. The user can then upload a list of GSE IDs and begin the analysis.
GEOracle analysis steps
- The user uploads a list of GSE IDs (simple.txt file, one GSE ID per line)
- The metadata for each GSE will then be analysed and clustering / labelling / matching will occur.
- The user decides whether to use the default filters for which GSEs to process, or manually set desired filters, then click "COMPUTE".
- GEOracle will now try to detect the names of the perturbed molecules and direction of perturbation for each GSE that passes filtering.
- Once the GSE IDs appear in the "Processed GSEs" table, the user clicks them one by one to modify / verify / remove the comparisons.
- Once the user is happy with the details of every GSE, they click "NEXT STEP" and enter a desired output directory.
GEOracle will then automatically perform differential expression using the limma method as implemented in NCBI's GEO2R. As well as differential expression results GEOracle will output a list of edges that can be used to instantly build a causal gene regulatory network based on the set of input perturbation experiments. This edge list can be loaded straight into Cytoscape or R's igraph package.
If you are having trouble installing or running GEOracle, please follow the below troubleshooting tips
- GEOracle works best on a relatively clean install of R (3.3+). You can perform a clean install of the latest version of R without removing your old versions.
- The most common problems occur from trying to use GEOracle with older versions of R (<3.3). Because GEOracle uses the latest features from Shiny, you will need to update your R and other core packages which Shiny depends on.
- Some users also encounter problems installing or updating packages due to permissions. Package install problems occur with R fairly frequently and are best managed by doing a clean install of the latest R with full administrator privilages.
- Some users report memory / lag issues after extended periods of time using the tool. If you have a long list of GSE IDs try to split them up into chunks of ~50 and process them individually. This will improve efficiency and make sure you don't lose any information in the case of a crash (R or web browsser).
- There are many cases where GSEs will not be represented in the final output. GEOracle will automatically remove GSEs which do not cluster confidently, or where a matched perturbation and control cluster can not be identified. Similarly many GSEs will not show significant results when using a standard differential expression approach. If you think some GSEs that should be present are missing, check the filters that were used and check for significant results using GEO2R on the GEO website for that particular GSE.
This website is still under construction. Please contact _EMAIL_ with any queries


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Master of Science
Dr. Bryan Neff
With global temperatures projected to surpass the limits of thermal tolerance for many species, evaluating the capacity for evolutionary and phenotypically plastic changes in thermal tolerance is key to our understanding of the biological consequences of climate change. Within quantitative genetic breeding designs and multiple rearing environments, I measured the thermal performance of cardiac function among families of two populations of chinook salmon (Oncorhynchus tshawytscha). I found significant indirect genetic, plastic, and additive genetic effects contributing to cardiac performance and thermal tolerance, representing a variety of adaptive mechanisms available to salmon populations faced with climate change. These results enhance our understanding of the mechanisms of thermal adaptation in fish and suggest a resiliency to rising temperatures among these ecologically, economically, and culturally important fish.
Muñoz, Nicolas, "The adaptive capacity of thermal tolerance in chinook salmon" (2014). Electronic Thesis and Dissertation Repository. 2220.


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Study wrongly implies LED to blame for van Gogh masterpiece damage
16 January 2013 09.30 GMT
(Netherlands) - Scientists use old LED data to highlight why some yellow colours in Vincent van Gogh's paintings are turning brown due to lighting exposure. Findings sensationalised by mainstream press.
It has been known for some time that the light yellow tones in Vincent van Gogh's paintings are particularly prone to darkening, but now an international team of scientists have produced a report which suggests that the blue bandwidth in lighting could be to blame.
The experiments were apparently carried out using a Xenon lamp high in UV-A, UV-B, and UV-C wavelengths. Unfortunately the research group, which included scientists from the Van Gogh Museum in Amsterdam amongst others, chose to highlight the danger of LED lighting by publishing a spectral distribution chart from a six year old LED system with a particularly high blue bandwidth. The chart is labelled 'Emission spectrum of a typical "white" LED, containing a substantial portion of harmful blue light'.
Even more unfortunately, the report was jumped on by media all over the world printing misleading headlines that LEDs were harmful to van Gogh paintings. Articles quickly appeared in the Daily Mail and The Independent in the UK and the Huffington Post in the USA.
In the report they suggest that all LEDs have a high amount of blue. However, recent developments in museum grade warm white LEDs with high CRI have greatly reduced the amount of blue wavelength present meaning that the bandwidth is now much closer to the black body curve locus.
The paint changes have been blamed on a chemical reduction of chromium, the principle element found in the chrome yellow paint favoured by van Gogh to depict sunshine. However scientists' were left baffled as to the cause of the changes and as to why the darkening was more apparent on some canvases rather than others.
Using synchrotron X-rays to better understand the problem, Deutsches Elektronen-Synchrotron (DESY) in Germany and the European Synchrotron Radiation Facility (ESRF) in France examined an extensive series of van Gogh paintings belonging to three museums in the Netherlands (including the Van Gogh Museum) and France. Speck-sized paint fragments taken from the masterworks were examined at the two synchrotron facilities and two heritage labs in Italy and Holland.
It was concluded that the artist did not always use the same type of chrome yellow paint in his work. Van Gogh liked to use a standard lead chromate paint named 'middle yellow' but also, due to his poverty, utilised a cheaper 'lemon yellow' and 'primrose yellow' from time to time. It was these non regular types of paint that were found to be reactive to light in the lab.
The paints affected, which have been found in Van Gogh's famous 'Vase with Sunflowers' and the 'Portrait of Gauguin', tended to have a higher sulfate content, with the paint becoming unstable the higher the sulphate levels rose. When exposed to green-blue light those paints containing unstable levels of sulfate turned a brownish/yellow, while 'middle yellow' remained unaffected.
Claus Habfast of the European Synchrotron Radiation Facility in France, told the Independent newspaper in London: "LED lights appear to have many advantages but museums should carefully consider that paintings from the Van Gogh era could be affected by them."
Ella Hendriks, Head of Conservation at the Van Gogh Museum in Amsterdam also commented: "Studies like these are very important to make museum curators aware that, even under ambient light conditions, the degradation of some sensitive materials proceeds continuously. Musea should carefully consider the potential impact of, for example, the new, LED-based, lighting systems that are now being installed in collections."
However, Rogier van der Heide of Philips Lighting, who acts as a lighting consultant at the Van Gogh Museum and Rijksmuseum in Amsterdam, states: "The use of LED in museums is safe. It is regrettable that the research was published in such a way. The research was correct but the interpretation was wrong."
Martin Krautter of ERCO, who also manufacture LED lighting for museums, commented: "Paintings using very unstable pigments have to be treated with extreme caution. But to believe that there is a 'less dangerous' light source available for these paintings than modern warm white LED is quite ridiculous. If you want to stop degrading, put the paintings away into the dark!"
There is no evidence that LED light damages artwork across the board. Museums that hold works by Van Gogh and Paul Cezanne, who are known to have used the paint in question, are being asked to consider their use of lighting systems with high blue bandwidths when lighting works by Cezanne or Van Gogh and to check masterpieces with infra-red light for the presence of the paint.


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Beliefs and performance
The cognitions, or thought processes, in which an athlete engages may be critical to performance. A 1996 study by Williams and Leffingwell, Cognitive strategies in sport and exercise psychology, found several assumptions underlie the use of cognitive-behavioral inventions:
- Cognitions can affect athletic performance.
- These thought processes can be changed.
- This change can influence behavioral change, and therefore, improve performance.
They identified several areas of irrational beliefs that may affect an athlete's performance. In particular, they indicated that perfectionist demands may cause a poor self-concept or feelings of inadequacy, which increase the likelihood of failure. However, they distinguish between perfectionist demands and perfectionist desires indicating that a perfectionist desire, which is achievable and not judgmental, may increase the likelihood of success. Other irrational beliefs include:
- Considering failure a catastrophe
- Basing self-worth on achievement
- Focusing on fairness in competition
- Generalizing from a single performance to overall competence


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Gatön Ngawang Lekpa Series
Holding the oceanic treasury of the profound and secret aural lineage
Of the lords of speech, Mañjughoṣas of the Sakya tradition,
You are without equal in creating a feast of excellent explanation,
Glorious guru, at your feet I pray!
Texts by and about the Sakya lama Gatön Ngawang Lekpa (sga ston ngag dbang legs pa, 1867–1941) of Tharlam Monastery, one of the foremost Lamdré (lam 'bras) teachers of recent times:
This short light offering prayer (mar me'i smon lam) by Gatön Ngawang Lekpa, which is commonly recited in the Sakya tradition, encourages the practitioner to visualize a lamp that is as vast as the universe and that shines with the light of a billion suns, as the basis for infinite 'offering-clouds'.
Long Life Prayers
In these five verses, Ngawang Lekpa praises the body, speech, mind, qualities and activity of Ga Rabjampa, the great scholar and founder of Tharlam Monastery. The author incorporates the syllables of the master's name, Kunga Yeshe (meaning total joy and wisdom), into every verse.


Take the 2-minute tour ×
I have the question:
compute $\phi(24)$ for each element Z/24 decide whether the element is a unit or a zero divisor, if the element is a unit divisor give its order and find its inverse.
Ive worked out $\phi(24)=8$
and the unit divisors to be ${1,5,7,11,13,17,19,23}$
however when I came to working out the order I got them all to be 2?
share|improve this question
Presumably, you mean all but one of them has order 2. – Gerry Myerson Nov 28 '12 at 12:16
yupp bar the number 1, could you confirm ive answered it correctly or have i gone terribly wrong? – jill Nov 28 '12 at 12:18
_USER_ You can write $(\mathbb{Z}/24)^{\times} \cong (\mathbb{Z}/8)^{\times} \times (\mathbb{Z}/3)^{\times} \cong \mathbb{Z}/2 \times \mathbb{Z}/2 \times \mathbb{Z}/2$ in which it's easy to see that all elements have order at most $2$ – Cocopuffs Nov 28 '12 at 12:27
2 Answers 2
$(2a+1)^2=4a^2+4a+1=8\frac{a(a+1)}2+1\equiv \pmod 8\implies c^2\equiv1\pmod 8$ if $(c,8)=1$
Now, $(3b\pm1)^2\equiv 1\pmod 3\implies c^2\equiv1\pmod 3$ if $(c,3)=1$
If $(c,8)=1$ and $(c,3)=1$ i.e., if $(c,24)=1, lcm(3,8)\mid (c^2-1)\implies c^2\equiv1\pmod{24}$
So, $ord_{24}c\mid 2$
But clearly, $ord_{24}c\ne1$ for $c>1\implies ord_{24}c=2$ for $c>1$ and $(c,24)=1$
share|improve this answer
If you look at the numbers mod 6 (the prime divisors of 24 being 2 and 3) you eliminate those equivalent to 0,2,3,4 - so you have left those equivalent to 1 and 5 (i.e. $6n \pm 1$). You could confirm your answer by looking at what happens to the numbers $(6n \pm 1)^2$ when they are taken mod 24.
share|improve this answer
Your Answer


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write_coeff file file = name of data file to write out
Write a text format file with the currently defined force field coefficients in a way, that it can be read by LAMMPS with the include command. In combination with the nocoeff option of write_data this can be used to move the Coeffs sections from a data file into a separate file.
The write_coeff command is not yet fully implemented in two respects. First, some pair styles do not yet write their coefficient information into the coeff file. This means you will need to specify that information in your input script that reads the data file, via the pair_coeff command.


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NYU's summer school began in 1895, when seven members of the faculty, with the approval of the Chancellor, offered courses in mathematics, physics, chemistry, biology, experimental psychology, and the theory and practice of teaching. The faculty members received no additional salary, only the tuition fees collected from students. The University Council officially took control in 1899 and the popularity of the program quickly grew to over 500 students, both men and women, by 1907. The program mostly attracted teachers who were interested in pedagogical courses.
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text:
General and Specific Objective
To advance education by providing books, equipment, and educational aids to students attending school in East Harage and West Harage in the Oromiya Region, Ethiopia.
To advance education by providing publicly available scholarships, bursaries, and other forms of financial assistance to students in Ethiopia to be used for elementary, secondary, or post-secondary education.
To Improve the standard of life of Ethiopian children and young adults, who currently live below the poverty level, by increasing the availability, basic education, and sponsorship. Our goals are to achieve the following:
- To improve the livelihoods of 3,700 low living students.
- To provide educational support for 4,780 students and OVC
- To intervene in the construction of one school accommodating from KG to high school consisting of library and laboratories with an enrollment capacity of 500 students per year. Moreover, dormitory and meal service will be provided for 300 students who came from remote areas. To facilitate scholarships opportunities as an educational intervention carried out on yearly bases for undergraduate and postgraduate students from OVC.
- To build a more sustainable way of life in Ethiopia and Africa as a whole by decreasing poverty.
- To give hope to disadvantaged and vulnerable children through basic education.
- To give students basic education and scholarship.
- To empower disadvantaged children hopes to build a more positive and stronger world.


text: Graph-to-text generation aims to generate fluent texts from graph-based data. In this paper, we investigate two recently proposed pretrained language models (PLMs) and analyze the impact of different task-adaptive pretraining strategies for PLMs in graph-to-text generation. We present a study across three graph domains: meaning representations, Wikipedia knowledge graphs (KGs) and scientific KGs. We show that the PLMs BART and T5 achieve new state-of-the-art results and that task-adaptive pretraining strategies improve their performance even further. In particular, we report new state-of-the-art BLEU scores of 49.72 on LDC2017T10, 59.70 on WebNLG, and 25.66 on AGENDA datasets - a relative improvement of 31.8%, 4.5%, and 42.4%, respectively. In an extensive analysis, we identify possible reasons for the PLMs' success on graph-to-text tasks. We find evidence that their knowledge about true facts helps them perform well even when the input graph representation is reduced to a simple bag of node and edge labels.


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About Seed Beads
Seed beads, also known as rocailles, are versatile beads used in embroidery, jewelry stringing, and all kinds of bead weaving applications. The smallest seed beads can go under trade names such as Antiques or Delicas, or they can be simply designated by size, where the bigger the number the smaller the bead. For example, 11 0 seed beads are very small (2mm), but 6 0 seed beads are bigger (4mm).
Although simple bead stringing projects are always a possibility, weaving with seed beads -- which can be done with a loom or off-loom -- is getting more and more popular. Bead weaving is nothing new, it has been practiced by Native Americans for centuries, and enjoyed a surge of popularity among Victorian women.
A common weaving technique for seed beads is peyote stitch. See our videos referenced above for demonstrations of this and other common bead weaving styles. Weaving involves the use of needles, so we've included the most appropriate beading needles above as well. Seed beads can also be used in a variety of sewing, threading, or wire projects.
Fireline thread is very good for bead weaving. It is pre-waxed, doesn't fray, and has very strong tensile strength. However, Nymo thread is good for loomwork because it's very thin, which is an advantage when your project requires that the needle pass through the same bead hole many times. Dandyline from Beadalon is also a nice thread that is strong, waterproof, and does not fray.
Basically, seed beads can be used in any design, whether it's loom weaving, threading, or embroidery, whenever you want to add small points of color or intricate detail. Other ideas include a bead-encrusted picture frame, monogrammed bags, and beaded zipper pulls. The possibilities are limited only by your imagination!
Getting to Know Seed Beads
How Many Seed Beads are in a Gram?


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Using the Display Interface
With BlueZone, users have the ability to remove session text from the display session and paste it onto the Windows Clipboard. The Clipboard text can then be pasted back into another screen of the display session or into another Windows application. To cut session text to the clipboard:
Hold down the left mouse button while dragging the mouse pointer over the desired text; or, use the keyboard select functions: Left, Up, Right, Down, All.
Once the desired text is selected, release the left mouse button.
From the BlueZone MenuBar select Edit, Cut.
De-select Highlighted Text
To de-select the highlighted text without cutting it click the left mouse button; or use the keyboard select function Cancel.
View Text on Clipboard
Use the Clipboard Viewer application that comes with Windows.
To view the text in the correct context make sure the Display, OEM Text option is enabled in the Clipboard Viewer.
NOTE When using Edit, Cut to remove session text, only unprotected input data will be cut to the clipboard. Also, The Edit, Cut operation always functions as if Copy with Columns Aligned is enabled. For additional information, see Edit Property Sheet below in related topics.
Copying Text to a File
Copying Text to the Printer
Pasting Text into the Display Session


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Senior secondary education is designed to prepare students for initial entry into the workforce, for vocational education and training and higher education studies. It is undertaken in Years 11 and 12.
There are two key senior secondary education accrediting bodies in Victoria, the Victorian Curriculum and Assessment Authority (VCAA), and the International Baccalaureate (IB).
The VCAA accredits the two Victorian senior secondary qualifications, the Victorian Certificate of Education (VCE) and the Victorian Certificate of Applied Learning (VCAL).
The IB accredits the International Baccalaureate Diploma, which is a globally recognised senior secondary qualification.
In Victoria, the VRQA is responsible for the:
- registration of senior secondary providers to deliver one or more senior secondary qualification:
- in schools
- in non-school settings.
- registration to become a senior secondary awarding body
- accreditation of senior secondary qualifications.
For information about applying to provide senior secondary education, see:
To search for registered senior secondary providers, see:
For information about becoming an awarding body or about accreditation of senior secondary qualifications, see:


Dynamic Pelvic MRI
For many of the 400,000 women who experience pelvic floor dysfunction each year, diagnosing their condition can be challenging, uncomfortable and time consuming. The pelvic floor is a complex area of the body that requires long experience and special expertise to allow for proper diagnosis.
The pelvic floor can be divided into three compartments:
 - Anterior (bladder and urethra)
 - Middle (vagina, cervix and uterus)
 - Posterior (rectum)
A complex network of muscles support the entire pelvic floor. Damage to even one of the muscles can lead to prolapse (one or more of the pelvic organs falls out of position), while stretching or tearing can lead to pelvic floor relaxation and a range of symptoms, including incontinence, pelvic pain and/or constipation.
Due to recent advances in sequencing speed, Dynamic Pelvic Magnetic Resonance Imaging (MRI) can now greatly aid in the diagnosis of conditions affecting the pelvic floor. A major benefit of Dynamic Pelvic MRI is enhanced patient comfort, as well as other benefits, including:
 - No IV contrast
 - No radiation
 - Relatively noninvasive (depending on technique)
 - In most cases, patient only has to bear down
 - In most cases, no enema
Dynamic Pelvic MR allows radiologists to directly see detailed images of the anatomy of the pelvic floor structures, which allows analysis of anatomy and function. Studies have shown that Dynamic Pelvic MRI is more sensitive than physical examination, making it the gold standard for diagnosing pelvic floor disorders.
Dynamic Pelvic MRI Procedure Information
Why Choose the S. Mark Taper Foundation Imaging Center for a Dynamic Pelvic MRI?
Android app on Google Play


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Abstract: In this paper an algorithm is presented for the fitting of a tube shaped B-spline surface of (3,2) degrees to another surface along a given connection curve. Satisfying prescribed first and second order boundary conditions at a finite number of interpolation points on the connection curve several vertices of the control net of the bordering patches are computed from a fairness condition. The resulting B-spline surface joins the second surface with almost curvature continuity at those common points in which the tangent planes and the normal curvatures in one prescribed direction of both surfaces coincide.
Keywords: Computer-aided design, B-spline surface, boundary conditions, fairing
Full text of the article:


text:
The highly complex steps in the mountain carving process at Crazy Horse can be summed up in relatively simple terms. We are making a very large duplicate of Korczak's sculpture to tell the story of North American Indian cultures. That artwork depicts the Lakota warrior, Crazy Horse, seated on his horse and pointing over the horse's head as he says, "My lands are where my dead lie buried." In order to convey that powerful story on a monumental scale on the mountain we follow three basic steps: 1) measure Korczak's model; 2) measure the mountain; 3) remove all the rock that doesn't fit! In reality each of these steps gets quite complex and requires the use of powerful tools and techniques, but the guiding principles remain quite simple.
The members of the Crazy Horse mountain crew are experts in precision blasting, equipment operation and engineering. They maintain a strong emphasis on safety in all steps of the operation and are proud to have an outstanding safety record. Here's a little closer look at each of the meticulously detailed steps this team carries out to carve the mountain:
Measuring systems have evolved steadily during the 60-year history of the mountain carving. Korczak relied on artistic estimates and his incredibly practiced eye and natural feel for dimensions and scale. After his death, his family and the mountain crew developed a mechanical pointing system to measure the 1/34th scale model of Crazy Horse's face. After completion of the face, we designed and built another mechanical pointing system to measure the 1/300th scale model of the entire carving. More recently laser scanning methods have been used to measure the 1/34th scale model and just in the past year brand new technology has been used to measure the 1/300th scale model with a laser scanning arm. Monique Ziolkowski is currently working to build a 1/60th scale model that will combine the artistic elements of Korczak's story with dimensions and geologic details from the mountain. Some combination of mechanical pointing systems and laser scanning technology will likely be used to measure this model when it is complete.
Korczak used a combination of his artistic eye, tape measures and a beautiful old theodolite (survey instrument) to determine the basic location of his model within the mountain and begin the process of removing excess rock. A 60-foot long measuring boom was fixed to the top of Crazy Horse's head in 1987 to direct the work on the face. A plumb bob suspended from that measuring boom was used to transfer numbers from the pointing system on the 1/34th model of Crazy Horse's face.
When work moved beyond the face in 1998, a survey control system was developed and a modern survey instrument was used to measure the entire mountain. This instrument, known as a total station, measures very precise angles and distances from known control points to calculate 3 dimensional coordinates for any point on the mountain. It uses an infrared beam reflected from a hand held prism to measure distances up to several thousand feet with accuracy to the nearest 1/1000th of a foot. Measurements from Korczak's models are transferred to the mountain using this same instrument and survey control system.
Laser scanning equipment has been used to measure the entire mountain on several occasions over the past 10 years. These instruments work on the same principle as the total station to measure angles and distances from known control points to points of interest on the rock. They use a laser beam reflected from the rock to measure the distances without need of a prism at each point. This allows for measuring huge numbers of points very quickly and accurately to build 'digital models' of the mountain in our engineering computers.
The next step in measuring on the mountain will be to apply the best possible methods to measure the geologic structure of the mountain in addition to the basic geometry of the mountain. This information becomes critical in refining the shape of the models and in planning for long term stability of the memorial.
Rock is removed from the mountain primarily with explosives. Again this complex process can be summed up in basic steps: Drill precisely placed holes in the granite; load explosives in the holes; time the detonation sequence of those explosives; push the blasted rock (known as 'muck' in the mining industry) off the mountain with heavy equipment and finally remove the last layer of rock in the finishing stage. All blasts at Crazy Horse are designed, drilled and executed to protect the rock that is left after the blast. This is the opposite of most blasting operations, where the main concern is the final size and location of the material being blasted away. The mountain crew prepares most blasts using a system that explosives engineers call "pre-splitting." It is similar to perforating a piece of paper to allow it to tear evenly. The rock to be removed is drilled on all sides with a series of parallel drill holes. Explosives are detonated throughout the entire length of each of the drill holes, cleanly removing the desired rock while leaving the remaining rock undamaged. Here's a more detailed look at each of the steps in the rock removal process:
Equipment has evolved from Korczak's use of a single-jack (sledge hammer and hand steel) to drill the holes for the first blast on the mountain. Korczak quickly advanced to pneumatic jack hammer drills powered by 'Buda', the ancient air compressor which quit frequently during the work day and forced him to make many trips down and back up the 741 steps to the top of the mountain. He then progressed to wagon drills, a larger drifter drill mounted on a D8 Cat and finally air track drills. These machines required less manual labor but still relied on gas or diesel powered air compressors to drive the hammer. The mountain crew did much of the drilling for Crazy Horse's face using hand held rotary hammer drills powered by more modern, efficient electric air compressors. We still drill 1 3/8 inch or 1 5/8 inch holes up to 21 feet deep using these hand drills on rare occasions when the track drills cannot be maneuvered to the drilling site. Hydraulic drills are now the standard and our fleet includes three of these very efficient machines mounted on tracks or rubber tires. Most of our holes are drilled about 20 feet deep using 2 inch diameter carbide steel bits. Our largest machines approach drilling rates up to 10 feet per minute! The next generation of these drills will be faster and more efficient and will have enclosed cabs to better protect the mountain crew from the noise and dust generated in the drilling process.
When most people think of explosives, they imagine dynamite. The primary types of explosives used here at Crazy Horse, however, are not dynamites but detonating cord and small diameter water gel or emulsion based pre-split products. Dynamite is very effective at fragmenting rock, but expends all of its energy in an area equal to the length of the cartridge – a very small portion of the drill hole. Our blasts using detonating cord and pre-split products can be designed to expend the same amount of energy over the entire length of the drill holes. This provides much better control of the explosive energy and does much less damage to the rock that is not removed by the blast. In a typical blast at Crazy Horse up to several hundred drill holes are loaded with the appropriate size of detonating cord or pre-split explosives. After the product is in place the holes are filled with small crushed stone. The stone fills the open space in the hole and better focuses the explosive energy to precisely split the rock.
The typical blast is actually a carefully timed series of smaller blasts spaced only a few milliseconds apart. The vibration and damage caused by the blast can be controlled by limiting the amount of explosive detonated in each section of the blast. The distance to what will be the finished surface of the mountain carving ("final grade") dictates the distance between drill holes and the type and amount of explosive used in each hole. The closer to final grade, the smaller the drill hole spacing and the smaller the explosives charge weight in each hole. Timing between the blast sections is controlled by the blasting caps (detonators). This is another area where advancing technology is making a big difference in our mountain carving operation. Electric blasting caps which are susceptible to premature detonation caused by static or nearby lightning strikes or radio transmissions are no longer used. Our most common method uses non-electric delay detonators fired by sending a spark through long plastic tube or with a highly secure 2-way radio controlled remote initiation system. We have also used the latest technology – a system of electronically controlled, programmable detonators which allow nearly infinite choices in blast timing. We expect systems like this to play a key role in controlling blasts as we work closer to finished grade in the future.
Removing the blasted rock or muck from the mountain is accomplished with heavy equipment. Here again there has been a steady improvement in the type, size and efficiency of the equipment used over the past 60 years. A typical blast today produces 2000 to 3000 tons of rock fragments. These rocks range in size from small gravel up to the occasional 10 ton boulder and most remain on the blasting bench rather than falling off the mountain from the force of the blast. The mountain crew spends 2 or 3 days with a combination of excavators and bulldozers to move this rock off the mountain and clear the way for the drills to prepare the next blast. To lend some perspective to the quantity of rock being handled – the average dump truck on the highway is hauling about 15 tons of material. It would take 200 truck loads to haul away the rock from just one large blast on the mountain!
When the crew returns to finishing work it will be accomplished as it was on Crazy Horse's face by drilling to isolate small blocks of rock (100 to 1,000 pound chunks).


text:
Home > News > Nanotechnology holds key to longer life: Research
December 12th, 2007
Nanotechnology holds key to longer life: Research
American scientists seem to have found the secret to extending the lifespan of brain cells, thus spawning hope for a longer life.
A molecular biologist and a nanoscientist at the University of Central Florida have found that nanomaterials developed for industry have an unexpected and potentially revolutionary side effect: They can triple or quadruple the life of brain cells.
The result is people could live longer and with fewer age-related health problems.
Beverly Rzigalinski, assistant professor in the Department of Molecular Biology and Microbiology and at the Biomolecular Sciences Center, and Sudipta Seal, associate engineering professor at the Advanced Materials Processing and Analysis Center and the Department of Mechanical, Materials and Aerospace Engineering, will receive 1.4 million dollars from the National Institutes of Health, National Institute on Aging to study the reasons behind the reaction and possible future applications.
Sound waves precisely position nanowires June 19th, 2013
Scientists Use Nanotechnology to Increase Thermal Stability of Essential Oils June 19th, 2013
Production of Bioactive Material for Quick Treatment of Bone Damages June 19th, 2013
Nanometrics Announces Participation in 5th Annual CEO Investor Summit: Accredited Investor and Publishing Research Analyst Event to be Held Concurrently With SEMICON West and Intersolar 2013 in San Francisco June 19th, 2013
Conceptual Nanomedical Lipofuscin Removal Strategy April 29th, 2013
utsandiego.com November 22nd, 2012
Nanoparticles against aging October 3rd, 2012
Frost & Sullivan Hosts Webinar: Can We Live Forever? Gauging the Future Trajectory of Medical Technology Development March 24th, 2011


watchfulness required to avoid corrosion problems. Well-built aluminum boats are more expensive than production fiberglass sailboats. Aluminum fabrication costs are based on the material expense of proper aluminum alloys for hull plating, frames and stringers, and on labor costs for skilled aluminum welders. The construction process is more labor intensive than fiberglass boats.
Potential corrosion sources in aluminum boats are well understood by builders these days. Following best practices in electrical wiring and equipment isolation from the hull eliminates most corrosion risks. An aluminum boat owner can prevent corrosion by learning a few unique requirements. For example, an isolation transformer must be wired in the boat if connected to shore power; a charcoal filter must be used when filling an aluminum water tank from a city chlorinated water supply; never moor the aluminum boat next to a steel boat; never use chlorine cleaners for anything (use vinegar); and always have installed and regularly check an LED light indicating a fault from a connection between the hull and the positive or negative side of the battery.
ON: What is your advice for voyagers considering an aluminum vessel?
DC&RS: They should follow the same process as with the considered purchase of any boat: Talk to sailors who have a similar boat, inspect as many aluminum boats as possible, and consider having a custom boat built by selecting a good naval architect and finding a small, experienced aluminum boatyard for the build.


ResultSets and streaming columns
To get a field from the ResultSet using streaming columns, you can use the getXXXStream methods if the type supports it. See Streamable JDBC data types for a list of types that support the various streams. (See also Mapping of java.sql.Types to SQL types.)
The following code fragment shows how a user can retrieve a LONG VARCHAR column as a stream:
 // retrieve data as a stream
 while ( {
 // use a to get the data ip = rs.getCharacterStream(1);
 // print the data
 char[] buff = new char[128];
 int size;
 while ((size =!= -1) {


text:
The Tomini Bay Programme (known locally as Programme Teluk Tomini), also referred to as SUSCLAM (Sustainable Coastal and Livelihoods Management) is a five year programme that ensures community prosperity through equitable and sustainable management of the coastal resources of Tomini Bay.
The Programme's goal is improved management of coastal and marine resources in Tomini Bay for the benefit of local communities.
- Increased collaboration between stakeholders in North Sulawesi, Gorontalo and Central Sulawesi to undertake community based coastal resource management.
- Increased local capacity for sustainable marine and coastal resource management in order to benefit community livelihoods.
- An information system to support the sustainable management of natural resources.
Scope of Activities:
- Support for collaboration between stakeholders to promote an increase in community based marine and coastal ecosystem management in Tomini Bay.
- Support for livelihood improvements and sustainable locally based management of marine and coastal resources.
- The development of an information system to support management decision making at all levels.
- The collation and distribution of lessons learned in the field of community based marine and coastal resources management.
- The provision of technical and administrative support to develop local capacity.
Tomini bay is one of the largest bays in Indonesia with an extent of around 59,500km2. It is the only bay in the world to be bisected by the equator. Read more


Let's suppose that a flight is being conducted under 14 CFR 135. The airplane is certified for single pilot operations, but two pilots who are both rated as PIC on the 135 certificate occupy the pilot seats. One of the pilots is a CFI. Does anything in 14 CFR 135 prevent the CFI from giving dual given time to the PIC while he flies?
 - 1
 $\begingroup$ Sounds like a 135 operator conducting type transition training to me... $\endgroup$ – UnrecognizedFallingObject Dec 18 '15 at 4:58
 - $\begingroup$ I'm not asking the question in that specific context, but that would apply. I'm asking if anything prevents instruction from being given during operations with passengers or cargo while operating under 14 CFR 135. $\endgroup$ – ryan1618 Dec 18 '15 at 14:15
 - 1
 $\begingroup$ _USER_ feel free to make that kind of edit yourself too... $\endgroup$ – Bret Copeland Jan 1 '16 at 21:51
It took me a little bit to figure out the underlying reason for asking this question and it has to do with logging flight time. For example, in a single pilot operation with an autopilot, the second pilot is not required and therefore cannot log the flight time at all even though their company may want them there. The FARs don't allow the second pilot to log the time.
The regulation that governs logging of flight time is 61.51.
61.51(h) Logging training time. (1) A person may log training time when that person receives training from an authorized instructor in an aircraft, flight simulator, or flight training device. (2) The training time must be logged in a logbook and must: (i) Be endorsed in a legible manner by the authorized instructor; and (ii) Include a description of the training given, the length of the training lesson, and the authorized instructor's signature, certificate number, and certificate expiration date.
So the question becomes what training was given during the revenue Part 135 flight and were you an authorized instructor?
The term Authorized Instructor is only found in Part 61.
61.1. Authorized instructor means— (i) A person who holds a ground instructor certificate issued under part 61 of this chapter and is in compliance with §61.217, when conducting ground training in accordance with the privileges and limitations of his or her ground instructor certificate; (ii) A person who holds a flight instructor certificate issued under part 61 of this chapter and is in compliance with §61.197, when conducting ground training or flight training in accordance with the privileges and limitations of his or her flight instructor certificate; or (iii) A person authorized by the Administrator to provide ground training or flight training under part 61, 121, 135, or 142 of this chapter when conducting ground training or flight training in accordance with that authority.
Since it is a Part 135 revenue flight I would believe the CFI would have to comply with section 135.338 and 135.340.
135.340(a) No certificate holder may use a person nor may any person serve as a flight instructor unless— (1) That person has satisfactorily completed initial or transition flight instructor training; and (2) Within the preceding 24 calendar months, that person satisfactorily conducts instruction under the observation of an FAA inspector, an operator check airman, or an aircrew designated examiner employed by the operator.
If the authorized instructor has complied with 135.338 and 135.340 they are also bound to the training program for the 135 company. If that training stipulates you can give dual given during revenue flights than you are more than welcome to do so. If there is no provision in the training program to provide instruction during revenue flight then it should not be done.
The best option is to request a legal interpretation on the validity of what you are wanting to do.
Short answer: NO
Long answer: In a flight where the CFI is certificated to provide instruction and the two are sitting in pilot seats then the PIC may log any part of that flight as dual instruction. It does not require the CFI to actually say a word in order for it to count as dual; even if he's merely observing, if something bad happens he'll open his mouth or take controls.
Part 135 is more about requirements for operations; it does not affect flight instruction, which is a part 91 regulated activity.
 - 2
 $\begingroup$ Nothing here gives any explanation why "no" is the correct answer to the question "Can instruction be given during a {Part 135 flight}?" Are you answering the question "does anything in Part 135 prevent..."? $\endgroup$ – Ralph J Jan 1 '16 at 2:00
 - $\begingroup$ You can't log training time unless a CFI endorses your logbook, per 61.51(h), so there's more to it than just being in the aircraft together (related question). And I assume that in your last sentence you meant to say that flight instruction is regulated by part 61 (not part 91)? $\endgroup$ – Pondlife Jan 2 '16 at 1:54
Your Answer


text:
The Joseph S. Rumbaugh Historical Oration Contest
The National Association of Secondary School Principals has placed this program on the NASSP National Advisory List of Contests and Activities for 2012-2013.
NASSP Student Contests and Activities Page
The Joseph S. Rumbaugh Historical Oration Contest is open to all students attending home schools, public, parochial, or private high schools who are in their freshman, sophomore, junior or senior (grades 9 through 12) year of study.
History of The Joseph S. Rumbaugh Oration Contest
In 1945 an Ohio SAR member, Douglass G. High, originated this creative exercise in a Cincinnati Senior High. Two years later the NSSAR assumed National sponsorship. Douglass G. High passed away in 1952. In 1953 the National Society attached his name to the contest title as a memorial. He was the first Chairman on the NSSAR Oration Committee, serving in this capacity for five years.
In honor of a Florida SAR member, this Oratorical event was renamed the Joseph S. Rumbaugh Oration Contest. For many years this Compatriot has shown an active interest in the welfare of youth and has been a creative promoter of this contest. The contest is designed to explore the influence of the Revolutionary war on present day America.
Purpose Of The National Contest
- To support historical research in our high schools by promoting oratorical presentations related to our Revolutionary War period _PHONE_.
- To emphasize American History to the high school student and focus on and intelligent relationship between the past and the present.
- To place a positive emphasis on the plans of our founding fathers.
The preliminary rounds of the contest are held by Chapters and/or State Societies of the Sons of the American Revolution to select one winner from each participating state. In regions (SAR Districts) where no State Society sponsors an entrant, an SAR District entry is permitted. Prizes may be awarded to winners of Chapter and State Society (or District) competitions. The State or District sponsor is responsible for informing the contestant how expenses of competing at the National Level will be made. For example, travel, hotel for two evenings and meal expense.
The National Society competition between State Society winners is held during the NSSAR's National Congress in June/July.
The National Rumbaugh Orations Committee is currently attempting to raise the level of scholarship awards for our national winners. Please consider contributing to the Orations endowment by accessing the fillable form "The Dr. Joseph Warren Medal". Our youth thank you for giving them this increased opportunity for education. You can download the form here.
Rules of the Rumbaugh Oration Contest
For further information about the contest, do one of the following
- Call, write, or Email the contact in a nearby Chapter or State Society
- Email to NSSAR National Chairman at goebeltaconic [dot] net (National Chairman)
- Write -- making sure to enclose a number 10, business size, self-addressed envelope -- to the
Chairman of the Rumbaugh Oration Contest c/o NSSAR Headquarters 1000 South Fourth Street Louisville, KY 40203-3208
Official Rules of the The Joseph S. Rumbaugh Historical Oration Contest
- The contest will be held in preliminary round(s) by state societies and/or chapters of the Sons of the American Revolution to select one winner from each participating state. In districts where no state society sponsors an entrant, a district entry is permitted. Each participating state society or district should provide information regarding the contest to senior high school, parochial, private and home-schooled speech and/or history teachers and principals or counselors as early as possible.
- The contest is open to all students of the freshman, sophomore, junior and senior classes (Grades 9 - 12) in the public, parochial, private and home schools within the jurisdiction of the sponsoring state society or district.
- The oration must be original of not less than five minutes or more than six minutes. The subject shall deal with an event, personality, or document pertaining to the Revolutionary War and show a relationship to America today. The oration must be essentially the same as the submitted manuscript. Notes and props (including military uniforms) may not be used in the presentation.
- The state society or district establishes the date and deadlines for its contest allowing adequate time to submit its winner as an entrant in the national competition. (Four weeks before the start of NSSAR Congress) Form A & B, which can be found below, (National) must be received by the National Chairman by the deadline.
- Before the chapter winner competes in the state contest, a copy of the oration, a photograph and biographical sketch of the entrant, and the completed Form B should be mailed to the state chairman following the chapter contest. Form A (State) will be sent by the Chapter Chairman to the State Chairman.
- At Congress the NSSAR will furnish awards and give recognition to all orators who participate in the national preliminary and final contests.
- Expenses involving lodging, meals, and transportation to, at, and from the NSSAR Congress may be borne by the sponsoring state society or district. Chaperon for the entrant may be provided by the state society or district.
- During the presentation of orations at chapter, state-district, or national contest, no applause is permitted until all orators have finished speaking.
- During the contest, no private videotaping or flash picture taking will be allowed.
- By action of the 1985 Congress, all judges in the Joseph S. Rumbaugh Historical Oration Contest must be members of the SAR. The judges will select the winners by the following criteria: A. Composition; B. Delivery; C. Significance; D. History. Time allocated for delivery is between 5 and 6 minutes. (A penalty is applied for going outside the time allocations.)
- The contestants must agree that the interpretation of rules and the decisions of the NSSAR and its judges shall govern without reservation. The judging sheets and notes are the property of the SAR.
- The first place winner at the national level of the Joseph S. Rumbaugh Historical Oration Contest may not compete in its future competitions.
- The first place National winner is expected to attend the youth awards luncheon the day after the final competition.
NATIONAL SCHOLARSHIP AWARDS:
Third Place…………………………………………. $1,000
The above winners also receive an Olympic-size medal
All other finalists…………………………………… $300
All other national Contestants……….……… $200
The winner of the state or district contest may receive expenses toward their trip to compete in the national contest. The state society or district may give a cash award and/or an Olympic-size medal.
The Joseph S. Rumbaugh Historical Oration Contest Procedures
Insofar as possible the chapter, state or district contest should follow the procedures of the NSSAR Congress contest. These procedures are known to the majority of our chairmen, but new chairmen may be unfamiliar with them. The national procedures are as follows:
- At the beginning of the program the rules are explained to the orators and the audience.
- Before the contest begins, preferably in private conference with the chairman, the orators draw numbers to determine the speaking order.
- All orators are introduced only by number
- In giving the oration, at no time may the orator use notes or props.
- There are at least three judges, all of whom are SARs in accordance with the 1985 NSSAR Congress action. Prior to the contest, the chairman discusses the rules, procedures and judging sheets with the judges. The judges are seated throughout the audience with their location unknown to the speakers. The chairman acts neither as coach nor judge.
- Before the first orator comes before the audience, the timer is introduced. For the benefit of the orator, the signals to indicate five minutes and six minutes are described to the orators and the audience. If the orator announces a title, timing does not begin until the oration itself begins. The orator at the end of six minutes may complete his/her sentence. If the orator begins the next sentence and/or continues, the timer records the excess time. If the oration is less than five minutes, the timer records the time not used.
- The chairman follows the manuscript. The changing of a word or a sentence is understood, but if a substantial portion of the oration deviates from the manuscript, the chairman indicates this on the record. The timer and chairman are seated together for recording purposes. The one who is following the manuscript can and should prompt. The timer notes these promptings on his record.
- When the contest is over the judges and timer have retired, the chairman introduces each orator either by name or number and asks the individual to comment on his/her activities, school, future plans, and any family members or support group persons that may be with them at the contest.
- When the judges return, they are introduced. The judging sheets and notes are the property of the SAR. The winners are announced and presented with monetary awards and Olympic-size medals. Some chapter, states, and districts give monetary awards along with Olympic-size medal for first place. The medal is available for chapters, states and districts and can be purchased from the NSSAR Merchandise Department. Check the merchandise catalog for details.


text:
Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)
Yuanzhi Li, Yingyu Liang
Neural networks have many successful applications, while much less theoretical understanding has been gained. Towards bridging this gap, we study the problem of learning a two-layer overparameterized ReLU neural network for multi-class classification via stochastic gradient descent (SGD) from random initialization. In the overparameterized setting, when the data comes from mixtures of well-separated distributions, we prove that SGD learns a network with a small generalization error, albeit the network has enough capacity to fit arbitrary labels. Furthermore, the analysis provides interesting insights into several aspects of learning neural networks and can be verified based on empirical studies on synthetic data and on the MNIST dataset.


Take the 2-minute tour ×
I've got a fixed solution space defined by a minimum and maximum float which has no divisible slice.
You then have 0..N Gaussian distribution probability sets which I need to combine.
In the end I neeed
 1. Method to define probability set with a numeric range (not sliceable) and 0..N Gaussian functions
 2. A function which can generate a random number in the range as defined by the calculated probabilities.
Also I know it is possible that some combinations will generate a zero solution space.
Now I'm thinking the way to do it is take the normalised probability density functions and multiply them to get a new space then normalising the result. I just can't seem to break it down into algorithmic form.
Any ideas?
share|improve this question
You would probably be better off asking this at math.stackexchange.com? – bummzack Aug 15 '10 at 10:59
I thought about that, but I'm mostly concerned with how to do it algorithmically. A pure maths solution would help but not be the answer. – Kimau Aug 15 '10 at 11:05
Then maybe try stackoverflow.com? It looks like a generic programming problem, I don't see the word "game" in your post anywhere (not that it's a requirement but that's a pretty good sign that you might want to look elsewhere) – Ricket Aug 15 '10 at 15:41
I need help with some terms, like no divible slice, zero solution space, normalized probility density. – Jonathan Fischoff Aug 15 '10 at 16:20
Hmm. the top hit for "divisible slice" on google is this question. Then a number of documents where "divisible" and "slice" occur next to each other, but are part of different sentences. You might want to explain that one, as it's obviously not uniform usage. – drxzcl Aug 16 '10 at 7:45
1 Answer 1
First let's make sure I understood your question correctly:
 - You have a probability function that is expressed as a sum of N parametrized one-dimensional gaussians, each with different mean and standard deviation.
 - You want to generate stochastic variables according to this distribution.
Is this correct?
If this is the case, I reccommend you use a variation of rejection sampling. The recipe is quite straightforward, but you might have to iterate a bit before you get an answer out of it. This is the basic outline.
 1. You generate a uniformly distributed random number in your desired interval, x.
 2. You calculate the value of your probability distribution, p(x)
 3. You generate another uniformly distributed random number between 0 and 1, q
 4. If q < p(x), return x
 5. If not, start from step 1.
No matter how large the temptation, do not re-use q for different iterations.
share|improve this answer
I cannot use this method because as I stated a floating range is non-divisible (not sliceable). So sampling is impossible. I already use this method for enumerations which are possible to sample. Also I've taken advice and moved this question to Math Stack math.stackexchange.com/questions/2584/… – Kimau Aug 21 '10 at 8:13
Ok, let's move there. – drxzcl Aug 21 '10 at 15:53
Your Answer


Why Are Words More Memorable Than Numbers?
Assuming that they are, I'm sure for some people it's actually the other way around.
Is it because numbers describe a relationship between entities rather than the entities themselves?
it's because like there's not much material difference between 1178 and 1179, they're too specific aren't they.
Like you could remember seeing a red car but could you remember what shade of red?
Numbers all mean the same thing, just different quantities of that thing
1 Like
It's only words
And words are all I have
To take your heart away
yeah they rely on something else to define them don't they.
So does that mean maths can't exist in a vacuum?
simply write numbers down as words and they become easier to remember
I guess until something has happened nothing can have any meaning,
Can someone give me the four one one on this thread please?
One of the only things that makes me remotely suitable for my job is that I find numbers very easy to remember.
1 Like
This is a good little memory trick
Say you had to remember this string of numbers
193 919 452 020
You'd probably forget after half hour if you were asked to repeat what they were because there's no context but if you put them together and they have a context it's easier so
193 919 452 020 becomes
_PHONE_ 2020 aka the start and end years of WW2 and the current year.
1 Like
yeah that is neat!
Can Discobot answer with word numbers?
Hey _USER_ roll 1d6
:game_die: 2
Human consciousness doesn't really work in numbers, thank heavens, it's another level of mathematical abstraction
1 Like


text:
Article in Mashable Tech
Big Idea: Jerry the Bear is a robotic teddy bear that "has" diabetes. Children are able to take care of Jerry by checking his blood glucose levels, giving him "insulin shots" and "feeding" him a variety of foods.
Why It's Working: Targeted specifically to children living with type 1 diabetes, Jerry helps sick kids not only learn about the procedures that are performed on them daily but also empowers them to understand the importance of symptom-checking and self-care.
People with type 1 diabetes, a lifelong genetic condition that prevents the accurate breakdown of glucose in the blood, rely on a steady amount of insulin to be delivered to their bodies every day. Since young children cannot manage an insulin pump, test their own glucose or deliver their own injections, parents with diabetic children must administer at least 3 finger-sticking blood glucose checks and frequent insulin injections every day to ensure diabetes is managed. For a five-year-old child, that's a lot of boo-boos in the name of love.
Enter Jerry the Bear, a fully interactive robotic teddy bear with type 1 diabetes and the brainchild of Northwestern students and Design for America fellows Aaron Horowitz and Hannah Chung. Horowitz, now CEO for the duo's company Sproutel, explains that Jerry the Bear was inspired by the teddy bears children often get after their diabetes diagnosis.


Archive for the 'the U.N.' Tag
Fixing the World, Bang-For-The-Buck Edition: A New Freakonomics Radio Podcast Leave a comment
Summary: Return on Investment (ROI) analyzes at the most efficient way to spend money. An example given is the difference between curing malaria and HIV/AIDS. To cure malaria, it would cost about $1,000 per person, while it would cost ten times that to cure HIV/AIDS, and it is decided that they would rather save 10 people from malaria before they save one from HIV/AIDS. The United Nations, with their Millennium Development Goals coming to a close, will be looking to set new goals in 2015, to be completed by 2030. One of the issued they will focus on is how they are setting goals, and how to be more efficient with the help of the Return on Investment analysis.
Original Air Date: October 2, 2014
Length: 43 minutes 34 seconds
Prompt / Discussion: You are a member of the United Nations, and are put in charge of coming up with new development goals for 2015. You have $100 billion to invest in various development aid. Discuss how you would prioritize between an important, expensive goal (such as getting all kids into school, which was one of the Millennium Development Goals), and something that might not be seen as highly important, but cost effective.


text:
Lafayette, Ind., 1859. Credit: Bass Photo Company Collection, Indiana Historical Society
Balloon Flight Through History
From smoke ballooning to modern hot-air balloon races and Paris to Civil War battlefields, ballooning has had a history rich in change and experimentation! Explore these different eras and adventures in ballooning by clicking on the links below.
Still want to know more? Check out these links on the history of ballooning:
- The Smithsonian's National Air and Space Museum in Washington, DC, has an extensive collection of art and photographs pertaining to the early history of ballooning. Over 400 images are available at the link below.
- The National Balloon Museum in Indianola, IA, has a good summary of the history of ballooning on their Web site.


text:
Learning Guide: Personal hygiene
Author: Alba Cecilia Báez Gómez – Description: This English selfstudy guide helps you practice giving instructions in written form. All the activities are related to the top of personal care habits presented in Way to Go 7 workbook Module 1 Unit 2 Lesson 3.
It starts with some vocabulary revision activities. Then you have to answer some questions about the language used to write instructions( Imperatives and sequential linking words) and end up writing the instructions for a personal care habit.


text:
Oct. 1, 2010 The role of a key nutrient which prevents cataracts in salmon has been revealed by eye specialists at the University of East Anglia.
Research published September 30 in the American Journal of Physiology -- Regulatory, Integrative and Comparative Physiology shows how the nutrient histidine, when added to the diet of farmed salmon, stops cataracts (clouding of the lens in the eye) from forming.
Following fears over BSE in the early 1990s, blood meal was removed from the diet of farmed salmon. This coincided with a large increase in the incidence of cataracts which cause economic losses and fish welfare problems.
Lead author Dr Jeremy Rhodes, from the Norwich Eye Research group at UEA, said: "The international research team of which we are a part have identified a key nutrient (histidine) that is present in high quantities in blood meal but was deficient in the post 1990s diet. We also found that by adding histidine to the salmon's diet, cataract could be prevented.
"During the life cycle of salmon the young salmon parr spend the early part of their life in fresh water before they enter the sea as salmon smolts where they grow to maturity before returning to fresh water to spawn.
"In this paper, the latest of several from the project, we show that histidine has a protective role in the lenses of salmon enabling them to withstand the considerable environmental stresses that their life cycle demands. When histidine is deficient in the diet, these environmental stresses lead to the development of cataract."
Salmon farming is worth $11 billion worldwide and Norway is the largest producer with a 33 per cent share. Fish farming is Norway's third largest exporter after oil and metals.
A multi-centre collaboration between the research labs of the University of East Anglia's Norwich Eye Research Group and the National Institute of Nutrition and Seafood Research (NIFES) in Norway and industrial partners Biomar Ltd (Scotland) and Marine Harvest (Norway) was set up in 2004 to investigate the cause of the cataract outbreaks in farmed salmon.
The Norwich Eye Research Group at UEA has been a key member of this team and in addition to their vital research into the mechanism of the cataract formation has hosted scientists from the NIFES labs in Norway and sent scientists to Norway to help with collection of samples and the development of new techniques.
The work of this collaborative group has had a global impact on the salmon farming industry and the dietary histidine content of farmed salmon has been increased as a direct result of this work.
A synthetic histidine compound has recently been approved for use within the EU and work from the group was quoted in the conclusions of the European Food Safety Authority.
The research has been funded jointly by the Norwegian Research Council and the industrial partners.
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- J. D. Rhodes, O. Breck, R. Waagbo, E. Bjerkas, J. Sanderson. N-Acetylhistidine, a Novel Osmolyte in the Lens of Atlantic Salmon (Salmo salar L.). AJP: Regulatory, Integrative and Comparative Physiology, 2010; DOI: 10.1152/ajpregu.00214.2010
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Charcoal on Your Hair and Skin!
activated charcoal
How Weird Does Charcoal on Skin Sound?
Briogeo founder, Nancy Twine always has been a problem solver. She conducted researches on scalp issues, which majorly are caused by debris buildup that can clog many hair follicles. She aimed at finding a strong ingredient that could eliminate that buildup, along with those flakiness, irritation, and itchiness that come with it. She discovered that binchotan charcoal had unique properties that can eradicate this buildup without any harsh ingredients.
Twine (who has advanced charcoal into Briogeo's well known and growing scalp resuscitating line) claimed it was important for her to create hair care products with mild, effective, gentle, and detoxifying ingredients in place of their harsh counterpart (such as sulfates), which can expose the hair and scalp of natural oils and hydration.
Styling products, natural, sweat, and sebum can accumulate on the scalp and hair for a long time leading to limp hair, scalp itchiness, clogged hair follicles, and irritation, and even alopecia (hair loss). Charcoal helps to soak up deep-rooted infirmities beyond what a well-respected shampoo can cleanse away. It is good for your scalp because it aims impurities at the tip of the hair that can put a blockage to the hair follicle and cause scalp problems.
Activated charcoal is a highly smooth, light black powder prepared from coconut bone char, shells, coal, petroleum coke, peat, olive pits, or sawdust. The charcoal is "activated" by processing it at a very high temperature that alters its internal pattern, reducing the pore sizes, and increasing its surface area. This yields more porous charcoal than the common and regular charcoal. It has a negative (-) charge, meaning when included in a product, it attracts positively (+) charged molecules, such as toxins or dirt.
Because of its high porous and purifying properties, activated charcoal is often seen in a wide range of health, cosmetic, and beauty products, from toothpaste to face masks. Parents are even encouraged by The National Poison Control Center to keep the charcoal powder in the home to help combat the absorption of accidental toxin intake by children. So you could see that the performance of charcoal is indeed active and real!
Over some past years, it has become one of the most-wanted ingredients in hair care products, with such brands as Dove, SheaMoisture, Kenra, and Huetiful, all launching several charcoal hair care products.
"We noticed that charcoal was a trend in skincare industries to pull out toxins and purifies," says a marketing manager at Inspired Beauty Brands, which recently launched their Citrus Oil & Hask Charcoal collection. Haircare brands then thought how they could bring such an amazing ingredient into hair care to offer the same benefits as it does in skincare."
Here are some few top reasons for its pronounced onymous:
In some regions of the world, where dust and heat mix with sweat to weigh down one's hair, we always crave additional care. Charcoal is so helpful that it has become a primary ingredient in many shampoos, separating them from other ingredients to provide sound hair care. Below, I have listed many of the main hair care importance of charcoal.
01. Suitable for All Hair Textures
Most charcoal treatments or shampoos can be used on several hair types with different texture without messing with color or drying out strands. For the desired beautiful hair textures, you might get to find out that beginning to use charcoal shampoo for at least twice in a week and continued in the succeeding weeks might be all you need, depending on your type of hair and the number of styling products you use. Giving your scalp and hair a regular detoxifying cleanse may prevent accumulation and the need for too often shampooing.
02. Gets Rid of Itchiness and Dandruff
hairThe process involved in turning charcoal into an activated type makes its particles highly porous as it is oxidized on exposure to carbon dioxide. This is why it is very capable of absorbing more and more toxins. If you are the type with an oily scalp with flaky dandruff, activated charcoal's absorption feature will help soak all those excess oils, thus getting rid of dandruff on your hair.
 1. It Helps Other Products to Work Better
Removing caked contents from the hair aids for better absorption of essential nutrients among hair treatments and enhances the entire glowing health of your hair.
 1. Adds Volume
Who does not crave to have bouncy hair like that of those TV stars? Using activated charcoal on your hair can revive the dull, thin hair, lifeless, and give it that bounce and much volume it needs! As it cleanses your hair from impurities, your hair doesn't feel weighed down any longer. You will now notice a yet healthy look on your hair immediately after the first use of activated charcoal in your hair. If you carry around enough oil and dirt, your hair will begin to sag, and frequent shampooing may not be getting them all out. Our hair can gain about 4 % of its weight in accumulation from scalp dirt, dry shampoo, and pollution. Regular shampoos only remove surface dirt, but activated charcoal pulls out even more.
 1. Soothes Your Scalp
Charcoal soothes irritated, itchy, and flaky scalps and moisturizes the scalp to prevent dryness. You cannot just forget to treat your scalp with just as much vital specific beauty routines as you do your skin.
 1. Promotes Hair Growth
Your scalp is skin also, which means just like the skin on your body and face, the scalp absorbs oil, dirt and has too much sebum, which may hamper the quality of your hair and affect its growth. Activated charcoal helps wipe out all impurities, remove sebum, and cleanses the pores deeply to allow your pretty hair to breathe. It unclogs all pores in your scalp and detoxifies the follicles. This helps your hair grow well.
 1. A Powerful Detoxifier
Activated charcoal is well known to behave like a magnet that attracts and removes dirt from our scalp and hair. This activated charcoal may absorb about 1000 times its weight in dirt/impurities. It is also very good post-swimming to get rid of all/any chlorine that is stocked with your hair's natural texture and color.
An activated charcoal-inclusive shampoo product should gently detoxify your skin by capturing dirt and toxins, and oil, which would later be washed off. And because it is mild, it won't disturb the natural moisture levels of your hair. This means that your hair will be clear, pure, healthy, and have some natural shine on it.
 1. Cleanses Off Your Skin from Dead Cells
Because of the "spongy" and binding properties of activated charcoal, it is very easy for it clear skin and hair dirt, skin oil, impurities, dead cells, and boosts your appearance into a clear and glowing one.
If you include activated charcoal in the composition of a cleanser, you will notice how brightened, and amazing your skin will become.
 1. Brightens Up the Skin
fresh skinOur skin cells regenerate every twenty (21) days. This means that the old cells die and possibly shed off the skin surface. However, dirt, skin oil, and several environmental factors could slow down this process, hence causing dead skin cells to accumulate on top of the surface. This often leads to many issues, including dullness and skin tone.
 1. Coordinates Skin Oil Production
Charcoal attracts unwanted excessive oil from our skin without causing any damage and dryness on the skin surface. Keep in your sub-consciousness that activated charcoal in skin treatment is recommendable for people with oily skin; this is because of charcoal's high potential to soak up oils. Should you have dry and very sensitive skin, you may consider other charcoal-inclusive skincare products.
How Can We Use Activated Charcoal in Our Hair?
There are more than a hundred ways of supplementing activated charcoal in our hair care routine (daily, weekly, monthly, etc.). The easiest method is to mix two tablespoons of activated charcoal smooth grounds alongside some coconut oil and massage it upon our scalp. Leave it on the scalp for up to 20 minutes before washing it off.
You may also add a few quantities of activated charcoal in our shampoo jars and shake well. Ensure your shampoo is a mild one.
Always endeavor to wash off the charcoal from your hair after some period to avoid too deep penetration into your skin.


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Decrement by 1, return previous
Atomically decrements by one the current value and returns the previous value of the counter. It is possible that multiple concurrent client requests may receive the same previous value. This occurs since only the decrementing part of the logic is atomic, the retrieval of the value before it is decremented is not.
Future Backendless.counters.getAndDecrement(String counterName);
IAtomic counter = Backendless.counters.of(String counterName);
Future counter.getAndDecrement();
Argument Description
counterName name of the counter to decrement.
Function callback = (counterValue) => print("previous counter value is - $counterValue");
Backendless.counters.getAndDecrement("my counter").then(callback);
IAtomic myCounter = Backendless.counters.of("my counter");


The sirloin is cut from the beef loin and is a muscle that does very little work, so the strip steak is particularly tender although not as tender as the tenderloin. It is also called a strip loin steak.
When attached to the bone, together with the tenderloin, the strip steak becomes a T-bone or porterhouse steak.
It is suitable for fast, dry heat cooking methods, such as grilling, broiling or pan frying.
Grilling is a popular method of preparing beef cuts, especially steaks. By grilling, one can take advantage of a high degree of heat which can quickly sear the outside of a steak cut, sealing in moisture and flavour while creating a desired crust.
Broiling is a cooking method where the meat is placed under direct heat such as flame.
Pan frying involves cooking in a shallow skillet. It can also give the meat a desirable crust and the tender cuts of beef are best suited for this method.


text:
Superior (Steamboat), 22 Dec 1821
- Full Text
It is stated in the Buffalo Journal that the proprietors of the steam boat WALK-IN-THE-WATER are about to commence the building of another boat, of smaller dimensions, and that she is intended to be ready for the lake by the first of May next.
December 22, 1821
(This vessel was to be the SUPERIOR. See Erie Gazette May 23, 1822.)
- Media Type:
- Item Type:
- replace WALK-IN-THE-WATER
- Date of Original:
- Local identifier:
- Language of Item:
- William R. McNeil
- Copyright Statement:
- Copyright status unknown. Responsibility for determining the copyright status and any use rests exclusively with the user.
Maritime History of the Great Lakes


text:
I am working on a web app that provides a visual programming environment to generate 3D models - Mobius
It involves creating a scripts by adding lines of coding and just editing parameters. We are using angular-tree-component to generate a tree to represent the code structure, like in the image below
The lines of code are draggable - but as the tree becomes bigger - dragging and dropping becomes cumbersome. Hence, we were thinking of adding a cut-paste functionality with which the user can select and cut lines of code and paste them somewhere else.
What would be the most user-friendly way of implementing this functionality?
Adding Ctrl+X, Ctrl+V shortcuts are one way - but I am not sure if it would be discoverable, given that this feature didn't exist before. What microinteractions should I be taking care of in this case?
Is there a better way to implement this other than keyboard shortcuts? Each line has a set of buttons that are visible when the line is focussed. Not sure if adding another button to that is a good idea?


Can anyone tell me why the control system designers do not prefer pure derivative controller? Instead they use something called a Pseudo derivative controller. What is this Pseudo derivative controller and how does it has an edge over the pure derivative controller?
 - \$\begingroup\$ By the way, I'm not sure how common the desire or need to avoid a directly expressed derivative term actually is (other than the roll-off pole to cut noise, as noted in the other answer). It is a nice trick to have at your disposal just the same. \$\endgroup\$ – Pete W May 21 at 3:11
Because ideal derivative operation is not causal. For example if you want to calculate the derivative of a function at point a, you actually need to use the value of that function at a very small time after a. Depicted here (taken from _URL_
enter image description here
For example, this is the s-domain representation of a sample PD Controller:
G(s) = K * (s + 3)
One of the first things we learn while stuyding s domain representations is, the fact that in order for a system to be causal; the degree of the numerator must not be greater than the denominator's degree. As you can see, the system above is non-causal; since the numerator degree is 1, whereas the denominator 0.
What you can do in that kind of situation is to, add a low-pass filter by simply adding a pole which is located at the far left-side plane. Such as:
G(s) = (K * (s + 3)) / (s + 40)
If you try to implement a derivative operation in a controller, you are probably going to experience some oscillations which are caused by the derivative action. When designing real-control systems I use, Backward Difference to make sure to be causal.
In the context of a controller, pseudo-derivative was a term coined by Phelan in the 1970s, e.g. Phelan 1971. He made some perhaps excessive claims about it and it was not well received.
In its simplest version, it is an alternative to PI. Two changes are made: First the zero is moved into the feedback path, which I won't discuss to keep this answer short.
Second is a loop rearrangement, which I sketched below, with P being the plant. pdf-loop
The loop on top is the final form giving the pseudo-derivative its name. Note there is no actual derivative. The loop on the bottom is the small-signal equivalent, with the derivative appearing explicitly.
The similarity to a PI controller \$\frac{K}{s}(1+{T_0}s)\$, should be visible. The loop gain, stability, and disturbance rejection are the same as the corresponding PI, but the PI has a closed-loop zero that does not appear in the corresponding PDF.
The closed-loop response of the PDF is also small-signal-equivalent to the corresponding PI, with an additional LPF \$1/(1+{T_0}s)\$ on the input.
If you look, you can also recognize this in a modern incarnation, in controllers like Messner's CPIL (Complex PI-Lead) or CPISL (Complex PI-Super-Lead), where the author refers to the same loop-rearrangement as the "parallel inner loop form".
Your Answer


text:
Learn how to change the WFBS Scan Method from Conventional Scan to Smart Scan or vice-versa.
To select the scan method, do one of the following:
If WFBS was freshly installed
- Log on to the WFBS console.
- Click Security Settings.
- Click a Servers (Default) or Desktops(Default) group.
- Click Configure.
- Click Smart Scan or Conventional Scan.
- Click Save.
If WFBS was upgraded from lower versions
Conventional Scan is the default method. The Smart Scan and Conventional Scan buttons are also not present in the console. To activate Smart Scan, refer to this solution: Enabling or disabling the Smart Scan function in WFBS.


Puneet Varma (Editor)
String trio
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String trio Fine playing of Lennox Berkeley by Dresden Trio Seen and Heard
Beethoven string trio no 1 in e flat major op 3
A string trio is a group of three string instruments or a piece written for such a group. The term is generally used with reference to works of chamber music from the Classical period to the present. From at least the 19th century on, the term "string trio" with otherwise unspecified instrumentation normally refers to the combination violin, viola and cello (cf "string quartet", "piano trio" etc.). This is how the term is used by major catalogs, including IMSLP.
String trio The Giardino String Quartet Fantasia Music
Serafino string trio jean sibelius string trio in g minor
String trio httpsuploadwikimediaorgwikipediacommonsthu
String trio String Trio No 1 in D Major YouTube
Beginning in the second half of the 18th century, although the trio configuration for two violins and cello was not wholly abandoned in classical chamber music (even during the 19th century), the scoring for violin, viola, and cello began to take precedence. Joseph Haydn appears to have been the first composer to use this combination (Tilmouth and Smallman 2001), though he was soon emulated by Luigi Boccherini (Kennedy 1994).
String trio SIMPLY STRINGS Yorkshire39s favourite string trio
String trio Schoenberg String Trio by Trio Battuto YouTube
String trio Bellini Trio Bellini Strings Bellini String Quartet amp Trio
String trio Wikipedia
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What's the difference between a "cold read" and a "prepared material" workshop?
Important question! A "cold read" means the workshop instructor (the casting director) provides material, usually from the shows he or she may have worked on, that you then read "cold" (without much time to rehearse). Usually the instructor gathers each actor's headshot, and then assigns scenes, sometimes pairing actors together. You then will have 5-15 minutes to work on your scene, and then perform them for the instructor (see classroom vs 1-on-1 style for more info). Generally you should hold your sides while performing a cold read.
A "prepared material" workshop means you must bring in your own scene or monologue (be sure to check if the studio provides a reader) and perform for the instructor. Whether or not you hold your sides/script is entirely up to you, but prepared material should be just thatprepared. Some workshop studios require you to get your own scenes approved prior to your workshop. When registering always be sure to ask what that studio's policy is, as well as how to get your scene approved, if need be.
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Modern History
Wikibooks Modern History
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The engines of change
19th century
20th century
21st Century
Major People
The major people in this time frame are:
 1. Queen Victoria
 2. Benjamin Disraeli
 3. Mahatma Gandhi
 4. Benito Mussolini
 5. Mao Zedong
 6. Adolf Hitler
 7. Jawahar Lal Nehru
 8. Deng Xiaoping
 9. George W. Bush
 10. The Human Race
 1. Kernigh
 2. Dr. C.J. (international relations articles-Cold War, First World War, American Civil War, Cuban Missle Crisis)
 3. Other and anonymous contributors


text:
AGSAS > Objectives
We strive for
authenticity in clothing, appearance, actions, attitude, and
personality. Specifically, our goals are to:
- Research and study diaries, letters, textiles, garments, images and original artifacts of the period.
- Share research with our peers and the public.
- Participate in civilian scenarios at battle reenactments and living history programs.
- Demonstrate and learn by doing period activities, not limited to, but including, knitting, sewing, quilting, spinning, needlework,rolling bandages, cooking, or doing laundry.
- Develop our first person skills, both for public interpretation and our own education, and our third person interpretative skills.
- Illustrate the impact that the War had on the lives of ordinary citizens including coping with separation or loss of family members, economic hardship, shortages, and substitutes and the impact of invading armies.
- Study and educate the public on the role of soldiers' aid societies and of the various ways in which civilians on the homefront aided the war effort.
- Raise awareness and contribute to non-profit organizations dedicated to preservation of historic sites.
We have raised money through raffles of quilts, various reproduction items, and other period activities.


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Can a regularisation of the determinant be used to find the eigenvalues of the Hamiltonian in the normal infinite dimensional setting of QM?
Edit: I failed to make myself clear. In finite dimensions, there is a function of $\lambda$ whose roots are the eigenvalues (or inverses of the eigenvalues) of a given operator $U$, namely, the characteristic polynomial $\det (I-\lambda U)$. Is there some way of regularising this determinant to do the same thing in infinite dimensions? In general? Or at least for unitary operators which describe the time evolution of a quantum mechanical system?
link to a related question What does a unitary transformation mean in the context of an evolution equation?
EDIT: Perhaps the question still is not clear. The question was, and still is, ¿if you regularise $\det(I-\lambda U)$ as a complex valued function of $\lambda$, for $U$ a unitary operator, will its zeroes be the values of $\lambda$ such that $I-\lambda U$ fails to be invertible? ¿Has a non-zero kernel? ¿Or does regularising the determinant lose touch with that property of the finite dimensional determinant?
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Can you please clarify the question? Do you mean, can you discretize the Schrordinger eigenvalue problem to a finite dimensional system, and then find the eigenvalues E of the finite dimensional matrix M using det(M-EI)=0, and recover the correct levels E in the limit that the dimension of the system goes to infinity? – Ron Maimon Jan 3 '12 at 8:37
That would be the best possible answer, but I could settle for less. I'll try to rephrase the question, too. – joseph f. johnson Jan 3 '12 at 8:50
Then your question is not about the determinant at all, but about regulating the Schrodinger operators computationally. This is very easy to do, it is normal in computational studies, but I am not sure how much is rigorously known about the continuum limit. – Ron Maimon Jan 3 '12 at 12:35
I don't know why you say "regularizing". I gave you the "regularized" form below. I think you mean something different, "regularization" means putting the theory on a lattice, or breaking the continuum limit some other way, like doing an infinite sum with additional factors. You are asking whether the determinants converges after appropriate rescaling in the large L small $\epsilon$ limit to a unique function of $\lambda$, and it might, for the appropriate class of potentials. Zeta-function regularization is often used. Convergence isn't necessary for PI. – Ron Maimon Jan 4 '12 at 18:12
I don't know whether this makes a difference, except in grammar, but I did not say « regularising », I said « regularisation », and that is because that is the normal word for altering the definition of a divergent function (or integral) to make it convergent yet still agree with the original if the original were convergent. E.g. zeta function regularisation of the determinant. Lattice methods are one method of regularisation but not the only one. AFAIK, the zeta function regularisation doesnt work for the characteristic poly, and even if it did, wouldnt have the eigenvalues as roots. – joseph f. johnson Jan 4 '12 at 22:12
2 Answers 2
The continuum eigenvalues and eigenvectors of the Schrodinger operator are the limiting low-lying eigenvalues and eigenvectors of the discrete lattice approximations. Given a Schrodinger operator
$$ H= \sum_i A_i \partial_i^2 + V(x_1,....,x_n) $$
Where V is of the appropriate class (smooth is too restrictive--- you can have delta functions too, and random potentials, but I don't know the best possible function class--- it might be any integrable potential, i.e., any potential at all EDIT: of course it can't, as the -1/r^n energy levels run away to be localized on top of the attractive spot. The correct condition on the potential is involved, but you can take it to be continuous for this discussion), you replace the x's by a square lattice of spacing $\epsilon$ and of total size L in each direction with periodic boundaries, replace the $\nabla_i$ by the lattice $\nabla_i$
$$ (H_L \psi) (x) = \sum_i {A_i\over \epsilon^2} (\psi(x_i + \epsilon) - 2\psi(x_i) + \psi(x_{i-1})) + V_L(x) \psi(x) $$
Where V_L(x) is the integral over one lattice volume of the continuum V(x) in an $\epsilon$ box centered at x, and the discrete second derivative is the difference between the forward difference and the backward difference.
Then the approximately smooth low lying eigenvectors of $H_L$ converge to the eigenvalues of H in the continuum limit, and as for the high eigenvectors, who cares, these are lattice artifacts. I am sure that it is possible to prove all this rigorously, although from the physical point of view, if it were not the case, the Schrodinger equation would be physically suspect.
You can see the convergence on a computer, if you simulate a discretized Schrodinger operator. You can prove the convergence of the discrete to continuous propagator relatively easily from the path integral. For the individual eigenvalues and eigevectors, things will be somewhat more involved. If you want a mathematical proof, I can try to sketch one.
EDIT: Determinant formula
If you look at the eigenvalue equation for the finite dimensional operator $H_L$,
$$det(H_L - \lambda I)$$
you find a finite degree polynomial, whose zeros are the eigenvalues of the equation in the limit $\epsilon\rightarrow 0$, $L\rightarrow\infty$.
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You mean $det(H_L - \lambda I)$. This is a finite degree polynomial in $\lambda$ whose eigenvalues are those of $H_L$. – Ron Maimon Jan 3 '12 at 23:16
you seem to be saying that it is the set of zeroes which has a limit? Not the polynomial? – joseph f. johnson Jan 3 '12 at 23:55
_USER_: yes--- it is not obvious that the polynomial is converging, but for sure the zeros are. But when you get a certain set of zeros, you can write an Euler product formula and make an analytic function which has these zeros, and perhaps this gives a unique correct continuum notion of infinite dimensional determinant, I am not sure. I always think of it regulated. – Ron Maimon Jan 4 '12 at 7:06
It seems, then, that the answer to my question is « no », but you are not sure. – joseph f. johnson Jan 4 '12 at 8:27
_USER_: The answer seems to be yes, I didn't work out the limit of the polynomial, but an analytic function is usually specified by its infinite set of zeros and some additional constraints, like a polynomial of infinite degree. I am not sure under what conditions the convergence is guaranteed, and convergence of the determinant is not necessary for any of the physics results, but the mathematical topic is Fredholm theory. – Ron Maimon Jan 4 '12 at 8:39
As you have already mentioned, there are many ways to understand'regularization' and it is not very often connected with discrete limit - rather, these are dirty tricks to give a meaning to certain sums/integrals which are clearly divergent. Here, the problem is different - we do not know a priori WHAT should be this divergent object - to have divergence we have to have a limit and we have no limit so far. So, the question is rather about the definitnion than about'regularization' which might be necessary in later steps.
So, i may suggest a definition - we have an identity for finite dimensional operators (let us assume U unitary), : $det(I-\lambda U) = exp(Tr(ln(I-\lambda U))$. This is always correct - because $I-\lambda U $ is normal and therefore diagonalizable.
We can expand ln in Taylor series around 1 to obtain (ordinary Taylor series when U is in eigenbasis, no problems with radius of convergence when looked upon U - as modulus of all U's eigenvalues is 1).
$$ det(I-\lambda U) = exp(- \sum_{n=1}^{\infty} \frac{\lambda^n}{n} Tr\, (U^n) ) $$
Now we have an expression explicitly containing a limit and at the same time well defined for U an operator in finite dimensional complex Hilbert space. Note, that the appearance of limit is a side-effect, not intentional. Now, we can ask if this expression makes sense when our space becomes infinite-dimensional. There are theorems that state, that if U is bounded (that is $\exists_{M>0}: \forall_{v \in V}\,\, ||U v||\leq M \, ||v|| $) and trace-class (so that trace always exists and is finite) the above formula is well defined in infinite dimensional case. For unit