|Number 20: 24/05/2003
A scientific publication by SGF and NEODyS
A rather popular word in NEO jargon is "keyhole". It was introduced by Paul Chodas to denote the following: suppose that a certain small body (a comet, an asteroid or, far more often, a small meteoroid) encounters the Earth in a certain year. It can happen that the perturbation imparted by the Earth to the small body puts the latter in a resonant orbit such that, on the same day of some later year, when the Earth is again at the same place, also the small body comes back there, and a collision takes place.
The "coming back" of the small body after a certain number of years is called a "resonant return", and the collision takes place only if the small body passes through a certain small region of the "target plane" in the vicinity of the Earth; this small region is the keyhole associated to the given impact.
Examples of keyholes can be seen on the JPL website (http://neo.jpl.nasa.gov/news/news018.html); they were computed by Paul Chodas in May 1999, when the impact possibilities of 1999 AN10 in the years following the 2027 encounter with the Earth were being analyzed.
To obtain such results one needs a state-of-the-art orbit computation program, able to take into account all the perturbations one can possibly think of, so as to compute with the highest accuracy the precise positions of the collision solutions. One wonders whether it is possible to have an idea of the location, size and shape of impact keyholes, leaving aside the achievement of great precision, in exchange of some geometric understanding. In fact, with the help of Opik's theory of close encounters, we can say a lot about location, size and shape of impact keyholes.
Let us start by discussing the location. As we said before, for a resonant return to be possible, the orbital period of the small body after the first encounter must be in a certain resonant relationship with the orbital period of the Earth: its value in years must be equal to a fraction like p/q, with p and q integer and not too large (say, up to something like 50 or so).
It turns out that, if we compute, using Opik's theory, the target plane points where the small body has to pass in order to be put by the gravitational pull of the Earth in an orbit of prescribed period, we find that these points lie on a circle, whose radius and center are simple functions of the initial orbit of the small body, and of the given period of the post-encounter orbit.
On the other hand, we know that, on the target plane, the region of uncertainty is essentially very narrow, so as to resemble a line segment. Its intersections with the "resonant" circle thus give us the locations of the keyholes; in fact, there are generally two keyholes associated to the same resonant return, and one of them is much smaller than the other, for reasons that will be clear in a moment.
We now discuss the size of keyholes, and especially why they are in most cases very small. Let us see what happens to two imaginary particles that cross the target plane of the first encounter, and let us further suppose that they are very close to each other at the beginning. As a consequence of their different positions on the target plane, between their orbital parameters after the encounter there will be slight differences; the most important of these is the one in semimajor axis, i.e., in orbital period, since it is the one that forces the two particles to become more and more spatially separated over time.
|The dotted line shows the circle, in the b-plane of the 7 August 2027 encounter of 1999 AN10 with Earth, leading to a resonant return in 2044. Units are Earth radii and the Earth is shown as a circle in the center. The continuous lines on the circle enclose the keyholes resulting in impacts on the Earth in 2044. The vertical line at about 5.8 Earth radii from the centre corresponds to the region of uncertainty.|
Thus, the recipe is the following: first, take the disk of the Earth of the second target plane and put it on the first target plane, at one of the intersections between the appropriate resonant circle and the region of uncertainty; second, squeeze the disk by the appropriate compression factor, in the direction normal to the resonant circle (i.e., radially). Voila', it's done: the keyhole resembles an extremely thin lunar crescent, lying on the resonant circle.


Thursday, June 07, 2012
Our days are numbered
No, Harold Camping isn't up to his old trick of predicting the end of the world. I was just fascinated yesterday when I noted the date was 6/6/12, because six plus six equals 12. I thought it was pretty profound and pointed it out to several of my co-workers. None of them seemed to share my enthusiasm about this phenomenon or see any significance in it at all.
Technically it isn't as impressive when you think of it as 6/6/2012, because six plus six doesn't equal 2,012 unless you were taught math in Arkansas. But 6/6/12 just reeks of profundity.
Oh, it's no 6/6/76 (which was the day the movie The Omen debuted in theaters...I saw it on that day so I know this is a fact). The movie producers were trying to play off the significance of the mark of the devil (666). They kind of glossed over the seven in 6/6/76.
I suppose you can read something in just about every date if you play with the numbers long enough. Calendars are a bit ludicrous anyway if you think about it. They are a vain attempt to quantify something infinite (time) with something finite (number of days there have been people on the planet). And the calendar we have is pretty arbitrary anyway. Who got to pick which day was 1/1/1 (which adds up to three and could therefore have religious significance...trinity an such)? I think it was Pope Gregory XIII. But who died and left him Pope? Well, technically Pius V.
But I digress.
I kind of wished I had written this on 6/6/12 instead of 6/7/12. Though six plus is 13 and 13 plus 12 equals 25. And two plus five equals seven which is today's date. Tomorrow is 6/8/12. Six plus eight equals 14. Fourteen plus 12 equals 26. And six plus two equals eight which is tomorrow's date.
I think I'm on to something.
I just can't wait until 7/5/12 when every thing adds up to 12 again. Though 12 plus 12 equals 24 and two plus four equals six which won't be the date. But six is half of 12.
Posted by Time at 3:31 PM


|ASSOCIATION CANADIENNE DES
PHYSICIENS ET PHYSICIENNES
PRESS RELEASE / FOR IMMEDIATE RELEASE
1999 CAP-CRM PRIZE
in Theoretical and Mathematical Physics
PROFESSOR DAVID J. ROWE
"I am deeply honoured to follow the four very distinguished previous winners of this award."
Ottawa, May 14th, 1999 - The Canadian Association of Physicists (CAP) and the Centre de recherches mathématiques (CRM) are pleased to announce that the 1999 CAP-CRM Prize in Theoretical and Mathematical Physics will be awarded to David J. Rowe, Professor at the University of Toronto for developing a microscopic foundation for the models and theories of nuclear collective states by the application of elegant techniques from group theory and mathematical analysis.
Together with his students and associates, Dr. David J. Rowe has been able to develop a detailed picture of important system, based on the underlying properties of the protons and neutrons that form the nucleus. In doing so, he also developed a number of new mathematical tools that have used to explain other classes of phenomena.
Rowe's research has introduced many techniques of modern mathematics into physics, a strategy that allowed him to make significant steps in the development of modern nuclear theory. Understanding the atomic nucleus has been considered an intractible problem, as it involves simultaneously describing the behaviour of hundreds of particles, all interacting strongly under the force that binds together the nucleus. Rowe's contributions have enable us to view this system as literally a fluid, albeit one with unusual properties. The mathematical techniques he has introduced have found application in many other areas of physics, especially in those cases where the underlying patterns or symmetries of the system change. Rowe's impact on theoretical physics has therefore extended far beyond the original scope of his work on the structure of the atomic nucleus.
Prof. Rowe received B.A.s in 1959 from Cambridge University and Oxford University. In 1962, he obtained his M.A. from Oxford University as well as a D.Phil (Thesis: ‘Studies of Nuclear Structure using Medium Energy Protons'). After spending a year as a lecturer at a Royal Air Force Radio School, Dr. Rowe worked as a Ford Foundation Fellow at the Neils Bohr Institute followed by a three years with the Atomic Energy Research Establishment (Harwell). He was a Research Associate at the University of Rochester from 1966-68 and joined the faculty at the University of Toronto as an Associate Professor in 1968. He became full Professor in 1974. He was elected a Fellow of the Royal Society of Canada in 1986.
Dr. Rowe has received a number of honours, including an A. P. Sloan Fellowship (1972), the Rutherford Memorial Medal (1983) of the Royal Society of Canada, Fellowship in the Royal Society of Canada (1986) and an Isaac Walton Killam Senior Research Fellowship from 1990-92.
The annual CAP-CRM Prize in Theoretical and Mathematical Physics was first introduced in 1995. Dr. Rowe will receive the 1999 Prize during the CAP's awards banquet to be held at the University of New Brunswick on June 8th, 1999.
The Canadian Association of Physicists, founded in 1945, is a professional association representing over 1600 individual physicists and physics students in Canada, the U.S. and overseas, as well as a number of Corporate and Departmental Members. In addition to its learned activities, the CAP also undertakes a number of activities intended to encourage students to pursue a career in physics.
The Centre de recherches mathématiques is a national research centre in mathematics and theoretical physics jointly supported by the federal government, the province of Quebec, and the Université de Montréal where it is based. Among the activities of the CRM are thematic years, summer schools, workshops, seminars, and the publication of monographs, proceedings, and lecture notes in mathematics and physics.
Çe communiqué est aussi disponible en français.
For more information, please contact:
Canadian Association of Physicists
Tel: (613) 562-5614 Fax: (613) 562-5615
or Centre de recherche mathématiques
Tel: (514) 343-7501 Fax: (514) 343-2254
- 30 -


Finding reliable expert help on the internet can be quite problematic because very often people claiming to be professionals end up being not able to solve even the most fundamental tasks, and of course the really tough ones. With the info available, you can calculate which loan is the ideal option for you. There are a couple terminologies which you ought to remember in knowing the forms of depreciation procedures.
Help Me Solve This Math Problem Secrets
The teachers are predicted to cover vast sums of material in a brief time period. First and foremost, maths isn’t taught strategically with a concentration. Some kids become scared when they see mathematical problems involving fractions since they’re not able to think of fast and fast means of simplifying fractions.
The Hidden Truth About Help Me Solve This Math Problem
Many different kinds of math questions and problems can be found on the internet on math help royalessays.co.uk sites. If you are you searching to find out more regarding math help geometry on-line check out our web-page. If you think an internet math problem solver is what you require, do an on-line search to acquire a list of services which you can select from.
WebMath is intended to help you solve your math issues. You’re not there to fix the math difficulties. So it is recommended to learn math in a sequential way.
The difficulty and content of the 2 sections are essentially exactly the same. Prior to taking any exam, it’s vital that you have solved lots of problems beforehand. Breathe at the start of an issue.
They need to see that they can do the work so that they can feel confident! It might be possible for some students not to find the solution in the very first, second, or even the third endeavor. Then, let they choose which one question from each task type they want to solve.
As a result of fixed center face, you just need to be worried about the remainder of the eight faces on each side. If your kid is struggling, provide them with a number line. From the start of eternity To the end of time and space To the start of every end And the end of each place.
If you do so, you won’t ever have to look for any other math word problem solver’ or some other wiring supplier. The exercises accelerate the cognitive retrieval and one is equipped to rapidly pick the most proper technique. The tape diagram is a good tool for building that understanding.
Help Me Solve This Math Problem – Overview
There’s no expert course on earth that may be completed without involving maths in it. Our experts will supply you with clear step-by-step calculations, thus providing you with a pretty great idea of the way the task was solved and making it really easy that you explain it to your fellow students. In reality, even individuals who aren’t in college may benefit from learning mathematics as it makes a more broad-minded individual.
Calculus is an important portion of mathematics. Equations are useful to fix our everyday life issue. It intimidates many people, but algebra is nothing more than an extension of the basic arithmetic you use every day.
Solving multiplication problems won’t be an issue anymore! Other variables could be involved also. You are able to try out the a variety of methods in heuristics math.
Using Help Me Solve This Math Problem
The job is to make a compressed archive of a specific 100MB file smaller than ever before as a means to create new compression algorithms. With each iteration, the procedure is enriched. If one chooses to fix a problem in any of Math areas, he’s got to go through it in a detailed manner and discover out solution with no doubt about the issue.
After you determine the issue, you can establish the unit of measurement for the last answer. You’ll frequently be directed to evaluate a specific function for a particular value of x. As you see now, calculating percent difference is quite a simple undertaking, as long as you just keep in mind the formula, which again, isn’t a really complicated endeavor either!
A great deal of students who are a bit confused by math see word troubles and just guess what things to do without the checking and refining part. Consequently, math word problems are an excellent approach to emphasize the value of math in everyday life. If you don’t have plenty of time left before test day, but don’t quit!
After you determine the issue, you can establish the unit of measurement for the last answer. The ratio of a single quantity to another can readily be become a proportion by multiplying both regions of the ratio by the very same number, and then setting the 2 expressions to be equal. To seek out the an elaborate function limit is needed with the assistance of limits an intricate function can be broken into small pieces.
It is clear that they’re not asking sincerely. Your work is to receive hundreds or thousands of individuals solving math difficulties, and you’ve got in order to easily and effectively communicate why something is important before anyone will be considering the weeds of the company.
The Bizarre Secret of Help Me Solve This Math Problem
As an example, for primary and middle school students there are 1st grade math complications, 2nd grade math issues, 3rd grade math issues, 4th grade math issues, 5th grade math complications, 6th grade math issues and 7th grade math troubles. The capability to understand Math problems in a course room environment can be challenging for Math anxious students. By the way, you’re not learning math to attend a college.
Bearing that in mind, here are a few ideas for new year’s resolutions which can help you turn into an even greater engineer in 2018. Our experts will supply you with clear step-by-step calculations, thus providing you with a pretty great idea of the way the task was solved and making it really easy that you explain it to your fellow students. In reality, even individuals who aren’t in college may benefit from learning mathematics as it makes a more broad-minded individual.
Top Help Me Solve This Math Problem Secrets
It’s possible for you to practice 20 questions daily free of charge. What’s more, there aren’t any answer explanations, which makes it tricky to figure out how to locate the correct answers for math questions that you get wrong. You will receive the answer, 16100.


The mathematics of poker by bill chen
The Mathematics of Poker by Bill Chen is considered by a fair amount of people to be one of the standards, it's very deep though. I haven't read ...
by Bill Chen and Jerrod Ankenman ... Applying the tools of computer science and mathematics to poker and sharing the information across the Internet, these ... Poker Mathematics | Using Math In Poker - The Poker Bank A quick overview of the mathematics that can be used during poker to help you ... mathematics, look no further than The Mathematics of Poker by Bill Chen . Jerrod Ankenman - Poker Training | Coach | IveyLeague.com In 2006, Jerrod co-authored The Mathematics of Poker with Bill Chen. The book is an introduction to game theory and quantitative techniques as they relate to ... Learning the math of poker - Learning Poker - CardsChat™
Книга The Mathematics of Poker (Bill Chen, Jerrod…
The Mathematics of Poker by Bill Chen and Jerrod… A book review of the Mathematics of Poker by Chen and Akenman.Chen and Ankenman have created a unique text, one that deals far more with a meta approach to the game of poker from a mathematical perspective and offers very little in the way of traditional, scenario-focused advice. The Mathematics of Poker by Bill chen and... | Cool … This book provides an introduction to the quantitative techniques as applied to poker and to a branch of mathematics that is particularly applicable to pokerBill chen and Jerrod Ankenman do a terrific job explaining how math can, amoung other things, show you exactly how to mix up your play in such a...
Review "For those who think poker math is only about probability, pot odds, and straightforward, rote play, think again. Chen and Ankenman do a terrific job explaining how math can, among other things, show you exactly how to mix up your play in such a way that even champion players cannot get the best of you.
Chen holds a Ph.D. in mathematics (1999) from the University of California, Berkeley. He was an undergraduate at Washington University in St. Louis triple-majoring in Physics, Math, and Computer Science, and was also a research intern in Washington University's Computer Science SURA Program where he co-wrote a technical report inventing an Argument Game. Top 100 Poker Books for Texas Holdem: Places 11 to 20 12. The Mathematics of Poker. by Bill Chen, Jerrod Ankenman. Poker has been dominated by players who have learned the game by playing it, people who cultivated an intuition for the game and are adept at reading other players’ hands from betting patterns and physical tells. The Mathematics Of Poker by Bill Chen - Booktopia "For those who think poker math is only about probability, pot odds, and straightforward, rote play, think again. Chen and Ankenman do a terrific job explaining how math can, among other things, show you exactly how to mix up your play in such a way that even champion players cannot get the best of you. Chen Formula - The Poker Bank
Book Review: The Mathematics of Poker – Thinking Poker
The Mathematics of Poker - Bill Chen.pdf磁力链接种子下载 The Mathematics Of Poker, Book by Bill Chen (Paperback) | chapters.indigo.ca Buy the Paperback Book The Mathematics Of Poker by Bill Chen at Indigo.ca, Canada's largest bookstore. + Get Free Shipping on Entertainment books over $25!
- Gala casino leeds poker results
- No deposit min payout 1 cent casino online
- 21 black jack online cuevana
- Colt inn casino battle mountain nv
- Free sea monkey slot machine
- Woman wins 8.5 million casino refuses to pay
- Free slot games 4u
- Pitch black x jack frost lemon
- Sac roulette reine des neiges
- 888 poker bonus 8 dolares
- Club 23 crown casino location
- Blazing sevens slot machine free
- Free bingo games online no download
- No deposit casino bonus codes cool cat casino
- Ni hao holland casino groningen
- Free slots las vegas
- Deposit dewa poker lewat hp
- Pokerstars european poker tour london
- Belterra casino group bus rates & bonus


Core Maths for Advanced Level [L. Bostock, S. Chandler] on * FREE* shipping on qualifying offers. Colour has been included to highlight all key concepts and formulas and enhance the illustrations. Summary sections have been extended to provide additional examination practice and preparation. Summaries. Buy Core Maths for 'A' Level on ✓ FREE SHIPPING on qualified orders. Buy Core Maths for Advanced Level 3rd by L Bostock, S Chandler (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders.
Core Maths for 'A' Level | L. Bostock, S. Chandler | ISBN: | Kostenloser Versand für alle Bücher mit Versand und Verkauf duch Amazon. This third edition takes this crucial information and incorporates it into a student- friendly format that focuses on the core concept of human genetics. Each chapter uses the same problem-based approach as the previous editions, and addresses the important role of genetics and disease by integrating molecular and clinical. Core Maths for Advanced Level has 33 ratings and 4 reviews. Written by the renowned author team of Bostock and Chandler, this best-selling textbook cover.. .
1 Nov Written by the renowned author team of Bostock and Chandler, this best-selling textbook covers all major A Level Mathematics specifications. Suitable for all points of entry to Advanced Level with appropriate supporting material in the early sections of the books. Each chapter contains a variety of exercises. 22 Jan Core mathematics for advanced level - Functions. Sarah Sue Calbio. Bostock and Chandler chapter3 functions. Sarah Sue Calbio. matemáticas puras understanding-pure-mathematics. Fernando Espinoza Camargo. Chapter 1 representation and summary of data & ANSWERS. Sarah Sue Calbio. Chapter. This third edition of Core Maths for Advanced Level has been extensively revised to cover the pure mathematics for AS of Edexcel Foundation (Edexcel). Oxford, Cambridge and RSA Examinations (OCR). Assessment and Qualifications Alliance (AQA). Welsh Joint Education Committee (WJEC). L. Bostock. S. Chandler.


These Are The Odds Of Being Dealt a Royal Flush in Poker - Curiosity Jul 20, 2016 ... When you sit down to a game of Texas Hold 'Em, what are the odds you'll get a royal flush on the flop? Each hand in Hold 'Em is some ... Texas Hold'em Odds - Poker Odds - Tight Poker A guide on calculating odds in texas hold'em poker. ... You should at least call on the flop any time the pot odds are offering you greater odds than the odds that ...
If you've got a flush draw (one card short of a full flush) after the flop, you'll make your hand 34.97% of the time. That's just over a third.
The odds of flopping one are one in 649,740. Of course the odds of making one by the river are better since you are making a five card hand from a possible seven cards. On th 16th of last month I was playing in an ultra low stakes cash game (25c/50c NL), while I was waiting for a tournament to start. Poker Math & Probabilities (Texas Hold'em) Poker Math & Probabilities (Texas Hold'em) The following tables provide various probabilities and odds for many of the common events in a game of Texas hold 'em. Odds % Example Win % 330-to-1 0.30% JJ v 77 80% v 20% ... Two suited cards will flop a flush Two suited cards will make a flush by the river The Probability that.... Straight Pair What Are the Odds? A List of Long-Shot Odds in Texas Holdem As a matter of fact, if two players start out with two suited cards of the same suit, the odds of both flopping a flush are not as small as one might think. Once every 206 attempts the flop will show three cards of the same suit.
Playing the flop tips. Don't get attached to weak flush and straight draws. Make continuation bets regularly. Don't be afraid to bet with strong hands right away – no need to wait for the turn. Consider using the float play if you know how. You have time to make your decision, so use it. There's no need to rush. Playing the flop overview.
Playing Flush And Straight Draws | Texas Hold'em Watch SplitSuit's video on Flushes and Flush Draws for 8 hand histories involving strategy on playing flushes in Texas Hold'em. You are on the flop with a pretty decent flush draw.Pot odds will tell you whether or not to call certain sized bets to try and complete your flush or straight draw. Holdem odds royal flush | Safe gambling on the Internet Texas Hold'em Poker Odds & Probabilities. What are the odds of a royal flush in texas holdem? Would you like to merge this question into it?It's easier to flop a straight flush with JTs than it is with J7s. This question has been asked and answered on the internet about a thousand times. How to Play Texas Hold'em Poker | Rules & Terms | Pala… Texas Hold’em Poker is a community card game that can be played with 2-10 players. Learn the rules for Texas Hold’em Poker and get your winningHold ’em consists of two cards (“hole cards”) being dealt face down to each player and then five community cards being placed face-up by the dealer — a...
Probability of flopping straight flush. the odds of flopping a straight flush are: 1 in ( Joining and rejoining a texas holdem poker game that is already in.Learning how to properly count your outs and calculate poker odds is a fundamental requirement of Texas Hold'em. While the math used to...
In poker, what are the odds of flopping a straight flush with ... In poker, what are the odds of making a royal flush after the flop in Texas Hold 'Em? What equation gives me the probability to get a flush in a Texas holdEM poker? What's so special about getting 2:1 odds pre-flop in poker? Poker Odds - HomePokerGames.com Here, I calculate the odds of NOT flopping a set and subtract it from 100%. To calculate the odds of not flopping a set, all the cards on the flop can't have the same rank as your pocket pair. For the first card there are 48 out of 50 cards that won't hit your set. Pyroxene’s Common Flop Odds | Flop Turn River
Poker Drawing Odds & Outs | Pokerology.com
Here, I calculate the odds of NOT flopping a set and subtract it from 100%. To calculate the odds of not flopping a set, all the cards on the flop can't have the same rank as your pocket pair. For the first card there are 48 out of 50 cards that won't hit your set. Pyroxene’s Common Flop Odds | Flop Turn River Pyroxene’s Common Flop Odds. ... Holding two unsuited cards and flopping a four flush. ... FTR is your home for Texas Holdem Strategy, ... Basic Poker Odds | Flop Turn River After the flop, the decisions in Texas Holdem get a bit tougher. Understanding pot odds will help determine your best action from here. Check out our Texas Hold’em Pot Odds article to learn more about pot odds, what pot odds are, calculating your pot odds, implied odds, etc. You can also view our Texas Hold’em Pot Odds Chart here.
Odds Of Flopping Flush In Holdem - Spielbank Wiesbaden 845 odds of flopping flush in holdem countrylink timetable casino to sydney Re: About That Royal Flush The ins and outs of that most elusive of hands By Henry Tamburin Do you have a comment or question about this article? Slotzinnen Voor Zakelijke Brief Aug 2011 Posts:The poker odds chart below shows the probabilities of obtaining various .. Strategy: Probabilities in Texas Hold'em - PokerStrategy.com In the case of Texas Hold'em, there's the 2 pocket cards and 5 on the board. This way of working out the probabilities would be the more accurate way - however, just to note, the probabilities worked out on 5 of 52 are practically the same, and far easier to calculate. Odds of straight or flush draw on flop - Learning Poker Odds of straight or flush draw on flop. $5 NLHE Full Ring: Nut Straight Vs. In this case, Google (or whatever search engine you prefer) is your friend. I put in "odds of making a straight in texas holdem" and got plenty of links to figure these out. Odds of flopping a flush is 118:1 or about 0.8% and odds of flopping a straight can be a bit higher (but not by so much). Odds Of Flopping a Flush In Texas Holdem - martinval.com


Youth Guitar Classes
Our youth guitar classes are designed to teach young children the basics of chord construction, proper fingering technique and strumming rhythm patterns to build a foundation for learning guitar. Our teachers utilize games and other fun activities to make learning fun and effective. Students experience immediate success which boosts their confidence and inspiring further exploration.
6 Benefits of Music Lessons
1.) It improves academic skills.
Music and math are highly intertwined. By understanding beat, rhythm, and scales, children are learning how to divide, create fractions, and recognize patterns. It seems that music wires a child's brain to help him better understand other areas of math, says Lynn Kleiner, founder of Music Rhapsody in Redondo Beach, CA. As kids get older, they'll start reciting songs, calling on their short-term memory and eventually their long-term memory. Using a mnemonic device to do this is a method that can later be applied to other memory skills, says Mary Larew, Suzuki violin teacher at the Neighborhood Music School in New Haven, Connecticut. Musical instrument classes also introduce young children to basic physics. For instance, plucking the strings on a guitar or violin teaches children about harmonic and sympathetic vibrations. Even non-string instruments, such as drums and the vibraphone, give big kids the opportunity to explore these scientific principles.
Parents Magazine - By Angela Kwan


Junior Maths Competition 201802 May 2018
Irish Junior Maths Competition Success
Congratulations to First Year student Emilie Borowski on coming third in the regional final of the Irish Junior Maths Competition held here in Cashel Community School on Friday evening April 27th. This event is a national competition organised annually by the Irish Maths Teachers Association and is open to all first year students. Eleven students from Cashel Community School qualified for this final. This is a great achievement for Emilie and for all eleven students on reaching the final – well done to everyone.


What Is Volumetric Weight Volume Calculator
Volumetric weight refers to the overall size of a parcel and is measured in volumetric kilograms. Volumetric weight can be calculated by multiplying the length, width and height of a parcel (in cm) and dividing that figure by 5000 (some carriers use a divisor of 4000).
You may often find that the price of your shipment is dictated by the volumetric weight of your parcel(s) rather than the physical weight. This is because our pricing is calculated based on whichever is the greater out of the volumetric weight and the physical weight.
For example, you could have a box of feathers that is quite large, say 100 cm X 50 cm X 50 cm but is relatively lightweight at 5kgs. Using the above calculation (length X width X height / 5000), the volume of this parcel is 50 volumetric kilograms. As the volume 'outweighs' the physical weight of 5kgs, the price is based on 50 kilograms. For this reason, it is extremely important to measure parcel(s) their widest, longest and highest points. Any bulge handles, tags or packaging that could break the beam of a measuring laser must be included.
It's worth noting that it works the other way around too. You could have a small box of heavy metal components (30 cm x 30 cm x 20cm) weighing 10kg in physical weight. The volume of this parcel is 5.4kgs. So in this instance, the volumetric weight is lower than the physical weight meaning that the price would be calculated at 10kg.


In the first post, we took a look at the types of machine learning (ML) algorithms. First one was the supervised learning. When we think the word supervise, we guess that we’ll use a data which is identified and separated properly (we know what result we get when we give specific input) to create a model. Some examples of supervised learning can be house prediction problems, understanding a handwritten text, spam mail detection. There are various algorithms in supervised learning. But as the first thing in supervised learning, we’ll start with Linear Regression.
Linear Regression (LR) is a basic statistical method which applies a linear function to data and predicts a scalar value. Commonly used example of this method is predicting house prices.
Why do we use Linear Regression
First, we want to predict in a better way, by looking at the data and approaching in a statistical way. Second, when there is a change in our feature, we want to know what will be the outcome. Lastly, for summarizing the data. Instead of dealing with all the data, we want to create a linear function to define a correlation between feature and output.
As a simple example of a linear function, we’ll use the following equation:
Let’s split this equation into the parts and check one by one. w is called a weight/parameter. x is the input/feature and b is the bias.
Parameters are the values that control the behavior of the system. In machine learning, they are mostly called weights because the value of the parameters affects the system. So, an increase in the specific part of the weight vector increases the effect of that part on the prediction. And also, a decrease in a specific part of the weight vector decreases the effect of that part on the prediction. When the amount of the weight value is huge, it has a greater effect on the prediction. If it’s zero, there is no effect.
Inputs or generally called features in ML are the values which represented by x in our equation. Features are the direct affecting values in our function. For example, if we would like to predict house prices, our features can be the number of rooms, size of the house and age. We’ll predict the price of a house by looking into those features with help from our parameters.
Bias is generally included in the definition of parameters. This is another value we would like to estimate. We can think of this value as the representation of our estimates when all features are equal to zero. In ML, we would like to learn weights and bias so-called parameters of our model (for now, linear regression function).
There are two types of Linear Regression, simple (univariate) and multiple (multivariate). We’ll define the general rules and strategy of linear regression mainly under linear regression for simplicity now. Then, we’ll focus on the multiple linear regression based on the learnings in here. In simple linear regression, we have only one feature. We can think the price of the house is only dependent on the size of the house. So, we only care about one feature. This is why it’s called simple.
The red dots in the graph above represents our data set. Let’s guess some parameters and bias and draw our linear line into our data set like above. This seems like a pretty good guess when you think the whole data. But we will have errors shown with gray vertical lines in the graph. Those errors are our cost of not being able to fit all the data. So, every approach will come with a cost and we’ll measure our prediction’s performance according to the cost.
Cost/Error Function (measuring the performance)
As we said, we are using the cost function to measure the performance of the model. But how do we calculate the error in general? As stated in the graph as gray vertical lines, the difference between actual value and the predicted value gives the error. By calculating the error we can measure the accuracy of our prediction function. After finding the error, our main idea will change and we’ll try to choose the parameter (w) and bias (b) values so that our cost will be minimum. Calculating the error comes from the simple mathematical approach; calculating the distance between two points. Therefore, we’ll use mean squared error.
We can see in the formula that we subtract the actual value from the predicted value. And we take squares to get rid of negativity. Lastly, we take the average of our error in the whole of our data set. So, this measures the error. When the y^and y are equal, the error will be 0. When the Euclidian distance between predicted value and actual value increases, the error increases as well.
Now, we have our model (or hypothesis) and we have a way of measuring how well it fits into the data. Next, we need to estimate parameters w and b to decrease the cost. Machine learning and deep learning is based on minimizing the cost with different approaches. We hear the terms like curve fitting, global minimum in the curve many times. It comes from the error function. As we saw above the error function takes squares to get rid of negativity. So, if we try to draw the graph of error function it will be in a curve shape (in simple linear regression case, parabolic). Finding the minimum point of a curve is the main idea.
What do you think about linear regression? Have you tried linear regression before? What advantages can you get using it? Let know your thoughts, comments or feedback on Twitter @candosten.


sGrapp: Butterfly Approximation in Streaming Graphs
This paper studies the fundamental problem of butterfly (i.e. (2,2)-bicliques) counting in bipartite streaming graphs. Similar to triangles in unipartite graphs, enumerating butterflies is crucial in understanding the structure of bipartite graphs. This benefits many applications where studying the cohesion in a graph shaped data is of particular interest. Examples include investigating the structure of computational graphs or input graphs to the algorithms, as well as dynamic phenomena and analytic tasks over complex real graphs. Butterfly counting is computationally expensive, and known techniques do not scale to large graphs; the problem is even harder in streaming graphs. In this paper, following a data-driven methodology, we first conduct an empirical analysis to uncover temporal organizing principles of butterflies in real streaming graphs and then we introduce an approximate adaptive window-based algorithm, sGrapp, for counting butterflies as well as its optimized version sGrapp-x. sGrapp is designed to operate efficiently and effectively over any graph stream with any temporal behavior. Experimental studies of sGrapp and sGrapp-x show superior performance in terms of both accuracy and efficiency.
Sheshbolouki, Aida, and M. Tamer Özsu. "sGrapp: Butterfly Approximation in Streaming Graphs." arXiv preprint arXiv:2101.12334 (2021).
Read the paper (Will update the most recent version soon)
Delightful Event: sGrapp is accepted to appear in ACM Transactions on Knowledge Discovery from Data!
EIC comment: "The paper discusses butterfly formation in graphs. A very well written paper that is a pleasure to read. Some minor changes are suggested"
Emergence of Global Synchronization in Directed Excitatory Networks of Type I Neurons
The collective behaviour of neural networks depends on the cellular and synaptic properties of the neurons. The phase-response curve (PRC) is an experimentally obtainable measure of cellular properties that quantifies the shift in the next spike time of a neuron as a function of the phase at which stimulus is delivered to that neuron. The neuronal PRCs can be classified as having either purely positive values (type I) or distinct positive and negative regions (type II). Networks of type 1 PRCs tend not to synchronize via mutual excitatory synaptic connections. We study the synchronization properties of identical type I and type II neurons, assuming unidirectional synapses. Performing the linear stability analysis and the numerical simulation of the extended Kuramoto model, we show that feedforward loop motifs favour synchronization of type I excitatory and inhibitory neurons, while feedback loop motifs destroy their synchronization tendency. Moreover, large directed networks, either without feedback motifs or with many of them, have been constructed from the same undirected backbones, and a high synchronization level is observed for directed acyclic graphs with type I neurons. It has been shown that, the synchronizability of type I neurons depends on both the directionality of the network connectivity and the topology of its undirected backbone. The abundance of feedforward motifs enhances the synchronizability of the directed acyclic graphs.
Ziaeemehr, Abolfazl, Mina Zarei, and Aida Sheshbolouki. "Emergence of global synchronization in directed excitatory networks of type I neurons." Scientific reports 10, no. 1 (2020): 1-11.
Synchronization is a phenomenon that occurs in systems of interacting units, and is widespread in nature, society and technology. Recent studies have enlightened us regarding the interplay between synchronization dynamics and interaction structure. However, most of these studies neglect that real-world networks may actually be directed and disconnected. Here, we study the synchronization of directed networks with multiple leaders using the Kuramoto model. We found that in networks with high driving strength, the steady-state frequency of each node is determined by the linear combination of leaders' natural frequencies, with structural coefficients that can be calculated using the eigenvectors of a network Laplacian matrix corresponding to zero eigenvalues. The steady-state frequencies of the nodes following multiple leaders are not fixed and have sharp peaks between consecutive time instances where leaders meet each other in the phase circle. The results suggest a new way of understanding how leadership style influences the synchronization dynamics of directed networks.
Sheshbolouki, Aida, Mina Zarei, and Hamid Sarbazi-Azad. "The role of leadership in the synchronization of directed complex networks." Journal of Statistical Mechanics: Theory and Experiment 2015, no. 10 (2015): P10022.
Are Feedback Loops Destructive to Synchronization?
We study the effects of directionality on synchronization of dynamical networks. Performing the linear stability analysis and the numerical simulation of the Kuramoto model in directed networks, we show that balancing in- and out-degrees of all nodes enhances the synchronization of sparse networks, especially in networks with high clustering coefficient and homogeneous degree distribution. Furthermore, by omitting all the feedback loops, we show that while hierarchical directed acyclic graphs are structurally highly synchronizable, their global synchronization is too sensitive to the choice of natural frequencies and is strongly affected by noise.


Dr. Fidel Gonzalez Department of Economics and Intl. Business Sam Houston State University 2 OPPORTUNITY COST MARGINAL ANALYSIS Elasticity Elasticity SUPPLY DEMAND MARKET EQUILIBRIUM CONSUMER SURPLUS PRODUCER SURPLUS AND TOTAL SURPLUS MARKET EFFICIENCY MARKET FAILURE Pigouvian Taxes Quotas Coase Theorem Command and control TAXES EXTERNALITIES PUBLIC GOODS COMMON GOODS ARTIFICIALLY SCARCE GOODS GAME THEORY 3 Opportunity costs and gains from trade The economic problem is a problem of scarcity and equity. Scarcity refers to the fact that we have a lot of desires and a finite number of resources. This topic talks about scarcity and introduces some important concepts. In particular we will talk about 1) Slope and equation of the line 2) Opportunity cost 3) Production possibilities frontier 4) Efficiency 5) Absolute and comparative advantage 6) Terms of trade 4 Opportunity costs I will explain this concepts using an example Consider Rob who lives in a desert island. For survival Rob can collect coconuts (C) or bananas (B) If he spends the whole day working he can collect EITHER 8 coconuts and 0 bananas (if he spends the day collecting only coconuts) OR 0 coconuts and 10 bananas (if he spends the day collecting only coconuts) Note that he is can NOT collect 10 coconuts and 8 bananas that is impossible. 5 So what is the scarce resource In this case time is scarce there is a fixed number of hours. If there were more hours then Rob will work longer and obtain more coconuts and bananas. Next I will graph the options for Rob. This point represents zero bananas and eight coconuts. C 8 This point represents 10 bananas and zero coconuts. 10 B 6 Now we allow Rob to collect any linear combination of the two point in the previous graph. Hence I can draw a straight line between the two points and any point on the line will be feasible. Why we allow Rob to have a linear combination and not some other kind We do this to keep things simple. We will relax this assumption later on. C For example before only the y and x-intercept were possible but now Rob can collect 4 coconuts and 5 bananas. Any point on the line. 8 Next lets obtain the slope of the line and the equation of the line (PLEASE refer to the power point presentation on how to do this). 4 5 10 B Slope -8/10 0.8 Equation of the line in a general form is y slopex y-intercept In this case C -0.8 B 8 7 The equation of the previous line is very useful because it gives me all the possible combinations of C and B that are feasible (that is the all possible points on the line). For example if B1 then C 7.2 B6 then C5.2 B4 then C4.8 Imagine that Rob decides to collect the following C8 and B 0 Eating only coconuts is very boring so Rob decides to eat one banana now we have the following C -0.8 (1) 8 7.2 Hence C7.2 and B1 Note that in order to increase bananas by one unit Rob has to reduce his consumption of coconuts by 0.8 (from 8 to 7.2 coconuts) C 8 10 B What if C4.8 and B4 and Rob decides to increase bananas by one unit then now he will have C-0.8(5) 8 4 that is C4 and B5 8 In every single case in order to increase the amount of bananas Rob has to give up 0.8 coconuts. This is the idea behind opportunity cost. The opportunity cost is the is the value of the best alternative to any choice. In our example the opportunity cost of one extra banana for Rob is 0.8 coconuts. Note that there is a relationship between opportunity cost of one banana and the slope of the line in the previous graph. In both cases we measure how much of C decreases when B goes up by one unit. Actually the absolute value of the slope is equal to the opportunity cost of one extra unit of B in terms of C. First why did I say the absolute value Because the slope in the graph is negative -0.8. The opportunity cost is not negative. Hence I need to take the absolute value of the slope. Remember that the absolute value of any number is the positive value of the number. The absolute value is denoted by . For example the absolute value of -10 is 10 the absolute value of 10 is also 10. Think of it as the positive version of any number. Using the notation -10 10 -5 5 6 6 etc. 9 In general the opportunity cost of one extra unit of the variable in the x-axis is equal to the absolute value of the slope in terms of the y variable. In our previous example The opportunity cost of one extra unit of B slope of C The opportunity cost of one extra unit of B 0.8 of C We have not talked about the opportunity cost of coconuts. Lets use the equation of the line first Start at B10 and C0 now increase C by one unit and obtain the value of B 1 -0.8 B 8 -7 -0.8B B 8.75 B decreased by 1.25 units What if B 4 and C4.8 increase C by one unit and obtain B 5.8 -0.8 B 8 -2.2 -0.8 B B 2.75 B decreased by 1.25 units 10 That is in order to get an extra unit of C Rob has to give up 1.25 units of B. That is the opportunity cost of one extra unit of C is 1.25 units of B. Notice the 1.25 is the inverse of the slope. That is In general the opportunity costs of one extra unit of the variable in the y-axis is equal to the inverse of the absolute value of the slope in terms of the variable in the x-axis. In the Rob example 11 Production Possibilities Frontier Now assume that Rob gets tired as the day passes by. In the morning Rob is very productive however in the afternoon Rob is not very productive because he is tired. These are Robs new options In the morning 3C and 0B or 0 C and 6 B In the afternoon 5 C and 0B or 0 C and 4 C We can graph the previous information C Afternoon Slope-5/4-1.25 Morning Slope-3/6-0.5 C 5 3 6 4 B B 12 Combining the morning and afternoon graph into one graph C C Morning Slope-3/6-0.5 Afternoon Slope-5/4-1.25 5 3 6 C C 4 B 8 Morning Slope-3/6-0.5 3 5 Afternoon Slope-5/4-1.25 6 10 B 13 Note that the slope changes from the morning to the afternoon. In fact the slope gets flatter. This means that the opportunity cost of B increases from morning to afternoon. In other words B is getting more expensive in the afternoon. The opposite is happening to C it is getting cheaper from morning to afternoon. Morning Slope-3/6-0.5 C 8 Afternoon Slope-5/4-1.25 5 B 10 6 Now imagine that we can reduce the day not in two parts but in milliseconds. In that case the previous graph will be a curve C 8 The slope of the curve on the left is always changing. The slope starts from almost zero at the origin and gets steeper and steeper and B increases. In other words the opportunity cost of B increases as we have more of B. B 10 14 The line that shows all the maximum different possible production combinations is called the production possibilities frontier (PPF). The production possibilities frontier can be a straight line or a curve like in the previous graph. If the PPF is a straight line the slope dos not change along the line and the opportunity cost is also constant. If the PPF is curved like in the last graph then the slope increases as the variable in the x-axis goes up. That means that the opportunity cost of the variable in the x-axis increases In the graph on the left you can see that a change in the x variable when y is big produces a very small decrease in the y variable. However the same change in x when y is big produces a large change in the y variable. That is in order to obtain the same extra x you give up of y when y is higher. Q Why does this happen Imagine that y is the amount of computers produced and x is the amount of car (see graph in the next) y x 15 Computers When we produce a lot of computers we have resources that are specialized (cars engineers) and non-specialized resources (assemblers). When we increase the production of cars most of the non-specialized resources moves to the cars industry. Why Because they have skills that can be used in either industry. Since most of the specialized computer workers stays in the computer industry then the drop in the production of computers does not change that much. If we continue increasing the production of cars we will be taking more and more specialized computer workers into car production. Therefore the production of computers will drop more and more. Cars At the end we will be transferring very specialized computer workers into the production of cars and the production of computer will drop significantly. 16 Computers C We want to know if point on the PPF are efficient. First we need to defined what is efficiency. We will use the definition Pareto efficiency (Pareto was an Italian economist) We say that an allocation is efficient if in order to make someone better of we have to make someone else worse off. In terms of the PPF we say that an allocation is efficient if in order to increase the production of one good I have to reduce the production on another good. B A PPF Cars The point A is below the PPF this means that we can increase the production of both goods at the same time so this is clearly and inefficient point. Allocations below the PPF are inefficient. The point B is efficient because in order to increase the production of any good we have to reduce the production of the other good. Any allocation on the PPF is efficient. No single allocation on the PPF is more efficient the others they are all equally efficient. The point C is above the PPF this means that this point is not feasible. We would like to produce at point C because it represents higher production but our resources are not enough to reach it. Allocations above the PPF are desired but unfeasible. 17 Trade Lets go back to our previous example with Rob and assume the PPF is a straight line. So far we have Rob is alone in the island. Because Rob has nobody to trade with everything that he produces he has to consume it. That is in the absence of trade production equals consumption WITHOUT TRADE PRODUCTIONCONSUMPTION Now Sam appears in the island too. There are only Rob and Sam in the desert island. Sam can collect 12 coconuts and 0 bananas OR 0 coconuts and 4 bananas Graphing Sams production possibilities frontier C 12 Slope -12/4 -3 PPF 4 B 18 Hence The opportunity cost of 1 B 3 C The opportunity cost of 1 C 1/3 C Now imagine they do not trade and each produce the following Rob decides to produce 5 B and 4 C Sam decide to produce 2 B and 6 C World Production and Consumption without Trade Total World Production of B is 7 and C is 10 19 Graphing the information in the table we obtain the PPF for Rob and Sam Sam Rob C C 12 8 6 4 2 4 B 5 10 B Remember that because there is not trade their production possibilities frontier also dictates how much they can consume. None of them can consume above their PPF when there is not trade. However they would like to consumer above their PPF. Both of them will enjoy to consume more of both goods. Remember points above PPF are desired but unfeasible without trade. 20 Before we move one we need to have some definitions. Absolute Advantage someone has an absolute advantage if he is able to produce more of a good or service with the same amount of resources. In our previous example Sam has an absolute advantage in the production of coconuts and Rob has an absolute advantage in the production of B. Comparative Advantage someone (or a country) has an comparative advantage in the production of a good or service if it has a lower opportunity cost than the other person (country) in the production of that good or service. In our previous example Rob has a comparative advantage in the production of bananas (its opportunity cost of one B is 0.8 C which is lower than Sams 3 C). Sam has a comparative advantage in the production of coconuts (its opportunity cost of one C is 1/3 which is lower than Sams 1.25 C). The concept of comparative advantage is key to understand trade. Having a comparative advantage in the production of a good means that it is cheaper for that person to produce the good. It is cheaper in the sense that the person has to give up less of the other good. That is for Rob is cheaper to produce bananas (in terms of the coconuts he has to give up) and for Sam is cheaper to produce coconuts (in terms of the bananas he has to give up). 21 Assume each person specializes in the production of the good in which they have a comparative advantage. In the example Sam will specialize in coconuts and Rob will specialize in bananas. The following table shows the new world production World Production with Specialization We have just showed the power of specialization based on comparative advantage. Comparing the world production with and without specialization we can see that the world production with specialization increase the total production of B by 3 units and the total production of C increases by 2 units. The theory of comparative advantage tell us that total production will increase if producers specialize in the good in which they have a comparative advantage. Because no one can have a comparative advantage in all goods 22 However with specialization the production is not equal to production. Part of the production is consumed by the producer and the rest is traded for other goods. WITH SPECIALIZATION (OR WITH TRADE) CONSUMPTION PRODUCTION Once Rob and Sam specialize in the production of B and C respectively they have to trade. The question now is What is the price at which they will be willing to trade In other words how many C for B are they willing to trade. This price is called terms or trade. Rob will love to have a price of 1 B for 12 C clearly Sam will not want this. Sam will love to have a price of 1C for 10 B but Rob will not like it. So what kind of price is Rob and Sam willing to accept 23 Lets start with Rob Rob can do two things 1) he can not specialize and trade with himself or 2) specialize and trade with Sam. If Rob does not specialize he is fact trading with himself and the price he is paying is his opportunity cost. For example imagine that Rob is producing 5 bananas and 4 coconuts. He now wants to have another coconut. He can figuratively trade with himself he will do that by increasing the production of coconuts by one. But this requires that he lowers the production of bananas by 1.25 bananas. In fact he has traded 1 coconut for 1.25 bananas with himself. The opportunity cost is the price of trading with himself. Rob will accept any price that is better than the price of trading with himself. In other words we will accept any price that is better than his opportunity cost. A good to see this is by using a number line. We will use the number line that you used in kindergarten. The number line goes from left to right and increases from zero to infinity 0 24 I will show the opportunity cost in the number line. Robs opportunity cost 1C 1.25 B Next put C on the other side Now graph 1.25 B/C in the number line B/C 0 1.25 We know that Rob has bananas and wants coconuts so he will love to have a price of very few bananas for a lot of coconuts. When B is low and C is high then B/C will be a low number. That is Rob prefers small B/C. This implies that Rob will be better off compared to trading with himself to the left of the opportunity cost. For example if the price happens to be 0.5 bananas for 1 coconut Rob will be better off because if he trades with himself he would have to give up 1.25 for 1 coconut. As long as the price is to the left of his opportunity cost Rob will be better off. 25 Robs opp. cost B/C 0 1.25 Rob is better off to the left of the opp. cost Now lets consider Sam. His opportunity cost is 1 C 1/3 B Again moving C to the other side Now let show Sams opportunity cost in the number line B/C 0 0.33 Sam has coconuts and wants bananas so he wants to have a price of very few coconuts for a lot of bananas. When B is high and C is low then B/C will be a high number. Sam prefers small B/C.. For example if the price happens to be 2 bananas for 1 coconut Sam will be better off because if he trades with himself he would have to give up 3 coconuts for 1 banana. As long as the price is to the right of his opportunity cost Sam will be better off. 26 Placing both opportunity costs in the same number line Sam is better off to the left of his opp. cost Sams opp. cost B/C 1.25 0.33 0 Robs opp. cost Rob is better off to the left of his opp. cost The place where both Sam and Rob can be better off is between 0.33 and 1.25 Both better off in this range B/C 1.25 0.33 0 We really do not know where in the range between 0.33 and 1.25 B/C the real price will be. This will depend on their negotiations but we know that for sure that they will trade. 27 Lets assume that they decide the price to be 1. bananas for 1 coconut. Actual price B/C 0.5 1.25 0.33 0 Also assume that Rob decides to sell two bananas. This implies that Sam has to pay 4 coconuts. The final allocation of coconuts and bananas is the following World Production with Specialization World Consumption After Trade 28 Finally lets compare consumption with trade and consumption without trade World Consumption without Trade World Consumption After Trade NOTE THAT WITH TRADE BOTH SAM AND ROB CONSUME MORE THAN WITHOUT TRADE We have reached our main conclusion Trade will be better than no trade for all parties involved IF AND ONLY IF 1) the parties specialize in the production of the good in which they have a comparative advantage AND 2) the terms of trade are better than their respective opportunity costs. 29 However the advantages of trade are not only that both can consume more but also they consumer above the production possibilities frontier. That brings us to our second main result If 1) the parties specialize in the production of the good in which they have a comparative advantage AND 2) the terms of trade are better than their respective opportunity costs. The involved parties will consume above their production possibilities frontier. A point that is not feasible (but desired) without trade The point 8C and 2 B is above the PPF so it is preferred over any point on the PPF but it is only available with trade Rob Sam The point 4C and 8 B is above the PPF so it is preferred over any point on the PPF but it is only available with trade C C 12 8 6 4 2 4 B 5 10 B
PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.
You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!
For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!


Wayne County Schools News Archives
Posted by Wanda Watts, 2012-03-15
TO: ALL WAYNE COUNTY EMPLOYEES...
Open enrollment for this year will be April 1-April 30, 2012. You will not have to complete a tobacco affidavit every year. PEIA will still base premiums on t...Read full article.Substitute Calling System
Posted by T Conzett, 2012-02-23
Wayne County Schools will begin using our new automated substitute calling system March 1, 2012. All employees and substitutes for Wayne County must register with the new system by PHONE. Please click...Read full article.School Calendar Voting
Posted by T Conzett, 2012-02-15
Employees can now log in to vote on a calendar for next school year. Please click HERE to open the access page.Middle School Math Field Day Winners
Posted by L. Hurt, 2012-02-11
6th, 7th, and 8th grade Math Field Day Teams from the six Wayne County middle schools competed at Vinson Middle School on Tuesday, Feb. 7, 2012. Students compete in a written exam, mental exact, ment...Read full article.Crum Middle on Letters About Literature
Posted by Tim Conzett, 2012-02-10
Crum Middle School recently submitted entries to the Letters About Literature contest and was featured on the LAL website. To see more please click HEREHigh School Math Field Day Winners
Posted by L. Hurt, 2012-02-06
Wayne County high school students participated in Math Field Day on Tuesday, January 31,2012, at Spring Valley High School Career Technical Center. Students in grade 10 - 12 compete against each othe...Read full article.
<<-First <-Previous Next -> Last ->>


How to Play Sudoku on your Android Device
This is a game, where you will have to blow your mind all the time. Its all about strategy of yours to find the right digit for the right place in the grid. Get the details about the game play and start playing it on your device.
- The game will have a grid size of 9×9.
- There will be 9 boxes in the entire grid, with nine spaces inside.
- Each of the grid will contain digits from 1 to 9, only once.
- There will be naturally 9 rows and 9 columns and each row and column will have digits from 1 to 9, only once.
- There will be no repetition of digits in any column, row or grid.
This is the rule of the game.
How to Play
- In the game you will be given some digits, from very beginning. In easy level, the number of digits provided will be more. As level in increased, you will be provided less number of digits.
- Based on the digits provided, you will have to blow your mind to fill the rest boxes, ensuring that each row, each column and each grid will contain all digits from 1 to 9, only once.
You will love to blow your mind for the game and in the mean time will also love to get the score updates. Just download the sudoku from the play store, install it and start playing.


04/28/2011: JUMPIN' MATH JAM FREE has just been released! It is a free ad supported trial version of JUMPIN' MATH JAM, but includes only addition and multiplication. Give it a try!
04/12/2011:Get a preview of JUMPIN' MATH JAM on YOUTUBE! You can learn how the game works, discover features, and determine if this app is right for you!
04/09/2011: JUMPIN' MATH JAM USERS: Thank you very much for your positive feedback!
v1.1 Has just been released in response to your requests for new features! Check it out on the Android Market!
APPTITUDE DEVELOPERS is pleased to announce the launch of its first mobile application for the Android platform, JUMPIN' MATH JAM!
JUMPIN' MATH JAM is a really fun way to practice addition, subtraction, multiplication, and division facts as you (a frog) try to beat the turtle in a race to the next level. It's a fun game that's more entertaining than math flash cards, and can be quite addictive! For 5th graders and older, the "random" mode is recommended as it takes you through all operations up to the 12's tables. For earlier elementary students, focusing on just one operation at a time can help reinforce skills. As you go through the levels, the game moves faster and faster! JUMPIN' MATH JAM can be found in the Android Marketplace.


Correlations between many elements in a system inevitably contain indirect correlations from other elements.
You should also be very careful when you calculate a correlation between Time series.
Table of Contents
Handling indirect correlation #
The indirect correlation leads us to inaccurate prediction. There are several ways to filter out those indirect edges with spurious correlation:
- Correlation of correlations
- Partial correlation
- Mutual information based approach (citation needed).
Methods for the Inverse Ising problem
network deconvolution: http://www.nature.com/nbt/journal/v31/n8/abs/nbt.2635.html
- Network link prediction by global silencing of indirect correlations
Aggregating correlation #
Sometimes, we want to average correlation values. A standard method is performing Fisher transformation and average the z values then transform it back to correlation coefficient.
- Averaging Correlations: Expected Values and Bias in Combined Pearson rs and Fisher's z Transformations
Constructing networks from correlation matrices #
Correlation Matrix #
Correlation and causation #
Generalized ways of inferring associations #
- Reshef et al. Detecting Novel Associations in Large Data Sets
- Kinney and Atwal, Equitability, mutual information, and the maximal information coefficient
- http://www.johndcook.com/blog/2008/11/05/how-to-calculate-pearson-correlation-accurately/ - don't expect that the small difference between two large numbers will be accurate.
- Cosine similarity, Pearson correlation, and OLS coefficients
- http://en.wikipedia.org/wiki/Partial correlation
- Graphical interaction models for multivariate time series by Rainer Dahlhaus
- Comparing association network algorithms for reverse engineering of large-scale gene regulatory networks: synthetic versus real data


Our Tutoring Program
The Yellowstone Strengths Academy recognizes the need to have a reliable tutoring service for students and parents in the current climate. We aim to provide individualized tutoring options that fit everyone’s needs. We understand the importance of having a solid educational foundation and strive to help students and parents strengthen that foundation as they navigate through this unique time.
The tutoring service is available to students ages 13 years through 19 years on a monthly, quarterly or full academic year basis. Students work with an online tutor to brush up on critical skills, finish homework assignments, review key concepts needed for class, time management or general accountability.
Meet the Tutors
John Doe is a computer scientist who loves math.


Po Shen Loh took an hour out of his day to sit down with the Going Deep podcast and discuss his company Expii that helps students learn difficult STEM topics.
He represented the USA Math team at the International Mathematical Olympiad as a high schooler in 1999, where he won a silver medal. He came back to the team as an deputy leader (assistant coach) in 2004 and 2010-2013. He took over the Head Lead role in 2014 and led the US to its first championship in 21 years in 2015.
Po founded Expii Inc. in January of 2014 as a learning tool to help replicate the most effective methods of teaching for students all over the world. Expii's mission is as follows;
"We believe that high quality educational resources should be available to anyone, no matter where they are or what they can afford. We also believe that students and teachers are the best at explaining things.
We build the tools ordinary people need to educate one another. So far, we've designed an approachable markup language that enthusiasts have used to create thousands of lessons. We've also created a free platform to interconnect these lessons."
Po got his PHD in Mathematics from Princeton in 2010, where his thesis discussed combinatorics (the study of discrete systems) and probability theory. Prior to his work at Princeton, Po-Shen received the equivalent of a masters degree in mathematics from the University of Cambridge in 2005, where he was supported by a Winston Churchill Foundation Scholarship. He received his undergraduate degree in mathematics from Caltech in 2004, graduating first in his class, and his undergraduate thesis later received the Honorable Mention for the 2004 AMS-MAA-SIAM Morgan Prize.
After getting his PHD, he went on to immediately begin an Assistant Professorship in Mathematics at Carnegie Mellon University.
1-hour lesson on probability
Math Olympiad World Championship
Po's Math Lessons


Jan. 18, 2016, 7:05 p.m.
Recurring deposit is scheme offered by banks where a person deposits monthly installment and banks gives higher interest rates than saving account. Recurring deposit is kind of fixed deposit and interest rates of recurring deposit is just little less than fixed deposit.
Recurring deposit is suitable for those people who have constant source of income, for example salaried people. It is best solution for medium term saving (6 months to 3 years) with higher interest rates.
Recurring Deposit Interest : The interest rates given by banks is generally above 8.0% and it is compounded quaterly (means when your money gains interest in a year).
You should know how to calculate compound interest in order to calculate recurring deposit maturity amount, you had studied compound interest in your school (formula is given below).
Lets take an example and then we will calculate recurring deposit step by step with explanation.
Example: Suppose you want to puchase a motorcyle next year and you want to save some money for it but you also want higher interest rates, so you chose to start RD. You start an RD of Rs.5000 for 1 year. So you are going to deposit Rs.5000 in the bank for next one year. And your bank gives you interest 8.25% for 1year compounding quaterly.
This means, for you first installment of Rs.5000, you'll get 8.25% interest for 12 months from the bank compounding quaterly. For the second installment, you'll get 8.25% interest for 11 months compounding quaterly, and for third installment of Rs.5000, you'll get 8.25% interest for 10 months compounding quaterly and so on.
Recurring Deposit Formula
A = Maturity amount.
P = Principal amount (In our case, it is Rs.5000)
R = Interest rate in decimal, convert interest rate into decimal by dividing it by 100 (In our case, 8.25/100 = 0.0825)
T = Time duration in months (In our case, it will be 12 months)
t = Time duration in years
N= compounding frequency (since it is quaterly, it will be 4)
Calculating recurring deposit maturity amount:
Now, we will calculate amount (A) from above formula for each installment we pay, starting from first month to 12th month and then add all of them. So the final maturity amount will be
A = A1+A2+A3+.....+A12
A1, A2, A3,,,A12 are the maturity amount for respective installment.
|1||5000||0.0825||12||12/12||4||A1 = 5425.44|
|2||5000||0.0825||11||11/12||4||A2 = 5388.64|
|3||5000||0.0825||10||10/12||4||A3 = 5352.10|
|4||5000||0.0825||9||9/12||4||A4 = 5315.80|
|5||5000||0.0825||8||8/12||4||A5 = 5279.75|
|6||5000||0.0825||7||7/12||4||A6 = 5243.94|
|7||5000||0.0825||6||6/12||4||A7 = 5208.38|
|8||5000||0.0825||5||5/12||4||A8 = 5173.05|
|9||5000||0.0825||4||4/12||4||A9 = 5137.97|
|10||5000||0.0825||3||3/12||4||A10 = 5103.12|
|11||5000||0.0825||2||2/12||4||A11 = 5068.51|
|12||5000||0.0825||1||1/12||4||A12 = 5034.14|
|A = 62730.84|
Using the above formula, we have calculated amount for each installment and then added all of them to get our final maturity amount.
For the first 500 that you deposited in the bank, you will get interest for 12 months (t = 12/12 = 1), and for the second installment that you paid, you'll get interest for 11 months.
Its not that hard to calculate RD maturity amount, you just need to understand the formula for calculating recurring deposit maturity amount.
I trid best to explain. Please let me know if you have any further queries.


Week Ten Essential Question: How can I differentiate through student product in my classroom?
This week I attempted to create a rubric that could be used to assess student learning through project-based use of simulation games such as Minecraft.
First, the Alaska Standards I chose to unpack in my rubric:
Standard for Mathematical Practice 4. Model with mathematics:
In grades 9-12 mathematically proficient students will:
- apply mathematics to solve problems in everyday life, society, and workplace
- identify important quantities in a practical situation and map the relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas
- consistently interpret mathematical results in the context of the situation and reflect on whether the results make sense
- apply knowledge, making assumptions and approximations to simplify a complicated situation, realizing that the final solution will need to be revised
- analyze quantitative relationships to draw conclusions
- improve the model if it has not served its purpose
Writing Standards for Literacy in History/Social Studies, Science and Technical Subjects grades 6-12: Production and Distribution of Writing
6. Use technology, including the internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically
Here’s a link to my rubric:


Material in this two-day course will assist operators with math problem solving in preparation to write certification exams (Small Systems, Level I, Level II or III/IV). It was specifically developed to increase your water & wastewater math knowledge and problem solving skills. Includes a focus on important math principles and the support systems used in water and wastewater operations.
NOTE: This course was completely re-developed in late 2016 and approved for new CEUs by Alberta Environment and Parks. Math and Support Systems are two components found in the provincial certification exams.
The CEUs from this course can be used toward the following discipline(s) for certification renewal:
• Water treatment
• Water distribution
• Wastewater treatment
• Wastewater collection
Dates & Locations
- Session #2
- May 18, 2023 8:00am - May 19, 2023 4:00pm
- Hotel Blackfoot - 5940 Blackfoot Trail SE - Calgary
Although not mandatory, it is recommended that participants take the Entry Level Training -or- the Level I Certification Preparation course prior to taking the Math & Support Systems for Operators.
-Basic Math - Units of Measurements, Unit Calculations, System Calculations
-Basic Math Worksheet - questions and answer review
-Water Operator Math Worksheets - questions and answer review
-Wastewater Operator Math Worksheet - questions and answer review
-Support Systems - Introduction, Pumps, Basic Hydraulics, Valves, Basic Electricity, Instrumentation and Controls
-Support Systems Worksheet - questions and answer review
-Basic Pump Components - Split Case Pumps
Inclass: No manuals will be forwarded to students in advance of this course – the instructor will provide all material on-site.
$460.00 Must have current AWWOA Membership
$345.00 (For in-class courses only) Must have a current AWWOA Membership and be an operator of a small public rural water/wastewater facility.


After writing my inaugural blog post, A First Grade Teacher Enters The Math World, I have spent some time searching for and thinking about mathematical leaders to follow in the primary grades. It is easy to find leaders at the high school and middle school levels, and I have come across many in the elementary level, but there are far fewer who really specialize in the primary grades, at least far fewer who are vocal and make themselves accessible in online learning communities like Twitter. Of course, I have learned so much from these higher grade teachers and leaders and for that I am so grateful, but sometimes it would be nice to be in touch with others who are working out the exact same things that I am. (Like right now in my room, my goal is to get my kids talking. It's tough at the beginning of the year! I just passed off all of my near perfectly trained mathematical conversationalists to the second grade team. You're welcome second grade!)
Saturday, August 29, 2015
Sunday, August 16, 2015
I have been teaching for about 14 years, all of which have been spent in kindergarten through second grade. The last 8 years have been in first grade. I’ve been reading some tweets about us elementary folk being left out of the math loop, and it is true for many, so I thought I would weigh in and share my journey.
Sometime after Christmas break during a staff meeting our principal introduces Ryan Dent to the staff. He is saying all kinds of crazy stuff like I do, we do, you do is backwards! Seriously? How are my little first graders supposed to come in and teach each other math they haven’t even learned yet? He wants teachers to talk as little as possible and the kids to do nothing but talk?! Classroom management nightmare, right? This guy is nuts… but he is really passionate… Then something weird happens, I go to a training at the county office and someone else (who I know is not crazy) says the same thing. I guess I better learn a little bit more about it.
Later in the spring I attend my first Standards of Mathematical Practice training offered by Ryan and Kristian Quiocho at my district office. I don’t know how else to explain the training other than it was like a giant epiphany. A huge Aha! Now it all makes sense. I see it now. It will take getting used to, but I get it.
After the training I start trying out some of what I learned. Success after success. I guess these guys are on to something. Later in the year they announce that our district is going to write our own math modules, but they want teachers from each grade level to come together and write tasks. I figure, this is new for me, but I know I will learn a lot so I do it with another first grade teacher and we work ALL SUMMER, and by all summer I mean from the day school gets out until we went back. We both felt like we had gone to college for the summer.
When school began I decided there was no better way than to dive in. I gave students tasks, I watched them struggle (NOT RESCUING THEM WAS EXCRUCIATING), I used samples of their own work, students explained and critiqued the work of others, they made connections, they talked to each other about math, they wrote about math in their math journals. I decided to use the same assessment I had used the year before to compare data. This is what happened:
(3 is high, 1 is low)
Seriously? I went to college. I got my bachelor’s and master’s degrees, and took more classes after that and my kids are better teachers than I am??? My students learn better when I hardly say anything at all??? How are my kids able to figure out how to do this math without me telling them how to do it? Then it hit me. It was that thing Ryan and Kristian shared at our SMP training only maybe I wasn’t quite ready to fully understand it yet… It was problem solving. My kids can problem solve. What is problem solving? Simply put, problem solving is what you do when you don’t know what to do.
What was I doing while the kids are running the show? I give them a task, I listen for common misconceptions, I choose work samples to fuel discussions,
and I do my best to ask probing questions that focus on conceptual understanding. (It’s easier to funnel them into the answer.) As Phil Daro would say, “What is the math they need to learn here?” I worked with my co-module writer to train other first grade teachers in our district on using the modules. It was exciting to see other teachers open up and try teaching math this way. It was even more exciting to read about their success in emails.
Then, I started to get more and more into math. I watched this talk by Dan Meyer: http://www.ted.com/talks/dan_meyer_math_curriculum_makeover?language=en Hello integrating multi-media, real world tasks, 3 acts! I loved it and was totally inspired to try some myself. Ryan introduced me to Graham Fletcher’s tasks for elementary. http://gfletchy.com/3-act-lessons/ Thank you very much!
After all of this I begged my district to go to NCTM’s national conference in Boston. For some reason, they said yes. My district sent 3 of us to represent our district. I was representing K-2, Ryan was 3-8, and Chris was 9-12. (Both Ryan and Chris’s mathematical intelligence intimidates me, but I have made peace with that and I choose to look at it this way. I am the lucky one, because I get to grow the most.) I couldn’t believe it! I was so shocked… and thankful… and humbled… and a little scared… Teachers don’t often (next to never) get to go to conferences out of state! I truly wanted to learn as much as I could and then use what I learned to help better any teacher willing to listen. While I was there I was given the opportunity to learn from the very best. I went to sessions by Phil Daro , Jason Zimba, William McCallum, Dan Meyer (I took a pic with him! There was a line! I’m not kidding. Math nerds unite at NCTM),
Marilyn Burns, Sherry Parrish, Ruth Parker, Karen Karpe, and Maria Blanton. Not only were the presenters amazing to learn from, but I got to meet other professionals like Steve Wyborney who is just amazing. All in all, it was phenomenal. I wish I could share every last detail of the training with people, but it’s exactly how Dan Meyer describes math class in the beginning of Math Class Needs a Makeover. (see video link above) Our math team (Ryan, Chris and myself) took back the message that we had received at NCTM and reported to the district and used that learning to plan future professional development for our teachers. I am soooooo looking forward to these!
I couldn’t be more pleased with the growth my students made last year. They are my math superheros. They taught me so much! This year my group of students is very different. My room is now the inclusive classroom in first grade and it’s more homogeneous, at least at the moment. My math goal as of right now is to focus on meeting these kids where they are right now. At NCTM Jason Zimba said, “Don’t let the standards be handcuffs for the children placed in front of you.” So I’m not. I’m also setting a goal to really work on my questioning technique with a strong emphasis on conceptual understanding.
As far as Literacy ＞ mathematics, I can’t say I agree anymore. Yes, students need to be able to read to do just about everything else, but they also have to use reasoning skills. They need to be able to choose tools to solve problems in and outside of a mathematical context. They need to be able to analyze and critique the reasoning of others to help make decisions for themselves. In the real world, people are not going to spoon feed them and give them everything they need. They are going to have to problem solve. Why not start cultivating this when kids are little?
Follow my blog with Bloglovin
Powered by Blogger.


⭐⭐ Shipping Available! - Free local pickup with any order - Free local delivery with any $25 order ⭐⭐
Robot Blues 9781610671248, New Friend 978161671255, Worry Monsters 9781610671262
Jack wants to win the math competition, but it's not his best subject. Luckily, he's been paired with a math whiz! Can they work together to win?


Welcome to the officially unofficial Pi Day website!
Pi Day is next celebrated on March 14th 2020 all over the world. Why March 14th? Well, that's because the Greek letter Pi (π) is used in mathematics to represent a constant - originally this was the ratio of a circle's circumference to its diameter, but it has various definitions now and is used in many mathematics and physics formulas.
Pi is most commonly shown as being 3.14159 but this is just an approximate value. It's an irrational number, and its decimal representation never ends.
Take a look at what one million digits of pi looks like!