In the case of Akshay Anant Matkar vs State of Maharashtra, a police search followed the filing of an FIR on November 15, 2022, at a public location in Satara district where a man named Satish Botalji was allegedly collecting money from customers based on computerised numbers. According to the police, Botalji violated the terms of the Maharashtra Prevention of Gambling Act, 1887 by operating an internet gaming or gambling site without a valid permit.
whether the win wingame is actually a game of skill or a game of mere chance
The petitioner claimed that the instruction manual for the game Wingame demonstrates that the player must solve mathematical quizzes based on various combinations of geometric figures that are given specific values. Based on the equations, a mathematical solution must be found, and the solution must be provided in the form of a multiple-choice question. The player proceeds through the game’s levels once the action is completed in a timely way; as a result, it is a skill-based game and does not fall under the gambling prohibited by the Maharashtra Prevention of Gambling Act, 1887.
Analysis of Order
The division bench of Justices Sunil Shukre and MM Sathaye Bombay High Court quashed a First Information Report (FIR) lodged against Wingame Enterprises proprietor Akshay Matkar booked for gambling’ under the Maharashtra Prevention of Gambling Act, 1887.
The bench looked at the game’s user manual, which revealed that a player had to solve mathematical puzzles based on various combinations of geometric figures that were given specific values. Based on the equations, a mathematical answer was to be found and the answer was to be given in the form of MCQ. This meant that the game was one of skill rather than chance and did not fall under the definition of gambling.
The bench believed that wingame required mathematical competence rather than being a gaming of chance. In addition to the aforementioned skill, it is also necessary to have the capacity to observe and solve mathematical equations quickly. The bench added that “wagering or betting” is not required for an activity to fall under the definition of “gambling” in the case of online gaming.
The panel ruled that the FIR should be quashed because, based on the facts and circumstances of the case, no offence is supported by the claims in the FIR as they currently stand, and subjecting the Petitioners to a trial would be an abuse of the legal system.


X Number Game
Today you acquaint yourself with one of the most edgy games to come to your iPhone. “Cross Numbers Puzzle” is not your old fashioned fill in the blank puzzle. It is an in your face, make you think, numbers challenge. Developed by HYPERLINK “http://zyousoft.com/”zYouSoft, this app will present a contest like no other. This game will test your eye-hand coordination as well as your ability to think quickly.
With a bright, colorful board, “Cross Numbers Puzzle” is sure to attract even the most seasoned puzzle player. The way the board is constructed will tell you right away; this is not an average puzzle. The playing area is a square on its side with a point at the top and bottom. On the bottom edges of the square are blocks with a two digit number. Inside the square are colorful circles with numbers connected in a line. Here is where it gets challenging. Some circles do not have a number in them. You pick a number from 1-9 to place in the correct circle. If you pick the correct number you will have completed the string to equal the number in the square. Would you like more? Ok, how about we add a timer so you’re really under pressure. When you complete the puzzle correctly, you will be directed to the Scoreboard where you enter your name. Of course the timer is there to show that your mind needs to be in overdrive to get better. Are you up for it?


Important announcements and information.
Check here for the latest information.
Welcome to the new website for Joseph J. Greenberg!
Please join us for a Parent Math Workshop and/or a Math “Live” Presentation! Click on the link below for more details.
Parent Math Workshop Flyer
Parent Math Workshop: Wednesday, December 6, 2017, from 5:00 to 6:30 PM in the Library.
Math “Live” Lesson Demo: Friday, December 8, 2017, from 9:00 to 10:00 AM in various classrooms.


Two multiplied by five equals ten.
If you multiply seven by five, you’ll get thirty-five.
Tom learned to multiply when he was five.
Three times three is nine.
The area of a rectangle is its height times its width.
Andy’s girlfriend has twenty of shoes, which is five times as many as Andy.
Ten divided by two makes five.
If you divide 10 by 3 , the remainder is 1.
3.14159 three point one four one five nine
13/353 thirteen over three hundred and fifty three（分母太長改用over）
15% fifteen percent
0.3% zero point three percent
12.05% twelve point zero five percent
A: Oh no, I failed my math exam. My mom is going to kill me.
B: Come on! It’s not the end of the world. Besides, I can help you. I’m quite good at math.
A: Oh Max, you are so kind. Could you teach me how to do division?
B: Sure, ten divided by two makes five. You can imagine that ten cakes have to be distributed to two people; therefore, each of them will get five.
A: Wow, that would be much easier. Wait, I also got some problems with multiplication. What is eight times three?
B: That would be twenty-four.
A: Okay, last question. How to calculate the area of a circle?
B: It’s its radius squared times three point one four(3.14).
A: Thanks! You really help me a lot.


What is Your Smartphone Thumb Zone? [INFOGRAPHIC] */?> What is Your Smartphone Thumb Zone? [INFOGRAPHIC]January 9, 2015 8:41 am ·
Smartphones have continued to increase in size, but our hands have not.
Have you ever wondered how big your hands would need to be to easily reach the entire screen only using one hand? The answer: Your hands would need to be as big as those of a professional football and basketball. Read about our calculations and sources below.
We also calculated how far the average man and woman can reach on four popular smartphone models: The iPhone 6, 6 Plus, Samsung Galaxy S5, and Galaxy Note 4. Be sure to check out how your hand compares with our two printouts as well.
Follow the links below for printer-friendly pdf versions of how large your hand needs to be to reach the entire screen of an iPhone 6 and a Samsung Galaxy S5.
This project aimed to estimate how much of the phone your right hand can reach using a “shelf grip” approach. Previous studies did not make any attempt to quantify how much of the screen people could reach, but rather took a subjective approach based on how a phone felt in one’s hands. Their “thumb zone” consisted of a sweeping arc from the bottom left corner to almost the middle-right of the phone.
Determining formulas to calculate their precise area was beyond the scope of this project. Rather, this project assumed thumb motion occurs in a radial fashion. We were able to perform our calculations using the Pythagorean Theorem, which states:
a2 + b2 = c2
We used a fixed location for the thumb, with the center along the right side of the phone, 1/4 the distance from the bottom. This fixed location was necessary for our calculations, when in reality people shift their grip while using their phone. The shelf grip is limited by physiology, and has an unreachable zone from half of the phone’s width on the bottom to 1/4 of the phone’s height on the right.
We estimated the base of your thumb is 1/4 the width of your hand above the phone. Assuming a 90 degree angle between the phone and your hand, we then used Pythagorean’s Theorem to figure out how far your thumb could “easily” reach, using the thumb length as the hypotenuse of the triangle.
To recap, 1/4 the width of the hand is one of the sides of the triangle, side b, the thumb length is the hypotenuse, c, and the green, “natural” zone radius is the other side of the triangle, side a.
Our formula is now: (green radius)2 + (hand width / 4)2 = (thumb length)2
Now we can solve for the green radius: green radius = √ (thumb length)2 – (hand width / 4)2
To calculate the yellow reach zone, we simply added 1 inch to the green natural zone. Anything beyond that was considered in the red, the unreachable zone.
We followed a very similar calculation to determine the hand size necessary to reach the entire screen of various smartphones. Using the dimensions of each phone, we were able to calculate the distance between the fixed thumb location and the upper left corner of the phone. We then subtracted 1 inch from these lengths to get the radius of the natural zone.
Going back to our formula, we have: (green radius)2 + (hand width / 4)2 = (thumb length)2
Except we know the green radius, and not the other two variables. After taking five measurements of men’s hands, we determined the average ratios between various parts of the thumb. We calculated that the thumb length = 0.866 * hand width, and hand height = 2.061 * hand width.
We can now simplify our formula to: r2 + (0.25w)2 = (0.866w)2
Solving for the width, we get: w = √ r2 / 0.687456
We also used these ratios to help calculate the hand height and width of the famous athletes, where often times only height or span was listed.
- Average hand size for men and women – http://www.theaveragebody.com/average_height.php
- Robert Wadlow – http://www.guinnessworldrecords.com/world-records/11000/largest-hands-ever
- LeBron James, Michael Jordan, Shaquille O’Neal – http://www.foxsportsradio.com/articles/the-locker-room-486404/the-largest-hands-in-the-nba-12467252 and http://www.insidehoops.com/forum/showthread.php?t=257270
- Russell Wilson, Colin Kaepernick – http://www.rotoworld.com/articles/nfl/47036/311/exploring-qb-hand-size
- iPhone 6, 6 Plus, Samsung Galaxy S5, Galaxy Note 4 – http://www.gsmarena.com/


The safest betting approach in current betting markets in Kenya and all over the globe is the arbitrage betting strategy. Arbs else referred to as Surebets, is a profit must approach since arbitrage betting is a risk-free opportunity rarely availed in some of the betting sites and sporting activities. In arbitrage betting, we are expected to compare odds offered by several betting sites which can be two or more. The profit will be earned as an advantage of the highly different odds offered by each bookmaker.
Categories of arbitrage bets
There are two methods of arbitraging; balanced odds arbitrage and unbalanced odds arbitraging. Finding an arbitrage opportunity is not that easy, but using our guide we will show you how to get an arbitrage bet. Using similar mathematical formulae used in the calculation of bookmaker’s commission margin, we will be able to find arbitrage bets. We add the implied probabilities of each of the best betting odds availed under every outcome. Therefore arbitraging demands that you involve only high odd wagers. Calculating implied probabilities will prompt us to divide each odd in decimal format by one.
Balanced odds Arbitrages
We can have two teams, Arsenal playing Tottenham and two betting sites A & B offering relatively high odds for each team. Using the above entities we shall understand the concept of balanced arbitrage betting:
Arsenal are assigned an odd of 2.8 by bookmaker A
Tottenham are assigned 2.8 in bookmaker B
This is a perfect arbitrage opportunity as upon betting with $100 for Arsenal and $100 for Tottenham; we are guaranteed a profit. The profit shall be $80 once any of the team wins, but a draw means you lose heavily.
Total stake invested= $200
Arsenal = +$280
Unbalanced odds arbitrage: Unbalanced arbitrage bets are hard to identify, and their calculation ends up presenting difficulties to arbitrage betting analysts. How can we identify arbitrage bets from unbalanced odds?
Arbitrage bets identification calculations
Here is a formula to use when calculating arbitrage odds in balanced and unbalanced odds scenarios.
1/Odds in decimal * multiplied by 100%
For instance, in the Arsenal and Tottenham example, we could identify the arbitrage opportunity through the following procedure
Arsenal= 1/2.80*100= 35.71%
Add the two percentages to get the arbitrage percentage, and it should give us 71.42% which is a great profit-making arbitrage. Arbitrage betting percentage is more favorable when lower than 100%, thus the lower the arb percentage value, the more profit you are set to take home.
Identifying an arbitrage opportunity from unbalanced odds
Take an example of Kim playing John in a badminton event. Kim is given an odd of 1.2 while John is at an odd of 8. Calculate their specific implied probabilities:
Kim= 1/1.2*100= 83.3%
John= 1/8*100= 12.5%
Total arbitrage= 95.8%
Note: Arbitrage betting works perfectly in events where a winner must be found, thus try to identify matches in which there is a very low possibility of ending up in a draw.
Arbitrage betting in football
Get arbitrage bets at 22bet Kenya;
We have considered betting in matches with only two outcomes. How about arbitrage betting in football market which has three possible outcomes, 1X2? Let’s consider a scenario where Arsenal Vs Tottenham match may end up with either side winning or a draw. We can still get arbitrage for this by including the draw’s implied probability in our calculations. After getting the implied probabilities of each selection that’s Home, Draw and away win possibilities, proceed to calculate the appropriate stake to wager on each selection. The stake amount will be gotten by first getting the total arbitrage value, and then proceed to apply the following stake calculation formulae for arbitrage markets in football:
Implied possibility/ Total arbitrage* (multiplied by) stake amount
The implied possibility will be one divided by each selection’s odds in decimal format. Calculate the stake amount to use in each of your arbitrage bet selections.


Using PCA to identify correlated stocks in Python06 Jan 2018
Principal component analysis is a well known technique typically used on high dimensional datasets, to represent variablity in a reduced number of characteristic dimensions, known as the principal components.
In this post, I will show how PCA can be used in reverse to quantitatively identify correlated time series. We will compare this with a more visually appealing correlation heatmap to validate the approach.
- Clean and prepare the data
- Check for stationarity
- Generate qualitative correlation matrix
- Perform PCA
- Generate loadings plots
- Quantitatively identify and rank strongest correlated stocks
Using PCA in reverse
This approach is inspired by this paper, which shows that the often overlooked ‘smaller’ principal components representing a smaller proportion of the data variance may actually hold useful insights.
The authors suggest that the principal components may be broadly divided into three classes:
- The top few components which represent global variation within the dataset.
- A set of components representing the syncronised variation between certain members of the dataset.
- Components representing random fluctuations within the dataset.
Now, the second class of components is interesting when we want to look for correlations between certain members of the dataset. For example, considering which stock prices or indicies are correlated with each other over time. This is the application which we will use the technique.
The raw data
First, some data. Three real sets of data were used, specifically. Daily closing prices for the past 10 years of:
- A selection of stocks representing companies in different industries and geographies.
- A selection of industry indexes.
- A selection of geography indexes.
These files are in CSV format. They are imported as data frames, and then transposed to ensure that the shape is: dates (rows) x stock or index name (columns).
Cleaning and pre-processing
Pandas dataframes have great support for manipulating date-time data types. However the dates for our data are in the form “X20010103”, this date is 03.01.2001. So a
dateconv function was defined to parse the dates into the correct type.
This was then applied to the three data frames, representing the daily indexes of countries, sectors and stocks repsectively.
trimmer = lambda x: x[1:] def dateconv(dataframe,func): dataframe = dataframe.reset_index() #reindex so we can manipultate the date field as a column dataframe['index'] = dataframe['index'].apply(func) #remove the trailing X dataframe['index'] = pd.to_datetime(dataframe['index']) #convert the index col to datetime type dataframe = dataframe.set_index('index') #restore the index column as the actual dataframe index dataframe = dataframe[1:] return dataframe countriesT = dateconv(countriesT,trimmer) sectorsT = dateconv(sectorsT,trimmer) stocksT = dateconv(stocksT,trimmer)
This is done because the date ranges of the three tables are different, and there is missing data. For example the price for a particular day may be available for the sector and country index, but not for the stock index. Ensuring pandas interprets these rows as dates will make it easier to join the tables later.
As the stocks data are actually market caps and the countries and sector data are indicies. We need a way to compare these as relative rather than absolute values. The market cap data is also unlikely to be stationary - and so the trends would skew our analysis.
So, instead, we can calculate the log return at time t, defined as:
Merging the data
Now, we join together stock, country and sector data. As not all the stocks have records over the duration of the sector and region indicies, we need to only consider the period covered by the stocks. To do this, create a left join on the tables: stocks<-sectors<-countries.
So the dimensions of the three tables, and the subsequent combined table is as follows:
Dims of stocks: (1520, 11) # 11 stocks Dims of sectors: (4213, 54) # 54 sector indicies Dims of countries: (4213, 25) # 25 country indicies Dims of combined data table: (1520, 90)
Now, finally we can plot the log returns of the combined data over the time range where the data is complete:
Checking for stationary data
It is important to check that our returns data does not contain any trends or seasonal effects. There are a number of ways we can check for this
1. ADF test
The null hypothesis of the Augmented Dickey-Fuller test, states that the time series can be represented by a “unit root”, (i.e. it has some time dependent structure). Rejecting this null hypothesis means that the time series is stationary. If the ADF test statistic is < -4 then we can reject the null hypothesis - i.e. we have a stationary time series.
adfuller method can be used from the
statsmodels library, and run on one of the columns of the data, (where 1 column represents the log returns of a stock or index over the time period). In this case we obtain a value of -21, indicating we can reject the null hypothysis.
2. Inspection of the distribution
We can also plot the distribution of the returns for a selected series. If this distribution is approximately Gaussian then the data is likely to be stationary. Below, three randomly selected returns series are plotted - the results look fairly Gaussian.
Calculating the correlation matrix
We can now calculate the covariance and correlation matrix for the combined dataset. We will then use this correlation matrix for the PCA. (The correlation matrix is essentially the normalised covariance matrix)
Before doing this, the data is standardised and centered, by subtracting the mean and dividing by the standard deviation.
#manually calculate correlation coefficents - normalise by stdev. combo = combo.dropna() m = combo.mean(axis=0) s = combo.std(ddof=1, axis=0) # normalised time-series as an input for PCA combo_pca = (combo - m)/s c = np.cov(combo_pca.values.T) # covariance matrix co = np.corrcoef(combo_pca.values.T) #correlation matrix
Using Plotly, we can then plot this correlation matrix as an interactive heatmap:
We can see some correlations between stocks and sectors from this plot when we zoom in and inspect the values. Some noticable hotspots from first glance:
- stock 7332687^ and the Nordic region (0.77)
- stock 6900212^ and the Japan Homebuilding market (0.66)
- stock 2288406^ and Oil & Gas (0.65)
Perfomring PCA involves calculating the eigenvectors and eigenvalues of the covariance matrix. The eigenvectors (principal components) determine the directions of the new feature space, and the eigenvalues determine their magnitude, (i.e. the eigenvalues explain the variance of the data along the new feature axes.)
First, we decompose the covariance matrix into the corresponding eignvalues and eigenvectors and plot these as a heatmap.
This plot shows the contribution of each index or stock to each principal component. There are 90 components all together. We can see that the early components (0-40) mainly describe the variation across all the stocks (red spots in top left corner). It also appears that the variation represented by the later components is more distributed.
The total variability in the system is now represented by the 90 components, (as opposed to the 1520 dimensions, representing the time steps, in the original dataset). The eigenvalues can be used to describe how much variance is explained by each component, (i.e. how the varaiance is distributed across our PC’s).
Below we plot this distribution:
As we can see, most of the variance is concentrated in the top 1-3 components. These components capture “market wide” effects that impact all members of the dataset.
Following the approach described in the paper by Yang and Rea, we will now inpsect the last few components to try and identify correlated pairs of the dataset
Developing the loadings plot
As mentioned earlier, the eigenvalues represent the scale or magnitude of the variance, while the eigenvectors represent the direction. The “loadings” is essentially the combination of the direction and magnitude. The loading can be calculated by “loading” the eigenvector coefficient with the square root of the amount of variance:
We can plot these loadings together to better interpret the direction and magnitude of the correlation. The loadings for any pair of principal components can be considered, this is shown for components 86 and 87 below:
The loadings plot shows the relationships between correlated stocks and indicies in opposite quadrants. Indicies plotted in quadrant 1 are correlated with stocks or indicies in the diagonally opposite quadrant (3 in this case). The length of the line then indicates the strength of this relationship.
For example, stock 6900212^ correlates with the Japan homebuilding market, as they exist in opposite quadrants, (2 and 4 respectively). This is consistent with the bright spots shown in the original correlation matrix.
Using the loadings plots to identify and rank correlated stocks
We can use the loadings plot to quantify and rank the stocks in terms of the influence of the sectors or countries.
To do this, we categorise each of the 90 points on the loading plot into one of the four quadrants. Then, we look for pairs of points in opposite quadrants, (for example quadrant 1 vs 3, and quadrant 2 vs 4). Then, if one of these pairs of points represents a stock, we go back to the original dataset and cross plot the log returns of that stock and the associated market/sector index.
Using the cross plot, the value is calculated and a linear line of best fit added using the linregress function from the stats library. A cutoff value of 0.6 is then used to determine if the relationship is significant.
Cross plots for three of the most strongly correlated stocks identified from the loading plot, are shown below:
Finally, the dataframe containing correlation metrics for all pairs is sorted in terms descending order of value, to yield a ranked list of stocks, in terms of sector and country influence.
The top correlations listed in the above table are consistent with the results of the correlation heatmap produced earlier.
This analysis of the loadings plot, derived from the analysis of the last few principal components, provides a more quantitative method of ranking correlated stocks, without having to inspect each time series manually, or rely on a qualitative heatmap of overall correlations. It would be cool to apply this analysis in a ‘sliding window’ approach to evaluate correlations within different time horizons.
Hope you found it interesting!
You can find the full code for this project here


A first in the examination of the interrelationship between words and numbers, through mathematical games and diversions, word and mathematical puzzles, and popular mathematical concepts
Odd Words, Even Numbers refers to the fact that standards of numeracy at all levels appear to be in decline. It proposes that by treating numeracy as a vital aspect of literacy we might be able to arrest this fall in standards. The main purpose is to stimulate and entertain readers of all ages which the author attempts to achieve by showing how we use the English language to describe a selection of mathematical concepts; by explaining many mathematical games and diversions; and by including a large number of word puzzles and mathematical puzzles each of which demonstrates the close interrelationship between words and numbers.
This book is also designed to appeal to those who might deny having any interest or expertise in handling or playing with numbers. Indeed, the book requires little mathematical ability of its readers to enable them to derive fun and enjoyment from its pages particularly if their interest is more inclined towards words and language.
A consistent theme of the book is that in order to be able to communicate effectively – whether in words or numbers – we must learn to communicate clearly and without ambiguity.
Ian Paterson has spent over five-sixths of his life collecting and studying books on recreational maths; mathematical puzzles, games and diversions and the English language. He is the author of best selling book A Dictionary of Colou’ also published by Thorogood.
‘I loved every word. Beautifully written and well researched this is a book for all ages who like a verbal or numerical challenge. An absolute must for those with children or grandchildren who like to be stimulated by words and numbers.’


I am a Postdoctoral Scholar at the Computing + Mathematical Sciences (CMS) Department at the California Institute of Technology (Caltech), hosted by Prof. Anima Anandkumar and Prof. Garnet Chan.
I obtained my Ph.D. in Computer Science from the Hebrew University of Jerusalem under the supervison of Prof. Amnon Shashua. I also have a B.Sc. in Physics, Mathematics and Computer Science from the Hebrew University. (Detailed CV).
My research focuses on investigating and further developing the theoretical underpinnings for deep learning methods, with some surprising connections to Quantum Physics.
If you are looking for my old class notes, you can find them here (website and notes are in Hebrew).


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Honors Algebra II
Hi, my name is Jason Clarke! My time at New West started in December 2021 when I came in as a teaching assistant for Algebra II. After teaching Algebra II myself during the 2022-2023 school year, I am back to teach it again for 2023-2024.
I moved to California from Chicago as a Trustee Scholar at USC, where I received my Bachelor’s degree in Economics. I spent the following three years tutoring students ages 4–25. My primary focuses were high school and college math in addition to ACT and SAT prep. Currently, I am working on completing my Master’s degree in teaching, expected by the end of 2023 from National University.
During my transition from tutor to teacher, my ultimate goal has been to utilize the lessons I have learned to ensure that students are engaged, motivated, and successful.


This calculator performs modular arithmetic computation. It can compute sum, difference, product, quotient, power and square root modulo any number up to 15 decimal digits.
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The app is currently available in English and it was last updated on 2012-12-31. The program can be installed on Android.
Modular calculator (version 1.3) has a file size of 36.86 KB and is available for download from our website.
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A few things happened since we last peaked in on you. For this post I will tell you about my decision to drop/withdraw from my Statistics class. Yep. I am working TOO hard to get a "D". Considering my last exam was another "F"--I think it's time to call it a day. Online classes are cool---however a math course was too extreme for me, and I like math. This is a required class so I MUST take it. Yet I need to have someone stand in front of me to explain why I should care about a binomial distribution in a random sample of 44 doctors, with the mean age of 43 to find the probability of how many doctors are 41.5 years old is really so important to me. Hence, I need to be able to see and say questions to the teacher. If all goes well, I hope to take a Statistics class in person starting January. After December, I will have 5-6 classes to finish my Bachelors in Sociology. For the future I've pondered the thought of a dual master's, or master's/doctorate and then I remember Statistics. I wonder my probability of either one and the certificate I would love to get from Harvard. Stay tuned.


The price at which you can buy 100% of the house is similar to the price when you make partial purchases. It is a variable price and corresponds to the initial cost updated to the moment you buy 100% of the house . To calculate the price of the house, the initial purchase cost (including purchase costs) plus the average variation of the prices of the houses in the area.
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Casum obtains the variation in the price of the house in the area based on reports and indices from independent bodies.
The main difference in price between buying a part of the house or buying the whole house, is that when you buy 100% of the house there is a minimum purchase price, which is equivalent to the initial cost of the house (including purchasing costs).These purchase costs will cover costs incurred by the investor at the time of purchase (notary, registration, agency, taxes, etc) for the percentage you are buying


Math teacher Ben Orlin writes and draws the (aptly named) blog Math With Drawings and is the author of a new book, Change Is the Only Constant: The Wisdom of Calculus in a Madcap World. To mark its publication, he devised this entertaining accompanying quiz. You can read the Ars interview with Orlin here.
Isaac Newton and Gottfried Leibniz have a lot in common. Birthdates in the 1640s. Fatherless childhoods. Colossal egos. Show-stopping wigs. Most of all, each had the honor of bringing calculus into the world. But when it comes to personalities, Newton and Leibniz are like night and day, or England and France, or derivatives and integrals. They’re rivals. Opposites, even. Do you belong on #TeamNewton or #TeamLeibniz? Take this quiz to find out!
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This calculator generates values which should be used for planning purposes only. The values are approximations and the actual bandwidth and harddrive capacity required may vary according to different recording environments.
The results assume that the camera settings for each camera are configured to the same settings.
How to use the NVR Calculator
- Enter the number of cameras being used.
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- Hit calculate to display the total bandwidth and total harddrive capacity required.
This lens calculator can provide the viewfield dimensions for a given focal length and distance, or provide the focal length for a given viewfield width/height and distance.
The values generated by this calculator are for the user's reference only, and may not meet the user's actual requirements (picture clarity, etc.).


In 1847, George Boole invented symbolic logic. Or so everyone thought. In actuality, Boole’s symbols were merely a code. When translated, the symbols revealed an ancient game — the key to saving the world.
That’s right: we’ve got lore. Lots and lots of lore. For a puzzle-solving card game I invented to teach my students symbolic logic.
When I was an algebra tutor, I began to wonder why I enjoyed algebra. Normal people hate math: it’s useless and confusing. And I’m not even that good at it. So, why was I having such a good time?
After I got my Ph.D. in philosophy, I was asked to teach a course on symbolic logic — and I encountered the same question all over again. Symbolic logic was just another kind of algebra. Most students found it frustrating and would never use it again after finishing the course. But even though I wasn’t particularly good at it, I really enjoyed it.
At some point I realized what was going on. I experienced both algebra and symbolic logic as puzzle-solving games. I didn’t do math problems. I solved puzzles. I didn’t do logic problems. I solved puzzles. I sometimes had problems solving those puzzles, but they were still puzzles — complete with mystery and discovery.
Algebra and symbolic logic are games, in other words. And not like Number Munchers
And I also don’t mean like Math Blaster:
It’s not that you could invent games that more or less arbitrarily forced players to do algebra or logic. It’s that algebra and symbolic logic already are games. The problem was that the curriculum we use doesn’t help students see that.
A lucky few get it on their own, of course. But most of us just see an incomprehensible mess of symbols that we somehow have to sort out to avoid getting an “F” on our report cards.
So, I decided to create a new curriculum that would show students that symbolic logic is a game — and that would help them use visual and emotional reasoning to master the subject. The original version of the game can be downloaded here. It was programmed in JavaFX over the course of two school years. My current project is to port the game to the Unity engine, incorporating animations, 3D graphics, and lots of other cool stuff.
One day I hope to do the same thing for algebra, though probably not as a card game. In the meantime, I’m having a ton of fun learning Unity (and Blender), and I hope other game devs will find what I’ve learned useful (and perhaps give me some hints about how to improve my code and approach).


On a project I am currently working on I needed to handle collision detection. I don’t have enough appendages to help me count the amount of times I have implemented collision detection. But this time it was a little different, I wanted to check whether or not someone was hovering over a segment of a circle. So I started to brainstorm possible algorithms to handle this particular kind of collision detection.
When I first started off I was thinking about it way too hard and way too mathematically instead of logically. I was trying to figure out the equation of a circle segment and blah blah blah. But after a little while of scribbling into my tiny notebook I came across a rather easy way to detect collision detection for circle segments.
Are we in the circle? If we aren’t in the circle then we aren’t going to be in the segment.
This is a super qualification to check for, lets just call dX and dY the coordinate relative to the center of the circle:
if (dX*dX + dY*dY) > radius*radius: return false;
This snippet of code checks the squared distance of the coordinate with the squared radius (no need to do a square root because a square is present on both sides of the equation and square roots are expensive computing-wise)
What angle is our point at? If it lies within the angles of our segment then we are in the segment since we just found out that we are in fact inside of the circle.
Using some vector math, we know that the arctangent2(y,x) is equal to the angle that the vector is at relative to the x-axis. This means we can find out the angle from the x-axis that our coordinate is at. This can be done with this code:
fi= atan2(dY,dX); return fi >= alpha && fi <= beta;
Here we call alpha the starting angle and beta the ending angle of the segment.
Here is an image:
In this image P is the point that was clicked and the resulting line and arrow is it’s vector. 0 is the starting point (unit circle!). If you aren’t familiar with Greek letters: the fish looking guy is Alpha, the “b” looking thing is Beta, and the O with a line through it is Fi.
Complete Algorithm in Semi-Pseudocode/Python:
function inCircleSegment(dX,dY,radius,alpha,beta): if(dX*dX + dY*dY > radius) return false; fi = atan2(dY,dX); return fi >= alpha && fi <= beta;
ONE LINE! (Because why not?):
return (dX*dX + dY*dY > radius) && (atan2(dY,dX) >= alpha && atan2(dY,dX) <= beta);
Seriously, don’t use that version though. At least save atan2(dY,dX) as a variable!
This was a fun little algorithm to come up with, one that is a lot easier to derive once you get your mind out of math and back into logic!


As the American education system continues to stress the importance of student performance, some institutions are finding that pupils may be at a disadvantage due to the curricula. According to a study published in the American Journal of Education, inconsistent math curricula revise across the country, particularly those who attend schools that do not have demanding lesson plans. The researchers examined the 1999 Trends in International Mathematics and Science Study, which covered 13 local school districts, nine states and institutions in more than 40 other countries. According to the findings, those who attended schools with a less demanding math curriculum could not keep up with the performance of students in other nations who had greater standards in the subject. "Overall, U.S. students are exposed to a less difficult school mathematics curriculum that places them at a disadvantage when compared to the students in many other countries of the world," the researchers wrote. However, as the nation pushes for education reform, more states are adopting a set of standards that will dictate the exact level of difficulty a math class should be.
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This article describes two stored procedures for the Analysis Server. The first one is to calculate the covariance matrix between all continuous attributes in the selected data mining model. The second one is to calculate the correlation matrix between all continuous attributes in the selected data mining model. In both cases it does not matter if the attributes are inputs or outputs of the model, the stored procedures ignore that fact.
The stored procedures are to be used with any model as the only parameter. The stored procedures will not work if any of the following is true:
- One or more columns contain nested tables
- The model does not allow drill through
- The model is not processed
Even if those conditions are met the stored procedures will only return a result for the continuous attributes. If none of the attributes are continuous the resulting matrix will be empty.
The stored procedures will return a table with three columns. The first two columns indicate the name of the attributes that were used to calculate the covariance/correlation. This table is a flatten version of a square matrix on size nxn where n is the number of attributes. Since covariance/correlation matrixes are symmetric the result only contains one half of the matrix (including the diagonal). This can be done because COV(X, Y) = COV(Y, X) so we only need one result. The diagonal or COV(X, X) represents the variance of X and is included in the results.
Deploying the stored procedure
The stored procedures are created using C# as a class library project. The project contains only 1 file: “MatrixRelationships.cs”. To create the library file with the stored procedures follow the next steps:
- 1. Create a new C# class library Project called MatrixRelationships
- 2. Download the MatrixRelationships.cs file into the MatrixRelationships directory
- 3. Add the source file to the project by pressing Shift+Alt+A (Add Existing Item) and delete the default Class1.cs element from the Solution Explorer
- 4. Add msmgdsrv to the references, select Project->Add Reference->.NET->Microsoft.AnalysisServices.AdomdServer
- 5. Build the project (Ctrl+Shift+B by default)
- 6. The dll file will be inside the bin\debug directory in the project
Once the project is built and the dll created we are ready to deploy the stored procedures into the Analysis Server. To deploy the stored procedures follow the next steps:
- 1. Open the Microsoft SQL Server Management Studio
- 2. Connect to the Analysis Server where you wish to deploy
- 3. On the object explorer (F8) and expand the server branch, you will see Databases and Assemblies, right click Assemblies
- 4. Select New Assembly and the Register Server Assembly will pop up, set the parameters as follows:
- a. Type: .NET Assembly
- b. File Name: Location of dll file with stored procedures
- c. Assembly Name: You can use the default name (MatrixRelationships) or you can set a new name here (The name should not be a duplicated assembly name)
- d. Include Debug Information: Check
- e. Permissions: Safe (by default)
- f. Impersonation: Use the credentials of the current user
- 5. The stored procedures are ready to be used
Executing the stored procedure
To execute the stored procedures you need to open a new Analysis Services DMX Query. To do this select File->New->Analysis Services DMX Query.
Once the DMX query window is open type the following command:
CALL MatrixRelationships.GetCovarianceMatrix( model name)
CALL MatrixRelationships.GetCorrelationMatrix( model name)
Note: MatrixRelationships will be substituted with whatever name was selected in Assembly Name.
The list of available models will show in the DMX query window under mining model.
Debugging the stored procedure
If the user wants to debug the stored procedures follow the next steps:
- 1. Open the project in Visual Studio
- 2. Deploy the stored procedures
- 3. In Visual Studio select Debug->Attach To Process
- 4. From available processes select msmdsrv.exe
Covariance matrix algorithm is based on the following formula:
The algorithm works as follows:
- 1. Extract continuous attributes from the model
- 2. Verify that:
- a. the model is processed
- b. the model supports drill through
- c. the model does not contain nested tables
- 3. Extract mean and variance for each attribute
- 4. Obtain the data from the model (all the Xi and Yi)
- 5. Create a triangular matrix to store the partial results for each X,Y combination
- 6. For each row in the data set from the model:
- a. Update the number of rows processed
- b. Obtain the values for each column and subtract the mean
- c. Update all combinations of (X,Y) by adding the appropriate
- d. If the value of a column is null for a given row, a 0.0 will be inserted (no covariance)
- 7. Divide every combination of (X,Y) in the triangular matrix by the total number of rows processed
- 8. Flatten the triangular matrix into a 3xM matrix where M is the number of continuous attribute combinations, given by where n is the number of continuous attributes.
Correlation matrix algorithm is based on the Pearson product-moment coefficient which is given by the following formula:
The algorithm to calculate the correlation is the same as the covariance plus it divides every (X,Y) combination in the triangular matrix by the product of X and Y standard deviation and the standard deviation is the square root of the variance.


The bandwidth or frequency response of the control amplifier or potentiostat amplifier is related to the maximum rate at which the output can change.
For a simple conversion, consider the 1 volt sine wave in the sketch below. From math tables, the maximum slope of sin(x) is 1.0 since
d sin(x)/dx = 1. at x=0
For our 1 Volt sine wave, the maximum slope corresponds to about 6 V/cycle, or 6×F V/s, where F is a hypothetical "maximum frequency." Because the bandwidth specification is often stated as the frequency at which the signal is attenuated by 30%, using 3×F V/s is a bit more realistic. Remember, however, that this is only a crude conversion.
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Analysis of sparse data in logistic regression in medical research: A newer approachS Devika1, L Jeyaseelan1, G Sebastian2
1 Department of Biostatistics, Christian Medical College, Vellore, Tamil Nadu, India
2 Department of Statistics, St. Thomas College, Palai, Kerala, India
Background and Objective: In the analysis of dichotomous type response variable, logistic regression is usually used. However, the performance of logistic regression in the presence of sparse data is questionable. In such a situation, a common problem is the presence of high odds ratios (ORs) with very wide 95% confidence interval (CI) (OR: >999.999, 95% CI: <0.001, >999.999). In this paper, we addressed this issue by using penalized logistic regression (PLR) method. Materials and Methods: Data from case-control study on hyponatremia and hiccups conducted in Christian Medical College, Vellore, Tamil Nadu, India was used. The outcome variable was the presence/absence of hiccups and the main exposure variable was the status of hyponatremia. Simulation dataset was created with different sample sizes and with a different number of covariates. Results: A total of 23 cases and 50 controls were used for the analysis of ordinary and PLR methods. The main exposure variable hyponatremia was present in nine (39.13%) of the cases and in four (8.0%) of the controls. Of the 23 hiccup cases, all were males and among the controls, 46 (92.0%) were males. Thus, the complete separation between gender and the disease group led into an infinite OR with 95% CI (OR: >999.999, 95% CI: <0.001, >999.999) whereas there was a finite and consistent regression coefficient for gender (OR: 5.35; 95% CI: 0.42, 816.48) using PLR. After adjusting for all the confounding variables, hyponatremia entailed 7.9 (95% CI: 2.06, 38.86) times higher risk for the development of hiccups as was found using PLR whereas there was an overestimation of risk OR: 10.76 (95% CI: 2.17, 53.41) using the conventional method. Simulation experiment shows that the estimated coverage probability of this method is near the nominal level of 95% even for small sample sizes and for a large number of covariates. Conclusions: PLR is almost equal to the ordinary logistic regression when the sample size is large and is superior in small cell values.
Keywords: Logistic regression, maximum likelihood, penalized maximum likelihood, profile penalized confidence interval
For analyzing binary type response variable, logistic regression is commonly used. Logistic regression enables researchers to estimate the effect of the exposure variable after adjusting for the effect of other potential confounding variables. An example of such binary type response variable is the case-control study finding the association between alcohol intake and heart disease after adjusting for confounding factors such as smoking, age, and gender.  Usually in logistic regression, the measure of association such as odds ratio (OR) is estimated by using the maximum-likelihood estimation (MLE) method. A common problem in estimating OR in logistic regression whenever with empty cell frequency in k × k table or with a small number of frequency count, is the failure of maximum likelihood estimate to converge [OR: >999.999; 95% confidence interval (CI): <0.001, >999.999].  This predominantly occurs in small to medium size datasets where the regression coefficient of at least one covariate value becomes infinitely large. Sparse data or separation data occur when the response variable is perfectly separated by a single covariate or linear combination of variables.  The problem of separation is by no means negligible and may occur even if the variable values are low in numbers.
A simple example of separation is a k × k table with "empty cell" frequency. [Table 1] presents the data on diabetics and obesity that were collected by the US National Institute of Diabetics and Digestive and Kidney Diseases.  One of the aims of the study was to find the association between obesity and diabetes after adjusting for age, number of pregnancies, blood pressure, etc. In this data, the separation is due to the presence of few/zero count values between obesity and diabetes. In the presence of separation, the model may converge but produce huge values of regression coefficients and standard error (SE) and CI may present with infinite values (OR: >999.999; 95% CI: <0.001, >999.999). This is due to the nonexistence of maximum likelihood estimates that makes it difficult for researchers to make appropriate decisions.
Some of the existing solutions that have been in practice for the problem of separation exclude the variable from the analysis. The second commonly used method is making modifications (usually by adding 0.5) in the data to eliminate the problem (Yates' correction in bivariate analysis for categorical data). But both these methods were strictly not recommended as they would lead to misleading results. Another alternative approach in the analysis of sparse/separation data is the exact logistic regression. , The idea behind this method is the same as the exact inference (Fisher's exact test) in 2 × 2 table. The exact logistic regression is based on the "exact permutational distributions of the sufficient statistics that correspond to the parameters of interest, conditional on fixing the sufficient statistics of the remaining parameters at their observed value."  Although this method is shown to be another option as compared to the above two, it is not used in regular practice due to the computational difficulty, provision of degenerate estimates, and not allowing the inclusion of continuous type covariates.
This paper disseminates the strategy and method of handling separated data in logistic regression using penalized maximum likelihood estimation method (PMLE).  We also examine the characteristics of this approach with the presence of separation data for small to large sample sizes with a different number of covariates using simulation.
The data used in this paper is from a case control study on hyponatremia and hiccups conducted in Christian Medical College, Vellore, Tamil Nadu, India.  The main aim of the hyponatremia study was to find an association between hyponatremia and hiccups after adjusting for potential confounding factors such as gender, age, renal disease, and creatine level in hospitalized patients. The dataset consists of 50 subjects with hiccups (cases) and 50 subjects without hiccups (controls). The hiccups groups were subdivided according to the severity of the disease so that among 50 subjects with hiccups, 23 subjects had mild hiccups, 12 subjects had moderate hiccups, and 15 subjects had a severe kind of hiccups. For an illustrative purpose, we have chosen 23 mild hiccup cases and 50 controls from the dataset and other confounding factors were randomly generated based on the given estimated values. Data were analyzed using SAS 9.2 for windows (SAS Institute, Inc., Cary, NC, 2000) software.
Maximum likelihood and penalized maximum likelihood estimates
Basically, the likelihood function is the joint probability of each data point under an assumed distribution for the outcome. The probability mass function of the Bernoulli random variable is written as f(y,p) = p y (1 - p) 1-y ; y = 0,1 & 0 ≤p ≤1. The logistic regression model is , with i = 1, 2…; n denotes n observations, r = 1, 2.., k denotes k-1 independent variables with r = 1 denoting the constant. The maximum likelihood estimate for the unknown parameter βr is obtained in such a way that it maximizes the probability of observing the data such that the likelihood function . The log likelihood (logL) is determined by taking the natural log of the likelihood function logL = ∑(y i logp i +(1-y i )log(1-p i )). The maximum likelihood estimate is obtained by solving the score equation, .
The problem in maximum likelihood estimate in the case of separation is that the function cannot have one maximum [Figure 1]a.
Hence, the idea behind penalized maximum likelihood estimate for logistic regression is that the method penalizes the likelihood by half of the logarithm of the determinant of the information matrix (I), that is, .  So, the modified score function becomes U(βr)* = ∑ni=1 (y i –p i +h i (1/2–p i)xir) = 0. Thus, the penalized maximum likelihood estimate provides a solution to the problem of separation in [Figure 1]b. For the calculation of CI, we used profile likelihood based CI as compared to asymptomatic based Wald-type confidence interval that is inaccurate in the presence of separation.  For comparing models fitted by maximum likelihood and penalized maximum likelihood for logistic regression, we used Akaike information criterion (AIC) and −2 log likelihood (−2logL) methods.  Given the different models, the one with smaller AIC/−2 logL fits the data better than the one with larger AIC/−2 logL values. Details of the software for execution of penalized logistic regression (PLR) are given below.
A simulation experiment was conducted to study the empirical performance of PLR with respect to coverage probability. Coverage probability is defined as the probability that the procedure produces an interval that covers the true (regression coefficient) value. In order to investigate the performance of this method in the presence of complete and quasi separations, we created 1,000 datasets, each with different sample of sizes n = (30, 75, 150) and with a different number of covariates k = (2, 3, 4). We used Monte Carlo method to obtain the 95% coverage probability of PLR. We conducted the simulation experiment by using SAS 9.2 for windows (SAS Institute, Inc., Cary, NC, 2000) statistical software. The R, STATA, and SAS codes for doing PLR are given in the appendix.
Twenty three cases and 50 controls were selected for the analysis of ordinary logistic regression and PLR. [Table 2] shows the demographic and clinical characteristics of the subjects. The primary exposure factor hyponatremia was present in nine (39.13%) of the cases and in four (8.0%) of the controls. Of the 23 hiccup cases, all were males and among the controls, 46 (92.0%) were males. Renal disease was present in five (21.74%) of the cases and seven (14.0%) of the controls. The mean [standard deviation (SD)] age of the subjects in the hiccups group was 51.61 (12.27) years and in the control group was 49.34 (11.94) years. The mean (SD) creatine level was more in the cases, that is, 2.23 (1.52) mg/dL than in the control group 1.45 (0.72) mg/dL. Our primary interest in this paper is to find the association between hyponatremia and hiccups after adjusting the potential confounders with the presence of separation due to zero cell frequency in the cross tabulation between gender and the disease group.
[Table 3] presents the results of the association between hiccups and its corresponding risk factors with 95% CI using both ordinary logistic regression and PLR methods. In the analysis of hiccups data, complete separation between gender and the disease group led to an infinite maximum likelihood estimate of gender (OR: >999.999; 95% CI: <0.001, >999.999) and intercept (OR: 47287; 95% CI: -) with large standard errors, whereas there is a finite and consistent regression coefficient for gender (OR: 5.35; 95% CI: 0.42, 816.48) and the intercept (OR: 0.05; 95% CI: 0.00, 1.30) using PLR. After adjusting for gender, age, and clinical characteristics, hyponatremia was associated with nearly 7.9 (95% CI: 2.06, 38.86) times higher risk of developing hiccups that is statistically significant (P value = 0.0057) using the penalized maximum likelihood method. Rather, there is an overestimation of OR: 10.76 (95% CI: 2.17, 53.41) between hyponatremia and hiccups by using ordinary logistic regression (P value = 0.0036). There is a statistically significant effect of the creatine level on hiccups in both the methods [OR: 2.16; 95% CI (1.16, 5.58)] using penalized methods (P value = 0.0493) and OR: 2.62; 95% CI (1.10, 6.27) the ordinary logistic regression method (P value = 0.0301)).
It is also noted that point estimates for each of the risk factors by the penalized maximum likelihood method was considerably smaller than the maximum likelihood estimates owing to the bias correction property of the penalized maximum likelihood method. In addition to this, the width of the 95% CI of the penalized maximum likelihood estimates was narrow as compared to the maximum likelihood estimates. PLR had a lower AIC and −2 log L values as compared to ordinary logistic regression using maximum likelihood estimate. This shows that PLR is preferred over ordinary logistic regression in the presence of separation.
It is also evident from the results of the simulation study that the estimated coverage probabilities of the CI of PLR were almost near the nominal level of 95% [Table 4]. This is even true for the studies with complete/nearly separated data with small sample sizes and an increased number of covariates. Instead, the coverage probabilities of ordinary logistic regression of almost 100% (where it is expected to be nearly 95%) indicates that this method is a poor choice when there is a presence of separation in the data. Thus, the simulation study implies that penalized maximum likelihood logistic regression can be applied for separated data even for small number of observations with increased number of covariates.
[Figure 2] plots the profile penalized maximum likelihood estimates for the effect of hyponatremia on hiccups, along with 95% CI. The circle denotes the point estimate with indications for lower limit (LL) and upper limit (UL).
In the analysis of the data, while the researcher may want to adjust for the effects of all confounding factors, including gender, omission of this risk factor cannot be considered here. Hence, we used the penalized maximum likelihood logistic regression method that provided a reasonable estimate of the effect of each of the risk factors on the disease status and greatly improved the interpretation as compared to the conventional method. All the ORs were nearly greater than 1; however, only hyponatremia and creatine level were statistically significant in both the models. The estimated OR of hyponatremia on hiccups is easily interpretable. After adjusting for all the confounding factors, hyponatremia was significantly associated with hiccups (PMLE OR: 7.88; 95% CI: 2.06, 38.86 as compared to MLE OR: 10.76; 95% CI: 2.17, 53.41). Excluding the covariate - gender, in both ordinary logistic regression and PLR models, the effect of hyponatremia on hiccups was lower as compared to the model with the presence of gender (PMLE OR: 6.95; 95% CI: 1.91,29.80 as compared to MLE OR: 8.62; 95% CI: 2.00,37.20).
Initially, the PMLE method was introduced to reduce the bias of maximum likelihood estimate in generalized linear models.  Currently, this method is used in many situations such as in multinomial logistic regression where it was suggested that this method was superior to other methods in small samples and equivalent to maximum likelihood estimate when the sample size increases;  in the analysis of complete/nearly separated data in logistic regression;  in the analysis of diagnostic and prognostic prediction models  where it has been shown that PMLE leads to smaller prediction error as compared to other methods such as bootstrapping technique. PLR has been used for finding the association between coronary heart disease (CHD) and smoking.  Comparison between maximum likelihood estimate and penalized maximum likelihood estimate were also done for separation case in which one of the cells in 2 × 2 table was equal to zero. Double penalized MLE has also been proposed for separation and multicollinearity in multiple logistic regressions.
In many medical researches, in dealing with binary type response variables the presence of separation is unavoidable. It arises most often when the sample size is small or strong relationships are present. The PMLE method is simple and easy-to-use and can be implemented via the most of the popular softwares. It also gives meaningful results that enable researchers to make appropriate decisions about important risk factors. In our data, the effect of gender on hiccups could not be studied using the conventional method while it would have been possible by using the penalized method (OR: 5.35; 95% CI: 0.42, 816.48). Thus, PLR provides an attractive, finite, and consistent regression coefficient against the conventional method. The OMLE method is approximately equal to the conventional method when the sample size is large and the cell frequency is more or equally distributed and is superior in small cell values. Hence, a recommendation can be made to always use PLR as compared to the ordinary logistic regression method.  The goal of considering the separation variable in the analysis is two pronged: firstly, how its impact on the exposure variable of interest as a co-variate or a confounder, for example: hyponatremia in this study; and secondly its effect on the outcome variable (OR and 95% CI).  The PLR analysis provides the correct estimate of OR and its 95% CI for the separation variables as compared to ordinary logistic regression analysis. However, many times the 95% CI is still wider despite its significance.
Hence, in the analysis of logistic regression with the presence of separation/sparse data the researchers need to make out two important points of information. One is that we need to review carefully the contingency table of separation variable and the outcome. It should provide biologically important data. Here in our example, men are more likely to have hiccups as compared to women. Second, we should not throw away such useful information due to a wider CI. The author should also provide the contingency table for the separation variable and the outcome to convey this message. Thus, the application of PLR in this study has provided a better picture of the effect of hyponatremia on hiccups after adjusting for other confounding variables.
PLR can be done using SAS, STATA, and R statistical software. In SAS, Proc logistic procedure with keyword "firth" was used to estimate the parameter of the covariates using PLR.  In STATA, "firthlogit" command is used to implement Firth-based PLR.  The "logistf" library in R software also has the function to perform PLR.
Financial support and sponsorship
This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.
Conflicts of interest
There are no conflicts of interest.
[Figure 1], [Figure 2]
[Table 1], [Table 2], [Table 3], [Table 4]


CHARLESTON, WV (WOWK) — West Virginia saw an improvement in overall student test scores for the 2022-2023 school year.
The West Virginia Department of Education shows that students are tested on English and math in third through eighth grade and in 11th grade. Students are tested on science in fifth, eighth and 11th grade.
According to the West Virginia Department of Education, there was a two-percent increase in both English and math scores and a one-percent increase in science scores compared to the 2021-2022 school year. Here is how students have done since the 2014-2015 school year. There was no testing in the 2019-2020 school year because of the COVID-19 pandemic.
English test scores dropped for seventh graders in the 2022-2023 school year, going from 41% to 39%, the Department of Education said. They said this is the only grade and subject to see a decrease in proficiency.