Shrimp Tank GH General Hardness
Shrimp Tank GH General Hardness
General hardness abbreviated as GH is also known as water hardness. GH is simply the measure of the total salts contained in your aquarium water. Calcium and magnesium are the primary salts dissolved in hard water.
Water abundant in GH is referred to as hard water, while one low in GH is regarded as soft. Generally, water that has little or no calcium and magnesium is considered soft, whereas water that has plentiful of calcium and magnesium is considered hard.
Even though GH is an essential component of water chemistry, there is no need for panic among people using tap water that dont know their GH because in general tap water will be made to have a specific GH depending on source and municipal area. (Hardy species of shrimp can be kept in these conditions)
This is why its very important that you first know your GH levels if you seriously want to get into shrimp and give them the best conditions possible, Most of the time this water will be more than adequate for easy to keep species of shrimp like cherry shrimp and ghost shrimp.
So, what are the reasons for monitoring the GH in your shrimp tank :
Your water is either hard or soft.
Hard Water Tank
Anyone who has ever breed fish can attest that not all fish can flourish in a similar environment and conditions this is the same for shrimp. If, for instance, your water source is too soft or too hard, it will be unlikely for you to keep specific types of shrimp that thrive in the middle of this range. You've to keep your GH in check, and based on the findings; you can either raise or lower it accordingly.
It's indisputable that some shrimp flourish in hard water while others do well in soft water. If you intend to keep these shrimp, you have to find out what parameters that type of shrimp does best in and setup your shrimp tank accordingly.
Importance of Aquarium GH to Your Aquarium
Osmoregulation is one of the main reasons why you should keep track of your aquarium GH. Osmoregulation is a natural process that takes place in your shrimp without stimulation. It's similar to breathing.
In simple terms, osmoregulation is the process by which shrimp counters the salts and water within the body with those from the outside.
In case of a disparity between the two, it can stress your shrimp, and in some instances, it can result in the death of your shrimp. This is where some of you will be familiar with the term "white ring of death."
This disparity is the reason why saltwater fish won't flourish in freshwater and vice versa, its also the reason drip acclimation is so Important, never under any circumstances throw healthy looking shrimp directly into another tank, in exceptional conditions if half the shrimp are already dead in a bag then yes do what you can to save whats left to avoid killing all of them.
Electrolytes are minerals and salts that transmit electricity when dissolved in water. Some of these minerals include calcium and magnesium.
These minerals play a crucial role in the development of muscles and bones, digestion, gills development, and strengthening the shrimps immune system to fight off various infections.
Electrolytes are a necessity if your shrimp is to remain healthy, thus the need to ensure they are plenty in your aquarium water.
Note that water that lacks GH is free from electrolytes for your shrimp to consume. This can result in adverse health complications for shrimp such as failing to molt properly.
Soft Water Shrimp Tank
Besides shrimp, aquatic plants demand electrolytes to some extent to support their growth. For instance, plants depend on calcium to grow.
In case your water is too soft, then your GH may be insufficient to provide your shrimp and plants with the electrolytes they require to flourish and stay healthy.
From the above, there is no doubt that adequate GH is paramount in your shrimp tank depending on the species. GH levels keep on changing from time to time because plants and shrimp consume, this is why water changes and good food rich in calcium are important.
It is also possible to have extremely high GH levels in your shrimp tank if the water is subject to evaporation leaving behind calcium and magnesium minerals.
Never top up shrimp tanks with tap water as this will increase the general hardness every time you do so.
We will of course go more into shrimp species specific details when we do some species profiles.
I hope this helps you understand a little bit more about GH and how it affects shrimp tanks.
Happy Shrimp Keeping
Marks Shrimp Tanks
Categories: Shrimp Tank Chemistry
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text: We present a detailed NMR study of the insulator-to-metal transition induced by an applied pressure p in the A15 phase of Cs3C60. We evidence that the insulating antiferromagnetic (AFM) and superconducting (SC) phases coexist only in a narrow p range. At fixed p, in the metallic state above the SC transition Tc, the 133Cs and 13C NMR spin-lattice relaxation data are seemingly governed by a pseudogaplike feature. We prove that this feature, also seen in the 133Cs NMR shift data, is rather a signature of the Mott transition which broadens and smears out progressively for increasing (p, T). The analysis of the variation of the quadrupole splitting νQ of the 133Cs NMR spectrum precludes any cell symmetry change at the Mott transition and only monitors a weak variation of the lattice parameter. These results open an opportunity to consider theoretically the Mott transition in a multiorbital three-dimensional system well beyond its critical point.

source: openbmb/Ultra-FineWeb


The d argument is an ordinary designator (e.g. (^ XCOMP) or sigma::^). The category's argument is a collection of atomic category labels enclosed in set-brackets. For example, the proposition
@(CAT (^ XCOMP) {NP' AP})
might be included in the English lexical entry for become to indicate that the XCOMP of become must correspond to some node labeled either NP' or AP. This would disallow strings like The girl became to go and The girl became in the park, even though the VP rule might allow VP', AP, NP', and PP all to be associated with the category-independent XCOMP function. If the XCOMP is assigned to the top of an ^=! head chain, then the constraint can also be stated in terms of just the lexical category labels:
@(CAT (^ XCOMP) {N A})
The CAT predicate is distributed to the elements of a set, so that this lexical specification for become would allow the mixed-category coordination John became a Republican and proud of it while the string John became a Republican and to go would be ruled out.
If only a single category is specified as the category's argument, the set-brackets may be omitted. Thus the proposition
@(CAT (^ XCOMP) V)
can appear in the lexical entry of verbs that take only verbal complements.
One advantage of a CAT specification over a VCOMP,... NCOMP arrangement is that a predicate such as consider that allows any kind of complement requires no marking at all instead of being four ways ambiguous.
d1 << d2
d1 >> d2
These propositions provide explicit grammatical access to the subsumption ordering of f-structures and other abstract structures. The subsumption ordering corresponds to a notion of information inclusion, in the sense that one structure (the subsumer) subsumes another if the second (the subsumee) contains at least the information found in the first. Thus, if d1 and d2 denote f-structures, d1 << d2 is true if and only if the structure denoted by the subsumee d2 contains all the attributes of the subsumer d1 structure, and on each of the common attributes, its value in d1 is either equal to or subsumes its value in d2. Subsumption provides for asymmetric propagation of information. If you assert that (^ OBJ NUM)=1 and (^ SUBJ)<<(^ OBJ), this does not establish a value for (^ SUBJ NUM): an existential constraint on the subject's number would not be satisfied. On the other hand, if you instead assert that (^ SUBJ NUM)=1 along with the subsumption, the number value will be propagated 'upwards' to the OBJ and would be inconsistent with any incompatible value independently asserted of the object's number. For convenience, d1 >> d2 is equivalent to d2 << d1.
If d1 and d2 denote sets, then d1 << d2 is true if and only if every element of d1 subsumes at least one element of d2. When the elements of both sets are simple symbols, d1 << d2 is equivalent to d2 contains d1. It also follows that if d1 and d2 both subsume some third set d3, then d3 contains d1 unioned with d2.
The explicit subsumption introduced by f1 << f2 is a little different from the implicit subsumption that is introduced when properties are automatically distributed from a set to its elements. For the purpose of set distribution, "properties" include constraining equations such as (^ TENSE) or (^ NUM)~=SG. Thus, ~(^ TENSE) on a set is satisfied if and only if ~(f TENSE) is true for all f $ ^. Explicit subsumption doesn't work this way. If f1 << f2, then ~(f1 TENSE) can be satisfied even if f2 has a TENSE (e.g the constraint doesn't get distributed to f2).
When displaying or printing unpacked f-structures, XLE checks whether a subsumee has the same content as its subsumer. If the defining constraints of the two f-structures are the same, then XLE makes the subsumee equal to the subsumer. Thus, a sentence like John wanted to arrive Monday and to leave Tuesday would have one f-structure with John as a PRED instead of three. If the defining constraints are different, then XLE does not make the subsumee equal to the subsumer. This can happen in a language where verbs assign quirky case, for instance. Sometimes the defining constraints are the same but the negative or sub-c constraints are different. To handle this case, XLE makes the subsumee equal to the subsumer unless sub-c and negated constraints are being displayed, in which case it displays separate f-structures for the subsumee and the subsumer.
Subsumption, particularly of reentrant structures, should be used with a degree of caution. When other propositions assert certain internal equalities in the subsumer, the f-description as a whole may be undecidable and XLE's sentence analysis procedure may not terminate. There have been proposals for restricted versions of subsumption that avoid the mathematical pitfalls, but the linguistic significance of these restrictions is not yet understood. Experience with the current relation in actual grammars may help to sharpen the issues and lead to theoretical refinements as well as improvements in XLE's implementation.
head precedence
f1 h f1
f1 h f2 means the same thing as f2 s f1
f1 s f2 at the same time. f2 >s f1 means the same thing as f1 s (^ OBJ). If you want the scoping relations to be determined by linear order, you can use the following constraints:
 { (^ SUBJ) s (^ OBJ)
| (^ SUBJ) ~s (^ SUBJ)}
This will have the effect of making the SUBJ outscope the OBJ when the SUBJ head-precedes the OBJ, and it will make the OBJ outscope the SUBJ otherwise.
surface adjunct scope
f1 $s f2
f1 $s f2 has the definition:
 f1 $ f2 and
for all x in the set f2, if x $s f2 and f1 s x.
The adjunct scope relations are useful for specifying relative surface scope within a set of adjuncts. They implicitly divide a set into three subsets of elements: the elements that were added using $s, and the elements that were added using $. The scope relations only apply within their own subset. For instance, the following rule will give left scope to the premodifiers and right scope to the postmodifiers, but will leave the premodifiers unscoped relative to the postmodifiers:
NP --> AP*:! $s (^ MODS);
AP*:! $s f2
f1 >s f3
f2 >s f3
f4 { N
| AP
N: (^ PRED ARG1


Map of North Korea
◆ Crudely calculated electricity bills
A common problem faced by all 3 surveyed regions is the lack of electricity meters for calculating household power consumption. The authorities have been attempting to install meters for every house since last year, but the prohibitive 30 USD price of each meter would have had to have been paid by each household. In the end, the plan could not be carried out after it met strong opposition from residents dissatisfied with the unreliable power supply.
As the meters were not installed, officials in charge of electricity distribution have to go door-to-door, cataloguing the appliances owned by each household and making crude calculations of each home's estimated power consumption. This primitive billing system is still in effect.
A reporting partner in Pyongyang complained of the system, saying, "The electricity distribution department always quarrels with residents because they set the rates entirely at their discretion. Lately, we've been paying 5,000 won a month for our house."
The authorities have announced, however, that meters for calculating exact power consumption will soon be required nationwide, starting from September/October.
Editor's notes on North Korean reporters
ARCHIVE(pdf) >>


text:
Hospital Ownership and Financial Performance: A Quantitative Research Review
Yu-Chu Shen, Karen Eggleston, Joseph Lau, Christopher Schmid
NBER Working Paper No. 11662
We apply meta-analytic methods to conduct a quantitative review of the empirical literature since 1990 comparing financial performance of US for-profit, not-for-profit, and government-owned general acute hospitals. We find that the diverse results in the hospital ownership literature can be explained largely by differences in authors' underlying theoretical frameworks, assumptions about the functional form of the dependent variables, and model specifications. Weaker methods and functional forms tend to predict larger differences in financial performance between not-for-profits and for-profits. The combined estimates across studies suggest little difference in cost among all three types of hospital ownership, and that for-profit hospitals generate more revenue and greater profits than not-for-profit hospitals, although the difference is only of modest economic significance. There is little difference in revenue or profits between government and not-for-profit hospitals.
This paper was revised on June 29, 2006
Document Object Identifier (DOI): 10.3386/w11662
Users who downloaded this paper also downloaded these:


text:
Very First Computer Game is as Old as Your Mom
Does anyone want to venture a guess as to when the first computer game was invented? And no – its not Pong.
This year marks the 50th anniversary of Spacewar, the very first computer game ever created. The game, a distant relative to what would eventually be known as Asteroids, puts the player in control of a spaceship that is buoyed by the gravity of a star in the city of the screen that shoots down rockets. It was originally developed at MIT by four students for the bulky PDP-1 minicomputer which more like a radar machine than it does a contemporary computer.
The classic game is still being updated to work on the latest browsers. If you can get past the dated graphics and obscene difficulty then give it a try here.
This means people have been vegging out, playing video games and yelling at computer screens since the early 60′s. Wow, what a long way man has come.
[via Daily Mail]

source: HuggingFaceFW/fineweb-edu


Taroko Xiangde Temple (太魯閣祥德寺)
Taroko Xiangde Temple 太魯閣祥德寺, Hsiang-Te Temple
Xiangde Temple
Xiángdé Sì
Why Should I Go?
Built into the mountainside on the opposite side of the river across the Pudu Bridge from Tianxiang Village in Taroko National Park, the Xiangde Temple is a Buddhist temple from which visitors can enjoy a bird-eye view of Tianxiang and the surrounding area.
This temple is known for having the world's highest-elevated statue of Ksitigarbha (地藏), a bodhisattva revered by East Asians for protecting those in hell (那落迦), as he has vowed not to attain buddhahood until all beings in all hells have been freed. He is generally depicted as a Buddhist monk with a bald head and halo carrying a staff with a Cintāmaṇi jewel at the top (如意寶珠, similar to a philosopher's stone) to light the dark and force open the gates of hell.
Completed in 1968, the main hall is also surrounded by the Tianfeng Pagoda and a white-robed Guanyin statue.
About halfway up the walk is a merchant area selling local tea and snacks.


_USER_ {export:144766, abstract = {
Static analysis tools aim to find bugs in software that correspond to violations of specifications. Unfortunately, for large and complex software, these specifications are usually either unavailable or sophisticated, and hard to write. This paper presents ANEK, a tool and accompanying methodologyfor inferring specifications useful for modular typestate checking of programs. In particular, these specifications consist of pre and postconditions along with aliasing annotations known as access permissions. A novel feature of ANEK is that it can generate program specifications even when the code under analysis gives rise to conflicting constraints, a situation that typically occurs when there are bugs. The design of ANEK also makes it easy to add heuristic constraints that encode intuitions gleaned from several years of experience writing such specifications, and this allows it to infer specifications that are better in a subjective sense. The ANEK algorithm is based on a modular analysis that makes it fast and scalable, while producing reliable specifications. All of these features are enabled by its underlying probabilistic analysis that produces specifications that are very likely. Our implementation of ANEK infers access permissions specifications used by the PLURAL [4] modular typestate checker for Java programs. We have run ANEK on a number of Java benchmark programs, including one large open-source program (approximately 38000 lines of code), to infer specifications that were then checked using PLURAL. The results for the large benchmark show that ANEK can quickly infer specifications that are both accurate and qualitatively similar to those written by hand, and at 5{\%} of the time taken to manually discover and hand-code the specifications.
}, author = {Nels E. Beckman and Aditya V. Nori}, booktitle = {PLDI '11: Programming Languages Design and Implementation}, month = {June}, publisher = {Association for Computing Machinery, Inc.}, title = {Probabilistic, Modular and Scalable Inference of Typestate Specifications}, url = {_URL_ year = {2011}, }


Do You Love Wild Animals?
Show me Wild Experiences
Published on : 27th January 2018
Are UK Wildlife Species Decreasing In Number?
The UK's endangered red squirrel
Based on studies, the UK has lost more than 16% of all animals including fish and birds since the 1970s. Reports also indicate that more than 10% of UK's wildlife species are in danger of becoming extinct. Meanwhile, the population of all endangered species in the UK have dropped by 65% from the 1970s to the present. The population of insects and other invertebrates have also decreased by almost 60%. Furthermore, as compared to the global average, the rate of loss of species in the UK is much faster. Given the aforementioned data, yes, UK wildlife species are decreasing in number.
What Are Causing The Decline In UK Wildlife Species?
Since the 1970s, the UK's population continued to grow together with its stable and developing economy. To address the increasing population, the UK government implemented changes in its overall agricultural approach. The UK used science and technology to make huge advances in farming. It became more efficient and scientific which made harvests better every year. However, as the farming became more sophisticated and successful, the effect on native animals also became worse. In fact, studies point to agricultural change as the primary driver of dropping wildlife population in Britain.
As animals needed to be kept out of the farmlands to ensure optimal crop growth, the clear effect was a large loss of natural habitat for several of them. The animals were forced to move elsewhere to survive. Loss of habitat is identified as one of the top reasons why the UK's wildlife species are decreasing in number. Aside from advanced agriculture, national urban development, which includes the building of infrastructure like roads, bridges, and buildings, also contributed UK's wildlife losing their homes.
The most affected animals due to habitat loss are hedgehogs, great crested newts, grasshoppers and sand lizards. In the 1950s, there was an estimated 36 million hedgehogs in the UK. It went down to around 2 million in the 1990s. It is believed that there are now less than a million hedgehogs in the UK. Similarly, newts, grasshoppers and sand lizards have also suffered a drastic decrease in population since the 1990s.
Another cause of the decrease in UK's wildlife population is the introduction of foreign species that compete with native ones. This is what happened to red squirrels after American native grey squirrels were introduced by the Victorians into the UK in the 1870s. The population of red squirrels, which was believed to be around 3.6 million some decades ago, is now down to an estimated 120,000. Apart from competition, grey squirrels carry a virus which does not seem to affect them but is lethal to red squirrels.
The native water vole is also suffering a similar fate as the red squirrel. However, the decline in the population of water voles is primarily caused by predation and not competition. In the 1920s, the American Mink was brought to the UK for fur farms. However, the minks escaped in the 1950s and bred in the wild. Now, they are the biggest threats to water voles. Since the 1980s, the water vole population declined by more than 90% because of the American Mink.
Scientists and conservationists are also sounding the alarm on climate change as one of the causes of the declining UK wildlife population. This phenomenon is said to be the leading culprit in the 70% drop in the number of seabirds in Britain for the past decades. Waters in Europe are changing which is affecting planktons. Consequently, sea eels which feed on these planktons are losing their food. Meanwhile, kittiwakes and other seabirds feed on these eels. With the scarcity of eels, these birds are forced to move out of their feeding areas and habitats.
With harsher storms and extreme weather, more animals are feared to lose their habitats, too. Also, with the disruption in the normal schedule of seasonal changes, animals are becoming out sync. If this persists, food supply would not be enough or available when needed.
Urbanisation, pollution and exploitation of natural resources have also contributed to the wildlife population concerns in the UK, since it has affected not only the habitats but also the air that animals breathe and the water that they drink. Bottom trawling, which has the objective to catch more fish in the ocean, has ruined sea beds and severely affected wildlife in the ocean.
What Has Been Done To Address The Declining UK Wildlife Population?
Several actions have been taken to prevent the problem from getting worse. Laws were implemented to protect certain species like what was done to the soprano pipistrelle, one of the country's smallest bats. This has caused a resurgence in the population of this species. Similarly, the protected status of the badger has resulted in an 88% increase in its number since the 1980s.
Reintroduction of some species was also done. The beaver, which disappeared in the 18th century due to hunting, has been successfully reintroduced in Knapdale Forest in Scotland. Currently, these animals are growing in number and are starting to be seen in other places in the UK such as the River Otter. Other animal species which were successfully reintroduced include the large blue butterfly, the short-haired bumblebee and the hazel dormice.
Creation of habitats is another step that was taken to address the declining wildlife population in Britain. For example, new reedbeds were made to provide bitterns with a natural habitat. This has helped grow their population by more than 14 times within the past 2 decades.
While there are positive signs that can be seen all over the UK, more needs to be done in terms of preventing the further decline of UK wildlife population. Some initiatives are headed in the right direction, but everyone should make their own contribution to ensure that no more animal in Britain becomes extinct.
The UK's Endangered Red Squirrel
Image Attribution: Photograph by Cameraman [CC BY-SA 2.0], via Wikimedia Commons
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Image Attribution: Photograph © Michael Gäbler / Wikimedia Commons, via Wikimedia Commons
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Image Attribution: Photograph by Mick Lobb [CC-BY-SA/2.0], via Geograph
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Image Attribution: Photograph by Cheryl Reynolds, Courtesy of Worth a Dam [CC BY-SA 3.0], via Wikimedia Commons
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Test Pit Investigation
Test pits are a common way to investigate the subsurface soils and collect soil samples if needed. This is done for purposes of delineating contamination in order to determine the location and size of a plume.Test pits are often requested over soil borings in landscapes where terrain is more extreme and to visibly see at what depth groundwater is at.
ENRC has the necessary equipment and experience in safety performing test pits with accuracy. If test pits aren't what you are looking for and you would need something with less ground disturbance, we can also perform soil borings up to 100 feet.


text:
Peter R. Griffin, an international lawyer who is the managing director of Slaney Advisors, a consulting firm based in London, points out an interesting fact showing just how much Germany can call the tune if trouble arises. Within the maze of documents explaining the Target 2 system, there is the following:
1. The bilateral relationship between the E.C.B. and participants in TARGET2-E.C.B. shall be governed by the law of the Federal Republic of Germany.
2. Any dispute arising from a matter relating to the relationship referred to in paragraph 1 falls under the exclusive competence of the courts of Frankfurt am Main, without prejudice to the competence of the Court of Justice of the European Communities.
Not being an international lawyer, I have no idea what it means to give one court "exclusive competence" — another way of saying exclusive jurisdiction — but then to add that that statement is "without prejudice" to the competence of another court.
Still, it sounds as if it is Germans who will judge any disputes if a central bank does default on loans, or if the Bundesbank tries to put a halt to the gigantic loans it is being forced to make.
"One might have expected the 'cornerstone' of monetary integration to be subject to European law and the European Court of Justice," says Mr. Griffin. "It raises the spectre of the various European central banks fighting each other and the E.C.B. in a German courtroom, under German law."


Asian Scientist Junior: Chang Meemann
Asian Scientist Junior: Chang Meemann
Regular price $18.00 SGD
Wildtype Books
Quantity must be 1 or more
by Jeremy Chan
About the book:
As a child, Chang Meemann was curious about animals and plants in nature. She decided to become a paleontologist— someone who learns about dinosaurs and ancient fish by studying their remains, known as fossils. With her keen research skills, she became the first woman director of an important research center in China studying fossils. Meemann's story demonstrates how passion, nurtured from a young age, can drive scientific excellence.
💡Download your free activity worksheets for the Asian Scientist Junior series here.
Collection: Asian Scientist Junior
This book series dives into the lives of extraordinary scientists who have made significant contributions to the science and technology space—from a pioneer of India's satellite program to the scientist who discovered a cure for malaria. Through these stories of courage and conviction, Asian Scientist Junior hopes to inspire all children, wherever they grow up, to dream of a better tomorrow.
 For more books from the Asian Scientist Junior collection, visit
ISBN: 978-981-11-7900-6
Publication Date: 23 September 2018
Dimensions: 240mm x 195mm
Pages: 36
Format: Hardcover


AR# 2224
VERILOG-XL: Error! Module (...) has a 'timescale directive but previous modules do not
Keywords: Verilog, Verilog-XL, timescale
Urgency: Standard
General Description:
When simulating with Verilog-XL, what does the following error mean:
The 'timescale compiler directive is optional. Designs that do not
contain this require no modification and the default of 1 ns / 1 ns is used.
However, if the design includes a 'timescale compiler directive for any
module definition, then all other modules definitions require this as well.
Otherwise, Verilog-XL flags this as an error.
The 'timescale can be declared in any file.
The UNISIMS has 100ps / 10ps.
The SIMPRIMS has 1ps / 1ps.
The glbl.v has 100ps / 10ps.
The smallest precision of all the timescale directives determines the time
unit of the simulation. For example,
'timescale 1 ns / 10 ps
module1 ();
'timescale 100 ns / 1 ns
module2 ();
'timescale 1 ps / 100 fs
module3 ();
The first timescale indicates that the time units for module1 are in multiples
of 1 ns and it is precise to 10 ps. Thus, the smallest timestep for the
simulator is 10 ps.
The second timescale is 100 ns / 1 ns. Since 1 ns is greater than 10 ps,
the smallest timestep remains 10 ps.
The third timescale is 1 ps / 100 fs. Since 100 fs is smaller than 10 ps,
the smallest simulator timestep now becomes 100 fs.
AR# 2224
日期 05/05/2004
状态 Archive
Type 综合文章
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text:
Last modified: 2011-12-23 by rob raeside
Keywords: vexilloid |
Links: FOTW homepage | search | disclaimer and copyright | write us | mirrors
Smith, 1975, p. 30 defines a vexilloid as:
An object which functions as a flag but differs from it in some respect, usually appearance. Vexilloids are characteristic of traditional societies and often consist of a staff with and emblem, such as a carved animal, at the top."
He further refers to an illustration on p. 13 showing an animal skull tied atop a rough wooden pole, captioned: "Victory over nature and victory over fellow human beings are common themes in flags throughout the history. These prehistoric vexilloids are only earlier, less sophisticated versions of the modern flagpole topped with a golden eagle (or lion or similar beast) and of the flag bearing emblems of warfare and power."
On p. 12 is shown an other primal vexillum - a rough piece of textile dyed red (possibly in the blood of a slain enemy or animal) tied up atop a rough wooden pole.
Other vexilloids shown in his book include: the Roman signum and the Norse metal vane (p.14), the German Schellenbaum (p. 21), set of various vexilloids to which he gave not special names on p. 34: 4th c. Iran, 7th c. England, 13th c. Mongolia, 14th c. Ethiopia, 16th c. Mexico. Also on pp. 34 and 35 are shown various Egyptian vexilloids some thousands years ago. On p. 36 are shown early Chinese vexilloids looking somewhat like large fans, then again various Roman vexillliods, on p. 37 some naval vexilloids on Antique coins. On p. 38 are mentioned parasols ("umbrella") used as vexilloids in SE Asia and West Africa and again some Chinese fans. On pp. 60-61 are stories of the Labarum and Dragon Flag which are on the edge between flags and vexilloids, I guess.
Page 92 repeats the image of the "first flag" captioned: "The first flag to be used on land may well have been a strap of material dyed with the blood of an enemy or slain animal."
On p. 104 are, as example of modern vexilloids shown Nazi standards. Page. 130 shows Roman-Gallic vexilloid with a cock atop, and p. 140 an Italian one. Pp. 164-171 include several Japanese vexilloids used by samurais, and p. 178 shows Soviet metal flags sent to the outer space.
I guess that this covers the topic of vexilloids quite exhaustively. I may
add that the municipal and religious gonfalons especially popular in Italy (and
modern Croatia) are also and edge case between flags and vexilloids - it is the
size of the textile part there that allows them to be counted as flags.
Željko Heimer, 31 January 2004


The Harley Therapy platform will always show times in the timezone that the device you are using is set to.
So if you visit another country and your phone or laptop is set to the local time, this is the time that you will see in your calendar and on all appointments.
However the first time you visit your calendar in this new location you will be presented with the following dialog:
What this means is that although you are viewing the calendar in your local timezone, your working hours are tied to a different one. If the relationship between the two timezones changes during the year this means that your working times may vary on a week to week basis in this new timezone.
Note in general you should not select Move my working times unless you are actually moving to this timezone permanently.
If you are planning on staying in this timezone you can Move your working times which will convert the times from the existing timezone to the new one based on the current difference between the timezones. In the above example a working time from 13:00 to 17:00 in the UK would move to a working time from 08:00 to 12:00 in New York (or 09:00 to 13:00 at some times of the year).
Anchoring working times to a timezone is required to manage changes in daylight savings time that occur at varying times around the world.
If you are just in that location temporarily you can click on Ignore, but if you then wish to edit your working hours they will be shown in your anchor timezone with a warning, e.g. if your timezone was set to New York and you were viewing in the UK the times you would still edit them in the New York timezone.
When viewing your working times in another timezone your working times may vary from week to week if the timezone you are located in does not have daylight savings time changes aligned to your normal time zone.
You can find out more out this in our article describing what the effect on your working hours is when you are outside your normal timezone.
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This paper summarizes and discusses the results of a survey on country practices in the management of sovereign assets and liabilities. Twenty-eight countries, mostly high-income economies, responded to the questionnaire. The survey responses provide detailed information about various approaches to the sovereign asset and liability management framework in terms of balance sheet production as well as objectives, priority areas, and challenges associated with integrated management. In addition to the survey results, where possible and relevant, this paper provides insight through prominent country examples. The survey results confirm that the number of countries that have developed such a framework is limited. Although most of the respondents indicated that they regularly produce an accounting balance sheet, the objective of this exercise is often limited to monitoring sovereign assets and liabilities rather than determining mismatches between them. In the cases where a sovereign asset and liability management framework is implemented, there are significant differences across countries. Most countries include state-owned enterprises in the sovereign balance sheet, but only a minority also considers central banks, in some cases only international reserves and sovereign funds. The challenges cited include institutional arrangements, uncertain or lacking mandate, coordination between institutions, data availability, and valuation of assets. Most of these challenges are related to the implementation of the approach. The development of sound practices for sovereign asset and liability management could benefit governments and facilitate the implementation of a holistic approach to manage their balance sheets and related risks, increasing their resilience to shocks.


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What effects do factors that impair or enhance performance in individuals have when these individuals act in groups? We provide a framework, called the GIE ("Effects of Grouping on Impairments and Enhancements") framework, for investigating this question. As prominent examples for individual-level impairments and enhancements, we discuss sleep deprivation and caffeine. Based on previous research, we derive hypotheses on how they influence performance in groups, specifically process gains and losses in motivation, individual capability, and coordination. We conclude that the effect an impairment or enhancement has on individual-level performance is not necessarily mirrored in group performance: grouping can help or hurt. We provide recommendations on how to estimate empirically the effects individual-level performance impairments and enhancements have in groups. By comparing sleep deprivation to stress and caffeine to pharmacological cognitive enhancement, we illustrate that we cannot readily generalize from group results on one impairment or enhancement to another, even if they have similar effects on individual-level performance.
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Journal article
Pers Soc Psychol Rev
Publication Date
3 - 28
caffeine, enhancement, group performance, group processes, impairment, neuroenhancement, pharmacological cognitive enhancement, process gains, process losses, sleep deprivation, stress, Caffeine, Group Processes, Humans, Motivation, Psychomotor Performance, Sleep, Sleep Deprivation


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The Safe 2 Race system was developed after we recognised the need for automating manual warnings and marshal systems during race events, to improve safety and response times. Our systems and hardware use wireless connections, artificial intelligence and unique algorithms to automate warnings and safety features to benefit circuits, race organisers, race control, marshals, drivers, teams and spectators. The S2R system updates every second on a range of interfaces and has various user functionality permissions.
Safe 2 Race System Key Functionality
The key functionality of the Safe2Race system for circuit, championships and driver use:
- Real time vehicle status awareness, tracking and timing vehicles for superior circuit and competition safety and compliance.
- Superior safety technology integrates vehicle to Race Control communications with instant notifications and automatic features.
- Instantly gives circuit and championship officials the information they need, whilst providing competitors and spectators real time race information – available on web and mobile interfaces.
- An electronic system with integrated AI designed to pair medical and impact data, offering currently unrivalled safety to competitors in Motorsport.
- Automated marshal flagging system benefits race marshals, race control and competitors.
- Instant in car notifications for drivers to notify of any change in race conditions, notification reaction within 1/10th second.
- Integrated systems for race control, team and spectator race timing information with a range of interface permissions.
- In-built penalty automation systems and post incident analysis.
- Tiers of access and custom permissions.
How It Works
The system tracks all vehicles locations each second, allowing flag conditions to be set within the entire circuit.
Safe2Race has been developed to combat the problems presented by human error and to provide safer racing conditions.
The system allows communication directly between every vehicle in a 'hot zone', pre-defined by race control.


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In 2013 Savaye and Mandisa created the Di Fthatani Project to help local people living in Townships in South Africa overcome hunger by teaching them a simple innovative farming method called tunnel farming. This method used people's basic knowledge of agriculture to plant fresh vegetables under a tunnel and allows them to grow in a controlled environment, using less water and space than a normal garden. The vegetables planted were carefully selected based on the vitamin and mineral deficiencies present within the community, such as vitamin A and zinc.
They also ran workshops on life skills, to teach the importance of individuality and self-awareness, basic financial skills, nutrition, and entrepreneurship. Today in each township Orlando – Soweto, Alexandra – Sandton, and in Tembisa – Midrand there are three thriving tunnel farms. The education received has enabled the people of those townships to feed and provide income to their local communities. Each tunnel has provided $5,000 to date. More importantly these tunnels are self-sustaining and run entirely by the communities.
Last updated: 25 June 2018


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|Uploaded:||February 17, 2012|
|Updated:||February 17, 2012|
I really didn't know what type of scene to make for a forest like theme with when creating this next landscape lesson with a 'for kids' theme. After thinking of what else I could create that could help aid people with drawing specific backgrounds, I came up with the idea to do a tutorial on "how to draw a jungle for kids", step by step. This lesson is going to be full of trees, leaves, foothills, and a bunch of moss filled ground. A jungle is a place that has heated temperatures, with a muggy, misty, sticky feel. I had so much fun making this jungle because my little eight year old sister helped me out with the concept. I think that there is a lot of potential with this background because you can add some tropical birds, insects and even reptiles to accent the whole drawing. I was going to include some wild life, but I thought I would leave that up to you guys. Well, that's it, have fun with drawing a jungle for kids, and I will return in a bit with some more fun for you all.


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THIS SURVEY EXPLORES CANADIANS' AND AMERICANS' PERSPECTIVES ON MORTGAGE RATES AND INFLATION.
As inflation remains high, many Canadians and Americans are exploring ways to reduce their expenses. In our latest North American Tracker, we explored how inflation is impacting Canadians and Americans, and how an increase in mortgage rates would impact Canadians and Americans who currently have a mortgage.
This survey is conducted in collaboration with the Association for Canadian Studies (ACS) and published in the Canadian Press. This series of surveys is available on Leger's website. Would you like to be the first to receive these results? Subscribe to our newsletter now.
MORTGAGE RATES AND INFLATION
- If mortgage rates went up by 1%, 13% of Canadians and 10% of Americans who have a mortgage would either face a significant financial burden, have to consider selling their home or have to sell their home. These figures balloon if rates were to increase by 3%.
- The proportion of Canadians (85%) and Americans (88%) who indicate that inflation is a serious problem for their household has increased since our last survey published on March 17, 2022.
- The top actions Canadians and Americans have taken due to rising inflation over the past few months are:
- Buying less expensive items at the grocery store (65% of Canadians, 49% of Americans)
- Eating at restaurants or ordering take-out less often (53% of Canadians, 41% of Americans)
- Reducing food waste to make their money go further (46% of Canadians, 40% of Americans)
This web survey was conducted from May 6 to 8, 2022, with 1,534 Canadians and 1,003 Americans, 18 years of age or older, randomly recruited from LEO's online panel.
A margin of error cannot be associated with a non-probability sample in a panel survey. For comparison, a probability sample of 1,534 respondents would have a margin of error of ±2.5%, 19 times out of 20, while a probability sample of 1,003 respondents would have a margin of error of ±3.094%, 19 times out of 20.
THIS REPORT CONTAINS THE RESULTS FOR THE FOLLOWING QUESTIONS AND MORE!
- If mortgage rates went up, what would be the impact on your household finances?
- How serious a problem is inflation/increasing interest rates for your household?
- How would you describe your own household's finances today?
- What is the impact of inflation on your household in the following areas? Has inflation had…


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Series Hybrid vs. Parallel Hybrid
April 18, 2012 by Ron Averill
Hybrid refers to something that is made up of two or more diverse ingredients. The goal in combining them is to capture and merge the advantages of each ingredient, while overcoming any disadvantages. But ingredients can be combined in many ways, resulting in considerable variation in performance depending on how they are combined.
In optimization search algorithms, as with electric vehicles, there are two main categories of hybrids: series and parallel. To better understand the basic
differences between the series and parallel hybrid approaches, let's consider a simple illustration.
Passing batonSuppose a team of people needs to carry an object a long distance. In a series hybrid strategy, one person will carry the object for a while, and then someone else will take the load and carry it a bit further. This "tag team" approach continues until the required distance is covered. This series approach might work well if the object is lightweight and small. But if the object is heavy or awkwardly shaped, then it will be difficult for one person to carry it even a short distance, if he or she can move it at all.
RowersIn this situation, it is clearly more effective for two or more people to carry the object together in a parallel hybrid approach. By working together in a well-coordinated effort, the load can be shared in a way that allows each participant to contribute to the task. Each contribution, however small, reduces the load on other team members, allowing the group to carry the load faster and further with less fatigue. Drivers of horse-drawn wagons, dog sleds and Christmas sleighs discovered this truth a long time ago.
Series hybrid optimization
Turning our attention to optimization, a series hybrid algorithm is developed by starting with one search algorithm, and then switching to another one (using a different strategy than that of the first algorithm) to continue the search. There is no limit to the number of different search strategies that can be used in this sequential manner.
Typically, a series hybrid algorithm begins with a search method that is good at global exploration, such as a Genetic Algorithm, and ends with a local refinement strategy, such as a gradient-based algorithm. Various other search methods can be sandwiched between these two. On some problems, this type of series optimization algorithm has been shown to perform reasonably well compared to monolithic (single-strategy) algorithms, when an appropriate set of algorithms and tuning parameters has been chosen.
How well a series hybrid optimization strategy performs depends on the specific algorithms and tuning parameters used at each stage of the search. Because each algorithm is working alone, the progress made at any time depends on how effective the selected method is for that problem and what it does with the information provided by previous search methods.
As I've mentioned in other posts, it is usually impossible to know which algorithms or values of tuning parameters will work well on a problem before it is solved. So, series hybrid algorithms have the same fatal flaw as most monolithic strategies, except the number of unknowns is now multiplied by the number of different strategies used.
Moreover, additional unknowns are introduced, such as the order of the strategies and when to stop one strategy in favor of another. Default values for these parameters may or may not work well for your current problem.
Parallel hybrid optimization
Parallel hybrid algorithms, like SHERPA (in HEEDS® MDO), overcome many of the shortcomings of series hybrid algorithms. In this strategy, multiple optimization methods actually work simultaneously to solve a problem in a collaborative fashion. Rather than contributing sequentially, these methods work together to search a design space and identify optimized solutions, like many hands helping to carry a heavy load.
As with any good team, a parallel hybrid algorithm requires good leadership, communication, coordination, and accountability. These attributes are built into the algorithm's infrastructure from the start.
Instead of separately exploring and refining at different stages of a search, a parallel hybrid algorithm enables these two essential activities to take place concurrently and synergistically! This not only speeds up the search but also makes it more likely to find the global optimum.
In a series hybrid algorithm, the search history can be used to determine which individual algorithm(s) made the most meaningful contribution to the search. But this is not possible with a parallel hybrid algorithm, because each algorithm behaves very differently as part of a team than it would individually.
Nevertheless, there are ways to hold an individual search strategy accountable for its contributions within a parallel hybrid algorithm, and those methods that do not contribute enough over time can be replaced by new methods or have their resources transferred to existing methods that are contributing at a higher level.
The characteristics of a well-designed parallel hybrid optimization algorithm include shared discovery, intellectual diversity, synergistic search, and greater robustness. Oh, and better designs, faster!
Collaborative Optimization
March 19, 2012 by Ron Averill
Collaborative optimizationMany engineers still resist the use of optimization algorithms to help improve their designs. Perhaps they feel that their hard-earned intuition is just too important to the solution process. In many cases, they are right.
At the same time, most optimization algorithms still refuse to accept input from engineers to help guide their mathematical search. The assumption is that the human brain cannot possibly decipher complex relationships among multiple system responses that depend upon large numbers of connected variables. Unfortunately, this is true.
Is this a case of irreconcilable differences? Or is it simply an example of everyone wanting to be the teacher, and no one wanting to be the student? I'm reminded of the Latin proverb:
Surely engineering intuition can benefit from the results of mathematical exploration, and vice-versa. It seems almost obvious.
So why do engineers and optimization algorithms prefer to work solo? I don't believe they prefer this. I think it is more a matter of not knowing how to collaborate, or not having the tools to facilitate this interaction.
Fortunately, modern optimization software tools like HEEDS now have features that encourage engineers to learn from the intermediate results of an optimization study and to share intuition-based insights with the optimization algorithm during a search. This collaborative optimization process leverages our two most powerful design tools – human experience and computers.
Consider the following example:
 - An engineer uses intuition and experience to define the goals of an optimization problem and a baseline (starting) design.
 - An optimization search algorithm then begins to explore the design space to uncover mathematical relationships that can lead to an optimized design, all the while sharing its progress and discoveries with the engineer.
 - While monitoring, validating and interpreting these intermediate search results, the engineer starts to learn what makes some designs better than others. This new understanding causes the engineer's intuition to practically blurt out, "If design B is better than design A, then design C should be even better!" Of course, the optimization algorithm might eventually discover design C on its own, but it would surely take a lot longer to do so.
 - The engineer shares his insight with the optimization algorithm, which happily accepts the input and puts it to use immediately. If the engineer was correct, then the algorithm now has new information that will accelerate its search. If the engineer's intuition did not lead to a better design, then the algorithm has only spent one design evaluation to discover this, and the new data may still have some valuable nuggets that can be exploited later in the search.
 - The circular process of exploring monitoring interpreting sharing is continuous throughout the search process, leading to better designs in much less time than was previously possible.
 - The enhanced communication between the engineer and the optimization algorithm builds a strong interdependent relationship between the two, leveraging the strength of each.
Collaborative optimization tears down one of the most common objections that experienced engineers have to using optimization methods. It not only makes full use of an engineer's intuition, but improves that intuition through experience gained from mathematical exploration of the design space. This is accelerated learning at its best.
Further, this is not one of those nice ideas that looks good on paper but doesn't work well in practice. This technique has already been used very successfully on many challenging design problems, including composite aircraft, crashworthy cars and insulated vaccine carriers.
There is now overwhelming evidence that a more intimate coupling of intuition with a hybrid, adaptive optimization algorithm can solve many challenging problems previously thought to be intractable.
Of course, in order to find the best solutions many optimization algorithms tend to explore a design space broadly, even spending some time in those regions of the space that don't yield any good designs. So the process helps us to understand not only what makes a good design, but also why some designs perform poorly. This reminds me of another important proverb:
"Wise men learn by other men's mistakes, fools by their own."
March 5, 2012 by Ron Averill
Clearly, the primary objective is to cross the finish line in the shortest time possible. But it's still important to remember that the total race time is the sum of the times necessary to complete three very different parts of the race – the swim, the bike and the run.
In optimization, this is often referred to as a summed objective problem. It is a good way to handle optimization problems containing multiple objectives that do not directly compete with one another. In other words, improving the value of one objective does not inevitably worsen another one. For example, swimming faster does not necessarily make you run slower, so these two objectives can naturally be summed together when seeking an optimal race strategy.
However, non-competing objectives might still be strongly coupled. In a triathlon, if you spend too much energy swimming faster, then you won't have enough energy remaining to bike or run at your best, resulting in a slower overall race time. Based on the athlete's level of skill and fitness,


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Government targets for England look to reduce by 40% overall the number of serious injuries and deaths on the nation's roads by 2010, (compared with a starting point - baseline - of the 1994-8 average figures). The target for those aged 15 or under is higher, at 50% reduction.
But when researchers compared police statistics (which the Government uses for its figures), and hospital statistics between 1996 and 2004, they found large discrepancies.
Police figures showed that by 2004, numbers of those killed or seriously injured had dropped by almost a third (from 86 per 100,000 population, to 59 per 100,000). However, the police statistics showed a much smaller decline in the number of people killed than the number seriously injured.
Police statistics showed a 32% drop in serious but non-fatal injuries. However, the researchers found that hospital figures for non-fatal road injuries showed that rates had hardly changed between 1996 and 2004.
The authors suggest the discrepancies are probably down to an increase in under-reporting of injuries in the police statistics and that, if there has been a decline in injuries, it is probably only in those considered by the police to have been minor.
More investigation is needed, say the authors, since the findings cast doubt on whether there has been much progress on the Government's target to date - and on its likelihood of being met by 2010. In practical and policy terms, much more needs to be done to ensure that there are real and substantial reductions in serious injuries on England's roads.


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From the c2wiki page on coupling & cohesion:
Cohesion (interdependency within module) strength/level names : (from worse to better, high cohesion is good)
 - Coincidental Cohesion : (Worst) Module elements are unrelated
 - Logical Cohesion : Elements perform similar activities as selected from outside module, i.e. by a flag that selects operation to perform (see also CommandObject). i.e. body of function is one huge if-else/switch on operation flag
 - Temporal Cohesion : operations related only by general time performed (i.e. initialization() or FatalErrorShutdown?())
 - Procedural Cohesion : Elements involved in different but sequential activities, each on different data (usually could be trivially split into multiple modules along linear sequence boundaries)
 - Communicational Cohesion : unrelated operations except need same data or input
 - Sequential Cohesion : operations on same data in significant order; output from one function is input to next (pipeline)
 - Informational Cohesion: a module performs a number of actions, each with its own entry point, with independent code for each action, all performed on the same data structure. Essentially an implementation of an abstract data type. i.e. define structure of sales_region_table and its operators: init_table(), update_table(), print_table()
 - Functional Cohesion : all elements contribute to a single, well-defined task, i.e. a function that performs exactly one operation get_engine_temperature(), add_sales_tax()
(emphasis mine).
I don't fully understand the definition of logical cohesion. My questions are:
 - what is logical cohesion?
 - Why does it get such a bad rap (2nd worst kind of cohesion)?
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Logical cohesion can be bad because you end up grouping functionality by technical characteristics rather than functional characteristics. For example, consider an application consisting of multiple modules. Each module represents some business domain and has corresponding data access code. If you group all data access code across all modules then you have logical cohesion. After all, it is all data access and it in some cases it is beneficial to be able to evaluate the data access patterns of an application. This however is problematic because the business domain provides the module boundaries, not the technical domain. By achieving logical cohesion you end up losing on functional cohesion. Typically, the business domain defines a well-defined unit of deployment and technical aspects are there to support the business domain.
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That's a good answer, although to avoid confusion, I'd mention that in the context of object oriented programming (and the examples on Wikipedia and c2wiki), a module is essentially a class. This means that the comment about the "huge if/else" also makes more sense. – Daniel B Oct 3 '12 at 7:05
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From how it is described, I would say it is about coupling code together that has some cohesion, but breaks object orientation.
Example: calculation of a polygon's area. When you put the calculation for the square together with the calculation for the triangle, and only choose by the input-param, then you have grouped two things logically by their outcome, not taking into account their real nature.
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A brief background: I'm working on a web-based drawing application and one of the tools I'm implementing is a 1-pixel thick pencil. The tool allows the user to draw 1px aliased lines on the canvas.
In order to determine where the user is drawing on the canvas, mouse coordinates are monitored. If mouse1 is held down, the pixel the cursor is over will change. Essentially it works just like the pencil tool in Photoshop.
NOTE: Bresenham's algorithm will not work for this situation. My input is submitted in real-time, so I'm not drawing a line from P0 to P1 where the distance between P0 and P1 is many pixels. In general, P1 is a neighbor of P0.
The issue I'm having is that my resulting lines do not have a perfectly clean 1px weight. Here's an example:
Line comparison
Note that both of the lines are hand drawn, so there is some variance. What's interesting is that Photoshop is able to make a much cleaner 1px representation of the line that I draw. The reason why my line looks dirtier is because of this:
Photoshop's line
My line
When drawing with the tool in my application, the red pixels are filled in. In Photoshop, the red pixels are not filled in. This makes sense because in order to move from a given pixel to, say, its south-east neighbor, either the east or south neighbor will likely be passed over. There is an extremely slim chance that the cursor will pass exactly over the corner into the south-east neighbor, avoiding the drawing of the red pixel, but this usually doesn't happen.
So, the question I'm left with is how Photoshop is able to skip the red pixels that are showing up in my lines. The only thing I could think of was waiting until two pixels are queued up before drawing either of them so I would know if a "corner-neighbor" was passed over. In that case I would just not draw the first of the two pixels because it would be equivalent to a red pixel in my diagram. This runs the risk of not drawing an intended pixel if the user draws a pixel, moves the cursor one pixel south, and then one pixel east. Both of the pixels should be drawn, but the algorithm would say otherwise.
Any ideas? How might Photoshop be handling this issue?
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What happens when you move the mouse fast? Does it skip pixels? – Hans Passant Dec 28 '10 at 22:07
_USER_ Passant Yes, when drawing quickly I get lines similar to what Photoshop produces. What's odd is that you don't have to draw quickly in Photoshop to skip those unwanted pixels. – Xenethyl Dec 28 '10 at 22:10
It stores the mouse points in a polyline. It doesn't add a new segment to it when it can simply extend the previous one. – Hans Passant Dec 28 '10 at 22:16
_USER_ Passant I'm not sure I follow completely. If I draw a line that passes though (50,50), (50,51), and (51,51), the ideal result would be skipping (50,51) because I was moving down to (51,51). But the points in the polyline would say that the line should move through (50,51)...? – Xenethyl Dec 28 '10 at 22:20
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up vote 3 down vote accepted
Original: Have a look at Bresenham's line algorithm. It can easily extended concerning smoothing etc.
Edit: Regarding the development of the question and the discussions (especially the comments below), I'd like to extract some interesting points: Photoshop's pencil tool does also draw very similar lines with "east" and "south-east" pixels as well, if the mouse is moved relatively slowly thus providing many samples for all those pixels. As soon as the mouse is moved faster, the trajectory does not provide samples for all directly neighbored pixels. The result would then be the desired 1-pixel thick line. In conclusion, we note: There is no "magic" behind Photoshop's pencil tool; it just seems to scan fewer samples. For details see discussions/comments below.
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I agree; look up Xiaolin Wu's line algorithm in wikipedia for example. – WebMonster Dec 28 '10 at 21:30
_USER_ Xiaolin Wu's line algorithm is for drawing anti-aliased lines. – Xenethyl Dec 28 '10 at 21:32
_USER_ I just had a look at Photoshop's pencil tool we are talking about. It draws lines with "east" and "south-east" pixels as well that are identical looking compared to your own solution, if I move the mouse relatively slow and thus provide samples for all those pixels. As soon as I move the mouse faster and thus do not provide samples for all directly neighbored pixels, the result is indeed similar to your desired Photoshop line. Did you observe this, too? Maybe your progam is too fast and scans for too many samples... ^^ – Flinsch Dec 30 '10 at 8:12
_USER_ I think you may have just helped me realize an issue with my current implementation. Right now I'm firing my draw event whenever the cursor moves to a new pixel. I didn't really give this much thought, as I figured it would be more efficient (if the user doesn't move their mouse, there's nothing new to draw). If I switch to polling instead of event handling, I then have the ability to offer brushes that build up paint over time (ex. an airbrush). I'll experiment with this tomorrow, but I think polling will work nicely. I'll just have to figure out the right interval. – Xenethyl Dec 30 '10 at 9:58
_USER_ I just finished moving my code over to 10ms polling instead of mouse move event handling. Not only is performance better (the browser isn't dropping any mouse move events), but my lines are of much higher quality (rivaling Photoshop). I never would have thought that my original approach was accurate to the point where the quality of my lines degraded. Paint build-up was a freebie with this change too, which I'm quite happy about. If you could edit your answer to note the discussion below and/or polling I'll mark this as accepted. Thanks so much! – Xenethyl Dec 30 '10 at 21:04
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The difference between both lines is basically that Photoshop is re-considering the n-1 pixel drawn AFTER drawing the pixel n, and erasing it if it gives positive with one of the following masks:
 x 1 x x 1 x
 1 o x or x o 1
 x x x x x x
 x x x x x x
 1 o x or x o 1
 x 1 x x 1 x
x= Don't mind
o= The n-1 pixel
1= Marked pixel after drawing pixel n
Or written as logic:
Suppose pixel n-1 is at a[i,j], so, after marking the pixel n, check:
If ( (a[i-1,j ]==1 && a[i ,j-1]==1) ||
 (a[i-1,j ]==1 && a[i ,j+1]==1) ||
 (a[i ,j-1]==1 && a[i+1,j ]==1) ||
 (a[i ,j+1]==1 && a[i+1,j ]==1))
 Unmark a[i,j];
You may want your to draw your line delayed one pixel just for not showing your "disappearing" pixels (although I doubt it'll be noticeable at that scale).
alt text
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Thanks for helping out with one of my questions again. The environment that I'm running this in very much favors a preemptive solution over a reactive one ("deleting" a pixel is an involved process, especially when you consider drawing over something that already exists). The issue here is deciding whether or not that one pixel should really be deleted. What if the user intended to draw the "L" shape in your diagram? The algorithm would blindly delete it. I'd find it hard to believe Adobe's implementation is insanely complicated with prediction and trajectory tracking... – Xenethyl Dec 28 '10 at 23:34
_USER_ If the user is picky about the corners in Photoshop, he will probably use another tool, and not a freehand pencil. But I agree in that PShop may have better algorithms in there. As for drawing over something pre-existent, I thought you have an "undo" command, so Unmarking!= Deleting. – belisarius Dec 28 '10 at 23:41
Agreed that user preference comes into this a little bit. Unfortunately, this issue is at the core of my drawing algorithm for any other drawing/painting tools (ie. pencil with different tips, paintbrush, etc). Every line that the user draws is treated as a 1px line, and if a tip (ex. a star) is being used it's just stamped at each pixel coordinate. Undo is not implemented yet, but the process would be similarly involved. Changing pixel data requires a copy, read, change, and write in this environment, unfortunately. – Xenethyl Dec 28 '10


Damage Threshold is a combat statistic in Fallout, Fallout 2, Fallout: New Vegas and Fallout Tactics. It was removed in Fallout 3, leaving Damage Resistance as the only armor statistic. However, it was restored in Fallout: New Vegas, before being removed yet again in Fallout 4.
Fallout, Fallout 2, Fallout Tactics
Fallout: New Vegas
See also: Combat damage
Imagine that there is an amount of damage that armor directly subtracts from damage… a "threshold" of damage, if you will. While a small percentage of damage may get through even the thickest armor, damage threshold can effectively neutralize a lot of small arms.J.E. Sawyer
Fallout: New Vegas mostly moves away from the exclusive use of Damage Resistance (DR) in Fallout 3, towards Damage Threshold (DT). Like in previous games, DT can function as an outright subtraction: if a shot is fired with a damage value of 40 against a DT of 10, then 10 damage will be ignored.
However, the sequence of calculations differs compared to previous games. DR is applied first. The value after this adjustment depends on any DR a player character has, which is capped to a DR of 85 (85%); however, DR above 80 does nothing, so the theoretical cap is 80.
DT applies after that, with a limit: the final damage taken cannot be lower than 20% of the base attack; if lower, it is overwritten to 20% instead.[1] For example, with 80 DR, DT will not do anything; however, with 70 DR against an attack of 10 damage, a DT of 1 will reduce the damage taken from 3 to 2, and DT above that will not help. Provided that a character's DR is 79 or less, any amount of DT is theoretically useful. Applying the previous example to an incoming attack of 100 damage, 70 DR and 1 DT would reduce damage instead from 30 to 29 - a much less significant reduction than 3 to 2.
So, to evaluate the earlier example, if an attack of 40 damage hits a character with 85 DR and 10 DT, the damage is first reduced to 6 (40 × 0.15 = 6), and then reduced by 10. The final result (-4) is less than 20% of the base attack (40 × 0.20 = 8), so the damage taken is raised to 8 instead.
Damage which is reduced to below the 20% minimum value is indicated with a shield icon next to the health bar (either the player character's, or the non-player character's). When all of an enemy's DT (if it is not 0 to begin with) is overcome with armor piercing attacks, then a broken shield icon will appear in its place instead. The shield icon is shown during V.A.T.S. and on the health bars once damage has been inflicted upon a target and will remain for 3 seconds afterwards.
The default value for DT is set at 0; this is then modified mainly by the DT value of armor and clothing worn. Other attributes can affect the DT value of a character, both permanently or temporarily. Perks and consumables can increase the player character's DT, while the Kamikaze trait reduces it. When attacking, the use of ammunition can modify the target's DT either way, with hollow point generally increasing their DT, and armor piercing decreasing it.
Difficulty and critical damage impact
As with the player character's damage, the difficulty multiplier of incoming damage is applied after the damage resistance and damage threshold calculations. For example, a regular deathclaw does 125 damage and Very Hard difficulty's inbound damage multiplier is ×2. If the player character has no DT and DR, the damage dealt is 250. If the player character has 40 DT and no DR, the damage becomes (125 – 40) × 2 = 170.
Unlike the difficulty multiplier, the critical damage is applied before the damage threshold calculations as it counts as the base damage. The deathclaw mentioned above deals an additional 125 damage when it crits, leading to an attack power of 250 on Normal difficulty. With 40 DT, the player character suffers from 210 damage instead, leading to 420 damage on Very Hard difficulty.
While unimportant in such a case, it becomes vital when the enemy has a low attack power, which is reset to 20% of the base damage due to the cap mentioned in the previous section. For example, a young deathclaw does 40 damage and if the Courier's DT is 40, the attack will deal 8 (40 × 0.2) damage on Normal difficulty. However, when a young deathclaw crits, it deals an additional 40 damage resulting in 80 total damage. With the player character's DT applied, the final damage becomes 40, surpassing the 20% cap and dealing the raw damage. On Very Hard difficulty, it leads to 16 (non-crit) and 80 (crit) damage, respectively.
Comparison between Damage Threshold and Damage Resistance. Implications
DR factor becomes much more important in extreme cases. Vanilla deathclaw (like any other enemy) will completely ignore the DT factor if the Courier has 80%+ DR (Med-X + Slasher + Battle Brew combo gives 85%) and deal 50 damage on very hard difficulty in any case, against any DT index, as the damage cannot be lower than 20% of its basic attack ((125 × 0.2 = 25) × 2 (very hard difficulty multiplier) = 50); its critical damage will be capped at 100 instead (compare to 500 raw crit damage against the Courier with no protection and 420 damage against the courier with 40 DT). The armor indicator will appear upon the hit as well, confirming the deathclaw is dealing it's minimum possible damage.
It means that when the Courier has to deal with high damaging opponents (like said deathclaws), the most reliable method is to increase DR to its maximum wearing no armor at all for faster movement – or the armor with the best possible buffs[2]. If the player has no Battle Brew (→ 50% DR), then, against the said deathclaw, 37.5 DT is needed to cap creature's damage to its minimum (125 × 0.5 = 62.5; 62.5 – 37.5 = 25).
As a more extreme example, take Legendary bloatfly from Old World Blues add-on. Its plasma damage is set to 300 (equal to that of deathclaw alpha male), becoming plain 600 on very hard difficulty. However, with 80%+ DR it's attack power is capped at 60 at normal and 120 at very hard difficulty, making it possible to survive several blasts for a high-level Courier. With 50 DT and no DR, surviving its attacks dealing 500 damage on very hard difficulty ((300 – 50) × 2) is possible only on a very high level. With 50% DR and 50 DT, the damage becomes 200 ((300 × 0,5 – 50) × 2) on very hard difficulty.
Interestingly, although no DT and DR of 50% makes very hard difficulty experience equal to no armor experience on normal difficulty, the DT factor alters the picture. If the normal difficulty deathclaw hits the player with no DR and DT of 40, it deals 85 (125 – 40) damage; however, the very high difficulty deathclaw hitting the Courier with 50% DR and 40 DT results in 50 damage instead (125 × 0,5 – 40 = 22,5; → override to 125 × 0,2 = 25; 25 × 2 = 50 (very hard multiplier applied)).
To sum up, high DT is enough against lowbut fast-damaging opponents (e. g., any fast-firing humanoids) unless they don't get critical hits; however, enemies with powerful attacks (mainly deathclaws and humanoids with explosives or single-action high-end weapon) should be countered with maximum DR instead.
 - Despite DT being the determining factor for armor in Fallout: New Vegas, when repairing armor, merchants will list DR instead. All armors when viewed from the repair screen have a DR of 0. This is fixed in patch 1.1.1.
 - In Fallout: New Vegas, the only articles of clothing that provide DR are the rebreather, which is acquired during the quest Volare!, the Vault 11 jumpsuit and the Scientist outfit.
 1. _URL_
 2. It is important to note that, due to a bug, any armor worn with high DR will receive immense amount of damage when hit and degrade extremely quick. This makes no-armor choice much more preferable.


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Mass and Energy Balance in Fire Ventilation
Milestone! As I was preparing to upload this post, I realized that this is the 200th CFBT-US Blog Post since its inception in August of 2008. Quite a lot has happened since then. In 2008 there were few people in the fire service focused on the importance of fire dynamics to firefighting operations. Today it is a significant research focus and an ongoing topic of discussion throughout the US fire service. Progress is being made, but much remains to be done.
This post focuses on questions posed by firefighters in Europe and North America. Art Arnalich, a Fire Officer from Spain recently sent me a message asking for clarification and further explanation of the application of conservation of mass as it relates to fire ventilation. As always, questions form an excellent basis to examine what we think we know and how it applies in a practical context.
In my previous post, Large Vertical Vents are Good, But…, I stated:
Conservation of Mass: The mass of air entering a compartment (single compartment or building) must equal the mass of smoke and air exiting the building. This means that other than in the extremely short term, if smoke is exiting the building, air must be entering. This may be through one or more openings functioning solely as inlets or openings may be functioning as both inlets and outlets (with either a bi-directional flow or alternating (pulsating) flow). However, the mass of the inflow must equal that of the outflow.
Art writes: The first condition for the Principle of Conservation of Mass to be applied is that the physical system must be closed to all transfers of matter and energy. While a closed compartment could be considered as a nearly "closed system", a venting structure suffers important transfers of matter and energy. If we were to consider a bigger system (let's say the 100x100x100m cube in which the house and all of its fire gases are included) the PCM [principle of conservation of mass] applies… Being the structure volume constant, any exiting gases will create an interior drop of pressure that will instantly drag an equal volume of gases to enter. Inlets with the bigger pressure differentials (lower side) will observe the larger flows. Outflow volume must equal inflow volume unless significant pressure changes can take place (not likely). Since there is an important difference between inflow/outflow temperatures (and densities), inflow mass (mass=density x volume) does not equal outflow mass.
The amount of gases coming out of combustion as a result of the new oxygen flow has been disregarded. In an actual fire, outflow volume should be larger than inflow volume because combustion of products generates new gases in within the interior.
But that doesn't mean that mass in = mass out if we just consider the house. Total mass of unburned air + mass of fuel + mass of all combustion products = constant. But to measure this we can't consider the volume of the structure itself but the volume that contains all fire gases, unburned gases and the house.
Art Asks: Could you please explain the implications of Principle of Conservation of Mass applies at a molecular level…If Mass-in=Mass-out then there is no mass variation over time (dm/dt=0). This would mean that the total mass of the house before the fire equals its mass after the fire. That doesn't make sense.
Conservation of Mass and Energy
Mass is neither created nor destroyed in chemical reactions. The mass of any one element at the beginning of a reaction will equal the mass of that element at the end of the reaction. If we account for all reactants and products in a chemical reaction, the total mass will be the same at any point in time in any closed system.
In combustion, if you consider the mass of the fuel and atmospheric oxygen before combustion, this must be the same as the mass of unburned fuel, unused oxygen, plus the products of combustion (this leaves out nitrogen and other thermal ballast that are not part of the combustion reaction). This is a bit different than the balance of the mass of smoke exiting the compartment and the mass of air entering.
I posed a similar question to Dr. Stefan Svensson from Lund University concerning the difference in the volume of products of combustion discharged and air intake from a single opening with a bi-directional air track. I discussed Art's question with Stefan to ensure that my answer was clear and as accurate as possible (while maintaining a practical context).
In actuality, I should have stated that mass and energy must be balanced. Application of the principle of conservation of mass and energy in practical fire dynamics is an estimate and it applies on the molecular level (i.e. molecular mass). Usually we look at the building as a system in which the principle of conservation of mass and energy works as a rough estimate. If you define the system as a large cube that contains the building, the cube becomes the system.
In considering mass balance in a compartment fire it is important to keep in mind that solid fuel in the compartment is undergoing pyrolysis; thermally decomposing into gas phase fuel. Some of the fuel burns producing a range of combustion products and some remains unburned. Smoke is comprised of air, products of combustion, and unburned pyrolizate.
As air, products of combustion, and pyrolizate are heated, the volume increases (but mass stays the same), cooler outside air flowing into the building is more dense (smaller volume, but the same mass). This results in approximate balance between of the mass of hot air and products of combustion exiting the building and the mass of cooler external air entering the building.
Density of Dry Air at 20o C: 1.205 kg/m3 (at Sea Level)
Density of Dry Air at 300o C: 0.616 kg/m3 (at Sea Level)
The implications of this difference in density is that if 1 m3 of hot air and products of combustion exit the building at 300o C, they will be replaced by approximately 0.5 m3 of cooler air (which will have the same mass as the exiting smoke and hot air. This differential will increase further if the temperature of the smoke is higher (resulting in lower density). It is important to note that the volume of air is not the same as the products of combustion and air that exit the compartment, but the mass is the same.
Pressure Differential and Flow
Smoke movement is due to both pressure and differences in density (gravity current). However, in general, the pressure differential between the interior of the building and the exterior is what causes smoke discharge. However, this pressure differential is not uniform and will be higher in the hot upper layer than in cooler air below (if a two layer environment exists inside the building). This is fairly simple to visualize when considering a single compartment. As shown in the following four photographs, hot smoke exits at the top of the door (above the neutral plane) and air enters at the bottom of the door (below the neutral plane). Movement of smoke in this case is the result of both the pressure resulting from increased temperature of the gases in the upper layer and the difference in density between the hot smoke (less dense) and the cooler air (more dense).
Mike Sullivan from Canada posed several related questions, focusing on a video included in the Large Vertical Vents are Good, But… post. Just to get everyone back up to speed on the video, this test was conducted by the National Institute of Standards and Technology (NIST) in Bensenville, IL. The building is a wood frame townhouse with a fire ignited on the first floor. The door on Floor 1, Side Alpha is closed and the window on Side 1, Alpha is open. The door to the second floor room where the open window is located is also open, providing a flow path between the window and the first floor fire.
Mike Asks: Although the Law of Conservation of Mass can be used to explain that for a mass of smoke to exit an equal amount of mass of oxygen must enter. But in reality is the mass of smoke inside the townhouse not an artificial mass—meaning—-typically all things in life are trying to reach an equilibrium. In this case I would think that the interior mass of smoke also elevates interior pressures and should continue exiting until an equilibrium with the exterior is met.
In the video the smoke does exit the window for quite a while. In this case if we were to discuss the Law of Conservation of Mass, would it be the mass of oxygen entering the lower part of the window that allows the smoke to exit OR with the fire burning in the living room is the mass of smoke being produced by the fire acting as a replacement for the mass of smoke exiting the window?
Both good questions! As previously discussed, smoke discharge (as well as movement on the interior) is the result of both differences in pressure and density. If considered simply from the perspective of higher pressure on the interior, smoke would discharge from the building until pressure equilibrium is reached (with the same pressure inside the building as outside). This is related to exchange of mass and energy, but only indirectly. If you opened a cylinder of compressed air, air would be discharged out of the cylinder into the atmosphere (no exchange). However, with a fire burning in the building, air must flow inward to sustain release of thermal energy, which in turn maintains (or increases) the temperature that causes the pressure increase.
Mike also had a question related to cooling of the upper layer with a solid stream, but that will be the focus of another post.
UL/NIST Video Series
Have a look at the seven part video series of Battalion Chief Derik Alkonis, LA County Fire Department; Steve Kerber, Underwriters Laboratories


four decimal digit day count system is derived from the truncation of the three most significant numbers of the present seven decimal digits of Julian Day Number (JDN), thus the name the Truncated Julian Day (TJD). TJD is arbitrar:ly chosen to begin from 0 at midnight May 24, 1969, (sic) and ends 9999 at midnight October 9, 1995 after which it recycles to zero. The repetition period is 27.4 years. A conversion table from TJD to calendar data in year, month, and day is given in Table II. The four decimal digits of a TJD number are represented by a 14-bit binary number.
By this definition, TJD is always a truncation of the Julian Day, and is never more than four digits, or 9999. Since it is a binary field represented by 14 bits, it could not physically exceed 16383. Furthermore, this is an integer value. The time of day is not represented as a decimal fraction, but by a count of seconds of the day from midnight, as well as optional milliseconds, microseconds and nanoseconds.
But that's not the whole story. A modified time code called PB-5J was later defined with 16 bits for TJD, which allows for integers up to 65535, corresponding to dates up to October 28, 2147. TJD values greater than 9999 can be found for the year 1995 and after, and a NASA web site converts to and from TJD for any positive value.
So there actually are two different definitions of Truncated Julian Day, one in PB-5 and the other in PB-5J, and it appears to me that the latter superseded the former.
TJD 56153/76300
Mars Time
At August 6, 2012, 05:14:39 UTC SCET (MJD 56145.21850) the Curiosity rover landed in Gale Crater on Mars. (SCET stands for Spacecraft Event Time, since it took until about 14 minutes later for the data transmission to reach earth.) In Mars time that was 05:50:16 AMT (MSD 49269.24), about 15:00 local time. AMT is Airy Mean Time, also known as Coordinated Mars Time (MTC), because it is the Local Mean Solar Time at Airy Crater, which marks zero longitude on Mars. MSD is Mars Sol Date, and like Modified Julian Dates it is a count of Martian days, which are called "sols", but from December 29, 1873 (MJD 5521.5).
Another sol count is started whenever a craft lands on Mars, so that was on Sol 0 for Curiosity. There is currently one other craft active on Mars, Opportunity, which was on Sol 3034. Opportunity is near the Martian Prime Meridian, one hour behind AMT, but Curiosity is on the other side of the planet, 9 hours, 9 minutes and 40 seconds ahead of AMT.
Note that sols are longer than earth days by nearly 40 earth minutes but are divided into 24 Martian hours, so each hour, minute and second is 2.7% longer than those on earth. Thus, the mission operators start their shifts 40 minutes later each day. To keep track, they use a Java program call Mars24, which you can download from NASA. By default it displays AMT and LMST for Curiosity and Opportunity, as well as MJD and MSD with two digits of decimal time. You can also find more information at Wikipedia.
MJD 56148.377
MSD 49272.317


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Lunch Seminar Mathematics & Statistics (LSE) - 2020/2021
Interviene: Marcella Mazzoleni, Università di Bergamo
Link: aula virtuale Teams
The joint models analyse the effect of longitudinal covariates onto the risk of an event. They are composed of two sub-models, the longitudinal and the survival sub-model. For the longitudinal sub-model, a multivariate mixed model can be proposed. Whereas for the survival sub-model, a Cox proportional hazards model is proposed, considering jointly the influence of more than one longitudinal covariate onto the risk of the event.
The purpose of the work is to extend the estimation method based on a joint likelihood formulation to the case in which the longitudinal sub-model is multivariate through the implementation of an Expectation-Maximisation (EM) algorithm which maximises the joint likelihood function, using Newton Raphson update and Gauss-Hermite quadrature rule.
The goodness of fit is tested using some diagnostics elements, such as the estimated survival function and the residuals for both survival and longitudinal sub-models, for instance longitudinal, martingale, deviance, and Cox-Snell residuals. Moreover, dynamic predictions are implemented for the survival and longitudinal sub-model, updating the survival function and the longitudinal trajectories at later points in time.


text:
Why do kissing gouramis kiss each other? Does this signify that I have a pair?
It seems most likely that this strange kissing ritual has actually
evolved as a way of settling disputes, without the fish having
resorting to more aggressive behaviour, rather than as a sign of
affection. It could be a trial of strength. Kissing gouramis (Helostoma temminckii
anchor their fleshy lips together, until one breaks the contact.
cannot sex these fish visually outside the breeding period - only when
the female then swells with eggs can they be distinguished. There are
two colours in existence - the natural grey form, and the more commonly-kept rose-pink domesticated variety. These do not reflect a difference


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If you think a pay bump would make you like your job more, you're probably right. But it's not quite as simple as you might think.
New research from career site Glassdoor suggests that more money can make employees more satisfied with their jobs — but not as much as other factors in the workplace.
The study is based on data from 221,000 Glassdoor users who contributed a salary report and an employer review for the same company since 2014. The users in the study earned up to $200,000 annually.
To be sure, higher salaries were associated with higher employee satisfaction. While 15% of users earning less than $30,000 a year gave their employer one out of five stars, just 10% of users earning upwards of $120,000 gave the same rating. On the flip side, while 40% of users making less than $30,000 gave their employer four or five stars, as many as 51% of users making more than $120,000 gave the same rating.
The caveat? A higher salary only makes employees a little bit happier. A more advanced data analysis revealed that a 10% increase in pay was associated with a mere 1% increase in employee satisfaction. So if you make $50,000 a year and you get a $5,000 raise, your satisfaction would theoretically rise from 75% to 76%.
When it comes to employee satisfaction, other factors could be more meaningful than salary. The researchers looked at different aspects of the workplace and found that employees valued them in this order:
 1. Culture and values
 2. Career opportunities
 3. Senior leadership
 4. Work-life balance
 5. Compensation and benefits
 6. Business outlook
This analysis adds to a growing body of research on the link between money and happiness.One study found that happiness levels off at incomes of $75,000 (or $82,000 in today's dollars). Another study found that the more money you have, the more money it takes to increase your happiness. The Glassdoor research is unique in that it puts salary in the context of other job attributes.
As Forbes' Susan Adams notes, it's likely that people making less than $30,000 would value compensation over other factors. But at the point at which you can take care of your expenses, save some money, and have a little fun, other aspects of your job may matter more than salary.
Ultimately, the difference between a job that pays $50,000 and one that pays $60,000 might not be that significant to your overall happiness. But the difference between a workplace where you'll stagnate and one where you can contribute to a team changing the world may be huge.
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Melting snow creates flooding crisis across Scotland
UK Today News: As temperatures rose rapidly in Scotland on Friday, the melting snow caused some chaos in the region and created floods throughout the country. Many schools and offices which were shut down over the past week due to excessive snowfall, reopened yesterday, and so did roads and railway routes.
The sudden rise in the temperature to 20 degrees has resulted in damaged pipes, flooded roads had disrupted normal traffic on the roads. The access to the Edinburg airport was reportedly closed due to flooding and created chaos for those who were due to catch their flights.
Many streets in Scotland had been closed, after fears that falling snow would hurt someone passing on the street. On Thursday morning, water from a burst water pipe filled Glasgow's Saltmarket. The water had destroyed several computer systems and phones.
The temperature compared to last week was 20C warmer in some parts of Scotland.
13 + 11 =


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Is there a standard or common way to write scientific notation in different bases that doesn't require repeating the base in both the coefficient and the exponent base?
For example, this notation is correct, but is quite verbose:
 - Implicit base 10: $100 \cdot \tau = 6.283 \times 10^2$
 - Explicit base 10: $100 \cdot \tau = 6.283_{10} \times 10_{10}^2$
 - Explicit base 16: $100 \cdot \tau = 2.745_{16} \times 10_{16}^2$
Most calculators & programming languages shorten this to an "exponent" notation such as:
Some rare ones even support a base, such as:
Unfortunately, these are not very nice notations outside of specific domains.
Ideally, I'm looking for an operator notation that concisely does the function:
 - $f(coefficient_{b},exponent) = coefficient_{b} \times b^{exponent}$
If there is no such standard or common notation, I'd be happy to hear any suggestions.
share|improve this question
How about "$\tau = 2.745 \times 10^2$ in base $16$" (or "τ = 2.745e2 in base 16", whichever you prefer)? – ShreevatsaR Jun 5 '11 at 22:42
what's a bit ugly is that you're still using base 10 to denote the base you're using. Maybe, in a way, it's more natural to denote your base by the highest number below the radix, instead of the radix itself, so you'd have base 9 or base F instead of base 10 or base 16 in'metabase' 10. – gfes Jun 5 '11 at 23:03
_USER_ I think your (base-1) notation has some appeal, but using 10 as the "metabase" seems to be the only way I've ever seen it done, and seems to be universally understood. "Base F" immediately makes one think of hexadecimal, but I think if you wrote "base 9" it would be confusing! – wjl Jun 5 '11 at 23:33
True. Although when working in base 10, probably anyone would omit the base 9 / base 10 altogether anyway. Also, I thought of a neater, but less practical way, namely writing the alternative expansion for the radix. I.e. 9._PHONE_ etc. or F.FFFFFFFFF etc. – gfes Jun 5 '11 at 23:37
_USER_ The alternate expansion is quite clever. It would work especially well with an overbar to indicate a the repeating fractional part. – wjl Jun 5 '11 at 23:43
1 Answer 1
Unfortunately, $2.546_{16}\times 10_{16}^{23}$ is cumbersome, and it isn't immediately clear if the exponent is being written in base $10$ or base $16$, and $2.546_{16}\times 16^{23}$ has a strange mixing of base $10$ and base $16$ elements. For programming things, there are explicit prefixes you can put on a number to denote whether it is base $2,8,10$ or $16$, but that isn't general, and it still doesn't really address any of the previous problems.
Maybe a notation like $(2.546\times b^{23})_{16}$ would work to indicate that everything is supposed to be taken base $16$, with $b$ being implicit for the base (as writing either 10 or the base 10 expression of the base is awkward). However, I'm not fully enamored with this notation either.
What is your application of this? In what circumstances is some sort of scientific notation required but base $10$ is undesirable?
share|improve this answer
I actually like the parenthesized notation better than anything else I've seen or thought of so far. As far as the application, this is more of a general question that has bugged me for a long time. However, this comes up a lot for me specifically because I often write up detailed mathematical descriptions of the behavior of low-level, digitial electrical engineering applications. For instance, one place a concise notation would be obviously handy is when writing things about DSP algorithms using IEEE floating point in hexadecimal. – wjl Jun 5 '11 at 23:38
Um, one possibility is also to use the shift operators a la C/C++. So $(2.546 \ll 23)_{16}$? – Willie Wong Jul 5 '11 at 23:47
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