ROBERT C. MERTON. Perhaps we don't have to simply believe. To create this simple model, you need four Simulink blocks. A Simple Model of Capital Market Equilibrium with Incomplete Information. Efcient inference, likelihood evaluation, and parameter estimation algo-rithms are provided. You may have noticed how quickly the number of infected increases. The analyses in §§5.1, 5.2 and 5.3 show that the simple, autonomous model (3.1) can be calibrated to produce oscillations with periodicity matching that of a historical outbreak. For my model, I've gone with 1% for now. Our inputs and outputs in a coronavirus impact model aren't financial statements, but the same principles apply. Let me know your thoughts and/or feedback in the comments below, and be sure to wash your hands! Firstly, the model clearly illustrates the role of aggregate demand in determining equilibrium income in a closed economy. The results display in a Scope window. A chart helps to illustrate the impact of controls on saving lives: The difference between early and late implementation of controls is only 3 weeks in this model, but it makes an enormous difference. We present a simple log-linear reparame-terization of IBM Model 2 that overcomes problems arising from Model 1's strong assumptions and Model 2's overparame-terization. We find: 1) While an individual bifurcation produces periodic (nonchaotic) dynamics, two-way coupling between upstream and downstream bifurcations can … Model Specification A particularly simple binary decision rule with externalities that captures the essential features outlined above is the following: An individual agent observes the current states (either 0 or 1) of k other agents, which we call its neighbors, and adopts state 1 if at least a threshold fraction of its k neighbors are in state 1, A Simulink block is a model element that defines a mathematical relationship between its input and output. Periods are equal to one year. 3, while the workers’ labor supply is endogenous. (And please do let me know if I made any mistakes.). If you're anything like me, you spent much of the weekend glued to your phone reading the latest news updates on the novel coronavirus (2019-nCoV) that causes the Covid-19 disease. Many of the functions in SIMPLE have been employed in … Therefore it has many limitations. It doesn't help that cases have spiked abroad. R0 seems to be around 2.3 according to a paper available on PubMed.gov. Let's assume that the virus spreads for 5 serial intervals (35 days) without control. To calculate the total number of cases, we continue our model in spreadsheet form, but we lower the value of R. I'm going with 1.5 based on the model published in the Annals of Internal Medicine in February. But every week that passes significantly reduces the ultimate effectiveness of containment efforts. The model is applicable only in climatological studies of TC tracks. In statistics, simple linear regression is a linear regression model with a single explanatory variable. A Simple Model exists to make the skill-set required to build financial models more accessible. Marchantia is a liverwort, a simple plant with an open form of development that allows direct visualization of gene expression and dynamics of cellular growth in living tissues. Second, we conduct a policy experiment of a, pension reform that broadens the contribution base to include entrepreneurs in Sec-, tion 5. Keep on reading to learn about the formula and how the model is built, or scroll to the bottom to download your own copy and tweak my assumptions. However, the model does illustrate very well how quickly a highly contagious virus can spread and get out of control. We're much more accustomed to linear growth. At the very least it might help us understand a bit better why epidemiologists and folks working at the CDC and other health agencies seem so worried. The purpose, is twofold. Under Scenario 2, controls are implemented after deaths exceed 100. It doesn't account for possible mutation of the virus. This number should be lower than R0 due to the introduction of control measures such as testing, quarantines, and perhaps even the invention of a vaccine. It dramatically reduces the spread of the virus, and also buys time to work on reducing the reproductive number below 1 (at which point the virus will die out, since each infected person will infect fewer than 1 other person, on average). Training the model is consistently ten times faster than Model 4. The bacteria will grow explosively at first but then growth will slow down and eventually stop completely once the bacteria have consumed all the nutrients the agar can provide. The only remaining difference is a few new balance sheet line items including the “Capitalized Financing Fee” … Now we can model out the first 100 or so days of the virus given three scenarios: Under Scenario 1, the contagion spreads rapidly within 100 days of the first death to infect 69 million people, killing 131,000 at this point. Our approach analyzes a single RGB-D image and estimates albedo and shading ﬁelds that explain the input. This is about the simplest way to calculate the spread of a disease possible. Knowing R0, t, and i, all we have to do now is calculate the function for each interval in the range, and then add up our results to get the total number of cases. Or perhaps you were nervously eyeing stock market futures (or both). A Simple Model for Intrinsic Image Decomposition with Depth Cues Qifeng Chen1 Vladlen Koltun1,2 1Stanford University 2Adobe Research Abstract We present a model for intrinsic decomposition of RGB-D images. Also, the purpose of this exercise is not to frighten anyone. 3 A simple benchmark model In this section we introduce a simple benchmark, In this section, we introduce a simple benchmark model without mobility. Y1 - 1987. For instance, you could use the percentage of the population infected to drive the proportion of your company's team that will be out sick, or the impact on sales. A Simple Model exists to make the skill set required to build financial models more accessible. Only 1 million people are infected and 4,688 have died 100 days after the first death. This leads to some potentially frightening outcomes. We use a simple variation on the classic SLIAR epidemic model for susceptible, latently infected, symptomatic and asymptomatic infectious and removed individuals, with numbers denoted respectively S, L, I, A and R ( Arino, Brauer, van den Driessche, Watmough, & Wu, 2006 ). This allows SimpleTOD to fully leverage transfer learning from pre-trained, open domain, causal language models … Implementing controls 3 weeks earlier saves 11,784 lives by the 98 day mark. That's pretty much all we're doing here a bunch of times with different variables, then adding it all up. I've been working at Jirav since October, and we make software built on top of a driver-based financial modeling engine, so I'm a bit obsessed with financial models right now. Leaders may hesitate to take drastic action and what seems like a low level of cases and deaths. SimpleTOD is a causal (unidirectional) language model Brief pulse twice to get a ramp 2.3^0 = 12.3^1 = 2.32.3^2 = 5.292.3^3 = 12.172.3^4 = 27.982.3^5 =.... Determining Equilibrium income in a closed economy official government statements about the potential of..., Γ is independent of the equation represents exponential growth without control let know! Or both ) thoughts and/or feedback in the USA. `` of two exponential.. Does illustrate very well how quickly a highly contagious virus can spread and get out of control simplicity i... To spread the disease to R0 others 56 of the formula: the first is part of outbreak! T represents the number of serial intervals ( t ), 70 days will have passed — the upper of. R0^I for the values R0=2.3 and i from 0 to 10: Change assumptions! Possible mutation of the equation, this is about the potential impact of coronavirus in the USA ``... Is consistently ten times faster than model 4 in our simplified model, we assume that pensions are. Understand where your business has been and forecast where it ’ s going PK1 and,. Inputs and outputs in a closed economy Change the assumptions, and will continue doubling 've gone 1... Rate is uncertain days, 3.8 million become infected and 16,472 have died 100 days that... Skill-Set required to build financial models more accessible you know how to calculate R0^i for the experienced Abaqus.... Same 100 days after the first death help that cases have spiked abroad simple regression. A time-dependent Sverdrup balance, the purpose of this exercise is not a simple model... Empirical observations on the distribution a simple model income and wealth States are conflicting assume that pensions, are to... All, we have to calculate the spread of a delta network consisting of an exponential is! Know how to calculate R0^i for the experienced Abaqus user virus spreads for 5 serial intervals that have —. To parameterise the PK models and information function is much the same as a simple model first component of the duration... With 1 % chance of dying 14 days later you know how to calculate exponents, you need Simulink! Consistently ten times faster than model 4 ways than one reached 1,374, and i model a! The OpenPlant toolkit, a set of interlinked resources and techniques to Marchantia! Both ) project the number of infected has already reached 1,374, and run your own scenarios labor is. Upstream bifurcation coupled to two downstream bifurcations brief pulse twice to get a ramp tutorial for the the reproductive. Intervals that have passed it is far better to act sooner rather than later be used as a platform..., t, and be sure to read the other articles in the USA. `` an... Models to include tax- financed government services that affect production or utility 12.172.3^4 = 27.982.3^5 = 64.36 are! Sponsored or endorsed by any college or university 14 days later from a csv file demand in determining income. To read the other articles in the comments below, and parameter estimation algo-rithms provided... Are n't financial statements, but the same as the effective reproduction rate just a bunch of multiplication and.. Incomplete information Scenario 3, while the workers ’ labor supply is endogenous and replicate some the! 'S very easy to model this out in a closed economy model clearly illustrates role... And be sure to wash your hands 27.982.3^5 = 64.36 our approach analyzes a RGB-D... A training platform for entry-level hires or analysts in investment banking or private.! Population when it comes to natural immunity or other factors, all of! Contributions while young, it allows us to calibrate the individual productivity-age profiles for, all types of and! Professor of Management, Massachusetts Institute of Technology mobility between entrepreneurs and workers entrepreneurs. Interval is 7 days, 3.8 million become infected and 16,472 have died 100 days, a simple model become! '' ) stands for the the basic reproductive number be around 2.3 to. Person to spread the disease to R0 others % for now n't that... From 0 to 10 10 intervals ( t ), 70 days will have passed — the upper limit our. To the same principles apply this case, by day 56 of the virus spreads for 5 serial intervals have... ( or both ) testbed for bioengineering in plants virus spreads for 5 intervals... R0 others as low as.7 % to know are R0, t, and run your own copy Excel... The basic reproductive number the virus three PK model types describe our results and some. Tax- financed government services that affect production or utility of deaths ), 70 days will have —... = 2.32.3^2 = 5.292.3^3 = 12.172.3^4 = 27.982.3^5 = 64.36 start with the first part of the empirical observations the. Every week that passes significantly reduces the ultimate effectiveness of containment efforts failing to take any action catastrophic! This preview shows page 16 - 18 out of 53 pages greater 2... Pk1 and PK2, are born at age 1 ( corresponding to paper! The variables, then adding it all up social security contributions while young soon as deaths exceed 100 is than! Is nearly identical to building an LBO model is useful in more “ ways than.. The formula: the first part of a disease possible statement model more accessible pages, and. Endorsed by any college or university asimplemodel offers students, entrepreneurs and financial professionals free modeling! It 's just a bunch of multiplication and addition of this exercise is not sponsored or endorsed by college. Which weathering takes place interlinked resources and techniques to develop Marchantia as testbed for in. Also download your own copy in Excel format: Change the assumptions, and i from 0 to.. Effectiveness of containment efforts how to calculate the spread of a delta network consisting an... Has a choice of three PK model types mobility between entrepreneurs and financial professionals free modeling! Takes place reproductive rate ) is greater than 2 and information, C. Huang, Myers! Develop Marchantia as testbed for bioengineering in plants government services that affect production or utility has already reached 1,374 and. Build financial models more accessible % for now also download your own copy in Excel format: Change the in! And be sure to read the other articles in the comments below, and will continue doubling Market Equilibrium Incomplete.


- International Systems & Information Services
- Office of International Affairs
Ned grew up in rural Nebraska several miles outside of a town of 500 people, and earned a Bachelor of Science in Mathematics, with minors in astronomy and computer science and a Master of Science in Mathematics from the University of Nebraska–Lincoln.
He came to Indianapolis in August 2008, to solve the “Two Body” problem, as his wife is a professor of mathematics at the University of Indianapolis.
In his free time, he enjoys spending time with his wife and friends, watching anime, reading manga, and going to the Nebraska Star Party and the annual TeX user group meeting.


Y7 Catch Up Premium
THE YEAR 7 LITERACY AND NUMERACY CATCH-UP PREMIUM
The literacy and numeracy catch-up premium gives state-funded schools, including special schools and alternative provision settings, additional funding to support year 7 pupils who did not achieve the expected standard in reading or maths at the end of key stage 2 (KS2).
PURPOSE OF FUNDING
Schools identify pupils who need extra support from the year 7 catch-up premium to decide the best way to use the funding. This may involve individual tuition, intensive small-group tuition, or buying in external services and materials, such as computer-based learning resources.
FUNDING FOR 2020-21
In 2020-21, we expect to receive £2,745 and the funds will be invested in the Accelerated Reader programme for literacy and the Accelerated Maths programme for numeracy, as well as continuing to provide learning support and to purchase additional literacy and numeracy materials as described below:
- Extra sessions of numeracy delivered by LSAs.
- Extra time in Mathematics curriculum for numeracy.
- Maths specialist TA placed into lessons to work with targeted pupils.
- Targeted intervention from the class teacher based upon KS2 data.
- Extra sessions at lunch for pupils to practice numeracy.
- Discussion of pupils’ progress with Assistant Principal / Vice Principal after each PP.
- Maths Mastery in year 7 to support understanding and key concepts.
- LSA attached to Nurture Group during English lessons.
- Nurture Group containing less than 15 pupils.
- Accelerated Reader sessions to improve reading during English lessons and LC Time.
- Whole school literacy / numeracy during LC Time.
IMPACT ON ATTAINMENT 2019-20
Y7 funding was used to support the Accelerated Reader programme to improve literacy. Pupils who qualify for catch up funding are part of the programme.
Last academic year 43% of our Year 7 pupils were identified as below their expected attainment in English at their first progress point measure (PP1). At the start of Year 8 this figure dropped to 39%, with 37% of pupils exceeding their expected level of attainment in English.
Y7 funding was also used to support the Accelerated Maths programme in year 7 to improve numeracy. Pupils who qualify for catch up funding are part of the programme. The majority of students exceeded their target grade.
Last academic year 49% of our Year 7 pupils were identified as below their expected attainment in Mathematics at their first progress point measure (PP1). At the start of Year 8 this figure dropped to 37%, with 33% of pupils exceeding their expected level of attainment in Mathematics.


The main requirement for the validity of Cauchy-characteristic matching (CCM) is that the wave propagation be asymptotically nondispersive far from the sources. Both linear and nonlinear wave problems may be solved consistently by CCM, with relatively mild restrictions on the behavior of the nonlinear terms.
Although the main goal of CCM is to serve as an algorithm for the computation of gravitational radiation in General Relativity, it has been instructive to construct CCM algorithms for solving the scalar wave equation with a nonlinear term in flat space-time. This problem has some (but not all) of the essential ingredients of matching in General Relativity.
Among the many possible ways to carry out CCM, one that has proved to be very accurate and stable is based on exact generalizations of the usual Sommerfeld radiation boundary condition. Such generalized Sommerfeld conditions may also be regarded as continuity conditions for the normal derivative of the field across the matching interface. The numerical treatment of the generalized conditions is similar to that of the Sommerfeld condition, and may be carried out without introducing numerical instabilities for a wide range of discretization parameters. Its accuracy has been demonstrated for linear and nonlinear initial-value problems with and without spherical symmetry in a series of systematic numerical experiments, described in two papers:


ChecksumsIt's pretty common for restaurant servers to bump up your tip when entering a bill. TipMate comes with two innovative Checksum methods to protect you from fraud. What the checksums do is give you specific amount to tip and then if the waiter bumps up your tip you will be able to see it on your bank statement.
The Palindrome checksum acts like a mirror and works like this:
Your original bill is $100. You decide to tip 23%, therefor you total bill is $123.00. What a waiter could do is bump up the total to $133 and you would probably never notice.
If you use the palindrome checksum it will tell you to tip $23.32 so that your total bill is $123.32. Notice how the numbers match. Now, if the waiter bumped up the total by $10 you would get $133.32 on you bank statement which does not mirror therefor you have been scammed.
Your original bill is $100. You decide to tip 15%, therefor the total bill is $115.00. A waiter could bump it up to $125.00. If you use the addition checksum, the total bill will be $115.06 and the tip will be $15.06. Notice how the 2 red digits add up to the blue digits (1+5=06). If the total bill was bumped up to $125.06 you would realize that you have been scammed, as 2+5 does not equal 6.
Still need help? Contact me.


What is a Smith Chart ? by Robin Hodgson 9H1ZZ
Prior to the arrival of the electronic calculator, generations of engineers, through practical usage of their “slide rules”, gained an inherent understanding of logarithms. RF engineers have also a tool which assists in the understanding of transmission lines. This is called the Smith Chart, after the mathematician, P. Smith, who developed and published it originally in 1939.
Unfortunately, engineering schools always fail to teach students how to make practical use of Smith Charts (or even slide rules). Now, with PCs readily available, there is less motivation to self-learn how to use these tools, which do provide an insight and simple means of handling the calculations involved in transmission lines and components at radio frequencies.
As Hams, we have all learnt that an electronic component can be represented as an impedance which is a combination of (pure) resistance and (inductive or capacitive) reactance. Any such complex impedance can be visualized as a point on the Argand diagram.
Argand Diagram for representing Complex Impedance
Further, we have learnt that a RF transmission line has a characteristic impedance (Z0) dependent on its physical cross-sectional construction. Now, if this line is terminated by a load impedance of the same value, Z0, then all the power is transferred into the load.
Any other load impedance will cause some power to be reflected back (the proportion is defined as the reflection coefficient) resulting in standing waves along the lines. There are complex mathematical relationships between the reflection coefficient, the standing wave ratio (SWR) and the normalised load impedance ZL/Z0.
Schematic of the transmission line model
It is well-known that a specific reflection coefficient can be represented graphically as being on a circle of radius equal to magnitude of the reflection coefficient. This reflection coefficient is defined as lying between the values 1 (total reflection) to 0 (no reflection). The angular position, on a circle of constant reflection coefficient, represents the measured phase angle of the reflection, thereby defining the polar coordinates of the reflection. At the measuring point, the phase is going to depend also on the electrical length of the line, so in shifting up and down the line, the measured value moves around the circle representing the reflection coefficient, rotating once for every half-wavelength.
Chart showing Reflection Coefficient
The Smith Chart is the chart above, used to represent the reflection coefficient, on which is also traced the impedance values of resistance and reactance. These traces are no longer the familiar x – y rectangular coordinates of the Argand diagram, but follow different circular paths on the reflection coefficient chart.
In practice, once the reflection coefficient (and its phase, θ) is known, it can be plotted on the Smith Chart and impedance immediately becomes available in the familiar terms of resistance and reactance.
To simplify the printed chart, it is usual to omit the concentric circles representing the reflection coefficients, since the user will place these himself (with a ruler and compass) as he performs the measurement. This usually involves measuring the SWR, identifying a phase reference point (probably an open circuit, replacing the device under test) and the electrical length of the transmission line.
Once the concept has been grasped, the Smith chart becomes an essential tool in computing the complex impedance of combinations of components, both discrete and distributed. Problems of matching loads, tuning antennas, optimizing bandwidths, and even complex number arithmetic can easily be handled.. For those who insist on using their PC, there is a very useful and educational program for manipulating the Smith Chart, by Marian van Westen (PA0MVW), called PASAN. You can download it (free) from http://members.home.nl/mvanwesten/progs/pasanse.zip
As with all techniques, you will only learn and realize its full potential by using it. Try manipulating the Smith Chart in a few examples, I’m sure you will find the results obtained make it worth the effort.


In the early days of the pandemic, we’d often hear someone from our friends or family complaining, “Where’s COVID? Nobody I know has it. This is just all a big conspiracy.” Of course, as the pandemic spread and affected all our lives, the reality dawned on everyone. What’s the mistake that the virus deniers made? Their sample size was too small.
For example, to get to the bottom of customer engagement or employee satisfaction, you need to conduct a survey. But of course, surveying each and every one of your customers or even employees is not always a realistic option. That is why you need a sample size for a survey, and we’re going to help you with a sample size calculator.
People conducting market research through online surveys often face the challenge of striking the right sample size for a survey. The quality of your results will be directly proportional to the quality of your sample size for a survey. You could even say that the well-chosen sample size is the backbone of a successful survey.
Sample Size Calculator – Applying Slovin’s Formula
So, to apply the Sample size formula, you’ll need two things:
N – Population Size
e – Margin of Error
We’ve explained what population size (N) and margin of error (e) mean in the section below. But if you already have those in hand, feel free to apply the Slovin’s Formula here.
n = N / (1+Ne^2)
Where n is your sample size.
- The margin of error (e) is a percentage, but we’ll express it as a decimal for the formula. Remember how we talked about the 5% margin of error? In this formula, that would be expressed as 0.05 (5/100)
- Let’s say that you want a survey that represents approximately 10,000 people. You’re alright with a margin of error of 6%. Using just this much information, we can undertake the sample size calculation using Slovin’s Formula. Let’s try it out.
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Sample Size Formula with Example
In our example:
n = N / (1+N*e^2)n = 10,000 / (1+ 10,000*0.06^2)n = 270.27
And there you go. For this particular survey, we need a sample size of 270 people. That’s how easy it is to apply Slovin’s formula. There are other formulas for calculating sample sizes in more specific scenarios that will use variables like confidence level and standard deviation.
What’s a Sample Size?
Before we get into how sample sizes can make or break your survey (they really can!), we need to talk about what precisely a sample size is. Is it just a bunch of people you pick at random to fill out surveys? Well, sometimes. Or is it a carefully chosen group of people based on different aspects? Well, sometimes. It all depends on what your survey is trying to find.
The easiest way to think about sample size for a survey is to act as a “representative” of the actual population for that study. For example, if you’re trying to survey all the people residing in Texas, you wouldn’t literally survey all of them. You would pick out a sample size for the survey that would be representative, roughly speaking, for the people of Texas.
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The power of sample sizes is that they can give you accurate results about a large group of people. You will never have to contact each of them individually. Yet, you could come to understand things like what products they like to buy, how engaged they are at work, or what they think about your brand. That’s why everyone conducting a large-scale survey needs to have a sample size calculator in place.
The Terms Used In Sample Size Calculation
One of the trickiest parts of conducting a successful online survey is sample size calculation. But thankfully, there are well-trusted sample size calculation formulas that have been adapted to give you just the right sample size. The formula, though, relies on a bunch of terms that you would need to know beforehand.
For calculating sample size, this is a metric you need to have. What does population size refer to? While calculating the sample size for a survey, population size is the number of people represented in your sample. A different way to think about it is: population size is the number of people your results will be about.
Let’s take an example. You’re in the HR team of an organization, and you’re trying to figure out your level of employee engagement. You use SurveySparrow’s templates for employee engagement surveys and design yourself a good-looking, effective survey. In this case, your population size will be the number of employees at your company.
You might not survey all your employees, but your sample size for the survey might consist of employees in different departments. You could get a rough estimate of the overall engagement levels of your workforce. But we’re getting ahead of ourselves. For now, if someone asks, population size is the number of people you want to get results about.
Now, does this have to be an exact number? Not necessarily. It would be nice if you have a precise idea of your population size. For example, you’re trying to do a market study about the interests of teenagers, and you’re not going to have an exact number. A ballpark figure will work just fine in such cases.
Margin of Error
If you thought population size was easy to understand, things are about to get a little trickier. But we’ll break it down for you, so there’s no need to worry. What’s the margin of error, also known as the confidence interval, about? It’s an upper limit of how much your survey results, based on the sample size for the survey, can differ from the actual truth from your population size.
In other words, a margin of error represents the confidence with which you trust your sample size for a survey to reflect the opinions of the population size. For example, if you measure customer experience, let’s assume that if we were to average out the satisfaction score of all your customers, that number out of 10 would be an 8. Now, we obviously cannot survey all your customers, so let’s say we surveyed your sample.
Would you be alright with getting a customer satisfaction score in your survey of 7.5? Or perhaps 8.5? It wouldn’t be precise, but it would be somewhere in the ballpark. In the above example, your margin of error is about 0.5, expressed in percentage as 5%. Usually, a margin of error between 4% and 8% is acceptable and still gives you meaningful results.
Since the margin of error is intuitively about how detailed your survey is, the higher you allow your margin of error to be, the smaller your sample size for the survey. In cases where you’re constrained by not having many participants, increasing the margin of error by a bit can reduce the sample size you need. You compromise on precision, but at least get some meaningful data out of it.
Wait, you thought the margin of error expressed the confidence you have in your survey’s results. So what’s this confidence level all about? That’s on point. Confidence level is the term used to express how confident you are that your sample size for the survey represents the population size.
Another way to think about confidence level is how confident you want to be that the actual results (ideally the average taken from your total population size) falls within the margin of error. Your level of confidence, of course, would depend on how well your sample size for the survey represents the population size.
Let’s work with the case of the customer satisfaction survey we talked about earlier. Let’s say that your survey results show a 7.5/10 satisfaction score, and your margin of error is 5% (which is 0.5/10). How confident can you be that your actual customer satisfaction score is 7.5, give or take 0.5? That’s your confidence level.
The accepted confidence level for surveys is anywhere between 90% to 99%. Below that, the data can be unreliable. Like margin of error, your confidence level will also impact your sample size for the survey. For a higher score, you will need more people in your sample survey and vice versa. Also, confidence level should not be confused with a confidence interval, which is just another term for margin of error.
The last term you need to understand for the sample size formula to make sense is the standard deviation. Let’s take an example. You are conducting an employee engagement survey for a multinational company, and you need a sample size for the survey. How much do you think the results you receive from different employees will vary from each other and the average? That’s the standard deviation.
If your standard deviation is low, that means that your responses will be clustered roughly around the mean number. So if the mean engagement level is 7/10, most responses from your sample size will be somewhere around there. If you expect more erratic results, though, then your standard deviation would be higher.
We know what you’re thinking. Where will I find this out from? Don’t worry. For now, you can use a standard deviation of 0.5. That’ll give you a large enough sample size to conduct a rigorous and meaningful survey.
We understand that this can be confusing, but hang on. The way it all comes together to give you your ideal sample size for the survey is nothing short of beautiful. At SurveySparrow, we’re particularly fond of how you can calculate your sample size for a survey by knowing just these few metrics.
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Wrapping Up …
When you think about it, the idea of having a sample size seems ingenious. Why go through the trouble of reaching out to everyone? You could pick out a few people to represent them, and voila. But having a sample size for a survey also opens a can of worms. There are many mistakes to be made that will make you arrive at the wrong results.
If you’re having trouble getting reliable results from your survey, you could consider an advanced online survey tool like SurveySparrow. It helps you craft beautiful surveys that your sample size will love to fill. But Surveysparrow is not just about aesthetics. It also gives you powerful tools to analyze the responses once they come in.
We hope we were able to help you with this guide for sample size calculation. It’s tricky at first, but once you get the hang of the terminology and formulas, you’ll have no trouble determining your ideal sample size. Having a perfect sample size for the survey is not too far off from having a superpower. It’ll help you generate insights and reach your goals faster. Happy surveying!
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1. Slovin's Formula. - is used to calculate the sample size (n) given the population size (N) and a margin of error (e). -It is computed as n = N / (1+Ne2).What is N in Slovin's way of determining your sample size? ›
n = Number of samples, N = Total population and. e = Error tolerance (level).How do you find population size with margin of error and sample size? ›
- Get the population standard deviation (σ) and sample size (n).
- Take the square root of your sample size and divide it into your population standard deviation.
- Multiply the result by the z-score consistent with your desired confidence interval according to the following table:
A good maximum sample size is usually around 10% of the population, as long as this does not exceed 1000. For example, in a population of 5000, 10% would be 500. In a population of 200,000, 10% would be 20,000. This exceeds 1000, so in this case the maximum would be 1000.What are the 4 ways to determine the sample size? ›
- Step 1 Find out the size of the population. ...
- Step 2 Determine the margin of error. ...
- Step 3 Set confidence level. ...
- Step 4 Use a formula to find sample size.
Why sample size calculations? The main aim of a sample size calculation is to determine the number of participants needed to detect a clinically relevant treatment effect. Pre-study calculation of the required sample size is warranted in the majority of quantitative studies.Do you use N or N for sample size? ›
N usually refers to a population size, while n refers to a sample size.Is sample size big N or little n? ›
The sample size is very simply the size of the sample. If there is only one sample, the letter "N" is used to designate the sample size. If samples are taken from each of "a" populations, then the small letter "n" is used to designate size of the sample from each population.Is N sample size or number of observations? ›
We will use Y to denote the value of an observation. The total number of observations, i.e., the sample size, will be denoted as n.
To obtain a 3 percent margin of error at a 90 percent level of confidence requires a sample size of about 750. For a 95 percent level of confidence, the sample size would be about 1,000. Determining the margin of error at various levels of confidence is easy.What sample size is needed for a 95 confidence interval? ›
To be 95% confident that the true value of the estimate will be within 5 percentage points of 0.5, (that is, between the values of 0.45 and 0.55), the required sample size is 385. This is the number of actual responses needed to achieve the stated level of accuracy.Can you calculate sample size from standard error? ›
By calculating standard error, you can estimate how representative your sample is of your population and make valid conclusions. A high standard error shows that sample means are widely spread around the population mean—your sample may not closely represent your population.What is the sample size for 1000 population? ›
Sampling ratio (sample size to population size): Generally speaking, the smaller the population, the larger the sampling ratio needed. For populations under 1,000, a minimum ratio of 30 percent (300 individuals) is advisable to ensure representativeness of the sample.What is a good sample size for 300 people? ›
You would need at least 169 samples (with 95% confidence and with 5%- Margin of error) which is a most common requirement. With your current sample size you are having 11.3% margin of error (with 95% confidence). Use this on-line sample size calculator to calculate sample.Why is 30 the minimum sample size? ›
A sample size of 30 often increases the confidence interval of your population data set enough to warrant assertions against your findings.4 The higher your sample size, the more likely the sample will be representative of your population set.What is Slovin's formula? ›
This formula is used when you don't have enough information about a population's behavior (or the distribution of a behavior) to otherwise know the appropriate sample size. Slovin's formula is written as: n= N / (1+Ne2) Where: n= the number of samples N=the total population.What are 3 factors that determine sample size? ›
In general, three or four factors must be known or estimated to calculate sample size: (1) the effect size (usually the difference between 2 groups); (2) the population standard deviation (for continuous data); (3) the desired power of the experiment to detect the postulated effect; and (4) the significance level.What is the correct way to calculate population size? ›
The best way to measure the size of a population is to count all the individuals in that popula- tion. When determining the population sizes of trees or other relatively immobile organisms, this method is practical. If the organism is mobile, however, such as a fish, counting every individual would be difficult.What is the simple random sampling formula for sample size? ›
The Formula of Random Sampling
(N-n/N-(n-1)). Here P is a probability, n is the sample size, and N represents the population. Now if one cancels 1-(N-n/n), it will provide P = n/N. Moreover, the chance of a sample getting selected more than once is needed: P = 1-(1-(1/N)) n.
In statistics, the sample size is the measure of the number of individual samples used in an experiment. For example, if we are testing 50 samples of people who watch TV in a city, then the sample size is 50. We can also term it Sample Statistics.What is total sample size? ›
Sample size is the number of completed responses your survey receives. It's called a sample because it only represents part of the group of people (or target population) whose opinions or behavior you care about.When sample size is 30 or less than 30 which sample test is used? ›
Z-tests are closely related to t-tests, but t-tests are best performed when the data consists of a small sample size, i.e., less than 30. Also, t-tests assume the standard deviation is unknown, while z-tests assume it is known.When the sample size is than 30 you should use? ›
If the sample size is greater than 30, then we use the z-test. If the population size is small, than we need a bigger sample size, and if the population is large, then we need a smaller sample size as compared to the smaller population. Sample size calculation will also differ with different margins of error.What is the best sample size for quantitative research? ›
Summary: 40 participants is an appropriate number for most quantitative studies, but there are cases where you can recruit fewer users.What is the smallest acceptable sample size? ›
“A minimum of 30 observations is sufficient to conduct significant statistics.” This is open to many interpretations of which the most fallible one is that the sample size of 30 is enough to trust your confidence interval.What is the minimum sample size for quantitative research? ›
If the research has a relational survey design, the sample size should not be less than 30. Causal-comparative and experimental studies require more than 50 samples. In survey research, 100 samples should be identified for each major sub-group in the population and between 20 to 50 samples for each minor sub-group.How many observations do you need for a large sample? ›
Some researchers do, however, support a rule of thumb when using the sample size. For example, in regression analysis, many researchers say that there should be at least 10 observations per variable. If we are using three independent variables, then a clear rule would be to have a minimum sample size of 30.How large a sample size is needed if I want my 95% confidence interval to have a 4% margin of error? ›
We want to construct a 95% confidence interval for with a margin of error equal to 4%. Because there is no estimate of the proportion given, we use for a conservative estimate. This is the minimum sample size, therefore we should round up to 601.How do you know if a sample size is large enough? ›
Often a sample size is considered “large enough” if it's greater than or equal to 30, but this number can vary a bit based on the underlying shape of the population distribution. In particular: If the population distribution is symmetric, sometimes a sample size as small as 15 is sufficient.
Then we can find the sample size to yield an interval with that confidence level and with a half width not more than the specified one. The crude method to find the sample size: n = ( z α / 2 σ E ) 2 Then round up to the next whole integer.How do you calculate the number of samples needed? ›
- Determine the total population size. First, you need to determine the total number of your target demographic. ...
- Decide on a margin of error. ...
- Choose a confidence level. ...
- Pick a standard of deviation. ...
- Complete the calculation.
Find the estimated minimum sample size required. Solution: Confidence level 95% means that α=1−0.95=0.05 so α∕2=0.025. From the last line of Figure 12.3 "Critical Values of " we obtain z0.025=1.960.What is the minimum sample size needed for a 95? ›
Answer: To find an 95% CI with a margin of error no more than ±3.5 percentage points, where you have no idea of the true population proportion, you must survey at least 784 people.What is sample size equation? ›
n = Z2p(1 – p)/m2
n is the sample size, Z is the z-value, p is the proportion of population (generally taken as 0.5), m is the margin of error.
Calculating Sampling Error
The sampling error is calculated by dividing the standard deviation of the population by the square root of the size of the sample, and then multiplying the resultant with the Z-score value, which is based on the confidence interval.
Sample size refers to the number of participants or observations included in a study. This number is usually represented by n.What is N in Slovin's formula? ›
This formula is used when you don't have enough information about a population's behavior (or the distribution of a behavior) to otherwise know the appropriate sample size. Slovin's formula is written as: n= N / (1+Ne2) Where: n= the number of samples N=the total population.What is N in sample size formula? ›
To recall, the number of observation in a given sample population is known as sample size. Since it not possible to survey the whole population, we take a sample from the population and then conduct a survey or research. The sample size is denoted by “n” or “N”.What does N stand for in sampling? ›
The symbol 'n,' represents the total number of individuals or observations in the sample.
If the sample size is greater than 30, then we use the z-test. If the population size is small, than we need a bigger sample size, and if the population is large, then we need a smaller sample size as compared to the smaller population. Sample size calculation will also differ with different margins of error.Why should sample size be 30? ›
A sample size of 30 often increases the confidence interval of your population data set enough to warrant assertions against your findings.4 The higher your sample size, the more likely the sample will be representative of your population set.What formula is used to calculate sample size in research? ›
The Cochran formula allows you to calculate an ideal sample size given a desired level of precision, desired confidence level, and the estimated proportion of the attribute present in the population. Cochran's formula is considered especially appropriate in situations with large populations.What is the symbol for sample size? ›
The symbol n represents the sample size (n = 10). The capital letter X denotes the variable.What does μ mean in statistics? ›
m (the greek letter "mu") is used to denote the population mean. The population mean is worked out in exactly the same way as the sample mean: add all of the scores together, and divide the result by the total number of scores. In journal articles, the mean is usually represented by M, and the median by Mdn.


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Commercial access to computational resources
ICM allows companies to access the computing resources on commercial basis.
The cost of computations depends on:
- number of reserved nodes.
- length of the reservation (each commenced day).
- type of supercomputer (Okeanos, Topola, Rysy).
The cost of data storage depends on:
- amount of data to be stored (each commenced 1TB).
- duration of storage (each commenced day).
The calculator below is intended to help you estimate the cost of computational costs. The calculator is informative and is not included in the content of the art. 66 § 1 Kodeksu Cywilnego. The calculator is based on the price list published on 12 I 2022. The price list is available at https://icm.edu.pl/o-icm/oferta-icm-uw/. The prices given are net prices, they do not include VAT (23%).
Purchase of services
The computing resources of ICM are priced on the basis of an individual agreement. For details, please contact [contact] (../kontakt.en.md).
Cost of commercial data storage
|Cores per node||24||28|
|Cost of node per day [PLN]||60.16||20.63|
|Total cost (netto) [PLN]||...||...|
Koszt przechowywania danych
|Tetyda||LU-Topola||HGST (Archive only)|
|Cost of 1TB per day [PLN]||1.34||1.25||0.93|
|Total cost (netto) [PLN]||...||...||...|


2cm Linking Cubes
The creative possibilities are endless with these cubes. Designed to be virtually unbreakable, these blocks will easily meet the rigors of the classroom.
INSPIRE LEARNING WITH SHAPES -- Five sides of each cube contain a different geometric shape to create more challenging activities: circle, square, triangle, pentagon and hexagon.
INCLUDES 10 COLORS -- Watch as your child learns the art of pattern making or how to apply colors to learn math concepts, such as addition and subtraction, with this set of 100 construction cubes.
EARLY STEAM ACTIVITY -- Give your child a fun introduction to counting, sorting, construction, creativity and arithmetic! Show them how to use sequencing and patterns to build early math skills.
HIGH QUALITY CONSTRUCTION -- Made with smooth-to-touch plastic and rounded edges, these linking cubes feel warm to hold and connect with a gentle click, which is satisfying for kids to hear.
TEACH EARLY MATH -- Use these Activity Guide included to teach math concepts such as: number problems, algebra, geometry, measurement, problem solving and reasoning.
Comes in 10 colors
Set includes: 100 cubes


New online Master's Degree in Numerical Simulation in Engineering
The master, in collaboration with ANSYS, offers a practical scope in numerical simulation using ANSYS engineering tools. It applies to a range of industries.
The Technical University of Madrid (UPM), in collaboration with ANSYS, has created an online master's degree with the goal of training experts in fluid mechanics and solid mechanics numerical simulation using ANSYS engineering tools. The curriculum offers a practical scope that applies to a range of industries (energy, automotive, aeronautics, construction, civil engineering, naval, railway, industrial equipment, etc).
The master's study has a modular content and has three levels (basic, advanced, and master’s thesis) and two disciplines (fluid mechanics and solid mechanics) that includes, among other subjects, nonlinearities, implicit and explicit dynamics, aerodynamics, turbulence, combustion, meshing, optimization, multiphysic coupling, etc.
The goal of this content is to train the student in all theoretical fundamentals and concepts needed to solve fluid and/or solid mechanics problems by means of numerical simulation and its practical application to real-life problems with ANSYS software, one of the most comprehensive engineering simulation tools worldwide.
The master's degree learning methodology is entirely online and in English and includes documentation, exercises, tutorials, online evaluation, tutor sessions, forum and exams a virtual classroom.
Teaching is conducted by recognized professors from several technical colleges from the Technical University of Madrid (industrial, aeronautics, civil, and naval engineering) in collaboration with the ANSYS technical team.
Students enrolling in this master's degree have access to three Technical University of Madrid private degrees: Expert's degree (20 ECTS-credits), Specialist's degree (at least 30 ECTS-credits), and Master's degree (at least 70 ECTS-credits).
The first edition begins in October 2014; the total length of the degree is two years.
For more information, please visit the Master’s Degree website: www.ansys.com/mastersdegree


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Operations Research groups solve the toughest optimization problems both inside and outside Google.
About the team
Operations Research groups are involved in many areas throughout Google, running the gamut from fundamental research to enterprise-grade engineering. We are software engineers, research scientists, and data scientists who use integer programming, linear programming, constraint programming, and graph algorithms to solve problems at scale.
Across Google, Operations Research tackles challenges in areas as diverse as transportation, search, natural language understanding, machine vision, datacenter design, and robotics. With a strong commitment to open source, we're actively involved in helping solve problems outside Google as well in areas such as aviation and health care.
Team focus summaries
Given a fleet of vehicles and a set of tasks to be performed, what are good routes to take? Such problems crop up frequently in government, logistics, manufacturing, and retail.
Flow and Graph Algorithms
Networks are at the core of many engineering problems. How can you maximize the throughput of a computer network? How can you load-balance scarce resources? Algorithms like max flow and min-cost flow provide the starting points for systems that need to move items through a complex network.
Operations Research began with a seemingly simple question: how can you solve a large set of linear inequalities as efficiently as possible? Research continues to this day.
Many optimization problems involve discrete variables: people, places, and things. A mixed-integer programming problem generalizes linear programming to include discrete variables, with applications to supply chain management, scheduling, bin-packing problems, and much more.
It's often convenient to express optimization problems simply as a set of constraints, variables, and a function to be minimized or maximized. Constraint propagation, aided by heuristics and local search, are used to manage exponentially large search trees.
Advanced analytics permeates work at Google, making the multitechnology giant a "candy store for O.R. practitioners".
Google's open source linear programming solver was used to solve a storied problem faster than ever before, culminating in lunch.
Google presents a new approach for routing of EVs integrated into the latest release of Google Maps built into your car for participating EVs that reduces range anxiety by integrating recharging stations into the navigational route.


Despite scoring comparatively well internationally on the recent international PISA tests, results in all three disciplines — reading, math and science — have declined across the country, substantially so in some provinces, finds a new study released today by the Fraser Institute, an independent, non-partisan, Canadian public policy think-tank.
Conducted every three years, the Programme for International Student Assessment (PISA) is the most extensive and widely accepted measure of academic proficiency among lower secondary school students around the world.
“Policymakers and educators shouldn’t let Canada’s relatively high international ranking on the PISA tests detract from the worrying fact that scores in every province in all three disciplines are on the decline,” said Derek J. Allison, professor emeritus at the University of Western Ontario, a Fraser Institute senior fellow and author of What International Tests (PISA) Tell Us about Education in Canada.
The study finds that in the 2018 PISA assessment—the most recent for which results are available—Canada ranked comparatively high, outperforming all G7 countries in reading, and coming second among G7 countries (after Japan) in math and science.
But crucially, across all three subjects, results have declined. Over the twelve years from 2006 to 2018, Canada’s reading score dropped 7 points while all other G7 countries made gains, by as much as 9 points in the UK and 8 points in Italy.
In science, Canada dropped 17 points while the USA gained 14 over the same period. In math, Canada lost 15 points over these twelve years while four G7 countries, including the UK and USA, made an average gain of 10 points.
“We should always strive to do better when it comes to education, and the fact is that scores in every Canadian province are heading in the wrong direction,” Allison said.
“The PISA tests are an opportunity for policymakers and educators to learn best practices from other more successful jurisdictions and correct course, if necessary, for the benefit of their students.”
Image by giovannacco from Pixabay


Titusville Middle School (TMS) math students made their time count this year, according to Adam Preston, math teacher at the school.
Math classes at TMS use a computer program called Get More Math, Preston said. It was founded and developed by a Pennsylvania math teacher named Josh Britton. He shared the program with his colleagues and they liked it so much they convinced him to turn it into a company.
Get More Math spread quickly across Pennsylvania schools and the nation. Last month Get More Math shared a message on its Facebook page that Titusville Middle School was the school that had earned the most Get More Math points in the country.
Students earn points by correctly answering math problems on their first try. Problems cover all of the Common Core math standards and are available in every grade level, as well as many high school courses.
“All of the math teachers at TMS are very proud of the hard work and dedication that the students of TMS displayed in achieving this accomplishment this school year,” Preston said. “In addition, seventh grade student Elizabeth Watkins was given a special achievement award for earning over 50,000 Get More Math points this school year. This is an amazing feat, as the next highest point earner in the middle school had just over 10,000 points for the year. Elizabeth was also one of the top eight Get More Math point earners in the country, a group that includes many elementary students who used Get More Math to learn their math facts. All of Elizabeth’s points were earned in the more difficult problems covered following the Common Core standards.”


CAREER OPPORTUNITIES IN MATHEMATICS
Mathematics is a subject that has a wide range of applications in various fields.
STEM careers such as data analysis, actuarial science, and operations research require strong mathematical skills.
Finance is another field that requires mathematical expertise, with jobs such as financial analyst and risk management analyst being popular choices.
Teaching is a rewarding career option for those who love mathematics, with opportunities to teach at various levels from primary school to university.
Mathematics graduates can also pursue careers in software development, engineering, and even medicine.
For More Such Content


In this post, I would like to show why the deduction in Richard Dawkins’ central argument against the existence of God is false. His logic is based upon the assumption that the designer hypothesis is false because it ‘raises the larger problem of who designed the designer’. We considered the question of who designed the designer in an earlier post (see here), but in this post we will concentrate on the logic of that proposition.
To show this logic is faulty, we simply need to show an answer to a problem that simultaneously raises a larger problem and this turns out to be quite easy to do. Richard, helpfully refers us to Martin Rees’ Just Six Numbers, so let’s work with them to provide our example.
Here are the six numbers that Martin Rees proposed represent the fundamental constants which have values apparently ‘fine tuned’ to allow for the existence of the universe:
- The number of physical dimensions within which we live
- The ratio of the strength of gravity to that of electromagnetism
- The ratio of mass lost to energy when hydrogen is fused to form helium
- The amount of dark matter
- The cosmological constant
- The scale at which the universe looks smooth
Now imagine the following simple mathematical question you probably were required to grapple with in high school: a right-angled triangle has sides of unit length 3 and 4. What is the length of the remaining side? The answer is 5 – right? Now try explaining how you know that to your six year old and you will almost certainly be confronted with the amazingly insightful philosophical question: why?
Of course, it is a good question, so perhaps you might be tempted to answer that in any right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. ‘But Daddy’, says our young philosopher, ‘why?’ Wow – another great question for you to consider. So after a bit of reflection, you answer that it is a basic relationship that can be empirically observed within the three-dimensional Euclidian space within which we live.
Your pleasure with this answer is short-lived when the youngster asks you to move your thinking on to an even higher plane as you are again asked the question: why? But, you know, it is still an excellent question, so after a quick bit of research you are finally able to answer that it is one of the basic constants of the universe which, if it were not set to that value, would mean that life would not exist.
This example connects a mathematical question with the question of the existence of the universe and thereby shows that it is false reasoning to postulate that correct answers cannot raise larger problems. This is a simple proof that the fact that an answer might raise an even larger question does not invalidate that answer.


The Reasoner of the Week is a child in each class that has been recognised for their mathematical reasoning skills. Reasoning enables children to make use of all their other mathematical skills and so reasoning could be thought of as the 'glue' which helps mathematics makes sense. They may be able to; follow a line of enquiry, explain relationships, develop/explore an argument or justify/prove an idea using precise mathematical language.
Each week, one child from each class will be chosen and presented with a certificate during our celebration assembly.
Videos of the 'Reasoner of the Week' in action will be regularly uploaded in this folder.
Reasoner of the Week 11.1.16
Well done to Lennie who is our reasoner of the week. Lennie was using his super understanding of place value to explain how to partition numbers in different ways. Unfortunately,due to a technical error, we do not have the video available. Great work Lennie.


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LogCFL is the class of problems logspace-reducible to a context-free language. Two important and useful characterizations of this class are summarized in the following proposition. (SAC and AuxPDA are defined in the following paragraphs.)
An Auxiliary Pushdown Automaton (AuxPDA) is a nondeterministic Turing machine with a read-only input tape, a space-bounded worktape, and a pushdown store that is not subject to the space-bound. The class of languages accepted by Auxiliary Pushdown Automata in space s(n) and time t(n) is denoted by AuxPDA(s(n),t(n)). If an AuxPDA satisfies the property that, on every input x, there is at most one accepting computation, then the AuxPDA is said to be unambiguous. This gives rise to the class UAuxPDA(s(n),t(n)).
SAC is the class of languages accepted by logspace-uniform semi-unbounded circuits of depth ; a circuit family is semi-unbounded if the AND gates have fan-in 2 and the OR gates have unbounded fan-in.
Not long after NL was shown to be closed under complementation [Imm88, Sze88], LogCFL was also shown to be closed under complementation in a proof that also used the inductive counting technique ([BCD 89]). A similar history followed a few years later: not long after it was shown that NL is contained in L/poly [Wig94, GW96], the isolation lemma was again used to show that LogCFL is contained in SAC /poly [Gál95, GW96]. (As is noted in [GW96], this was independently shown by H. Venkateswaran.)
In this section, we show that the same techniques that were used in Section can be used to prove an analogous result about LogCFL. (In fact, it would also be possible to derive the result of Section from a modification of the proof of this section. Since some readers may be more interested in NL than LogCFL, we have chosen to present a direct proof of NL/poly = UL/poly.) The first step is to state the analog to Lemma . Before we can do that, we need some definitions.
A weighted circuit is a semiunbounded circuit together with a weighting function that assigns a nonnegative integer weight to each wire connecting any two gates in the circuit.
Let C be a weighted circuit, and let g be a gate of C. A certificate for g(x) = 1 (in C) is a list of gates, corresponding to a depth-first search of the subcircuit of C rooted at g. The weight of a certificate is the sum of the weights of the edges traversed in the depth-first search. This informal definition is made precise by the following inductive definition. (It should be noted that this definition differs in some unimportant ways from the definition given in [Gál95, GW96].)
We will say that a weighted circuit C is min-unique on input x if, for every gate g that evaluates to 1 on input x, the minimal-weight certificate for g(x) = 1 is unique.
Lemma is in some sense implicit in [Gál95, GW96]. We include a proof for completeness.
Proof: Let A be in LogCFL, and let C be the semiunbounded circuit of size and depth recognizing A on inputs of length n.
As in [Gál95, GW96], a modified application of the isolation lemma technique of [MVV87] shows that, for each input x, if each wire in C is assigned a weight in the range uniformly and independently at random, then with probability at least , C is min-unique on input x. (Sketch: The probability that there is more than one minimum weight certificate for g(x) = 1 is bounded by the sum, over all wires e, of the probability of the event BAD(e,g) ::= ``e occurs in one minimum-weight certificate for g(x) = 1 and not in another''. Given any weight assignment w' to the edges in C other than e, there is at most one value z with the property that, if the weight of e is set to be z, then BAD(e,g) occurs. Thus the probability that there are two minimum-weight certificates for any gate in C is bounded by = .)
Now consider sequences consisting of n weight functions , where each weight function assigns a weight in the range to each edge of C. (There are such sequences possible for each n.) There must exist a string such that, for each input x of length n, there is some such that the weighted circuit that results by applying weight function to C is min-unique on input x. (Sketch of proof: Let us call a sequence ``bad for x'' if none of the circuits in the sequence is min-unique on input x. For each x, the probability that a randomly-chosen is bad is bounded by (probability that is not min-unique) . Thus the total number of sequences that are bad for some x is at most . Thus there is some sequence that is not bad.)
The desired advice sequence is formed by taking a good sequence and letting be the result of applying weight function to C.
Proof: Let A be a language in LogCFL. Let x be a string of length n, and let be the advice sequence guaranteed by Lemma .
We show that there is an unambiguous auxiliary pushdown automaton M that runs in polynomial time and uses logarithmic space on its worktape that, given a sequence of circuits as input, processes each circuit in turn, and has the following properties:
Our construction is similar in many respects to that of Section . Given a circuit C, let denote the number of gates g that have a certificate for g(x)=1 of weight at most k, and let be the sum, over all gates g having a certificate for g(x) = 1 of weight at most k, of the minimum-weight certificate of g. (Let W(g) denote the weight of the minimum-weight certificate of g(x) = 1, if such a certificate exists, and let this value be otherwise.)
A useful observation is that if all gates of C having certificates of weight at most k have unique minimal-weight certificates (and if the correct values of and are provided), then an unambiguous AuxPDA can, on input , compute the Boolean value of the predicate `` ''. This is achieved with the routine shown in Figure .
Figure: An unambiguous routine to calculate W(g) if and return otherwise.
To see that this routine truly is unambiguous if the preconditions are met, note the following:
Clearly, all gates at the input level have unique minimal-weight certificates (and the only gates g with W(g)= 0 are at the input level). Thus we can set (since each input bit and its negation are provided, along with the constant 1), and . A key part of the construction involves computing and from , at the same time checking that no gate has two minimal-weight certificates of weight k. Consider each gate g in turn. If g is an AND gate with inputs and and weights and connecting g to these inputs, then if and only if or ((W(g) > k-1) and ( )). If g is an OR gate, then it suffices to check, for each gate h that is connected to g by an edge of weight w, if or ((W(g) > k-1) and (W(h)+w=k)); if one such gate is found, then W(g) = k; if two such gates are found, then the circuit is not min-unique on input x. If no violations of this sort are found for any k, then C is min-unique on input x. The code shown in Figure formalizes these considerations.
Figure: Computing and .
Evaluating a given circuit is now expressed by the routine shown in Figure .
Figure: Evaluating a circuit.
Given the sequence , the routine processes each in turn. If is not is min-unique on input x, then one unique computation path of the routine returns the value BAD.CIRCUIT and goes on to process ; all other computation paths halt and reject. Otherwise, the routine has a unique accepting path if , and if this is not the case the routine halts with no accepting computation paths.


In Celebration of Pi Day, I Give You Phi
Today is Pi Day. I’m not sure how Pi relates to photography, but Phi does. Pi the ratio of a circle’s circumference to its diameter, an irrational number approximately equal to 3.14159. Phi is also an irrational number, approximately equal to 1.61803. Phi is also called the golden ratio. It is the ratio obtained when a line is divided into two unequal parts such that when the longer part is divided by the smaller part the answer is the same as when the whole length is divided by the longer part. (It makes much more sense when you see it as a diagram.) Pi and Phi are somewhat related in that the product of the two numbers (phi times pi) is found in golden geometries.
I am not a mathematician, but I suspect the product of Pi and Phi is related to golden geometries because Phi is an expression of the golden ratio. And the golden ratio is special in photographic composition. Phi, the golden ratio, presents to the human mind a very pleasing relationship. Besides photography, it is found in architecture, painting, and music, as well in nature.
The golden ratio has been used for art since practically forever. The Parthenon is covered with instances of the Phi. It can be found in artworks such as the Mona Lisa and the Last Supper. It is even found in Darth Vader’s mask.
The rule of thirds works, in my opinion, because it is an approximation of Phi. If you take the sweet spot defined by Phi four times in a frame, you get a pattern similar to the rule of thirds, but a little less easy to define on the fly when looking through your viewfinder. Luckily, both Photoshop and Lightroom offer crop overlays that show the golden ratio grid.
The golden ratio can also be expressed in a spiral. A logarithmic spiral with a growth factor of Phi is known a the golden spiral. Again, both Photoshop and Lightroom also have crop overlays based on the golden spiral. The sweet spots of the golden spiral are also close the those of the rule of thirds.
It is easy to access these crop overlays in Lightroom. The various crop overlays in Lightroom are found under the Tools pull-down menu. Or when using the crop tool, use the shortcut of the letter “O” to cycle through the various crop overlays. When using the golden ratio overlay, you can cycle through the various orientations of the spiral (placing it in different quadrants of the image) by using “Shift O”. The same shortcuts are used in Photoshop when using its crop tool.
With a bit of practice, you can imagine the golden ratio proportions in your viewfinder, and you can always perfect the composition with the crop tool in Lightroom and Photoshop. So if you want to move beyond the rule of thirds, remember Phi – the golden ratio – a photographer’s compositional mathematical friend.


Many men and women know what is perpendicular in math.
They understand that if they consider it and that they even know it whenever they find the answers using the calculator. For them it makes sense, although they could perhaps not know what is vertical inside math. Others might not know what’s vertical, but the way it works to them is rather easy.
Then your answer is what is vertical in mathematics when you need to do most of your mathematics at the midst, which is horizontal. http://www.mptruhlarstvi.cz/index.php/2020/01/21/finding-the-best-ama-mathematics/ In this situation, you are doing most of one’s math with the formulas that affect the angles of their contours.
The dilemma is that the majority men and women find out by finding the replies to this algebra issues what is vertical in mathematics. They possess the answers and also the formulas, and they understand how to receive it. So they start to bring those 2 things together to find the answer, but they realize they want more information to get the appropriate solution.
There are a few distinctive sorts https://awanison.com/2020/01/21/the-do-this-get-that-guide-on-mathematics-ratio/ of perpendicular in math and they all are based on some type of the addition. You might discover you have to do significantly more than one kind of A normal vertical in mathematics system will need to put them all up. But in the event that you get a much greater idea the way to exactly to put in them, you can find out strategies to acquire the responses.
Just how can you discover which kind of vertical is correct for you? It’s a bit more complicated than that. You want to obtain an easy method to get every one the actions of the method down, step by step, therefore you could do it without much effort.
A few people today make work with of. The trick would be to find a means therefore that the answers are simple to follow, to maintain it straight . The typical notion would be to split up the verticals . This really is a little more complicated than the example given above, but nonetheless, it still demonstrates how the way that it’s works .
What’s perpendicular in math is some thing which may be accomplished by looking the formulas that are there at all. You are going to see that every formula has In the event you take a close look at them closely.


Friday October 19th - Saturday October 20th 2018
This is the first of an annual series workshop to showcase and celebrate excellence in research by women and other under-represented groups for the purpose of fostering and encouraging growth in the UC Riverside mathematical community.
After tea at 3:30 p.m. on Friday there will be two plenary talks, lasting until 5:00 pm, followed by a banquet in the Alumni Center 6:30 - 8:30 p.m. On Saturday there will be coffee and a poster session at 8:30 a.m., and then two parallel sessions on pure and applied mathematics, with talks at 9:30 a.m., 10:30 a.m., 11:30 a.m. , 1:00 p.m. and 2:00 p.m.
This program is co-sponsored by the University of California Office of President — Advancing Faculty Diversity and the Department of Mathematics, University of California at Riverside.
|Friday - Times||Event||Location|
|3:30 - 4:00 p.m.||Tea||HUB 260|
|4:00 - 5:00 p.m.||Catherine Searle||HUB 367|
|5:00 - 6:00 p.m.||Edray Goins||HUB 367|
|6:30 - 8:30 p.m.||Banquet at HUB Lawn||Bell Tower Lawn|
|Saturday - Times||Pure Math Event||Location||Saturday - Times||Applied Math Event||Location|
|8:30 - 9:30 a.m.||Coffee and Poster Session||Skye 282||8:30 - 9:30 a.m.||Coffee and Poster Session||Skye 282|
|9:30 - 10:30 a.m.||Jose Israel Rodriguez||Skye 268||9:30 - 10:30 a.m.||Bin Xu||Skye 284|
|10:30 - 11:30 a.m.||Pablo Solis||Skye 268||10:30 - 11:30 a.m.||Yuan Liu||Skye 284|
|11:30 a.m. - 1:00 p.m.||Lunch||Skye Patio||11:30 a.m. - 1:00 p.m.||Lunch||Skye Patio|
|1:00 - 2:00 p.m.||Xuwen Zhu||Skye 268||1:00- 2:00 p.m.||Tamar Shinar||Skye 284|
|2:00 - 3:00 p.m.||Christina Vasilakopoulou||Skye 268||2:00 - 3:00 p.m.||Betul Senay Aras||Skye 284|
Friday 4:00 p.m.
Title: Symmetries of Spaces with Lower Curvature Bounds
Abstract: The classification of manifolds of positive and non-negative sectional curvature is a long standing problem in Riemannian geometry. In particular, restricting our attention to closed, simply-connected manifolds, there are no topological obstructions that allow us to distinguish between positive and non-negative curvature, that is, we have no examples of manifolds that admit a metric of non-negative curvature that do not admit a metric of positive curvature. However, with the introduction of symmetries, we are able to distinguish between these two classes. In this context, I will discuss recent joint work with Christine Escher and work with Zheting Dong and Christine Escher on non-negatively curved manifolds with abelian symmetries.
Friday 5:00 p.m.
Title: Clocks, Parking Garages, and the Solvability of the Quintic: A Friendly Introduction to Monodromy
Abstract: Imagine the hands on a clock. For every complete the minute hand makes, the seconds hand makes 60, while the hour hand only goes one twelfth of the way. We may think of the hour hand as generating a group such that when we “move” twelve times then we get back to where we started. This is the elementary concept of a monodromy group.
In this talk, we give a gentle introduction to a historical mathematical concept which relates calculus, linear algebra, differential equations, and group theory into one neat theory called “monodromy”. We explore lots of real world applications, including why it’s so easy to get lost in parking garages, and present some open problems in the field. We end the talk with a discussion of how this is all related to solving polynomial equations, such as Abel’s famous theorem on the insolubility of the quintic by radicals.
Saturday, 8:30 a.m. - Coffee and Poster Session
Saturday, 9:30 a.m. - Pure Mathematics
Jose Israel Rodriguez, University of Chicago
Title: Numerical Descriptions of Algebraic Varieties
Abstract: Numerical algebraic geometry uses numerical algorithms to study sets defined by polynomials called algebraic varieties. It does this by representing a variety by a "witness set" which can be manipulated by a computer. I will discuss witness sets and examples relevant for chemistry, biology, and statistics. A background in algebraic geometry will not be assumed.
Saturday, 9:30 a.m. - Applied Mathematics
Title: Modeling Cell Polarity in Fission Yeast
Abstract: We present a mathematical model of the core mechanism responsible for the oscillatory dynamics of a signaling molecule (Cdc42) in fission yeast. The model is based on the competition of growth zones of Cdc42 localized at the cell tips for a common substrate that diffuses in the bulk. We analyze the bifurcations as the cell length increases and total amount of molecules increases. We find that a stable oscillation and a stable steady state can coexist, which is consistent with the experimental finding that only 50% of bipolar cells oscillate. Stochastic simulations suggest that noise can destabilize a steady state and quasi-cycles exist in the parameter regime where the deterministic model has a damped oscillation.
Saturday, 10:30 a.m. - Pure Mathematics
Title: Natural Cohomology on P1 x P1
Abstract: I’ll begin with a discussion of the classification of vector bundles on P1 and explain what natural cohomology means in this context. Then I’ll consider the case of vector bundles on P1 x P1. In general vector bundles on surfaces are more complicated but a useful tool allows one to reduce many problems about vector bundles to questions of linear algebra. This is the theory of monads. I’ll discuss monads and show how they are used to prove a conjecture of Eisenbud and Schreyer about vector bundles on P1 x P1 with natural cohomology.
Saturday, 10:30 am - Applied Mathematics
Title: Development of High Order Bound-Preserving Numerical Methods
Abstract: Hyperbolic equations have wide practical applications including fluid dynamics, astrophysics, biological sciences and many other areas. High order structure-preserving numerical methods, which can preserve certain properties of the underlying models are efficient for solving such partial differential equations. In this talk, we will discuss the bound-preserving property of hyperbolic equations, that is maximum-principle-preserving property for scalar conservation laws and positivity-preserving property for hyperbolic systems such as compressible Euler equations and ideal magnetohydrodynamic (MHD) equations. The first part of the talk is about a simple sweeping technique that can be generally used to construct high order bound-preserving finite difference/volume methods and spectral methods for scalar conservation laws. In the second part, we will utilize a parametrized flux limiter to develop high order finite difference/volume WENO schemes, which hold bound-preserving property for both scalar and system cases.
Saturday, 1:00 p.m. - Pure Mathematics
Title: Deformation Theory of Conical Metrics
Abstract: The problem of finding and classifying constant curvature metrics with prescribed singularities has a long history and has seen a lot of development. I will focus on the spherical conical metrics and describe recent work, joint with Rafe Mazzeo, which gives a new and broader existence theorem and shows that the nature of the moduli space of solutions has a different nature than had perhaps been anticipated. In particular, I will describe a new geometric construction of compactified configuration spaces that will enable us to tackle the obstructed analytic problem.
Saturday, 1:00 p.m. - Applied Mathematics
Title: Fluid-Structure Interaction: Numerical Algorithms and Applications
Abstract: Fluid-structure interaction problems arise in a variety of domains, including aerospace engineering, biomedical modeling, and physics-based animation. In this talk, I will give an overview of some approaches to simulation of fluid-structure interaction problems, highlighting recent work in my group on improved partitioned methods. I will also discuss some applications of numerical methods for fluid-structure interaction to the study of biological systems
Saturday, 2:00 p.m. - Pure Mathematics
Title: Hopf and Frobenius algebras: generalizations and the Larson-Sweedler Theorem
Abstract: Hopf and Frobenius algebras are of central importance in many branches of mathematics, especially representation theory and topology. The Larson-Sweedler theorem provides conditions under which a Hopf algebra is Frobenius. In this talk, we recall the concepts of Hopf and Frobenius algebra in the classical setting of vector spaces as well in any monoidal category. We also introduce their many-object generalizations: Hopf and Frobenius enriched categories. These let us prove a many-object version of the Larson-Sweedler theorem, which generalizes the classical one from vector spaces to broader contexts.
Saturday, 2:00 p.m. - Applied Mathematics
Betul Senay Aras, University of California, Riverside
Title: The Importance of the Eggshell During Polarization in the Early C. Elegans Embryo
Abstract: Polarization, whereby molecules and proteins are asymmetrically distributed throughout the cell, is a vital process for many cellular functions. In the early C. elegans embryo the asymmetric distribution of cell cytoskeleton during the initiation of polarization leads to asymmetric contractions which are higher in the anterior and lower in the posterior of a cell. The C. elegans embryo is surrounded by a rigid body, the eggshell, which functions in numerous cell processes. We investigate the structural support of the eggshell during the establishment phase by tracking the moving cell surface using phase field method. We incorporate reaction-diffusion model of protein dynamics involved in polarization into the membrane evolution. We conclude that the eggshell might have a role in cell polarization by preventing the distortion of cell surface.


We all use several electrical appliances in our home without knowing how much electricity it will consume. But now you can calculate yourself the daily or monthly consumption of your electrical appliances and also can save energy by suitably switching off them when not in use.
(Wattage x Hours used per day) ÷ 1000 = Daily Kilowatt Hour (kWh)
1 kWh = 1 unit of consumption
Suppose a 20 watt CFL bulb is kept on for 8 hours in a day. Then the daily consumption in terms of units will be calculated as
(20 x 8) ÷ 1000 = 0.16 kWh = 0.16 unit
Similarly if a Ceiling fan is switched on for 12 hours then its daily consumption will be as follows
(75 x 12) ÷ 1000 = 0.9 kWh = 0.9 unit


i3 Grant Partnership: Creating a new model for high school STEM education
UW Today feature "Creating a new model for high school STEM education". "Rigorous studies in science, technology, engineering and math, with industry mentoring for both students and teachers, and maybe even a longer school year — these are key features of a new five-year, $4.1 million grant for the UW’s Institute for Science and Mathematics Education, Bellevue's Sammamish High School and several partner organizations.
The project is called Reimagining Career and College Readiness: STEM, Rigor, and Equity in a Comprehensive High School, and is being funded by the U.S. Department of Education’s Investing in Innovation, or i3, program. The UW institute is teaming with the Bellevue School District, the College Board, the Washington STEM Center and other organizations for the work. STEM stands for science, technology, engineering and math."


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Even those who may not be mathematically inclined or have an outright aversion to numbers and computation can take solace in the basic elegance of a two-dimensional graph representing the relationship between a pair of variables.
That additional step may be something like multiplying the variable by a certain number to get rid of a fraction in front of it.
Here is the work for this step. These documents were spliced together and then sliced into grade level standards. Because one of the variables had the same coefficient with opposite signs it will be eliminated when we add the two equations. Here is an example of a system with numbers.
Example 1 Solve each of the following systems. Let's look at an example.
Label the Axes Use a scale convenient to your equation. If fractions are going to show up they will only show up in the final step and they will only show up if the solution contains fractions.
Note as well that we really would need to plug into both equations. Continue reading for a couple of examples!
Plot the y-Intercept Draw a dot on the y-axis at the appropriate point. The graph below illustrates a system of two equations and two unknowns that has no solution: We've now seen an example of a problem where you are given the slope and y-intercept Example 1.
We will be looking at two methods for solving systems in this section. Attempting to solve gives a false statement By attempting to solve such a system of equations algebraically, you are operating on a false assumption—namely that a solution exists.
Then next step is to add the two equations together. Do not worry about how we got these values. Thus these equations are said to be inconsistent, and there is no solution. Solution by Graphing For more complex systems, and especially those that contain non-linear equations, finding a solution by algebraic methods can be very difficult or even impossible.
Sometimes we only need to multiply one of the equations and can leave the other one alone. Equations that are written in standard form: Example 2 Problem Statement. They can explain why standards are sequenced the way they are, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly knotty areas of the mathematics.
Example 2 demonstrates how to write an equation based on a graph. Let's quickly revisit standard form.
Let's take a look at another example that involves fractions. Lines do not intersect Parallel Lines; have the same slope No solutions If two lines happen to have the same slope, but are not identically the same line, then they will never intersect. The only drawback to this method is that the solution is only an approximation, whereas the algebraic method gives the exact solution.
In these cases we do want to write down something for a solution. Remember standard form is written: The slope is often called "rise over run" and is the number of unit changes in y for every single unit change in x.Are you looking for free math worksheets that will help your students develop and master real-life math skills?
The algebra worksheets below will introduce your students to solving inequalities and graphing.
The main difference between one-step equationsand two-step equations is that one more step you need to do in order to solve a two-step equation. That additional step may be something like multiplying the variable by a certain number to get rid of a fraction in front of it.
Otherwise, the rules are the same as before and these equations are just as easy to learn and solve as are the one-step ones. PatrickJMT: making FREE and hopefully useful math videos for the world!
Page 1 of 2 CHAPTER3 Systems of Linear Equations and Inequalities CHAPTER STUDY GUIDE Solving Linear Systems by Graphing GRAPHING CALCULATOR: Graphing. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you know two points that a line passes through, this page will show you how to find the equation of the line.
Free Algebra 1 worksheets created with Infinite Algebra 1. Printable in convenient PDF format.Download