text:
Volvo EX30 Will Be as Cheap as Possible
CUPRA reiterated last week that its second 100% electric model, the CUPRA Tavascan, will be manufactured in China, something increasingly common among European and American manufacturers. Now it is Volvo that confirms that it will shape a key product in its range of electric cars in China, the Volvo EX30, a model destined to be the most affordable in its range.
During the presentation of the Volvo EX90, Volvo's absolute flagship for the coming years, the brand revealed the first image of the EX30. While it is true that the brand did not comment on the model at the event, its CEO later did so to Automotive News Europe.
Without going into too much detail, Jim Rowan, CEO of Volvo Cars, referred to the model as the EX30, stating that it is a "really important car" for the brand as it will allow them to "reach a different price demographic." .
That is to say, it will be positioned in the lower part of the Volvo range to be located in the compact segment, a market niche that the brand abandoned with the cessation of production of the last compact, the Volvo V40. It will be based on Chinese group Geely's SEA platform and is expected to share key technical elements with Smart #1, which sits on the same basis.
The Smart model starts in Spain at 40,980 euros, a price that, based on the comment of the head of Volvo, should be lower than the EX30 when it hits the market. Currently, the most affordable electric car sold by Volvo is the XC40 Recharge, and it starts in Spain at 44,000 euros. Since this is a C-SUV, and the EX30 is expected as a B-SUV,
China and the manufacture of electric cars
China is gaining ground in an unstoppable way in the automotive landscape. To the projection that Chinese manufacturers are building outside their borders, such as BYD or SAIC, we must add that many foreign manufacturers are deciding to take the production of key electric cars on their journey to Chinese soil.
The reasons why they do so are clear. To a much more affordable workforce and a labor force that is equally qualified and voluminous, we must add the cost of materials, in addition to the cost of the cells that make up the batteries. Let's remember that China is currently the largest battery producer in the world, something that seems to not stop in the medium term with the flight of European manufacturers to China.
All of the above gives rise to the manufacturers that take the production of key models to China, and celebrate having done so. Without going any further, last week Tesla announced that during November the firm managed to shape more than 100,000 electric cars at its Shanghai I factory, which is a record for the brand itself, but also shows that its growth can lead to turning the factory into the largest car factory in the world, electric or not.
Volvo Plans to Make an Electric Minivan
Volvo EX30 hunted on test drive for the first time
Volvo thinks more affordable version for the EX90 family
Volvo is developing a new electric coupe SUV called the C60
Volvo believes electric and combustion car prices will be equal


This video is about creating a simple scene with Blend4Web.
I would love to see a walk-through of how to add a redirect link with the new node editing, add a sound and add an animation. I think those three things would be a great start for anybody starting out with Blend4Web.
If you need English voice-over, let me know.
I have a Blend4Web SDK tour video in processing, I will post a link when it is done.
Just watched your video - it is awesome! I agree that walk-throughs you mentioned would be very useful.
See an example blend file in the SDK for making page redirects without coding.
Sound can be added as described in this tutorials: , , . See also the manual page and sources for the Island demo.
For different animation types see the doc page and tutorials throughout the blog.
If you find some time and decide to create video tutorials by yourself, I'm pretty sure it would appreciated by our community very much! We are ready to provide you with whatever assistance you may need, including promotion.
Thanks for the links. I am starting to learn a few things. I may pester you with a few questions but once I understand a concept, I will do a video for it. I think there will be people who learn Blender specifically because of Blend4Web. There are many web development technologies that are becoming obsolete. Web developers who have never authored 3D content will be looking to keep up with the times. So I think videos that show each step assuming no knowledge of Blender would be cool.
So I think videos that show each step assuming no knowledge of Blender would be cool.
By coincidence, we just discussed that today and planned to expand the user manual with topics related to general Blender use. Indeed, this will be very helpful for newcomers to start with the Blend4Web workflow.
New video posted, Blend4Web Tour and Overview.
Let me know if I got anything wrong. I can still make changes.
Great! This is the most detailed and cool Blend4Web video review on youtube so far! Didn't know about the "Kick the bucket" idiom.
You might create and maintain a separate topic for your videos in the Projects section of the forum.
We'll also share it via our social media. Looking forward to more videos!


text:
Help Us Document the Historic Insect Pressure in Desert Lettuce
This Season With the produce season winding down rapidly, now is a good time to reflect on pest activity and insecticide usage you experienced this season in desert lettuce. The 2022 Lettuce Crop Losses Workshop will be held live, in-person Wednesday, April 20th at the Yuma Agricultural Center from 11:30 until 3:00 pm (see agenda below). Get there early as lunch will be provided. The meeting has been approved for 2.5 CA/AZ CEUs. Participants will be asked to complete two short surveys to document pest pressure and control tactics used on lettuce this season. This workshop has been invaluable to our Vegetable IPM Team over the past 18 years because it allows us to develop accurate "real world" data on crop losses and pesticide usage which is important to the assessment of IPM programs in Arizona. It's also valuable to PCAs, as it can translate their efforts into economic terms for their growers and confirms their value to the lettuce industry by showing the importance of key insect pests and their cost-effective management in desert lettuce production. It's no secret, the insect activity this year was exceptional, particularly for aphids. Lettuce and green peach aphids are still quite abundant on romaine in our late season trials at the Ag Center. As I've reported previously, I think this is by far the heaviest aphid year I've seen since Lettuce aphid was first reported in Yuma in 2000. Previous Lettuce Insect Losses surveys from theses workshops estimated that over a 15-year period, PCA made on average 1.5 sprays on lettuce for aphids (ranging from 1.0 to 2.5 sprays). For the complete report see: Insect Losses and Management on Desert Lettuce: A 15-year Summary. Based on reports from PCAs this spring, it is likely that considerably more sprays were applied this spring. Also, a wide variety of insecticides products were reportedly used by PCA's, some with mixed results. You can review the historical database of insecticides used for aphids and other insects here: Insecticide Usage on Desert Lettuce, 2020-2021. The bottom line: from a historical perspective, it would be quite useful to document aphid pressure and sprays applied this year compared to previous years. If results from the workshop show that aphid pressure was indeed heavier this year, then we can start asking why, and perhaps what we can do differently in the future. Finally, Marco Pena will be providing the latest results of herbicide trials and his areawide weed survey, and I will be providing the latest efficacy trial results on lettuce aphids, thrips, worms, and whiteflies. So, we hope you can make it to the workshop and participate in this important process.
Lettuce Crops Losses Workshop April 20, 2022 11:30-3:00 pm
Yuma Agricultural Center Conference Room
11:30-12:00 pm Lunch (It will be yummy)
12:00- 12:30 pm Impact of IPM on Lettuce Insect Losses John Palumbo
12:30-1:00 pm Individual Completion of LIL Questionnaires Attendees
1:00-1:30 pm Historical Results of Insect Losses /Insecticide Usage John Palumbo
1:30-2:00 pm Weed Management Research Update Marco Pena
• Recent herbicide trials
• Areawide weed surveys
2:00-3:00 pm Insect Management Research Update John Palumbo
• Worm and Whitefly efficacy trials
• Spring aphid and thrips efficacy trials
• INSV update
Crop Nutrient Management and Changing Market Conditions
Rapidly changing conditions are a common feature in the agricultural arena. Things are in a constant state of flux in terms of climate, economics, methods of operation, etc. However, in the past few years, principally during the pandemic and post-pandemic times, changing conditions in agriculture for the desert Southwest have been extremely rapid and substantial.
Supply chain issues have been disruptive to many sectors of the economy and that has certainly affected agricultural operations. Things that have commonly been standard or easy things to manage in the past such as the simple need of replacing equipment or parts have become complicated and expensive.
We have become aware of fragile supply chains and the exposure of single points of failure that can have huge domino effects in many facets of our society, including agricultural industries. For example, during the pandemic it cost nearly $40,000 to move a shipping container from Asia to the U.S. and now things are starting to catch up and it has been reported that containers can now be shipped from Asia to the U.S. for less than $3,000.00.
Fertilizer prices for many materials have more than doubled in recent years, primarily due to basic supply and demand pressures. Fertilizer supplies have been subject basic economic pressures and further exacerbated by the war in Ukraine and the associated changes in natural gas supplies.
Fertilizer Supply and Cost
In a recent report from DTN market analysis (Formerly: Telvent DTN, Data Transmission Network) for the second week of November, retail U.S. fertilizer prices were not substantially different than in October but did have some slight variations with five fertilizers showing marginally lower prices than in October and three other key fertilizers tracking slightly higher. It is important to note that DTN designates a "significant" difference in prices with a move of 5% or more.
The five fertilizers that were marginally lower in price included monoammonium phosphate (MAP), potash, urea, 10-34-0, and anhydrous ammonia. Di-ammonium phosphate (DAP), urea ammonium nitrate (UAN)-28, and UAN-32 were slightly higher in price in mid-November, Table 1. Costs per pound of nitrogen (N) is shown for primary N sources in Table 2.
UAN-28
Table 1. Mid-November retail prices in U.S. markets for several fertilizers. Source: DTN
Anhydrous Ammonia
Table 2. Comparative prices per pound of N. Source: DTN
Crop commodity prices have been higher recently, sometimes to the extreme. However, the increasing costs of crop production have generally overrun the increasing returns on a strong market. In a recent report on western crop production conditions, estimates of cost of production increases in the past year are 135% higher than in 2020 while the return values to farmers have been about 127% higher. Thus, a nearly 10% negative differential exists which exerts a strong impact on the crop production systems of the desert Southwest.
The American consumer is seeing this as well. In the American Farm Bureau Federation's 37th annual cost survey from volunteer shoppers for Thanksgiving dinner has shown that prices are up 20% this year. This increase is in addition to the 14% increase experienced in 2021.
Developing a conservative approach to nutrient management is often considered a risky venture in crop production systems, particularly with a short season crop like a leafy green vegetable that has a premium on quality as well as yield. However, under high fertilizer price conditions and/or tight supply, there is a greater incentive to develop and employ a more conservative approach to nutrient management.
To maximize nutrient management efficiency, the 4R concept of plant nutrient management and application can be helpful. The 4R concept consists of applying:
1. Right fertilizer source at the
2. Right rate, at the
3. Right time and in the
4. Right place
Along with the 4R nutrient management approach, assessing plant-available forms of the nutrients present in the soil by evaluating soil tests with appropriate indices is a good step in the develop of a more efficient nutrient management program. Then splitting nutrient applications, particularly mobile nutrients such as N in line with crop uptake and utilization are good steps towards higher fertilizer use efficiency by the crop. Thus, timing, methods, and rates of nutrient applications are critical (e.g, 4R management).
In agriculture we know quite well that we have no control over markets and the costs of crop production inputs. However, we can control these inputs in the field, and we do have some tools at our disposal that can be helpful in the process.
2021-2022 Sclerotinia Drop of Lettuce Fungicide Trial
This study was conducted at the Yuma Valley Agricultural Center. The soil was a silty clay loam (7-56-37 sand-silt-clay, pH 7.2, O.M. 0.7%). Lettuce 'Magosa' was seeded, then sprinkler-irrigated to germinate seed on Nov 2, 2021 on double rows 12 in. apart on beds with 42 in. between bed centers. All other water was supplied by furrow irrigation or rainfall. Treatments were replicated five times in a randomized complete block design. Each replicate plot consisted of 25 ft of bed, which contained two 25 ft rows of lettuce. Treatments were applied with a tractor-mounted boom sprayer that delivered 50 gal/acre at 100 psi to flat-fan nozzles spaced 12 in. apart.
Sclerotia of Sclerotinia minor were produced in 0.25 pt glass flasks containing 15 to 20 sterilized 0.5 in. cubes of potato by seeding the potato tissue with mycelia of the fungus. After incubation for 4 to 6 wk at 68°F, mature sclerotia were separated from residual potato tissue by washing the contents of each flask in running tap water within a soil sieve. Sclerotia were air-dried at room temperature, then stored at 40°F until needed. Inoculum of Sclerotinia sclerotiorum was produced in 2 qt glass containers by seeding moist sterilized barley seeds with mycelia of the pathogen. After 2 mo incubation at 68°F, abundant sclerotia were formed. The contents of each container were then removed, spread onto a clean surface and air-dried. The resultant mixture of sclerotia and infested barley seed was used as inoculum. Lettuce 'Magosa' was seeded and then sprinkler-irrigation was initiated to germinate seed in double rows 12 inches apart on beds with 42 inches between bed centers. Plants were thinned Jan 6, 2020 at the 3-4 leaf stage to a 12-inch spacing. For plots infested with Sclerotinia minor, 0.13 oz (3.6 grams) of sclerotia were distributed evenly on the surface of each 25-ft-long plot between the rows of lettuce and incorporated into the top 1 inch of soil. For plots infested with Sclerotinia sclerotiorum, 0.5 pint of a dried mixture of sclerotia and infested barley grain was broadcast evenly over the surface of each 25-ft-long lettuce plot, again between the rows of lettuce on each bed, and incorporated into the top 1-inch of soil. Treatment beds were separated by single nontreated beds. Treatments were replicated five times in a randomized complete block design. Each replicate plot consisted of a 25 ft length of bed, which contained two 25 ft rows of lettuce. Control plots received sclerotia but were not treated with any fungicide. As a point of reference, the original stand of lettuce was thinned to about 65 plants per plot.
For treatments first applied at seeding, sclerotia were introduced into plots before the first application of treatments. The first application for at seeding treatments was made on Nov 8, with an additional application on December 16th. For treatments first applied after thinning, sclerotia were introduced into plots after thinning before the first application of these treatments, with additional applications as noted in the data sheets. An initial sprinkler irrigation supplied water for seed germination, with subsequent furrow irrigations for crop growth. The final severity of disease was determined at plant maturity by recording the number of dead and dying plants in each plot due to Sclerotinia minor or Sclerotinia sclerotiorum (March 8th, 2022). As a point of reference, the original stand of lettuce was thinned to about 65 plants per plot.
In nontreated plots, 16-17% of lettuce plants were dead or dying due to infection with Sclerotinia minor and about 11 % due to S. sclerotiorum, at the end of the trial. Please refer to the data tables to compare treatments of interest, using the Least Significant Difference Value listed at the bottom of each table to determine statistically significant differences among treatments. (UA-3)+Silwett, (UA-2)+Silwett, and Endura fb Merivon +Silwett were most effective against Sclerotinia sclerotiorum. Endura+Silwett, (UA-3)+Silwett, (UA-2)+Silwett, Merivon+Silwett and Luna Sensation + silwett gave the best results against Sclerotinia minor (see table). Phytotoxicity was not noted in any of the treatments in this trial.
Precision Spot Sprayers (1-cm Resolution) for In-Row Weed Control
Over the last couple of years, we identified and developed two high speed, precision spot sprayers to apply herbicides to weeds with minimal off-target spray while traveling at speeds that are viable for commercial vegetable farming operations (2 mph). The first is a spray assembly designed for controlling in-row weeds that are close to crop plants (1-cm spot spray resolution). The second is a high precision (sub-centimeter spot spray resolution) sprayer designed for spot spraying cotyledon stage weeds in spinach and leaf lettuce crops. We tested the device in the laboratory and found that weed control efficacy was greater than 95% (3 species), percentage of off-target spray was less than 3% and no crop injury was observed. The work was presented at the 2021 California Weed Science Society Annual Meeting. Click here or on the image below ) to view the presentation and see video of the devices in action.
We are now working towards developing a high precision, automated/robotic weeding machine for vegetable crops. This fall, Evan McGinnis, Biosystems Engineering Ph.D. candidate, initiated work to develop AI-based imaging software for detecting and targeting weeds. Once developed, the software will be integrated with the precision spot sprayer and tested in the field. Stay tuned for updates!
This work is supported by the Arizona Specialty Crop Block Grant Program and the USDA NIFA Specialty Crops Research Initiative USDA-NIFA-SCRI-004530. We greatly appreciate their support. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the view of the U.S. Department of Agriculture.
Fig. 1. Images from "Centimeter Scale Resolution Sprayer for Precision In-Row Weed Control" presentation given at the 2021 California Weed Science Society Annual Meeting. Click here or on image to view the presentation.
Broccoli Weed Control Question
The IPM team frequently receives questions from our friend PCAs in Yuma regarding possible injury with herbicide combinations. A recent inquiry was about the addition of Prowl (pendimethalin) to Prefar herbicide preplant.
We found in our archives an evaluation that was done in 2002 by Barry Tickes from Arizona Cooperative Extension that addressing this question. The evaluation was located on 8th Street and the Levee in Yuma CO and included the following treatments: Dacthal at 10 and 12lb, Prefar at 6qt alone and with the addition of 0.5pt Prowl. All treatments were applied in 20 gallon/A spray volume as a 50% band on 42-inch beds. The plot size for this experiment was 600 ft. x 8 beds. Immediate incorporation was done with sprinkler irrigation. The results reported are in the following table:
Phyto (%Stunting)
Control: Nettleleaf Goosefoot
Control: Groundcherry
1. Dacthal
3. Prefar
4. Prefar+Prowl
6qt+0.5pt
5. Untreated
As can be seen the addition of 0.5pt of pendimethalin to 6qt of bensulide produced 20% stunting in this case.
Area wide Insect Trapping Network (April 6, 2022)
CEW moth counts increased in most locations over the past 2 weeks; but remain average for this time of the season.
Trap counts remain low in all locations, increased slightly, but remain below average for late season.
Cabbage looper trap counts increased in all locations, but still below average for late season.
Adult activity increased in some locations in the past two weeks. Overall, activity is below average for this time of year.
Thrips adult movement increased in all locations recently particularly in the Tacna/Roll are. Activity is well below average for late season.
Aphid movement low in most locations but increased slightly in Gila Valley. Trap captures well below average for this time of the season.
Adult activity increased in many areas, and below average for this time of season.

redpajama_set_name: RedPajamaCommonCrawl


The trailer of the romance-drama Ek Ladki Ko Dekha Toh Aisa Laga, featuring Anil Kapoor, Sonam Kapoor, Juhi Chawla and Rajkummar Rao, has been released. A new poster was unveiled on 26 December, where Sonam Kapoor described the film as "the most unexpected love story of 2019". The first look poster was launched on Anil Kapoor's birthday on 24 December.
In a meta-theatrical moment, the trailer begins with Rajkummar Rao narrating the tale of an 'unexpected romance' of a girl. As the girl grows up believing in fairy-tale romance, her garrulous father (Anil Kapoor) kickstarts the search for an ideal groom for his daughter. However, the seemingly perfect father-daughter relationship is strained when his daughter's secret comes out in the open. The cryptic trailer puts the notion of love in question, as the family struggles to come to terms with the daughter's choices in life.
Anil Kapoor shared the video clip with the hashtag, #LetLoveBe, captioning it as 'See love in a new light'. The trailer urges audiences to stop discriminating against love on the basis of caste, gender, race and other binaries.
This is the first time that the father-daughter duo Sonam and Anil Kapoor will be sharing screen space. In this context, the actress had said that though they have been offered a lot of films in the past, this one was apt for them to collaborate. She said, "I never found authenticity or idealism in any of the other films. I felt nobody besides me and my father (were apt) to do Ek Ladki Ko Dekha Toh Aisa Laga. We are glad to know that we were the first choice of the director", as per an earlier report.


text:
Q: Nonhomogeneous Poisson Process question I just have a quick question about the nonhomogeneous poisson process.
Say I am looking for E[N(1)|N(2) = 4] where N(t) is the number of arrivals by time t.
Since N(1) is before N(2),
is $$ E[N(1) | N(2) = 4] = E[N(1)] $$
?
Thanks for any answer.

A: No, this is not true. To generalize your question a little, you are asking if the value of $N(2)$ has any influence on the value of $N(1)$, and it certainly has. I can write up the similar expression
$E[N(1) | N(2) = 0].$
In this case, you know that at time $2$, you have had no arrivals, and since $N(1)\leq N(2)$, you also know that you must have $N(1)=0$. This means that
$E[N(1) | N(2) = 0]=0.$
On the other hand, you have that
$E[N(1)] = \lambda_1,$
where $\lambda_1$ is the Poisson parameter of $N(1)$, so the two expressions are not equal.
Concerning your case, given that you know $N(2)=4$, you must have that the value of $N(1)$ is some number in the set $\{0,1,2,3,4\}$, so $N(1)|N(2)=4$ is no longer Poisson, since it can take only a finite number of values.
I hope this helps.

redpajama_set_name: RedPajamaStackExchange


We talked about this icey treat last month as a heads up. Now the final day is upon us and tomorrow Italian ice is on the house at Rita's. They seem to be doing this every year as a sort of nod to the beginning of spring. Kinda ironic considering Spring is about the whole ice and snow meltnig away thing happening. Still, free is free and hopefully this will be the last time you see ice besides those Cinco de Mayo margaritas and summer ice tea.


text:
Q: SQL0199N error when trying to connect HammerDB to Db2 for z/OS I'm trying to generate some data for DB2 11.1 z/OS using HammerDB v3.1 which is running on a Windows remote host. There is no ability to run HammerDB on the same host with DB2.
According to the HammerDB documentation I need to set up IBM Data Server Driver for ODBC and CLI.
What I did:

*

*Downloaded and set up the driver for 11.1 on HammerDB host - v11.1.4fp4_ntx64_odbc_cli.zip as described here

*Configure db2dsdriver.cfg file
<configuration>
   <dsncollection>
      <dsn alias="TPCC" name="<my database name>" host="<my host name>" port="50000"/>
      <!-- Long aliases are supported -->
      <dsn alias="longaliasname2" name="name2" host="server2.net1.com" port="55551">
         <parameter name="Authentication" value="SERVER_ENCRYPT"/>
      </dsn>
   </dsncollection>
   <databases>
      <database name="<my database name>" host="<my host name>" port="50000">
         <parameter name="CurrentSchema" value="OWNER1"/>
         .......

*Add environment variable DB2DSDRIVER_CFG_PATH

set DB2DSDRIVER_CFG_PATH=C:\ProgramData\IBM\DB2\C_IBMDB2_CLIDRIVER_clidriver\cfg

*Run HammerDB GUI, try to build a schema and receive

Error in Virtual User 1: [IBM][CLI Driver][DB2] SQL0199N  The use of the reserved word "INDEX" following "" is not valid.  Expected tokens may include:  "ORGANIZE APPEND VOLATILE AUDIT VALIDPROC EDITPROC OBID IN DATA".  SQLSTATE=42601```

A: Probably the easiest way to understand the root cause of the problem is to trace the CLI driver.
Tracing the CLI driver by using the db2trc on -cli command
Something like this on the DB2 Data Server Client side:

db2trc on -cli -f trc.dmp
steps to reproduce the problem
  db2trc off
  db2trc fmt -cli trc.dmp trc.dmp.txt

The trc.dmp.txt file will have exact statements the client tried to run.


text:
Q: Elegant and efficient way to find the median value based on different columns I have a dataframe like as shown below but my real dataframe has millions of rows
te_df = pd.DataFrame({'subject_id':[1,1,1,2,2,2,3,3],
                      'test':['test1','test2','test3','test1','test2','test3','test1','test4'],
              '0-24hrs':[1,1,1,2,1,1,np.nan,np.nan],
              '24-48hrs':[np.nan,np.nan,np.nan,1,1,1,2,1],
              '48-72hrs':[2,3,1,3,3,np.nan,np.nan,np.nan]
                    })

I would like to find the median number of times a test is conducted (identify using test column) every 24hours (using 0-24hrs, 24-48hrs, 48-72hrs)
I tried the below
df_out = pd.DataFrame()
df_out['1st_24'] = te_df.groupby('test')['0-24hrs'].median()
df_out['2nd_24'] = te_df.groupby('test')['24-48hrs'].median()
df_out['3rd_24'] = te_df.groupby('test')['48-72hrs'].median()

Instead of repeating the same line thrice, is there any other efficient and elegant way to find this? Because my real dataframe has million of rows

A: Why not try
out = df.groupby('test')[['0-24hrs', '24-48hrs', '48-72hrs']].median()
       0-24hrs  24-48hrs  48-72hrs
test
test1      1.5       1.5       2.5
test2      1.0       1.0       3.0
test3      1.0       1.0       1.0
test4      NaN       1.0       NaN

A: You can also do this by:-
df_out=te_df.groupby('test').median().drop(columns=['subject_id'])

#output

       0-24hrs  24-48hrs    48-72hrs
test
test1   1.5     1.5         2.5
test2   1.0     1.0         3.0
test3   1.0     1.0         1.0
test4   NaN     1.0         NaN

Note: In @BENY 's method access column values by passing a list you will not get a warning:
out = df.groupby('test')[['0-24hrs', '24-48hrs', '48-72hrs']].median()


text:
Claudia Zhu
The World's Biggest Game of Memory
An Overview of Segmenting Scenes by Matching Image Composites
How do we derive meaning by matching visually similar images? Image and caption from paper.
One of the major goals in computer vision is semantic object segmentation, which is essentially identifying different objects that have semantic meaning (toothbrush or tree) within an image. This is a difficult endeavor because objects in semantic classifications take on a variety of forms and can rely on context spread throughout an image.
Beyond basic methods such as canny edge detection, where we look for a large difference (in intensity) between a series of neighboring pixels, we wish to identify entire objects. This presents technical challenges such as how do we identify windows as part of a building even though canonical edge detection will highlight the windows as something different. How do we identify a grey car in front of a grey lamp post in front of a grey building as different objects even if they are the same color. Much of this information relies on further information of the objects in the image that we are interested in parsing.
In the following paper we will present written by Russell et. al., we will explore the idea of obtaining such information by looking at visually similar images (in this case we mean that the images look very similar to one another in positive/negative space, where objects are, lighting, etc.).
This paper presents a model that finds matching images via a low-dimensional descriptor (think color, shape, texture, region in the image) and then transferring the associated labels from the matching images to the new image. Russell et. al. continue to show that this has achieved stellar results for object recognition, detection, annotation; image location, completion, exploration, colorization; and scene recognition and estimation.
Prior Work & Intuition
There has been much prior work done to produce an image using a stack of pre-aligned images that show the same scene. One of the most successful has been work done by PhotoMontage. The PhotoMontage framework selects regions from the aligned stack of images by optimizing a quality score to create a visually appealing image. In an effort to perform image segmentation and region filling (inserting computer generated image into gaps of another image), recent work has used PhotoMontage to automatically align images that contain the same scene (semantically).
The approach used by Russel et. al is different because they use a stack of visually similar images that are semantically different. Intuitively, this means that we only care about the shape of the picture (shallow similarity) and not the objects in it, in an effort to obtain semantic results. This is beneficial because finding similar scenes (semantically) as PhotoMontage does is both difficult to find/compute and does not always generate good results as semantically similar scenes does not work better than visually similar scenes in segmenting semantic objects.
To learn more, check out this paper on generating computer graphics based on datasets of globally similar images. And this paper on selecting objects based on large sets of images.
Motivation & Overview
Due to the internet, iPhones, accessibility of camera and pictures, we have a surplus of images, which allows us to compile massive collections of images. In this case, since we are specifically taking a look at scenery, we could compile road pictures, mountains, lakes, etc. From here, we select an image stack, which is a set of 5000 images by matching images (using standard image matching technique that we discuss more later on) to a given input image.
From here, we try to use the image stack of "similar" images that we found to give a semantically meaningful explanation of the new given input image. This means that we are searching for things by object and their purpose instead of by color or texture. All of this relies on a fundamental assumption that the image stack is already aligned such that the regions of objects that we care about are roughly in the same position. For examples, mountains will always be at the bottom of an image. The sky will always be near the top.
Then, we can use these semantic objects from our image stack to explain the input image. Using a large stack of images to explain the new input image instead of current methods such as CNN which relies on matching to a couple training images and then interpolating, we can compute a matching image composite (by matching each region in the input image to a semantically similar region in other images in the image stack. Note that this is informed by the difference in images as explained in the next paragraph). We can then use the image composite to explain the input image.
However, scene matches are never perfect. Specifically, parts of an image get matched up very well while others do not. Consider if you have a picture of a typical road with a tree and a building. This Scene Segmentation via Matching method takes advantage of the matching of parts property. For example, for a street scene, one matching image could have a building match very well, but getting the shape of the road wrong, while another matching image could get the road exactly right, but have a tree instead of a building. The differences actual tell us more about objects images and help us identify semantic boundaries since we can aggregate all of the images to create a matching composite image.
The top row shows matches for semantically similar images, which are very varied although they all depict crosswalks while the bottom row depicts visually similar images. These are much less visually varied even though they do not share meaning. Image and caption from paper.
Russel et. al's approach combines boundary-based and region-based segmentation processes together within a single MRF framework. The boundary process (Le Boundary Process) tries to figure out the semantic boundaries between objects using the stack. The region process (Le Region Process) groups pixels that belong to the same object based on consistent objects in the stack. This is aggregated in an MRF framework which is solved using GraphCut optimization (Le MRF Process).
Le Boundary Process
Russel et. al is able to exploit the stack of images for edge detection by relying on the assumption that objects in an image (which are difficult to detect from a single image due to coloring similarities/lack of features) do not rest at the same relative locations. For example cars could be parked anywhere on the street, or people could be anywhere in the image. Internal object structures, however such as windows relative to a building or wheels relative to a car will always be in the same place. Therefore the success of this approach is measured by the consistency of matches made locally (in the internal structures) in images in the stack.
Further, instead of matching the entire image, we find regions in an image where objects will match up to other regions of images in the stack. Regions outside of the boundary belong to a different region and will match with other images.
Formally, given an oriented line passing through an image point p at orientation θ, we independently search for matches in the stack of images by forming a local image descriptor modulated by a weighted mask for both sides of the line. Again, remember that the images in the stack are assumed to be "coarsely aligned" and therefore we only look for matches on both sides of the line at point p and orientation θ across the stack. In other words, matching is not translation invariant. See figure below.
Data driven boundary detection. Left: Input image with a line at a point and orientation. Right: The top 9 matches in a large collection for both sides of the queried line. Image and caption from paper.
Notice that for point B both sides look similar, resulting in a high rank correlation score. Point A lies on a boundary so the the sets of retrieved images are very different, resulting in a low rank correlation score.
The ordering in the list is given by the L1 distance between the local descriptors g(p, θ) of the target image and each image in the stack. They then compute Spearman's rank correlation coefficient between the two rank-ordered lists see below:
Spearman's Rank Correlation
High rank correlation indicates that point p lies inside an object's extent, whereas a low correlation should indicate that point p is at an object boundary with orientation θ.
Note that this data driven boundary detection is different from image based edge detection (ex. PB). This is because strong image edges (detected edges) can receive a low score since the query will result in similar pictures (at windows, the query will pull up the same picture since windows are likely to be in the same spot). Weak image edges can also result in a high score if such a boundary is uncommon. For example, a grey car parked at a grey building.
Further, data driven boundary scores are determined based on occurrence and matching statistics of similar scenes therefore requiring no additional manual supervision.
Data driven boundary detection: (a) Input image (b) Ground truth boundaries (c) PB Boundary detection (d) Proposed data driven boundary detection. In d, we observe clearer object boundaries and suppressed false positive boundaries (leaves of tree) in object. Image and caption from paper.
Le Region Process
The second part is the group pixels in the input image to form the region of the object. This entails finding clusters within the stack that are "self-consistent" and "explain the input image well". Again, the paper presents a data driven grouping approach. The paper starts off with a hypothesis that regions of semantically meaningful objects are similar across the stack (cars look similar, trees look similar).
Russel et. al's approach is to "find clusters of image patches that match the same images within the stack". This means that two patches in the input image will be regions in the same object if their respective matching images from the stack are similar.
Similar to the boundary process, the query images are compared at a particular patch location so again, the matching is not translation invariant. Again, compared with standard image region processing, patches with very different appearance can be grouped together if they query the same images. For example, a car wheel and car window look very different but will return similar images. This will reveal more semantic objects than only visually similar results.
In the figure below, patches that were matched to similar images and therefore belong to the same object or "major scene components" are highlighted. This again shows that local regions with different visual similarity map to the same object since their queries pull up visually similar images. Also note that there can be multiple hypotheses (multiple different interpretations of the semantic objects in an image) for a patch.
Data driven image grouping. Left: input image. Right: heat maps indicating groupings of pixels belonging to the same scene component, which are found by clustering image patches that match the same set of images in the stack (warmer colors correspond to higher similarity to a cluster center). Image and caption from paper.
Finally, we find cluster centers c_k for k ∈ {1,…,K}. Intuitively, we can understand the object clusters as "topics of an image stack" or different possibilities of objects. These cluster centers can be found via k-means or any other standard topic discovery methods. Further, as we aren't aiming to find all the semantic objects in the stack and only those that can explain the query image, we rely on a relatively small k ~ 5.
Le MRF Process
From the data driven boundary process, we were able to estimate clear boundaries and from the data driven region process, we were able to grow regions of semantic objects. However, even though the two processes pull from the same data, they complementary information. This is because the region process groups as many pixels as it can and is precise in location. The boundary process focuses on local image behavior at specific points.
An MRF based optimization framework ties the global region process and well-localized boundary process together. The paper presents a a multi-state MRF on pixels for segmentation. MRF is formulated as follows, but we will only go over a general explanation from the paper paraphrased as follows: Below, x_i ∈ {0, 1,…,K} is the state at pixel i that corresponds to one of the K different image stack groups. φ_i are unary costs, which are defined by similarity of a patch at pixel i. This is described by an indicator vector y_i to each of the K image stack groups. Then ψi,j are binary costs for a boundary-dependent Potts model.
Novel Methods
One of the challenges in scene-matching, which is the process of selecting images of the dataset so that we have a stack of images to use our process on, is that it is difficult to obtain good matches despite training/having a massive databases. This is because we rely on low-level image descriptors (no semantics) so it is difficult to find good matches that allow us to label parts of our new image. Several approaches such as synthetically increasing the dataset with transformed copies of images, which helps by adding translational diversity to the dataset; cleaning matching results using clustering, which aids by limiting our error, or simply picking good matches by hand. However, these do not resolve the fundamental issue that "because there is a potentially infinite cardinality of possible images to match, it is very unlikely to obtain a good overall match".
Instead, Russell et. al. propose that the new image is better matched by breaking the image into chunks that have good matches in the database, but are large enough to be meaningful as a chunk.
The figure to the left shows a precision-recall curve for the data-driven boundary detector. Precision-recall curves measure precision (number of true positive instances in all instances labeled to be positive) and recall (number of true positive instances in all positive instances regardless of what they were labeled as). Ideally we want both to be high. The curve comes from setting different thresholds to examine performance of various models.
Evaluation of the boundary detection task on the principal occlusion and contact boundaries extracted from the LabelMe database. We show precision-recall curves for PB (blue triangle line) and our data-driven boundary detector (red circle line)
Notice that Russel et. al.'s method achieves higher precision at all recall levels. At the same recall level, PB and the data-driven boundary detector achieves 0.45 and 0.50 precision, respectively. In other words, the Average Precision is higher for this method and therefore more desirable.
The star (output segmentation) produced the highest precision (0.55) at 0.09 recall. Improved performance at lower recall is due to the model suppressing interior contours in objects in the image. At higher recall, the model tends to miss small, moveable objects.
Left: Output segmentation produced by our system. Notice that the segment boundaries align well with the depicted objects in the scene. Top right: Top matches for each recovered segment, which are stitched together to form a composite. Bottom right: Top whole-image matches using the gist descriptor. By recovering the segmentation, we are able to recover improved semantic matches. Image and caption from paper.
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The love Tobi has for Alex seems to be getting deeper and deeper by the day.
Last night at the Pepsi show, BBNaija 2nd runner up Tobi Bakre opened up once again on his feelings for Shaku Shaku queen, Alex, but this time around on stage and in front of thousands.
Recall some weeks ago during the live eviction show when Ebuka asked Tobi if he would like to date Alex, Tobi quickly said yes which shocked Alex who never imagined such a thing was going through his mind.
Well, at the Pepsi show last night, Tobi revealed that he loves Alex with all his heart.
Few moments later and in response to Tobi's declaration, happy Alex came out and they both hugged each other deeply on stage.


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Nellie Irene Thurk
September 16, 2020 / Daily Dodge / Obituaries
Nellie Irene Thurk (nee Straveler) age, 88 of LeRoy passed away peacefully at her daughter's home after a short battle with cancer on Monday, September 14, 2020 with her family by her side.
Nellie was born the daughter of Joseph and Laura (Eastling) Straveler on December 1, 1931 in Brantwood, Wisconsin. On November 15, 1951 she was united in marriage to her one and only love George C. Thurk, Sr. in Oshkosh. Together they built their home and farm in the town of LeRoy where they raised their two children.
Besides farming Nellie worked numerous jobs. Over the years she worked at a canning factory in Brownsville, National Rivets in Waupun, and Grande Cheese. She also did home care for numerous people and her last job was a custodian worker for the town of LeRoy. She was a member of St. Paul Lutheran Church in Mayville.
In her spare time, Nellie enjoyed hunting, fishing, gardening, cooking, canning, and drinking a good beer along with spending time with her family and friends. She also enjoyed going on casual car rides, looking at nature and wildlife and stopping at the casino.
She is survived by her daughter- Christine (Larry) Kraemer of Theresa. Her grandchildren- Richard Kraemer, Joan (Jacob) Breitkreutz, Jennifer (Christopher) Davison, George (Kari) Kraemer, Keith Kraemer, and Penny Kraemer. Her 10 great grandchildren- Jacob (Amanda) Kraemer, Tristan Breitkreutz, Brandon Breitkreutz, Skyler White, Justin Davison, Derek Davison, Kayla Kraemer, George Kraemer, Dominick Kraemer, and Jonathan Kraemer. Great grandchildren- Parker Giese and Izabella Kraemer. Her sister- Josephine Schutt of Vestal, New York. She is further survived by other relatives and many friends.
She was preceded in death by her parents, her husband George Sr., her son George, Jr., her sisters Catherine Weisinger and Rosemary Cooley, her 5 brothers, Joseph, Norman, Hubert, Ernest, and Eugene Straveler.
A visitation for Nellie will take place on Friday, September 18 from 11 a.m. until 1 p.m. at the St. Paul Lutheran Church in Mayville with a private family funeral service (due to current health restrictions) to follow at 1 p.m. with Rev. Sara Gillespie officiating. Burial will be held at Graceland Cemetery in Mayville.
The family wishes to extend a heartfelt thank you to Kenny and Theresa Schraufnagel for your great kindness and a thank you to the hospice Metro team.
The Koepsell Funeral Home in Mayville is serving the family. For online condolences and other information please visit www.KoepsellFH.com
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Overall size including frame: 70 x 81cms 27.5" x 32"
A compelling scene to paint! Lots going on - the sunlight picking out bright colours contrasting with cool interesting shadow shapes, people moving around browsing, some standing and looking, others in conversation. I made lots of rapid sketches and settled on the flower seller as my main focus.


text:
\section{Introduction}
\label{sec:introduction}
Fragmentation processes are important in several different fields, including
powder technology~\cite{PFROA05,DTGPS04}, soil
physics~\cite{RSFFS91,PFMF97,ESDA03,MGAOTF03} nuclear
physics~\cite{RWMMA01,DD-GLTTM05}, astrophysics~\cite{BKGFOT83,OMBSAO98},
genetics~\cite{MLMOF91,MCDI91}, sprays~\cite{VMDLSF04,MVOSF04,SRWCAO99}, fuel
combustion~\cite{SLBSID94,SGTTTS98}, brittle
fracture~\cite{WKHBOS05,WKHFOS04,ASMO06} and geology~\cite{XLWPDO02,JRFDA03},
just to name a few.
\\
Because of the nature of the fragmentation process, only the final
distribution of fragment sizes is usually observable, thus becoming the main
quantity of interest.  Size-distributions have been characterized by different
empirical and theoretical statistical laws in the past.  The lognormal
distribution can be expected whenever a breakdown process can be described as
a multiplicative cascade, and has been applied in many fragmentation
examples~\cite{ASMO06,SGTTTS98,DLBASS96,BSMSAF96,IMFOL92}.  Simmons'
law~\cite{CHFTPO97,HFDPA93,HFNDD92} appears to hold universally for sprays,
and states that the mass distribution is Gaussian when written in terms of the
square root of drop diameters.  Villermaux~\cite{VMDLSF04,VUIO04,MVOSF04}
discusses the breakup process of ligaments in liquid jets, and concludes that
each ligament gives rise to a distribution of droplet sizes that is
essentially a Gamma distribution.  The Weibull distribution can be derived
from first-principles for the fragmentation of solids by
cracking~\cite{BWDOT95,ZGPATW99}, and reads \hbox{$ \%N(>m) = e^{-(m/\hat
    m)^{q}}$,} where $\%N(>m)$ is the fraction of droplets with mass larger
than $m$.  Brown and Wohletz~\cite{BWDOT95} remark that the Weibull
distribution may look similar to the lognormal, and suggest that the apparent
goodness of fits using lognormal could be fortuitous in some cases.  Other
authors have used the (empirical) {\it Rosin-Rammler}
form~\cite{BWDOT95,DTGPS04,ALBCOF97}, which applies to the accumulated mass
density in clusters of diameter larger than $D$, and states that
\hbox{$\%M(>D) = e^{-(D/D_m)^{q}}$}.
\\
In contrast with these approaches, which postulate exponential, or else
rapidly decaying size distributions, Oddershede et al~\cite{ODBSCI93} have
claimed that the size-distribution of fractured objects is an inverse
power-law, and furthermore suggested that a form of self-organized criticality
(SOC)~\cite{BTWSC88} might be responsible for this.  Power-law distributions
are often found right at second order phase transitions, in which case one or
more parameters must take precisely defined values.  However there are systems
whose dynamics converges to a stationary state that is critical, a phenomenon
termed SOC~\cite{BTWSC88} and for which no parameter tuning is needed.  Later
investigations~\cite{MBCPL96,TRMOF99,SRRDCI00,TSMOF00,OPLDDM00,OLCFEA07}
report ``composite'' power-laws, or transitions between lognormal and
power-laws as the fragmentation energy is
increased~\cite{IMFOL92,SMLCID96,SGTTTS98}.
\\
Recent works~\cite{KHTFD99,AHTUIF00,KSHSOI03,WKHBOS05,HWKF06} have reported
that fragmentation processes are only critical (and the ensuing
size-distribution a power-law) at a precisely defined value of the impact
energy. Within this picture, the fragmentation phenomenon goes through a
nonequilibrium phase transition at some well-defined value of the impact
energy. Evidences of criticality at a well defined energy where also found in
nuclear multifragmentation (NMF)~\cite{RWMMA01,DD-GLTTM05} experiments, and
have been interpreted in the context of a percolative
transition~\cite{CMNB86}, or else in relation with liquid-gas
coexistence~\cite{FCRFYA85,MBCEOP88,PMRPTN95,BLBCEO95,MPGPCI96,PD-GGFOP98,GFFPTL01,EMPLTV02,DBGESO04}
in nuclear matter.
\\
In this work, water-glycerine drops are broken by a controlled-pressure gas
blow, and the resulting droplets are counted and sized by computerized methods
that involve scanning and image-processing. The only control parameter, the
gas pressure, varies between 11 and 100 psi, and this in turn determines the
amount of energy available for the breakdown event.  Various statistical
measures characterizing the resulting size-distributions are obtained and
analyzed, for a minimum of ten and a maximum of fifty breakdown events at each
pressure. Our main finding is the existence of a phase transition around
\hbox{$P_c \approx 17 \hbox{psi}$}, where the size-distribution becomes a pure
power-law with an exponent $\tau_{min} \approx 1$ within a limited size-range.
Away from $P_c$, the size distribution is well described by the product of a
power-law and an exponentially decaying term (\Eqn{eq:14}), as given by
Fisher's model at coexistence~\cite{FTOC67}.
\\
The rest of this article is organized as follows. In
\Sec{sec:size-distributions} a brief discussion is done of some theoretical
approaches which have been used to characterize size-distributions in the
past.  \Sec{sec:exper-setup-data} describes our experimental apparatus, as
well as the data processing techniques we use to obtain statistics on size
distributions. Our results are presented in \Sec{sec:results}. In
\Sec{sec:size-distribution} the resulting size distributions are characterized
by means of a simplified Fisher expression (\Eqn{eq:14}), essentially a power
law with an exponential cutoff.  The total surface is discussed in
\Sec{sec:excess-surface}. \Sec{sec:observ-trans-perc} discusses whether the
observed transition can be characterized as percolative. The mass of the
largest fragment (\Sec{sec:largest-fragment} ) and moment correlations
(\Sec{sec:moment-correlations}) do not support such interpretation.
\Sec{sec:ashurst-holi-theory} discusses the behavior of the largest and
average mass fragment in the context of recent theoretical
elaborations~\cite{AHDFB99,AHDSD99}. In \Sec{sec:domin-prob} the concept of
dominance is introduced and applied to our data.  Finally, our results are
discussed in \Sec{sec:discussion}.
\section{Size distributions}
\label{sec:size-distributions}
In recent years, several brittle fragmentation~\cite{WKHFOS04,WKHBOS05,HWKF06}
and NMF~\cite{CMNB86,RWMMA01} experiments have been interpreted in the context
of Percolation Theory~\cite{SAITP94}. A percolation transition is claimed to
exist between a ``connected'' phase and ``disconnected'' phase, as the impact
energy is increased. In the connected phase, a large cluster (drop, fragment)
exists after the fragmentation event, that contains a significant fraction of
the total mass.  In the disconnected phase no such large cluster exists. The
natural order parameter for a percolative transition of this type is the
average size of the largest fragment. Measurements of this order
parameter~\cite{CMNB86,WKHFOS04} have shown that it goes to nearly zero at and
above the transition, in a way that is consistent with the proposed
interpretation.
\\
At the percolation critical point, the number distribution $N(x)$ of clusters
of mass $x$ becomes a power-law $N(x) \sim x^{-\tau}$, where the exponent
$\tau$ takes values close to $2.3$ in three dimensions.  NMF experiments have
been reported to give results consistent with $\tau \approx
2.3$~\cite{CMNB86,RWMMA01} as well, while brittle fragmentation experiments
seem to produce different values of $\tau$.
\\
NMF experiments are sometimes more generally
discussed~\cite{MNWCBI05,DBGCBI03,RBCEO01,EMPNMP00,SRLNMP97,FBKSOP96,BLBCEO95}
in the context of Fisher's Droplet Model~\cite{FTOC67}, which states that the
number of clusters (droplets, nuclei) of mass $x$ is given by
\begin{equation}
  N(x) = N_0 x^{-\tau} e^{B(p,T)x - C(p,T) x^{\sigma}},
  \label{eq:11}
\end{equation}
where $\tau$ and $\sigma$ are independent critical exponents.  Coefficients
$B(p,T)$ and $C(p,T)$ depend on surface tension, temperature, and chemical
potentials in the ``liquid'' and ``gas'' phases:
\begin{equation}
  B(p,T) = \frac{\Delta \mu}{T} = \frac{\mu_{gas} - \mu_{liq}}{T},
  \label{eq:12}
\end{equation}
and
\begin{equation}
  C(p,T) = \frac{c_0 \epsilon}{T}.
  \label{eq:13}
\end{equation}
Here $c_0$ is a constant that depends on surface tension, and
$\epsilon=(T_c-T)/T_c$ measures the departure from the critical temperature.
\\
The term $B(p,T) x$ measures the bulk contribution to the free energy of a
droplet of size $x$.  In a $(p,T)$ phase diagram, $B<0$ if the ``Gas'' phase
is thermodynamically stable, i.e. its chemical potential is lower than that of
the ``cluster'', or ``liquid'' phase.
\\
The term $C x^{\sigma}$ measures the surface energy of a droplet of size $x$,
so that $\sigma$ is the critical exponent that relates the dimension of the
surface to that of the volume of a droplet. For compact droplets in 3d one has
$\sigma=2/3$. For the liquid-gas transition $\sigma$ takes values close to
$2/3$.
\\
On the coexistence line, $\mu_l = \mu_g$ and thus $B=0$, so
\begin{equation}
  N(x) = N_0 x^{-\tau} e^{- C x^{\sigma}}.
  \label{eq:14}
\end{equation}
Furthermore, at the critical point one has $C=0$, and the size-distribution
becomes a pure power-law with exponent $\tau$.
\section{Experimental Setup and Data Acquisition}
\label{sec:exper-setup-data}
\subsection{Setup}
\label{sec:setup}
Our experimental setup is schematically shown in \Fig{fig:setup}.  An open,
straight glass tube (T) of 6 cm length and 7 mm inner diameter, has a solid
coaxial glass rod (1mm diameter) attached to its inner surface, with the rod's
tip protruding 5 mm downwards from the lower end of the tube.  From this tip
hangs a small (11.5 $\mu l$~\footnote{This is about the maximum volume that
  can be held by the liquid's surface tension.}) liquid drop (D) of an opaque
solution obtained by mixing equal quantities of glycerol and water, plus a
small amount of water-soluble black dye. The upper end of this glass tube is
connected to a pressurized chamber (C) via a 40cm length plastic (H1) hose,
and isolated from it by a solenoid valve (SV).  The tube is fixed so that the
droplet hangs 15 cm above the glass window of a flatbed scanner.
\\
\begin{figure}[h!]
  \centering
  \epsfig{figure=setup.eps,width=8cm,angle=0}
  \caption{Experimental Setup }
  \label{fig:setup}
\end{figure}
A nitrogen cylinder is connected to the chamber through a plastic hose (H2),
and a pressure regulator (R), which is provided with a manometer (P). The
chamber is formed by a 10 cm length, 3/8 inch inner diameter plastic hose and
is limited by two bypass valves, one manual (MV), the other electromagnetic
(SV).
\\
For each droplet breakdown experiment, the nitrogen pressure was selected with
regulator R, and the manual valve was opened until the pressure in chamber C
equilibrated, after which it was closed again.  Then, the electromagnetic
valve was opened by means of an electric switch, releasing the gas contained
in chamber C, which then flowed through tube T, fragmenting the droplet and
projecting its fragments downwards.  The resulting droplets, adhered to the
scanner's glass window, were scanned and subsequently counted and sized with
the help of specialized computer software.
\\
Before each breakdown experiment, the scanner glass was treated with a
hydrophobic solution containing Teflon.  Because of this treatment of the
glass surface, the contact angle of the liquid onto the glass was close to 90
degrees, so that the droplets turned out to be very similar in shape to
semi-spheres. After the fragmentation, a thin spacing was inserted between the
scanner lid and its glass window, and a high-resolution (600 dpi) scan was
performed.  Several (from 10 to 50) fragmentation experiments were carried out
varying the jet pressure P, from 11 psi to 100 psi.  The number of droplets
obtained varied, from a few ones at 11 psi to tens of thousands at 100 psi.
\subsection{Data Processing}
\label{sec:data-processing}
After each fragmentation, a scanning operation was performed.  All scanned
images were obtained at 600 dpi-grayscale, and stored using a lossy compressed
graphic format, for later processing.  Because of the non-negligible height of
the droplets, most images contained faint shadows, which were removed by image
thresholding~\footnote{Using Adobe Photoshop}.  Subsequent image processing
and droplet identification, counting, and sizing, was performed with the help
of ImageJ~\footnote{http://rsb.info.nih.gov/ij/}
\\
\begin{figure}[h!]
  \centering
  \psfig{figure=area.volume.fit.ps,width=6.0cm,angle=270}
  \caption{Data used for fitting \Eqn{eq:avolrelation} (squares) and the
  resulting fit (solid line). }
  \label{fig:avolfit}
\end{figure}
The output from ImageJ consisted essentially of a set of droplet areas, in
pixels.  In order to estimate droplet volumes $V_i$ from the observed areas
$\Omega_i$, we did the following. If gravity effects were negligible then all
droplets would be plane sections of a sphere and their volumes $V_i$ would be
given by
\begin{equation}
  V_i = \lambda_1 \Omega_i^{3/2},
\label{eq:vfromarea0}
\end{equation}
with $\lambda_1$ some constant. However (\ref{eq:vfromarea0}) is a good
approximation only for the tiniest droplets, whose shapes are less affected by
gravity. Larger droplets suffer a significant flattening and therefore
\Eqn{eq:vfromarea0} must be corrected.
\\
Under the effect of gravity, the height $h(\Omega)$ of a liquid droplet on a
flat horizontal surface is proportional to $\sqrt{\Omega}$ when $\Omega$ is
small, but saturates to a constant value $h_\infty$ for large values of
$\Omega$, in which case the fluid forms a flat ``lake'' of approximately
constant height. Thus $V$ satisfies (\ref{eq:vfromarea0}) for small $\Omega$,
but is proportional to $\Omega$ for large $\Omega$. Assuming, for simplicity,
a stretched exponential crossover, we write
\begin{equation}
  V(\Omega) =
    \lambda_1 \Omega^{3/2} e^{-(\Omega/\Omega_0)^\beta} +
    \lambda_2  \Omega \left [ 1-e^{-(\Omega/\Omega_0)^\beta} \right ],
\label{eq:avolrelation}
\end{equation}
where $\lambda_1, \lambda_2, \Omega_0$, and $\beta$ are to be obtained from
fits of calibration data (See \Fig{fig:avolfit}). The resulting values where
$\lambda_1=3.15 \times 10^{-5}$, $\lambda_2=8.3\times 10^{-7}$ $\Omega_0=10^5$
pixels, and $\beta = 0.366$.  In order to obtain the data required for the
fit, the projected areas were measured for several droplets having known
volumes.  Their volumes were obtained using calibrated pipettes (for the
larger ones), and glass capillaries (for the smaller ones).  The data used for
the fit, together with the resulting fit, are displayed in \Fig{fig:avolfit}.
Our final expression for the volume/area relationship extrapolates to \hbox{$V
  \sim 2 \times 10^{-5} \mu$l} when \hbox{$\Omega =$ 1 pixel}, implying that
the smallest detectable volume is \hbox{$V_{min}=$0.02 nl}.
\begin{figure}[h!]
  \centering
  \psfig{figure=Vol.Ndrops.ps,width=6.0cm,angle=270}
  \caption{Average total observed volume $V_T$ (squares) and
    average number of droplets $N_{drops}$ (circles) as a function of jet
    pressure $P$.  The initial volume of the droplet is 11.5 $\mu$l.}
  \label{fig:avgVN}
\end{figure}
\Eqn{eq:avolrelation}, together with the parameter values obtained from the
fit, were embedded into a C program, which read droplet areas (as calculated
by ImageJ), and used this expression to calculate volumes from them,
additionally implementing the statistical analysis of size distributions to be
described in \Sec{sec:results}.
\section{Results}
\label{sec:results}
\begin{figure}[h!]
  \centering
  \psfig{figure=allplotsps.ps,width=6cm,angle=270}
  \caption{$N(x)$, the number of  drops of relative mass $x=V/V_0$, for (from
  top to bottom)
  $P=$11, 15, 17, 25, 60, and 100 PSI. Solid
  lines are fits of \Eqn{eq:14} with $\sigma=2/3$. Plots have been displaced
  downwards for clarity. }
  \label{fig:Ndens.in.x}
\end{figure}
For each breakdown event, a set of droplet volumes $V_i$, $i=1,2,\ldots,n$ was
obtained as described in \Sec{sec:data-processing}, and the moments $M_k =
\sum_i x_i^k$ were calculated in terms of \hbox{$x_i=V_i/\sum_{j=1}^n V_j$},
the droplet volume fractions. The average number of droplets, as well as the
average total volume $V_T =\sum_i V_i$, are displayed in \Fig{fig:avgVN} as a
function of jet pressure P. The fact that $V_T$ remains almost constant and
equal to the initial volume confirms that most of the mass resulting from each
fragmentation gets caught by the scanner window, i.e. that there are no
significant mass losses, even at the largest pressures considered.
\subsection{Size distributions}
\label{sec:size-distribution}
\Fig{fig:Ndens.in.x} shows log-log plots of the normalized fraction of
droplets $N(x)$ with volume fraction $x$, for several values of the breakup
pressure $P$. Continuous lines in \Fig{fig:Ndens.in.x} are the result of
fitting Fisher's Model in the form indicated by \Eqn{eq:14}, which is
appropriate for the coexistence region.  We fixed $\sigma=2/3$ and adjusted
$N_0(P)$ (not shown), $C(P)$ (\Fig{fig:coeff}) and $\tau(P)$ (the
\emph{apparent} exponent, see \Fig{fig:effexp}) independently for each
pressure $P$. We checked that the qualitative features of these fits did not
change much for $\sigma$ ranging from $1/3$ to $2$.
\\
\begin{figure}[h!]
  \centering
  \psfig{figure=C.of.P.ps,width=6.0cm,angle=270}
  \caption{Amplitude $C(P)$ (circles) of surface correction term in \Eqn{eq:14}, for
    $\sigma=2/3$. The solid line is an empirical fit (see text).}
  \label{fig:coeff}
\end{figure}
\begin{figure}[h!]
  \centering
  \psfig{figure=tau.ps,width=6.0cm,angle=270}
  \caption{Fits of Fisher model (\Eqn{eq:14}) to the droplet density $N(x)$ (\Fig{fig:Ndens.in.x}),
    produce an apparent exponent $\tau$ (circles) showing a deep minimum
    \hbox{$\tau_{min} \approx 1$} around 18 PSI.}
  \label{fig:effexp}
\end{figure}
\\
The ``surface'' correction term $C(P)$ (\Fig{fig:coeff}) changes sign around
$P_0=17$ PSI, implying that the size distribution is similar to a pure
power-law there, and giving the first hint for the existence of a phase
transition. The resulting curvature change that is apparent in
\Fig{fig:Ndens.in.x} has been reported and discussed in NMF experiments as
well~\cite{GFFPTL01,BLBCEO95}. The solid line in \Fig{fig:coeff} is a fit of
the form
\begin{equation}
  C(P) = a \left [ \left ( \frac{P}{P_0} \right )^{\mu} -1 \right ]
\end{equation}
and results in $P_0=15.5$ and $\mu=-1.5$. This suggests that
\begin{equation}
C \sim (P-P_0)
\label{eq:Clin}
\end{equation}
near the crossing point $P_0$.
\\
The exponential term in (\ref{eq:14}) can be written, as is usually done in
the scaling description of critical phenomena, as
\begin{equation}
e^{-C x^\sigma} = F_{\pm}( (x/x_0)),
\end{equation}
where the subscript $\pm$ means $P>P_0$ or $P<P_0$ respectively. The
``cutoff'' $x_0$ satisfies
\begin{equation}
x_0= |C|^{-1/\sigma}.
\label{eq:x0}
\end{equation}
For compact droplets we can furthermore write
\begin{equation}
x_0 = \xi^3
\label{eq:xi}
\end{equation}
in three dimensions, where $\xi$ is a correlation length (the linear size of
the typical droplet). Considering (\ref{eq:Clin}), (\ref{eq:x0}), and
(\ref{eq:xi}) one finds that, near $P_0$,
\begin{equation}
  \xi \sim |P-P_0|^{-\nu}
\end{equation}
with $\nu =1/2$, i.e. a classical value for a thermal critical exponent. Of
course, this specific result ($\nu=1/2$) depends on the validity of
(\ref{eq:Clin}), which in view of the quality of our data cannot be taken for
granted.
\\
The apparent exponent $\tau(P)$ (\Fig{fig:effexp}) goes through a steep
minimum $\tau_{min} \approx 1$ around 18 PSI. A similar minimum in $\tau$ has
been taken as an indicator for the location of a phase transition in NMF
experiments~\cite{PCTEFA84,MBCEOP88} in the past.  In fact, Richert and
Wagner~\cite{RWMMA01} \emph{define} the critical temperature $T_c$ as the one
that minimizes $\tau(T)$. We may thus consider this steep minimum as a further
indication of a phase transition in the breakdown process, occurring somewhere
in the range 16-18 PSI for our specific experimental setup.
\subsection{Excess surface}
\label{sec:excess-surface}
The total normalized surface $\Omega_F=\sum_i x_i^{2/3}$ of the final set of
drops in each breakdown process gives an estimation of the total amount of
energy transferred to the system of drops (i.e. neglecting kinetic energy) and
is thus an interesting physical quantity in the breakdown experiment. We
define the relative excess surface as
\begin{equation}
  E(P) = \frac{\Omega_F - \Omega_0}{\Omega_0}
\end{equation}
where $\Omega_0=1$ is the initial surface. By taking averages over breakdown
events at pressure $P$, the results displayed in \Fig{fig:surfincrease} are
obtained. It can be seen in this figure that the pressure-dependence is
approximately linear everywhere, but there is a sharp discontinuity in its
slope, again happening around 17 PSI. Fitting two straight lines intersecting
at $P_0$ to the data shown in \Fig{fig:surfincrease} (dotted line) one obtains
the estimate $P_0=17.6$\ PSI.
\\
If the excess surface is interpreted as an ``energy'' and the jet pressure as
a measure of the effective ``temperature'', the discontinuous slope in
\Fig{fig:surfincrease} is analogous to a discontinuity in the specific heat.
\\
\begin{figure}[h!]
  \centering
  \psfig{figure=specific.heat.ps,width=6.0cm,angle=270}
  \caption{Surface increase versus Pressure  has a discontinuous derivative
    around 17.6 PSI. The dotted line is a linear fit, with the location of the
    kink as a fitting parameter.}
  \label{fig:surfincrease}
\end{figure}
\subsection{Is the observed transition percolative?}
\label{sec:observ-trans-perc}
\subsubsection{Largest fragment}
\label{sec:largest-fragment}
Recently there have been suggestions that brittle
fragmentation~\cite{WKHFOS04,WKHBOS05,HWKF06} and NMF~\cite{CMNB86,RWMMA01}
experiments can be rationalized in the context of a percolative~\cite{SAITP94}
phase transition. The validity of such interpretations rests, to a great
extent, upon the identification of a relevant order parameter which has the
properties of the infinite-cluster density in percolation. Within this
picture, the connected or percolating phase must be characterized by the
existence of macroscopic fragments, while no such fragments must exist in the
disconnected phase (at large breakdown energies). The average size of the
largest fragment, which goes to zero \emph{abruptly} at the critical energy,
plays the role of an order parameter in brittle
fragmentation~\cite{WKHFOS04,WKHBOS05,HWKF06}, so it is natural to first
consider the largest droplet size as a tentative order parameter also in the
case of our experiments.
\\
\begin{figure}[h!]
  \centering \psfig{figure=holian.predictions.ps,width=6.0cm,angle=270}
  \caption{ Maximum droplet size $Z_{max}$ (circles) and average droplet size
    $Z_{avg}=M_2$ (squares), as a function of jet pressure $P$. Straight lines
    are of the form $c_1 P^{-2}$ and $c_2 P^{-3/2}$ respectively.  Assuming
    that the system's \emph{expansion speed} $\eta$ is proportional to the jet
    pressure $P$, the observed dependencies $Z_{max} \sim P^{-3/2}$, and
    $Z_{avg} =M_2 \sim P^{-2}$ are consistent with recent predictions of a
    simple energy-balance theory of Ashurst and
    Holian~\cite{AHTUIF00,AHDFB99,AHDSD99}.}
  \label{fig:holianpred}
\end{figure}
The average mass $Z_{max}$ of the largest fragment is shown in
\Fig{fig:holianpred} from our droplet fragmentation experiments.  It turns out
that $Z_{max}(P)$ has a smooth pressure dependence of the type $Z_{max}(P)
\sim P^{-3/2}$, without any traces of a singular behavior. Notice that, if
there where a percolative transition, the mass of the largest droplet (the
infinite cluster) should go to zero at the critical point. Therefore we
conclude that the behavior of $Z_{max}$ does not support the existence of a
percolative transition in this system.
\subsubsection{Moment correlations}
\label{sec:moment-correlations}
In his discussion of NMF experiments, Campi~\cite{CMNB86} notices that
correlations among some moments of the size distribution are similar to those
found in Percolation. In particular, a plot is presented of $Z_{max}$ versus
$S_2=M_2/M_1$ (moments are calculated excluding the contribution of the
largest cluster) and it is argued that the rounded ``nose'' of events with
large values of $S_2$ corresponds to the percolative ``critical region''.
\\
\begin{figure}[h!]
  \centering
  \psfig{figure=ZmaxvsS2.lambdamodel.comparison.ps,width=6.0cm,angle=270}
  \caption{Inclusive (all pressures) scatter plot of the mass $Z_{max}$ of the
    largest piece versus $S_2=M_2/M_1$, where the moments have been calculated
    without the contribution of the largest piece. Points near the ``nose'' of
    events with large values of $S_2$ correspond to pressures in the range
    16-18 PSI. Notice, however, that the existence of this feature is by
    itself not indicative of critical behavior, since it is there even for the
    trival partition described in the text (solid line).}
  \label{fig:ZmaxvsS2}
\end{figure}
\Fig{fig:ZmaxvsS2} shows a scatter plot of $Z_{max}$, the largest cluster's
mass, versus $S_2$, for each fragmentation event in our experiments. This plot
is similar in many aspects to the one considered by Campi~\cite{CMNB86}, in
particular with respect to the existence of a ``nose'' of events with large
values of $S_2$. It can be easily seen, however, that this feature by itself
is not indicative of critical behavior. In order to see this, consider the
breakup of a droplet of unitary volume into an infinite succession of droplets
$i=0,1,2,\ldots$ of volume $v_i=(1-\lambda) \lambda^i$, for $0<\lambda<1$.  As
$\lambda$ goes from almost zero to almost one, the resulting size distribution
changes from being dominated by essentially one large drop, to being composed
of a ``mist'' of tiny droplets. Clearly there is no phase transition in this
system.
\\
For this simple partition, the largest mass is $Z=v_0=(1-\lambda)$.
Furthermore, it is straightforward to show that $S_2=Z(1-Z)/(2+Z)$. A plot of
$S_2(Z_{max})$ for this simple partition is displayed in \Fig{fig:ZmaxvsS2}
(thick line). It can be seen that its overall features are the same as
reported by Campi~\cite{CMNB86}, i.e. $S_2$ goes through a maximum and then
decreases, as $Z_{max}$ decreases ($\lambda$ increases). Thus we conclude that
the rounded ``nose'' in these plots is not by itself indicative of a phase
transition, and cannot be taken as evidence of percolative behavior.
\subsection{Ashurst and Holian theory}
\label{sec:ashurst-holi-theory}
Recently Ashurst and Holian (AH)~\cite{AHDFB99,AHDSD99} (see also \"Astrom,
Holian and Timonen \cite{AHTUIF00}), considering a $d$-dimensional fluid
system that expands uniformly at rate $\eta$, predicted that the
\emph{maximum} droplet size $Z_{max}$ should behave as $\eta^{-d/2}$ while the
\emph{average} droplet size $Z_{avg}$ should decrease as $\eta^{-2d/3}$ with
increasing expansion rate~\footnote{The average considered here to is not the
  \emph{number average}
  $1/N_{drops}$ but the \emph{mass average} $\sum_i x_i^2/\sum_i x_i = M_2$.}.\\
Since in our experiments the expansion rate $\eta$ is not a control parameter,
the applicability of AH results is not obvious.  However we find (See
\Fig{fig:holianpred}) that $Z_{max} \sim P^{-1.5}$ and $Z_{avg} \sim P^{-2}$,
which is consistent with AH predictions in 3 dimensions, if the (unknown)
expansion rate $\eta$ is \emph{assumed} to be proportional to the jet pressure
$P$.
\subsection{Dominance Probability}
\label{sec:domin-prob}
We now set to try and identify the nature of the phase transition at $17$ PSI,
by defining a useful order parameter that we call \emph{dominance
  probability}.  Although, as seen already, the largest fragment size is a
smooth function of $P$, we have noticed that, at low pressures, most of the
mass is concentrated in a few large fragments, while at larger pressures the
mass is evenly distributed among a large number of small droplets.  More
precisely, at very low pressures the mass distribution appears to be composed
of one large fragment plus many tiny droplets. Upon increasing the jet
pressure $P$, often two large droplets appear, next events with three large
fragments become prevalent, and so on. At large enough pressures, however, the
original droplet mass is more evenly distributed among a large number of
droplets, without a clear size distinction between large and small ones.  We
then seek to define an order parameter that quantifies the property that the
mass distribution be ``dominated'' by a few large fragments or not.
\\
For an arbitrarily defined ``dominance factor'' $\gamma$ taking values
slightly smaller than 1 (one can take e.g.~$\gamma=0.9$ to exemplify the
ideas), we say that there is \emph{dominance} at level 1 if the largest
fragment's mass is larger than $\gamma$ times the total mass.  If this
condition is not satisfied, the largest fragment is removed and we check
whether the second largest fragment's mass is larger than $\gamma$ times the
total remaining mass (after removing the first largest). If this is the case,
we say that there is dominance at level 2. If not, the second largest droplet
is removed and we proceed to do the same check with the third largest one, and
so forth, until only the last droplet remains.
\\
These ideas can be formalized as follows. First all droplets in a given
fragmentation event are ordered by size: $x_1 > x_2 > \ldots > x_n$. Then for
a given value of the ``dominance parameter'' $\gamma$, check whether the
dominance condition
\begin{equation}
  x_k > \gamma \sum_{k}^n x_i
  \label{eq:3}
\end{equation}
is satisfied for some $k<n$. Stop at the smallest value of $k$ that satisfies
(\ref{eq:3}). In other words we will say that there is dominance at level $k_d$ if
condition (\ref{eq:3}) is satisfied at $k=k_d$ but not at $k_d-1,
k_d-2,\ldots,1$. If (\ref{eq:3}) is not satisfied for any $k<n-1$ then we say
that there is no dominance. \\
\begin{figure}[h!]
  \centering
  \psfig{figure=dominance.ps,width=6.0cm,angle=270}
  \caption{Probability of dominance $P(k_d,P)$ at $k_d=$ 1 (plusses), 2 (crosses),
    3 (asterisks), 4 (empty squares), and 8 (full squares); mass of dominant
    drops $M_D(P)$ (empty circles), and total dominance probability $P_D(P)$
    (full circles) as a function of pressure $P$.}
  \label{fig:dominance}
\end{figure}
Whenever there is dominance at level $k_d$, the first $k_d$ drops are
substantially larger than all of the remaining ones. This means that the mass
distribution can be separated in two components: one made of $k_d$ massive
drops, the other constituted by one or more (usually many) tiny droplets.  If
on the other hand condition (\ref{eq:3}) is never satisfied, it is said that
there is no dominance and this means that the distribution has no
distinguishable size scale.
\\
In NMF, events where the excited nucleus emits a few small fragments composed
of one or two nuclei, remaining otherwise almost unaltered, are called
\emph{evaporation} events.  Those events where the original nucleus splits
into two large fragments (plus eventually a few much smaller ones) are called
\emph{fission} events, and those for which three large fragments are formed
are called \emph{ternary fission} events.  Within the dominance concept we
have introduced, the NMF classification mentioned above corresponds to
$k_d=1,2$ and $3$ respectively.
\\
In order to apply these ideas to our experimental data, for each pressure $P$
we determine the probability $P_D(k_d,P)$ that there is dominance at level
$k_d$, by averaging over fragmentation events (typically fifty) at pressure
$P$. The resulting dominance probabilities are displayed in
\Fig{fig:dominance} for several values of $k_d$. It is apparent from these
data that evaporation ($k_d=1$) events are predominant at low pressure, next
fission ($k_d=2$) events appear as $P$ is increased, followed by a
predominance of ternary fission($k_d=3$) and so forth. As shown in
\Fig{fig:avgk}, the average dominance level $k_d$ grows on approach to $P=18$
PSI, beyond which there is no longer any detectable dominance.
\\
The sum over $k$ of $P_D(k,P)$ gives probability $D(P)$ that there is
dominance at some level, and is also shown in \Fig{fig:dominance}, together
with the average mass $M_D(P)$ of all dominant droplets. The fact that
$M_D(P)$ is roughly equivalent to $D(P)$ indicates that, whenever there is
dominance, almost the total mass of the system is contained in the $k_d$
dominant drops.
\begin{figure}[h!]
  \centering
  \psfig{figure=dominance.avgk.ps,width=6.0cm,angle=270}
  \caption{Average number of dominant drops, versus pressure. For pressures
    larger than 18PSI, no dominance was ever detected.}
  \label{fig:avgk}
\end{figure}
The total dominance probability $D(P)$ goes to zero at around $18 PSI$, in a
way that is consistent with all previously mentioned evidence indicating a
critical point around that pressure. Of course the precise numerical values of
the dominance observables $P_D(k,P)$ depend on the arbitrary choice of the
dominance parameter $\gamma$, but we have checked that the fact that the
dominance probability goes to zero around $18$ PSI holds qualitatively
unaltered for $\gamma$ ranging from $0.8$ to $0.95$.  We also explored a
different definition of dominance, namely replacing (\ref{eq:3}) with
\begin{equation}
  x_k > \gamma x_{k+1}.
  \label{eq:otherdom}
\end{equation}
This means that a comparison is established between each mass-sorted droplet
and the next, stopping at the first level at which the ratio between them is
larger than a given prespecified factor. The use of definition
(\ref{eq:otherdom}) instead of (\ref{eq:3}) did not alter our findings
qualitatively.
\\
We thus feel justified to conclude, based on the data presented in this
section, that there is a \emph{dominance transition} in the neighborhood of
$P_c=18$~PSI. On the low-pressure side of this transition, a few large
(dominant) drops contain most of the original mass, and there is a size-gap
separating these large drops from the accompanying ``mist'' of tiny droplets.
Beyond $P_c$, on the other hand, one has a collection of droplets which
populate homogeneously the whole range of sizes without a systematic size gap.
\section{Discussion}
\label{sec:discussion}
We have presented a statistical analysis of droplet-size distributions
obtained when a liquid drop is broken by a sudden gas jet blow. A flatbed
scanner and image processing software were used to automatize the process of
counting and measuring the resulting fragments, enabling us to collect
statistics for breakdown processes resulting in up to tens of thousands of
tiny droplets. The resulting size-distributions $N(x)$, displayed in
\Fig{fig:Ndens.in.x}, can be fitted by a simplified Fisher-model expression
(\Eqn{eq:14}) and it was found that $N(x)$ behaves like a pure power-law only
at \hbox{$P_c \approx 17\hbox{~PSI}$}, providing the first hint for the
existence of a phase transition there. Further evidence suggesting a phase
transition is given by a deep minimum in the apparent Fisher exponent $\tau$
(\Fig{fig:effexp}), and by a sharp slope discontinuity in the relation between
pressure and surface increase (\Fig{fig:surfincrease}), both of them occurring
at $P_c$.  We argued that it is not possible to identify $P_c$ as a
percolation critical point, as was done in NMF~\cite{RWMMA01,DD-GLTTM05} and
Fracture~\cite{WKHFOS04,WKHBOS05,HWKF06} experiments, because: a)
$\tau^{min}\approx 1$ (\Fig{fig:effexp}) is far from the value $2.3$ that
would be expected for a percolative transition, and b) in our case, the mass
$Z_{max}$ of largest fragment does not become zero at $P_c$, but instead
behaves as $P^{-3/2}$ in the whole pressure range considered (See
\Fig{fig:holianpred}). Low values of the apparent exponent $\tau$ have been
previously reported in NMF experiments\cite{PCTEFA84,PCSFII85,MBCEOP88}.
\\
Furthermore, the behavior of the largest and average fragments, in our
experiments, was found to be consistent with recent predictions of Ashurst and
Holian (AH)~\cite{AHDFB99,AHDSD99}, if the original droplet is assumed to
expand at rate $\eta$ that is proportional to $P$ (\Fig{fig:holianpred}).
\\
Analysis of moment correlations through a scatter plot (see
\Fig{fig:ZmaxvsS2}) reveals a behavior similar to the one already found by
Campi~\cite{CMNB86} in NMF experiments, and which was invoked as evidencing
percolative critical behavior. We showed, however, that the shape of the
scatter plot displayed in \Fig{fig:ZmaxvsS2}, i.e. the existence of a maximum
in the values of $S_2(Z)$, is in no way related to criticality, since it is
there even for a simple, non-critical, partitioning model, as discussed in
\Sec{sec:observ-trans-perc}.
\\
We introduced the concept of ``dominance'' in an attempt to quantify the
observed fact that a few large droplets contain most of the original mass at
low pressures, while no dominant droplets are observed at larger pressures.
The dominance probability, as we defined it, although is dependent upon an
arbitrary parameter $\gamma$, shows a sharp fall (\Fig{fig:dominance}) to zero
at a critical pressure $P_c \approx 18$ PSI, that is roughly independent of
$\gamma$. Of course the precise value of $P_c$ is not interesting by itself,
since it will depend upon many parameters like the volume and viscosity of the
original droplet, the amount of gas contained in the pressurized chamber, the
diameter of the outlet (and thus the exhaust velocity), etc, whose variation
we did not consider in this experiment. Conceptually more interesting is the
fact that, as the energy available to break the droplet increases, a sharp
transition occurs between two breakdown regimes, and that this transition can
be characterized by statistical methods as discussed in \Sec{sec:results}.
\\
Future work could include the use of fast imaging techniques in order to put
these results in the context of what is known about rupture modes in the field
of sprays~\cite{PEUOB87,HFNDD92,JBBBOA99,LREOL01}. The following picture
emerges for isolated droplets subject to a sudden gas blow.  At low excitation
intensity (low Weber number) the prevalent rupture mechanism is vibrational
breakup, whereby collective oscillations break the drop into a small number of
roughly equal-sized droplets.  Upon increasing the breakdown energy, bag
breakup appears, which is characterized by the deformation of the drop into a
torus-shaped rim, which subsequently disintegrates. A variant of this is
called bag-and-stamen breakup, in which a central ``stamen'' is also formed.
Next come shear breakup, where small droplets are continuously stripped off
the rim of the drop, and catastrophic breakup, where strong surface waves
disintegrate the drop violently. The limit Weber number between vibrational
and bag breakup is around 10. At 20-60 shear breakup appears, and at 1000
catastrophic breakup.
\\
Since our experiments were conducted on droplets hanging from a thin glass
tip, the presence of which certainly modifies the gas flow and the ensuing
breakup modes, we do not expect a direct correspondence with the above
classification, although a comparison with the rupture modes of free droplets
would certainly be instructive.
\\
Also interesting is to establish a comparison of our results with recent
analyses of NMF data in the context of phase
transitions~\cite{RWMMA01,DD-GLTTM05}. Common characteristics are: a sharp
minimum in the apparent $\tau$ exponent~\cite{PCTEFA84,MBCEOP88,RWMMA01}, a
strong curvature change in a log-log plot of $N(x)$\cite{BLBCEO95,GFFPTL01},
and the fact that $N(x)$ is, to a good approximation, a pure power law at
criticality~\cite{PCTEFA84,MBCEOP88,BLBCEO95,RWMMA01,GFFPTL01}.
\begin{acknowledgments}
  This work has been partially supported by Conacyt, M\'exico, under Grants
  No.  46709-F and 48783-F.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
Q: Running parallel pipelines on different branches These are two branches of a project www.example.com: branch logan and branch bella.
The 33rd pipeline is the logan branch of www.example.com, and the 34rd pipeline is the bella branch of www.example.com.
When the 33rd pipeline is not over, the 34rd pepeline will always be in the pending stage.
If the pepeline of one branch is pending, the pepeline of the other branch will be affected?
This is very strange.How can I solve this problem?

A: If you have your own runners, you can modify the config.toml file, specifically changing the request_concurrency property:
[[runners]]
  name = "super-runner"
  request_concurrency = 10
  ...

If using kubernetes executor you can add the env variable RUNNER_REQUEST_CONCURRENCY and it will set the desired request_concurrency for every runner created.


Baltimore mayoral candidates filed campaign finance reports with the Maryland State Board of Elections April 15. Here's a look at the top earners.
Businessman David Warnock spent more than $1.6M in two months on his campaign for Baltimore mayor.
Headed into the final month Baltimore's race for mayor, former Mayor Sheila Dixon has a $100,000 cash advantage over her chief rival, state Sen. Catherine E. Pugh.
According to the latest campaign finance reports filed Tuesday, Dixon slightly outraised Pugh during the past two months, giving her $476,000 in her account compared with $371,000 for Pugh. During that time, Pugh outspent Dixon nearly 4 to 1 — $589,000 to $148,000.
The two women, who are competing in the Democratic primary, were virtually tied for the lead in a poll conduced this month for The Baltimore Sun and the University of Baltimore.
"I am proud to have the largest grassroots Baltimore fundraising base in this campaign," Dixon said in a statement.
The report shows Dixon's campaign has received donations from 1,227 individual contributors since the start of the campaign. In the most recent filing, she picked up $12,000 from members of Baltimore's Paterakis family, who developed the Harbor East area; $6,000 from Spinello Cos., a New Jersey contractor; and $1,000 from the State Center LLC.
Pugh's donations include many from business leaders and General Assembly members, including $6,000 from state Sen. Joan Carter Conway of Baltimore and $5,000 from Sen. C. Anthony Muse of Prince George's County. Her expenditures include more than $217,000 on media.
Businessman David L. Warnock, who was third in the recent poll, reported $73,000 on hand. He has spent more than $1.6 million on his campaign in the past two months — including nearly $1.5 million of his own money. He spent more than $1.3 million on media.
City Councilman Nick J. Mosby had $133,000 in his campaign account. He raised $73,000 over the past two months, largely through small donations. At the same time, he spent $143,000, mostly on campaign staff and fundraisers.
On Tuesday, six leading Democrats running for mayor of Baltimore made various claims — mostly true, but some false or exaggerated — during the first televised forum of the campaign sponsored by The Baltimore Sun, WJZ-TV, the University of Baltimore and Baltimore City League of Women Voters.
Lawyer Elizabeth Embry reported $246,000 in the bank. She raised $124,000 but spent $272,000 over the past two months. Among her contributions were $200 from former city health commissioner Peter Beilenson; $600 from city solicitor George Nilson; $750 from lawyer John Angelos, a relative of Orioles owner Peter Angelos; and $1,000 from developer J. Joseph Clarke, husband of City Councilwoman Mary Pat Clarke.
City Councilman Carl Stokes reported about $143,000. He raised about $36,000, with much of it coming from smaller donations of $50, $100 and $250. He collected about 10 donations worth $1,000 each and one $6,000 donation from J4P Associates, a company that owns the building the state leases to run the city's District Court on the east side.
Prominent Black Lives Matter activist DeRay Mckesson reported $97,000 cash on hand with $223,000 in donations from nearly 5,000 contributors — dwarfing the number of contributors of any other campaign. Many donations came in small denominations of $3, $5 and $25. He collected about a dozen donations of $6,000. He received checks from people from every state in the country and D.C. — and also some from famous names, such as Susan Sarandon, the actress who recently endorsed him on Twitter.
They are among 13 Democrats vying to replace Mayor Stephanie Rawlings-Blake, who is not seeking re-election. The Democratic primary is scheduled for April 26. Whoever emerges from the primary faces the winner of five Republicans and three Greens in November's general election. Democrats outnumber Republicans nearly 10-to-1 in Baltimore.
City Council President Bernard C. "Jack" Young, who is seeking re-election, had $664,000, the most cash on hand of any city politician, the reports shows.
Others showing fundraising strength were: Comptroller Joan Pratt, who had $223,000; 11th District City Councilman Eric T. Costello, who had $100,000; Council Vice President Ed Reisinger with $80,000; 4th District City Council challenger Brian Hammock with $88,000; and 1st District Council contenders Zeke Cohen and Scott Goldman with $86,000 and $80,000, respectively.
The race for Circuit Court judge also was proving expensive. A slate of sitting judges reported $145,000 on hand, while challenger James B. Kraft had $123,000.
Pugh has spent more than $1.1 million on her campaign.
Dixon has spent more than $850,000 on her campaign.