Introduction to likelihood-free inference and distillation of the paper Recurrent Machines for Likelihood-Free Inference, published at the NeurIPS 2018 Workshop on Meta-Learning.
Article jointly written by Arthur Pesah and Antoine Wehenkel
There are usually two ways of coming up with a new scientific theory:
- Starting from first principles, deducing the consequent laws, and coming up with experimental predictions in order to verify the theory
- Starting from experiments and inferring the simplest laws that explain your data.
The role of statistics and machine learning in science is usually related to the second kind of inference, also called induction.
Imagine for instance that you want to model the evolution of two populations (let’s say foxes and rabbits) in an environment. A simple model is the Lotka-Volterra differential equation: you consider the probability that an event such as “a fox eating a rabbit”, “a rabbit being born”, “a fox being born”, etc. happens in a small time interval, deduce a set of differential equations depending on those probabilities, and predict the evolution of the two animals by solving those equations. By comparing your prediction with the evolution of a real population, you can infer the best model parameters (probabilities) in this environment.
Modern theories require simulations in order to be linked to observations. It can be either a simple differential equation solver as in the case of the Lotka-Volterra model, or a complex Monte-Carlo simulator as they use in particle physics for instance.
By comparing the results of a simulation, i.e. the predictions of a model, with real data, it is then possible to know the correctness of your model and adjust it accordingly. If this process of going back and forth between the model and the experimental data is usually done manually, the question that any machine learning practitioner would ask is: can we do it automatically? Can we build a machine that takes a tweakable simulator and real data as input, and returns the version of the simulator that fits best some real data?
That’s the object of our recent work1, where we trained a neural network to come up with the best sequence of simulator tweaks in order to approximate experimental data, capitalizing on the recent advances in the fields of likelihood-free inference and meta-learning.
Let’s rephrase our problem in a more formal way. We can model a simulator (also called generative model) by a stochastic function that takes some parameters
\theta and returns samples
x drawn from a certain distribution (the so-called model).
This formalism applies to any scientific theory that includes randomness, as it’s very often the case in modern science (particle collisions are governed by the law of quantum physics which are intrinsically random, biological processes or chemical reactions often occur in a noisy environment, etc.).
Experimental data consist in a set of points living in the same space as the output of the simulator. The goal of inference is then to find the parameters
\theta such that the simulator generate points as close as possible to the real data.
Scientific fields using such simulators include:
- Population genetics. Model: Coalescent theory. Observation: the DNA of a current population. Parameters: the DNA of the common ancestor.
- High-energy particle physics. Model: Standard Model of particle physics. Observation: output of the detector during a collision. Parameters: coupling constants of the Standard Model (like the mass of the particles or the strength of the different forces).
- Computational neuroscience. Model: Hodgkin-Huxley model. Observation: evolution of the voltage of a neuron after activation. Parameters: biophysical parameters of the neuron.
So how can we predict the parameters of a simulator given some real observations? Let’s consider the simple example of a Gaussian simulator, that takes a vector
\theta=(\mu,\sigma) as parameters and returns samples from the Gaussian distribution
The classical way to infer the parameters of such a simulator is called Maximum Likelihood Estimation (MLE). The likelihood is defined as the density of the real data under a parametric model. It means that if most data points are located in high density regions, the likelihood will be high. Hence, the best parameters of a model are often the ones that maximize the likelihood of real data. If you are unfamiliar with likelihood-based inference, you can read this excellent introduction to the subject.
If you have explicitly access to the underlying probability distribution of your simulator, as well as the gradient of this distribution, you can for instance perform a gradient descent in the parameters space, in order to maximize the likelihood and infer the best parameters of your model.
However, many real-life simulators have an intractable likelihood, which means that the explicit probability distribution is too hard to compute (either analytically or numerically) . We must therefore find new ways to infer the optimal parameters without using neither the likelihood function nor its gradient.
To sum it up, we have a black-box stochastic simulator that takes parameters and generates samples from an unknown probability distribution, as well as real data that we are able to compare to the generated ones. Our goal is to find the parameters that lead the simulator to generate data as close as possible to the real ones. This setting is called likelihood-free inference.
How can we likelihood-free infer?
Let’s try to come up progressively with a method to solve our problem. The first thing we can do is to start from a random parameter, and simulate the corresponding data:
By doing so, we can see how far our generated data are from the real data, but we have no way to know where to move in the parameter-space. Instead, let’s simulate several parameters:
To do so, we consider a distribution in the parameter-space, called proposal distribution and noted
q(\theta|\psi). If we choose
q to be a Gaussian distribution, we will have
\psi=(\mu,\sigma). The first step consists in initializing
\psi randomly. In the figure above, we considered
\psi=\mu for simplicity. Then, we can perform the following step until convergence:
- Sampling a few parameters from the proposal distribution: 4 parameters around
\psiin the figure.
- Generating data from them: the 4 cloud of points on right.
- Choosing a good direction to move
The third step is the hard one. Intuitively, you would like to move
\psi towards the orange and green parameters, since the corresponding predictions (orange and green cloud of points) are the closest to the real data. A set of methods, called natural evolution strategies 2, allow you to link the performance of each
\theta (in terms of similarity between its predictions and the real data) to a direction in the parameter space. A recent paper 3 use for instance the similarity measure given by a Generative Adversarial Network (GAN) to find the best direction. Even though those algorithms perform well in the general case, one can wonder if for a given simulator, it is not possible to find a better algorithm that would exploit the particular properties of this simulator. That’s where meta-learning comes into play!
Meta-learning for optimization
The idea behind meta-learning is to learn how to learn, and in our case to learn the optimization process. The main idea, introduced in the paper Learning to learn gradient descent by gradient descent4, is to use a recurrent neural network (RNN) to find the best descent direction at each iteration. Below is an example of sequence of points produced by a randomly initialized RNN:
Each descent direction is random and the last point produced is far from the minimum. During training, it should learn to exploit the gradient information at each point in order to move toward the minimum, giving something like:
So how to train it? Generate many functions whose you know the minimum, and ask the RNN to minimize the distance between the last point of the sequence and the real minimum.
Learning to learn scientific models
In the case of likelihood-free inference, the RNN should return a sequence of proposal parameters
\psi, given the real observations and the generated cloud of points at each step.
Now, same question as for learning to learn by gradient descent, how do we train the RNN? Here, the trick is to generate many random parameters θ and to pretend for each one that it is the “true parameter”. We can then simulate each θ generated and obtain a set of “real observations”. The RNN can then be trained by passing it those real observations, looking at its final proposal distribution, and comparing it to the true parameter (that we know because we have generated it).
Let’s go through an example to clarify all of that. In the figures below, the proposal distribution is represented in color (red = high density). At the beginning, the RNN is initialized randomly and we evaluate it on our first generated true parameter
\theta (in red).
We can then backpropagate the loss into the RNN. After repeating this process for 200 different “true parameters”, this is what is should look like:
We can see that it has learnt to exploit the information of the observation space to move towards the good parameter.
We evaluated our model on different toy simulators, some where we the likelihood is known and some where it is not.
Non-likelihood-free problem: Poisson Simulator
The first simulator takes a parameter λ and draw samples from a Poisson distribution
P(\lambda). The goal of this example was to see if we obtain comparable performance as the maximum likelihood estimator. Here are the results:
We can see that the performance are comparable, even though we didn’t give our model access to the likelihood.
Likelihood-free problem: Particle Physics Simulator
To evaluate our model in a true likelihood-free setting, we considered a simplified particle physics model that simulate the collision of an electron and a positron turning into a muon and an antimuon.
The parameters of the simulator are the energy of the incoming particles and the Fermi constant, and the output is the angle between the two muons.
To evaluate our method, we compared the real observations with the ones generated by the last parameter found. Here are the results:
We saw what likelihood-free inference is and how meta-learning can be used to solve it by learning the best sequence of simulator tweaks to fit a model to the reality.
As most meta-learning models, a limitation is that it is hard to train. We had trouble scaling our method to more complex simulators, since meta-training requires a lot of simulator calls, which might be very slow in real-world settings. However, as the field of meta-learning makes progress, we hope that new methods will emerge to alleviate this problem and make it more scalable.
G. Louppe, J. Hermans, K. Cranmer, Adversarial Variational Optimization of Non-Differentiable Simulator (2017), arXiv e-prints 1707.07113 ↩
M. Andrychowicz, M. Denil, S. Gomez, M. W. Hoffman, D. Pfau, T. Schaul, B. Shillingford, N. de Freitas, Learning to learn gradient descent by gradient descent (2016), NIPS 2016 ↩


Ranger College is looking for students interested in careers in Science, Technology, Engineering or Math. A $2,300 in scholarship is available. Qualifications include; A high school degree with a 3.0 GPA in math and science. Enrollment in a T-STEM instructional program, completion of 30 semester credit hours within a year at Ranger College, work no more than 15 hours a week in a chosen program, related field, or business participating in the T-STEM Scholarship Program, and register with Selective Service. The scholarship review process starts immediately. For more information and to complete registration, go to; firstname.lastname@example.org.


This function returns the length of compartments by computing the distance between the two end points of a compartment.
Function Output Type : Real
Calculated : At each tracing point
Returns a value : For each compartment
Values to consider : All
Output Interpretation :
The above example, shows the total length as 16734 microns.
Total_Sum = 16734 gives Total_Sum, Minimum = 1.11802 gives minimum, Maximum = 656.878 gives maximum for given input neuron.
Examples of Distribution Plots :
The compartments that form the soma are not considered for this study.


Online Slot is a casino game that allows players to win real money based on the probability of the numbers generated by a computer. The random number generator creates new combinations every millisecond, making it impossible for players to predict when they will win or lose. This is why many people become addicted to slots, because the constant “almost wins” make players want to spin just a couple more times.
Modern online slot games can be very complex and feature many different symbols. Traditional slots usually have three reels with between 1 and 5 paylines, and the player wins when they line up matching symbols on a payline. Online slots, however, can be themed around any subject and can have as few or as many reels as the player wants. The game may also have additional features such as Scatters, Wilds and Bonus rounds.
The Bonus round in any slot is usually what players are after, as it’s where the big wins are normally found. These can be anything from free spins to pick and click games, random prizes or re-spins. The newer kinds of slot machines are now able to offer players the chance to trigger a bonus round without even having to bet.
The first thing to understand about slot is that no two slot games are the same. Each will have different RTP and volatility/variance characteristics that determine how often a player will be rewarded. This is why the math behind slots is so important for players to understand.


Welcome Year 5!
A start of a brand new year, where the use of the immersive classroom will enhance your learning and creativity.
We start our year off with the topic of Chocolate! We will look into Charlie of the Chocolate Factory in English and learning in history how chocolate was born in the Mayans time. In Reading, we are focusing on the novel Clockwork and discovering the different Reading Content Domains.
Our focus in Maths will be place value, addition and subtraction along with developing your reasoning skills.
Other topic we are covering include Forces in Science, Christianity and The Big Frieze in RE, Life Skill in Computing. Spanish, Music, Art and many more fun and exciting subjects.
Our PE day is Wednesday. This term Mandela are swimming on Wednesday’s.
Spellings will go out on Friday to be tested on the following Friday. You will receive your homework sheet at the start of the term and will be expected to work through it each week.
We have an exciting term ahead and we are looking forward to teaching you!
Miss Fitzgerald, Miss Wright and Mr Grimwood


Can You Solve Amazon’s Hanging Cable Interview Question?
Thanks to a MindYourDecisions YouTube video, we have a tiny sneak peek of one of the questions that are asked in interviews. And it’s, well, pretty arbitrary.
When we first heard the question, we were really confused. How in the world are you supposed to answer that right on the spot? We don’t envy anyone who stared blankly at their interviewer after hearing this question! However, thanks to the video, it makes much more sense and helps us solve the riddle.
A version of the question is as follows:
A cable of 80 meters (m) is hanging from the top of two poles that are both 50 m from the ground.
What is the distance between the two poles, to one decimal place, if the center of the cable is:
(a) 20 m above the ground? (b) 10 m above the ground?
Can you figure it out?
If you can’t, no worries! With a little help from the internet, the person who created this video goes on to find formulas to be able to solve the problem. He draws out the question in picture form and explains it—which still takes him several minutes and math equations to get there.
In the end, he runs into a problem: “This equation has no solution!”
The point of the problem is to think about it logically. And once he actually does that, it starts to make a lot more sense. And actually—equations aren’t even required.
The point of the question? “Many employees can mindlessly calculate the answer…but how many will think before they calculate?”
People were equally befuddled by the problem.
“I guess I wouldn’t have gotten the job, no wonder why they don’t have same day delivery anymore..lol,” someone commented.
“I’d point out that the answer is ‘not far enough’ as low-hanging cables are a safety risk,” another said.
“Always nice to learn ridiculously complicated formulas that replace a tape measure for scenarios that don’t exist. THANKS!” someone else joked.
See for yourself how to “solve” this problem in the video below!
What did you think of this “math” problem? Did you catch on right away to what they were looking for, or did it take you a few minutes? What would you have done if you received this question in a job interview?


Midian Mendes love to write about on kids training topics, like how he training kids on self controlling . She is a part-time writer at...Read more
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Scroll down if you are looking for the CAGR Calculator
How To Calculate CAGR?
CAGR is compound annual growth rate and it is used to calculate what your principal would grow to – if your interest earned is invested back at the same rate.
So if you invest 100 bucks at 10% – at the end of first year, you would get 10 bucks as interest, but at the end of the second year you would earn interest on 100 (original investment) + 10 (interest earned at the end of first year) = 110 and your interest would be 11 instead of 10.
CAGR is widely used in business to calculate the growth rate of revenues and profits, as the assumption in business is that the money that is made is – reinvested for future growth (the part which is not given as dividends to shareholders)
CAGR is a helpful tool when you are looking at a particular stock to buy, and have its historic revenues and profits available. You can input the revenues at a year 2003 and then at the year 2008, enter the number of years as 5 and see what the CAGR comes out to be.
This will give you an idea of the rate at which the company has grown.
CAGR Calculator is also helpful to calculate the amount of money that you would have after a certain period of time, if you were to invest a certain sum now at a given rate of interest. So in the above example 100 bucks will become 121 in two years time at a CAGR of 10%.
In this CAGR calculator you could calculate both, if you know what is the principal you are going to invest, number of years and rate of interest you could calculate the amount it would result in after the period.
Or if you knew the number of years, initial principal and then the resultant amount you could key in that to see at what CAGR the growth took place.
12 thoughts on “CAGR Calculator”
Value fund Series 13
10000 installation & something Returns show plzz
Plzzz m suggest…
SIP MUTUAL FUNDS growth equity funds Per Month 1000? .. & Returns to 20 year later How it’s value in it..
CAGR is the concept that makes rich more rich and poor more poor. Stock market investments are calculated on CAGR basis. CAGR shows it affects only in long term after good time period. Those who are not earning compounded returns are surely paying it. The good example to earn good growth rate in long term is through investment in multibagger stocks which converts meager thousand rupees investments into crores in few decades. We suggest you those multibagger stocks that have potential to convert your money from thousands to crores to know more do visit our site http://www.multibaggers.co.in
useful formula to know the real rate of return.
If I save Rs 2220/- per month for 15 years and get Rs 785000/- at the end of
15 years along with insurance cover of Rs 4 lakhs, what is my IRR and CAGR. these returns are available to devence employees under Postal Life insurance.is this a good option or terminsurance plus SIP optionis better
cagr is the good thing to use in the real life


Graduate programs in economics aim to train students in such a way to enable them to carry out independent research. For this purpose, the programs are designed to ensure that the students get a solid background in both economic theory and the techniques used in empirical research. While the Department offers both M.A. and Ph.D. degrees, the M.A. degree is considered, in principle, as an intermediate step that is passed en route to the Ph.D. The core requirements common to both programs leave little room for choosing the courses to be taken in the first year, but the students are offered considerable flexibility as to their choice of the fields of specialization later on.
Students admitted to graduate studies in the department are expected to have a strong background in undergraduate level economics and some training in mathematics and statistics. Sufficient (though not necessarily a pre-condition) background would consist of an undergraduate degree in Economics, or a year-long calculus sequence that includes multivariate analysis, a course in linear algebra, and a course in probability and statistics. (Also refer to the “Graduate Admissions” section in the introduction of this catalogue for the general graduate admission requirements.)
Prospective students must have completed Bilkent University’s requirements for a Bachelor of Arts degree in Economics or approximately equivalent training. Since students will be required to take some of the same courses as the Ph.D. candidates, similar preparation in mathematics and statistics is generally expected.
A grade point average of at least 3.00 must be maintained for the duration of Master’s level work.
For more information about the graduate program, please contact email@example.com.
For information on the MA curriculum, please click here and choose “Master of Arts in Economics.”
Information on the admissions process for graduate level economics programs can be found here.


I don't remember if I learned numbers using number blocks when I was a kid, but that's how I'm learning them now.
Technically, I supposed I started learning Danish numbers in the informal class I took this past fall, but I definitely prefer the Rosetta Stone method. When I was taking that class, I found myself trying like hell to cram and memorize those numbers before each class, leaving me with barely any time to even look at everything else he'd tried to teach us. Rosetta Stone makes the basics far more intuitive.
Here's the thing: I get that repetition is part of the method, but maybe three quarters of the way through each lesson, I find myself distracted. And since I already basically know one through ten in Danish, I even found my eyes drifting up to the TV... which was showing "Honey" on mute in the background.
"Honey" of all things...
I'm going to try to move through numbers as quickly as I can, and hope that the next unit keeps my attention a bit better.


D. Karaboga and E. Kaya, “Training ANFIS using artificial bee colony algorithm for nonlinear dynamic system identification,” in: IEEE 22nd Signal Processing and Communications Applications Conference (SIU), 2014, pp. 493-496.
P. Liu, W. Leng and W. Fang, “Training ANFIS model with an improved quantum-behaved particle swarm optimization algorithm,” Mathematical Prob. in Eng. vol. 2013, 2013.
V.S. Ghomsheh, M.A. Shoorehdeli and M. Teshnehlab, “Training ANFIS structure with modified PSO algorithm,” In Control and Automation, Med’07. Mediterranean Conference on IEEE, 2007, pp. 1-6.
M.A. Shoorehdeli, M. Teshnehlab, A.K. Sedigh and M.A. Khanesar, “Identification using ANFIS with intelligent hybrid stable learning algorithm approaches and stability analysis of training methods,” Applied Soft Comput. vol. 9, no. 2, pp. 833–850, 2009.
M.A. Shoorehdeli, M. Teshnehlab and A.K. Sedigh, “Training ANFIS as an identifier with intelligent hybrid stable learning algorithm based on particle swarm optimization and extended Kalman filter,” Fuzzy Sets and Systems. vol. 160, pp. 922–948, 2009.
D. Simon, “Training fuzzy systems with the extended Kalman Filter,” Fuzzy Sets Syst. vol. 132, pp. 189–199, 2002.
E.G. Carrano, R.H.C. Takahashi, W.M. Caminhas and O.M. Neto, “A genetic algorithm for multiobjective training of ANFIS fuzzy networks,” IEEE Congress on Evolutionary Computation, pp. 3259–3265, 2008.
F. Cus, J. Balic and U. Zuperl, “Hybrid ANFIS-ants system based optimisation of turning parameters,” Journal of Achievements in Materials. vol. 36, no. 1, pp. 79-86, 2009.
S. Uzundurukan, “Determination and modeling of basic parameters that affect the swelling properties of soils,” Ph.D. Thesis, Suleyman Demirel University, Turkey, 2006.
J.S.R. Jang and C.T. Sun, “Neuro-Fuzzy modeling and control,” The proceedings of the IEEE. vol. 83, no. 3, 378-406, 1995.
M. Mitchell, “An Introduction to Genetic Algorithms,” MIT Press, 1998.
S.Lek, M.Scardi, P.F.M. Verdonschot, J.-P. Descy and Y.-S. Park, Modelling Community Structure in Freshwater Ecosystems. Berlin, Germany: Springer-Verlag, 2005.
D.E. Rumelhart and J.L. McClelland, “Explorations in the micro-structure of cognition,” parallel distrubuted processing 1. Cambridge, MA: MIT Press, 1986.
C.F. Juang, “A TSK-type recurrent fuzzy network for dynamic systems processing by neural network and genetic algorithms,” IEEE Transactions on Fuzzy Systems. vol. 10, no. 2, pp. 155–170, 2002.
A. Kalinli, “Training Elman network using simulated annealing algorithm,” Journal of the Institute of Science and Technology of Erciyes University. vol. 19, pp. 28-37, 2003.
A. Kalinli and D. Karaboga, “Training recurrent neural networks by using parallel tabu search algorithm based on crossover operation,” Engineering Applications of Artificial Intell. vol. 17, pp. 529-542, 2004.


- The problem assumes the radius of the robot as 0.5 units.
- The obstacles are only rectangular in shape.
- The area is limited to 15 x 15 units (for visualization purposes).
Reading the Plot:
- The solid filled rectangles represent the obstacles.
- The dotted lines around the obstacles represent the offset for the robot.
- The green lines represent edges of the visibility graph that were not finally selected.
- The red lines represent edges constituting the shortest path from start to goal.
- The start and goal points have been exclusively mentioned on the plot.
- The blue curve is the final path the robot will undertake.
- The points marked with ‘*’ are the intermediate points.
- Initialization of start, goal, obstacles, offsets.
- Constructing an adjacency matrix
- Revising the adjacency matrix based on intersection with obstacle.
- Feeding the adjacency matrix to dijkstra(), implemented as a separate function.
- The output of dijkstra() is used to compute the Bernstein curve, as done in the last part of the project.
- The code is now generalized for maximum 3 intermediate points, order has been set constant at 5.
- The graph is plotted in sequence, and can be visualized as an animation.
Graphs related to 2 testcases are shown.


Java provides a rich set of operators to use in manipulating variables. A value used on either side of an operator is called an operand.
For example, in the expression below, the numbers 5 and 8 are operands of the plus operator:
int a = 5 + 8;
Java arithmetic operators:
1. + addition
2. – subtraction
3. * multiplication
4. / division
5. % modulo
Arithmetic operators are used in mathematical expressions in the same way that they are used in algebraic equations.
The + operator adds together two values, such as two constants, a constant and a variable, or a variable and a variable. Here are a few examples of addition:
int a = 40 + 10; int b = a + 34; int c = a + b;
The – operator subtracts one value from another.
int a = 100 - 15; int b = a - 5; int c = a - b;
int a = 100 * 6; int b = a * 3; int c = b * c;
The / operator divides one value by another.
int x = 500 / 5; int y = x / 4; int z = x/ y;
In the example above, the result of the division equation will be a whole number, as int is used as the data type. You can use double to retrieve a value with a decimal point.
The modulo (or remainder) math operation performs an integer division of one value by another, and returns the remainder of that division.
The operator for the modulo operation is the percentage (%) character.
int value = 36; int result = value % 5; // result is 1
Dividing 36 by 5 returns a quotient of 7, with a remainder of 1. Thus, the value of 1 is assigned to the result variable.


, where he learned and later carried to Italy the now popular Hindu-Arabic numerals.Hindu
is a pure place-value system, that is why you need a zero. Only the Hindus, within the context of Ind-European civilizations, have consistently used a zero. The Arabs, however, played an essential part in the dissemination of this numeral system.Numerals, a time travel from India to Europe
The discovery of zero and the place-value system were inventions unique to the
Before adopting the , people used the Roman figures instead, which actually are a legacy of the Etruscan period. The Roman numeration is based on a biquinary (5) system.. As the Brahmi notation of the first 9 ...
To write numbers the Romans used an additive system: V + I + I = VII (7) or C + X + X + I (121), and also a substractive system: IX (I before X = 9), XCIV (X before C = 90 and I before V = 4, 90 + 4 = 94). Latin numerals were used for reckoning until late XVI century!
The graphical origin of the Roman numbers
Other original systems of numeration were being used in the past. The "Notae Elegantissimae" shown below allow to write numbers from 1 to 9999. They are useful as a mnemotechnic aid, e.g. the symbol K may mean 1414 (the first 4 figures of the square root of 2).
Chinese and Japanese contributions
The Ba-Gua (pron. pah-kwah) trigrams and the Genji-Koh patterns, antique Chinese and Japanese symbols, are strangely enough related to mathematics and electronics. If all the entire lines of the trigrams (___) are replaced with the digit 1 and the broken lines (_ _) with the digit 0, each Ba Gua trigram will represent then a from 0 to 7, and each number is laid in front of its complementary (0<>7, 1<>6, 2<>5, etc...).
Write "a", "b", "c", "d" and "e" under the five small red sticks of each Genji-Koh pattern. By doing so, you will have the 52 manners to CONNECT 5 variables in boolean algebraics. The binded sticks form a "conjunction" (AND, .), and the isolated sticks or groups of sticks form a "disjunction" (OR, +). The pattern at the top left represents: [("a" and "d") or ("b" and "e") or "c"]


Sumdog is a site Lily's school uses to practice math at school. With her login, she can use the site at home as well. By solving math problems, kids earn coins to spend on their avatars. Every so often, they go up a rank. Everyone starts as a brown rat, and they go up through the ranks, they level up to the next animal, going through common chimpanzee to blue whale to dhole to harpy eagle, or however the progression goes.
That was my first surprise. Apparently the dhole is a real animal. It's some kind of wild dog from Asia. It's kind of cute.
The only dhole with which I was familiar was the one from the Cthulhu Mythos, the miles-long nightmare worm monsters, which I had to admit, would have been an unusual choice for an intermediate rank in a children's math game.
|Solve for paw|
Overall, it's a decent tool for a parent, and I like to be able to track her progress.


Noetic Math Learning Competition
An impressive 114 of Mrs. Damar’s math students competed in the Noetic Learning Math Contest, which is a national elementary math problem solving contest that is held twice a year. 19,367 young mathletes representing 1,279 teams across the country participated in this year’s fall contest.HSA Belmont had SIX team winners and FIVE students that received National Honorable Mention, an honor that is awarded to approximately the top 50% of participants. Team Winners: Jasmine Jones, Dylan Figueredo, Dakota Adams, Selena Ward, Kenya Smith and Martavion Easterling. National Honorable Mention Students: Jasmine Jones, Amya Washington, Iari Figueredo, Dylan Figueredo and Dakari Thomas.
Horizon Science Academy Belmont Charter School
Discover our School
Horizon Science Academy Belmont is a public charter school serving Kindergarten through eighth grades that opened in 2013. We provide our students with an innovative world class education, rich in math, science and technology. HSA Belmont focuses on preparing students to become bold inquirers, problem solvers and ethical leaders, with skills ready to meet the challenges of a competitive global workforce.


Each and everyday, Huntington Beach Union High School District (HBUHSD) educators take extra care to empower minds and build futures through innovative learning. On a normal Tuesday afternoon, Mr. Kimes, along with other Huntington Beach High School math teachers, could be seen doing just that, but using a teaching tool not typically utilized on a high school campus – LEGOs.
That day, Mr. Kimes Algebra 2 students were given the task of managing a tiny furniture store with LEGO-made products as their only inventory. In groups of three, students were provided 16 small Legos and 12 large Legos to construct tables and chairs. At the tiny furniture stores, LEGO tables sell for $16 while LEGO chairs sell for $10. With the information given, students were then instructed to manufacture the combination of tables and chairs that generates the most profit.
During this activity, students could be seen absorbing the math lesson with the added educational excitement of the LEGO component.


If you like to do any of the following, a career in math might be right for you!
Work with computers
play chess or checkers
Keep track of your money
Do challenging math problems
Build or fix things
Watch Nova or the Discovery Channel
Observe the stars
Follow sports stats
Figure out how things work
Math Related Careers
Studying math can lead to a career as a mathematician or statistician. Most people, however, use their math and problem-solving skills to succeed in careers in computer science, the skilled trades, business, science, or engineering.
Computer Science Careers
Every business and industry today relies on computers. If you like math and you want to work with computers, take a look at these careers.
Computer software engineer
Computer support specialist
Information systems manager
The Skilled Trades
There are excellent job opportunities in the skilled trades, and many of these careers require 2 years or less of education/training. If you’re good at math and like to work with your hands, consider one of these careers.
Heating and AC technician
Tool and die maker
Math Related Business Careers
People with good math skills are in demand in all areas of business. If you think you might like working in a business setting, consider on of these careers.
Math Related Science Careers
People working in science careers generally need to have good math skills. They use math to analyze data, calculate medications, do lab tests, and read test results. Below are just a few of the many careers that students who like math and science can choose from.
Medical lab technician
Engineering (requires a 4 – year college degree)
Engineers use math and science to solve all kinds of technical problems. Engineers produce and analyze designs, develop and test products, and supervise production. Most engineers specialize in one of the following:
Math Fun Fact
How much is a billion?
The moon is about a billion feet away.
A billion hours ago it as the Stone Age.
It would take 30 years to count to a billion.
Google came from a misspelling of googol.
A googol is 10100 or 1 followed by 100 zeros.
Another way to say 10100 is ten duotrigintillion.
In 1999, a Mars satellite costing $125,000,000 crashed because English units were used in some of the calculation instead of metric units.
Assuming Rudolph is in front, there are 40,320 ways to arrange the other eight reindeer.
National Pi Day is March 14, at 1:59 (3.14159…)
You cannot fold a piece of paper in half more than 7 times.
It takes 8 minutes for sunlight to reach the earth. Light from the next closest star takes 4 years.
WOODBURN PRESS Career InfoGuide Careers in Math – Item 603 www.woodburnpress.com Copyrighted Material 2014 Edition


a quick-playing dice game for three to five players
by Jonathan Leistiko
inspired by a comment by Ben Gibbs and Malisa Dijacimo
Gather clusters of similar cheeses, either from the Cheese Shop, or from the other mice.
Note: You can play this game with normal six-sided dice. If this were a commercially published game it would use 25 custom dice with the following die faces: Gouda (red), Swiss (white w. black circles), Bleu (white with blue lines & spots), Cheddar (yellow), American (Orange wrapped slice), Brie (white/yellow pie wedge). You can print out this die-to-cheese reference sheet to help you.
Put the Fromage á Trois dice in the center of the table. This is the Cheese Shop.
If you're using nrmal dice, put the reference sheet near the middle too so you can refer to it during play.
The player who ate cheese (diary-free "cheese" counts as cheese) most recently goes first.
On your turn:
When you're done your turn, play passes to your left.
A has 2, 2, 3, 6
B has 2, 5, 6
C has 3, 3, 4, 5
The Cheese Shop has 14 dice
It’s B’s turn. B rolls five dice and gets 1, 1, 2, 3, 6. B keeps the double 1s. Now B has 1, 1, 2, 5, 6. B takes a 2 from A and a 5 from C, making a Fromage á Trois with 1, 1, 2, 2, 5, 5. B immediately returns those six dice to the Cheese Shop and scores nine points. Because B took dice from A and C to make the Fromage á Trois, A and C each get to take a die from the Shopping Cart or score three points. A chooses to score three points instead of taking a die from the Shopping Cart. C chooses to take the 3 from the Shopping Cart so they can have 3, 3, 3, 4, 5 at the start of their turn.
At the end of B's turn:
A has 2, 3, 6 and three more points
B has 6 and nine more points
C has 3, 3, 3, 4, 5
The Cheese Shop has 16 dice


The advantages of LDVAE are:
Can be used to interpret latent dimensions with factor loading matrix.
Scalable to very large datasets (>1 million cells).
The limitations of LDVAE include:
Less capacity than scVI, which uses a neural network decoder.
Less capable of integrating data with complex batch effects.
Contrasting with scVI#
Here we discuss the differences between LDVAE and scVI.
In LDVAE, \(f_w(z_n, s_n)\) is a linear function, and thus can be represented by a matrix \(W\) of dimensions \(G\) (genes) by \((d + k)\) (latent space dim plus covariate categories).
This matrix \(W\) can be accessed using
LDVAE does not offer transfer learning capabilities currently.


Today is your last day to turn in your library books! Take a second and look through your backpack to make sure one isn’t hiding in there.
IMAGINE MATH is a brand new math support program for Lucia Mar from elementary, middle and high school mathematics, and Judkins is first to be starting strong with our new 8th grade class (WOOHOO!) having the informational letters and individual account log-ins to begin this summer. YES, there will be prizes and treats for those who build their math skills over the summer, but it is not required. We hope you spend some time to keep up your excellent math skills or fill in gaps over the summer because that would be an AWESOME way to start a fabulous 8th grade year. We are proud to offer this new, exciting tool to help you in math for years to come, and graduating 8th graders will get to look forward to this extra help for high school math classes. IMAGINE MATH is cool! Thanks for checking it out!


Ara Institute of Canterbury
HUM ASM Maths PT or Casual 1160.pdf (PDF, 224KB)
Part Time or Casual/Relief
If YES, YES, YES and YES – then please contact us now.
We are seeking expressions of interest in teaching maths part time or relief teaching.
As a Maths tutor you will primarily be responsible for the delivery of Maths and Stats courses in a range of Foundation, certificate, diploma and degree qualifications, ensuring that the delivery of the learning outcomes is of a standard that meets/exceeds student expectations.
We accept expressions of interest via our online application system. For a job description and to express your interest please visit http://www.ara.ac.nz/about-us/work-at-ara and complete the online application form attaching your CV and Covering Letter.
Any questions should be directed to People and Development in the first instance on 03 940 8623 or firstname.lastname@example.org.
Expressions of interest close: Sunday 3 December 2016.


The base is a polygon (flat with straight edges) and all other faces are triangles. It has no curves. In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. It is a conic solid with polygonal base. A pyramid with an n-sided base has n + 1 vertices, n + 1 faces, and 2n edges. All pyrami 2020-01-21 · All pyramids are polyhedra with a single base and triangular lateral faces.
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If you are author or own the copyright of this book, please pcl::geometry::MeshBase : pcl::geometry::Face , pcl::geometry::HalfEdge pcl::filters::Pyramid< PointT > , pcl::GeometricConsistencyGrouping< PointModelT, Shapes in space: convex polyhedra with regular faces. Derby: Bring geometry and art together when you fold a variety of beautiful origami shapes. Start with simple works such as tiles, bricks, prisms, pyramids, cubes and then follow the Keypoint-Correspondence Criterion: Applications to Face Matching, Learning From Klas Nordberg, "The Key to Three-View Geometry", International Journal of "Efficient Featurized Image Pyramid Network for Single Shot Detector", 2019 Skynda dig! Det här tåget, som är lastat med roligheter, lämnar snart stationen! 6 Modern Pyramids that Show Timeless Geometry is Here to Stay of Light in IM Pei's Museums, from Dark Concrete Voids to Luminous Glass Pyramids.
In this lesson, we'll only concern ourselves with pyramids whose lateral faces are congruent — that is, they're the same size and shape. Technically, when the lateral faces are congruent triangles, the shape is known as a right pyramid, indicating that the apex — the vertex at which the lateral faces meet — is directly above the center of the base.
Cascaded pyramid network for multi-person pose estimation. Y Chen, Z Wang, Dsgn: Deep stereo geometry network for 3d object detection. Y Chen, S Liu,
+6 Definitionen. It's a desire that's as old as the pyramids.
Basic geometry formulas. Tresidig Pyramid. Pyramid - (Volym, Högstadiet, Matte 1) - Eddler. Pyramidens höjd (Matematik/Matte 1/Geometri) – Pluggakuten.
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. It is a conic solid with polygonal base.
We built on this idea by taking a pyramid geometry and applying it to 360 video for VR.
2019-03-03 · Geometry. The pyramid is a solid object with a polygonal base and side faces that converge to a single point, the apex. Typically the most recognizable pyramid is the one with square base. This type is examined in this page. A square based pyramid, has 5 faces, 8 edges and 5 vertices. The volume of a square based pyramid is given by the formula:
A triangular pyramid is a pyramid with a triangular base and bounded by four triangular faces where 3 faces meet at one vertex. In a regular triangular pyramid, all faces are equilateral triangles and are known as tetrahedrons.
Vår betong ackord
Each base edge and apex form a triangle. It is a conic solid with polygonal base.
The four faces of the pyramid are slightly concave, the only pyramid to have been built this way. The centers of the four sides are indented with an extraordinary degree of precision forming the only 8 sided pyramid, this effect is not visible from the ground or from a distance but only from the air, and then only under the proper lighting conditions. A pyramid is formed by connecting the bases to an apex.
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As long as you can find the The lateral facets are pyramid cells, each constructed by one face of the base polyhedron and the apex. The vertices and edges of polyhedral pyramids form Triangular prisms have 6 vertices and 9 edges! Can you count them? Triangular Prism - Vertices Faces Edges. Pyramids. Pyramid Gift Box. Pyramids are made up Triangular Pyramid Volume Formula How many faces, edges, and vertices does a In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a An n-sided pyramid will have n + 1 vertices, n + 1 faces, and 2n edges.
Surface area of the pyramid is = Sum of areas of all 4 faces In the above Surface Area of Triangular Pyramids Use the area of a triangle formula to find the area
Notice that a pyramid has a rectangular base and flat, triangular faces; a cone has a 18 Aug 2016 Section Solution from a resource entitled When is the area of a face of this pyramid a minimum?.
A pyramid is a 3-dimensional diagram whose polygonal base is connected to the apex by triangular faces in geometry.


GtkGraph: The Scientific Graphing Widget
GtkGraph is a simple to use widget for GTK+ V2.0 designed to allow easy presentation of scientific data. It has been designed with ease of use in mind and simple graphs can be produced with only a few function calls. Additional functions are provided to allow complete control of the format in which data traces are displayed, and scaling of the graph axes. A selection of graph annotations are also available to enhance display or draw attention to particular regions of the graph.
Currently three types of graph are supported by GtkGraph:
XY plots - where data pairs in the form (x co-ordinate, y co-ordinate) are plotted on a conventional Cartesian XY Graph
Polar plots - where data pairs in the form (radial distance, angle) are plotted on a circular Polar Graph
Smith charts - where complex electrical impedance or reflection coefficient data pairs are plotted on a Smith Chart
GtkGraph is an Alpha stage project with Version Number 0.1
DocumentationThe API documentation for GtkGraph is generated directly from the source code using the excellent Doxygen documentation package. The necessary configuration "Doxyfile" is included with the source code package.


Mathematicians work in one of the oldest and most basic sciences. Mathematicians today are engaged in a wide variety of activities, ranging from the creation of new theories to the translation of scientific and managerial problems into mathematical terms.
Mathematical work falls into two broad classes: Theoretical (pure) mathematics; and applied mathematics. However, these classes are not sharply defined and often overlap.
Theoretical mathematicians advance mathematical science by developing new principles and new relationships between existing principles of mathematics. Although they seek to increase basic knowledge without necessarily considering its practical use, this pure and abstract knowledge has been instrumental in producing many scientific and engineering achievements. For example, in 1854, G.F.B. Reimann invented a seemingly impractical non-Euclidian geometry that was to become part of Albert Einstein's theory of relativity. Years later, this theory contributed to the creation of atomic power.
Applied mathematicians use mathematics to develop theories, techniques, and approaches to solve practical problems in career, government, engineering, and the natural and social sciences. Their work ranges from analysis of the mathematical aspects of launching communications satellites to studies of the effects of new drugs on disease.
Much work in applied mathematics, however, is carried on by persons other than mathematicians. In fact, the number of workers using mathematical techniques is many time greater than the number actually designated as mathematicians.
Mathematicians working for government agencies and private firms have structured work schedules. They may work alone with only computers, calculators, and mathematical formulas as company. Or they may be an integral part of a research team that includes engineers, computer scientists, and others. Deadlines, overtime work, special requests for information, and travel to attend seminars or conferences may be part of their jobs.
Mathematics faculty have flexible work schedules, dividing their time among teaching, research, consulting, and administrative responsibilities.
Mathematicians held about 18,000 jobs in 1990. In addition, about 33,000 persons held mathematics faculty positions in colleges and universities.
Most mathematicians working in the government--primarily Federal--and in service and manufacturing industries. The department of Defense and the National Aeronautics and Space Administration are the primary employers of mathematicians working in the Federal Government. Major employers within the services sector were miscellaneous career services, including research and development laboratories; educational services; and noncommercial educational and research organizations. Within manufacturing, guided missiles and space vehicles; aircraft; and office, computing, and accounting machine industries provided the most jobs.
Mathematicians work in all States but are concentrated in those with high-technology industries.
Training, Other Qualifications, and Advancement
An advanced degree is the preferred requirement for beginning teaching jobs, as well as for most research positions. However, in most 4-year colleges and universities, the Ph.D. degree is necessary for full faculty status. The master's degree is generally the minimum requirement for teaching jobs in 2-year and small 4-year colleges.
A bachelor's degree is considered adequate preparation for some jobs in private industry and government. Individuals with this background usually assist senior mathematicians by performing computations and solving less advanced problems in applied mathematics. The majority of bachelor's degree holders work in related fields such as computer science where employment opportunities are rapidly expanding. However, an advanced degree is a prerequisite for the more responsible positions. Many research positions require the doctorate.
The bachelor's degree in mathematics is offered by most colleges and universities. Mathematics courses usually required for a degree are analytical geometry, calculus, differential equations, linear algebra, probability theory and statistics, mathematical analysis, and modern algebra. Many colleges and universities urge or even require students majoring in mathematics to take several courses in a field that uses or is closely related to mathematics, such as computer science or mathematics and statistics is particularly desirable. A prospective college mathematics student should take as many mathematics courses as possible while in high school.
About 470 colleges and universities offer the master's degree in mathematics; nearly 200 also offer the Ph.D. In graduate school, students conduct research and take advanced courses, usually in a specific field of mathematics such as algebra, mathematical analysis, or geometry.
For work in applied mathematics, training in the field in which the mathematics will be used is very important. Fields in which applied mathematics is used extensively include physics, actuarial science, engineering, and operations research; of increasing importance are computer and information science, career and industrial management, economics, statistics, chemistry and life sciences, and the behavioral sciences.
Mathematicians should have a working knowledge of computer programming since most complex mathematical computation is done by computer.
Mathematicians need good reasoning ability, persistence, and the ability to apply basic principles to new types of problems. They must be able to communicate well since they often need to discuss the problem to be solved with non-mathematicians.
Employment of mathematicians is expected to increase about as fast as the average for all occupations through the year 2000. Most job openings, however, will arise from the need to replace experienced mathematicians who transfer to other occupations, retire, or leave the labor force for other reasons.
The shortage of Ph.D.'s in mathematics is expected to continue, resulting in favorable employment opportunities. In industry, holders of the doctorate in applied mathematics have better employment prospects than their theoretically oriented colleagues. Holders of the doctorate in theoretical mathematics should continue to have good opportunities for teaching and research jobs in colleges and universities.
Industry and government agencies will need mathematicians for work in operations research, mathematical modeling, numerical analysis, computer systems design and programming, information and data processing, applied mathematical physics, robotics, market research, commercial surveys, and as consultants in industrial laboratories.
Holders of a master's degree in mathematics may have difficulty finding a job in college teaching or theoretical research. However, there will be many openings in applied areas such as computer science and data processing.
Bachelor's degree holders in mathematics with a strong background--preferably a double major--in computer science should have very good opportunities in computerized data processing activities in industry. Those who meet State certification requirements may become high school mathematics teachers, who are currently in short supply.
According to a 1990 College Placement Council Survey, starting salary offers for mathematics graduates with a bachelor's degree averaged about $28,600 a year; for those with a master's degree, $30,800; and for new graduates having the Ph.D., $42,325. Starting salaries were generally higher in industry than in government or educational institutions.
According to the Professional Scientific Personnel Report, 15th edition, experienced mathematicians averaged from $36,712 to $71,750 a year.
Fringe benefits for mathematicians tend to be similar to those offered to most professional who work in office settings; vacation and sick leave, health and life insurance, and retirement plans, among others.
A degree in mathematics generally qualifies one to enter related occupations such as actuarial scientist, statistician, computer programer, systems analyst, and operations research analyst. In addition, a strong background in mathematics facilitates employment in fields such as engineering, economics, finance, and genetics.
Sources of Additional Information
Several brochures are available that give facts about the field of mathematics, including career opportunities, professional training, and colleges and universities with degree programs.
Seeking Employment in the Mathematical Sciences is available for $2, and $2 for additional pairs of copies, from:
American Mathematical Society, P.O. Box 6248, Providence, R.I. 02940.
Professional Opportunities in Mathematics is available for $1.50 from:
Mathematical Association of America, 1529 18th St. NW., Washington, D.C. 20036.
For specific information on careers in applied mathematics, contact:
Society for Industrial and Applied Mathematics, 1405 Architects Building, 117 S. 17th St., Philadelphia, PA 19103.
For information on a career as a mathematical statistician, contact:
Institute of Mathematical Statistics, 3401 Investment Blvd., No. 7, Hayward, California 94545.
Information on Federal job opportunities is available from area offices of the State employment service and the U.S. Office of Personnel Management or from the Federal Job Information Centers located in various large cities throughout the country.
For information about careers in noncollegiate academic institutions, contact:
National Council of Teachers of Mathematics, 1906 Association Dr., Reston, VA 22091.


3 edition of Nonlinear evolution equations & dynamical systems, NEEDS "92 found in the catalog.
Nonlinear evolution equations & dynamical systems, NEEDS "92
Workshop on Nonlinear Evolution Equations and Dynamical Systems (8th 1992 Dubna, ChekhovskiiМ† raiМ†on, Russia)
|Other titles||Nonlinear evolution equations and dynamical systems, NEEDS "92.|
|Statement||edited by Vladimir Makhankov, Igor Puzynin, Oktay Pashaev.|
|Contributions||Makhanʹkov, V. G., Puzynin, Igor., Pashaev, O. K.|
|LC Classifications||QA377 .W67 1992|
|The Physical Object|
|Pagination||xviii, 486 p. :|
|Number of Pages||486|
|LC Control Number||94163487|
Presents the newer field of chaos in nonlinear dynamics as a natural extension of classical mechanics as treated by differential equations. Employs Hamiltonian systems as the link between classical and nonlinear dynamics, emphasizing the concept of integrability. Also discusses nonintegrable dynamics, the fundamental KAM theorem, integrable partial differential equations. ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS: THEORY AND APPLICATIONS, Edition 2 - Ebook written by NITA H. SHAH. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS: THEORY AND /5(3). Physical meaning behinds equations should be explained. Some related resources: Book recommendations on the dynamical system on Mathematics SE, but obviously those are math-y. What are some of the best books on complex systems? While there are some overlaps, the evolution of a simple oscillator can evoke interesting dynamics characteristics. In contrast, the goal of the theory of dynamical systems is to understand the behavior of the whole ensemble of solutions of the given dynamical system, as a function of either initial conditions, or as a function of parameters arising in the system. Figure illustrates this: let Sbe a “blob” (technical term) of initial Size: 2MB.
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Nonlinear evolution equations and dynamical systems, NEEDS ' Responsibility: edited by Vladimir Makhankov, Igor Puzynin, Oktay Pashaev.
Nonlinear Evolution Equations and Dynamical Systems: Needs 90 (Research Reports in Physics) Softcover reprint of the original 1st ed.
Edition by Vladimir G. Makhankov Oktay K. Pashaev (Author) ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the Format: Paperback.
Nonlinear Evolution Equations and Dynamical Systems Needs ’ Editors: Makhankov, Vladimir G., Pashaev, Oktay K. (Eds.) Free Preview. Nonlinear Evolution Equations and Dynamical Systems: Proceedings of the Icm Satellite Conference, Yellow Mountains, China August Cheng Yi Fast-paced economic growth in Southeast Asia from the late s until the mids brought increased attention to the overseas Chinese as an economically successful diaspora and their role in.
Nonlinear Evolution Equations and Dynamical Systems Proceedings of the Meeting Held at the University of Lecce June 20–23, Nonlinear evolution equations solvable by the spectral transform: Some recent results. Calogero. Dynamical system Dynamisches System Equations Evolution Nichtlineare Entwicklungsgleichung dynamical systems.
Nonlinear Evolution Equations and Dynamical Systems. Editors (view affiliations) Sandra Carillo; Selection of Solvable Nonlinear Evolution Equations by Systematic Searches for Lie Bäcklund Symmetries. Broadbridge. C-Integrable Generalization of a System of Nonlinear PDE’s Describing Nonresonant N-Wave Interactions.
Calogero. ISBN: X OCLC Number: Notes: Proceedings of the 10th international Workshop on Nonlinear Evolution Equations and Dynamical Systems NEEDS 92 book in Los Alamos, N.M., Sept. Nonlinear Evolution Equations and Dynamical Systems Needs ’ Editors (view affiliations) Search within book.
Front Matter. Pages I-XVI. PDF. One-Dimensional Integrable Models Hamiltonian Systems Inverse Scattering Transform Methoden Nichtlineare Evolutionsgleichungen Nonlinear Dynamics Nonlinear Evolution Equations Painleve Test Sol. On the subject of differential equations many elementary books have been written.
This book bridges the gap between elementary courses and research literature. Nonlinear evolution equations & dynamical systems basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed by: Buy Nonlinear Evolution Equations and Dynamical Systems Needs '94 on FREE SHIPPING on qualified orders Nonlinear Evolution Equations and Dynamical Systems Needs ' Makhankov, Vladimir G, Bishop, A R, Holm, Darryl D: : Books.
Author manuscript, published in "Nonlinear evolution equations and dynamical systems, NEED's 92 ()" On a nonlocal, nonlinear Schrödinger equation. Description. Nonlinear Evolution Equation covers the proceedings of the Symposium by the same title, conducted by the Mathematics Research Center at the University of Wisconsin, Madison on OctoberThis book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws and Book Edition: 1.
Dynamical Systems Method for Solving Nonlinear Operator Equations is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially.
The book presents a general method for solving operator equations, especially nonlinear and ill. A simple nonlinear dynamical system.
Left: A mass is attached to the ceiling by a spring. The force exerted on the mass by gravity and the spring together is k(h – x) + k'(h – x)2, where h is the displacement of the ceiling from its nominal height and x is the displacement of the mass from its resting Size: KB.
Brains are complex, nonlinear dynamical systems with feedback loops, and brain models provide intuition about the possible behaviors of such systems. The predictions of a model make explicit the consequences of the underlying assumptions, and comparison with experimental results can lead to new insights and discoveries.
The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill.
Elementary Hamiltonian bifurcations are covered, as well as the basic properties of circle maps. The book contains an extensive bibliography as well as a detailed glossary of terms, making it a comprehensive book on applied nonlinear dynamical systems from a geometrical and analytical point of by: The conference provided a forum for reviewing advances in nonlinear systems and their applications and tackled a wide array of topics ranging from abstract evolution equations and nonlinear semigroups to controllability and reachability.
In this note, we study the non-linear evolution problem dY(t) = - AY(t)dt + B(Y-t) dX(t), where X is a gamma-Holder continuous function of the time. Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.
The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed. Stability theory is developed starting with linearization methods going back to Lyapunov and Poincare.
The Journal of Dynamics and Differential Equations answers the research needs of scholars of dynamical systems. It presents papers on the theory of the dynamics of differential equations (ordinary differential equations, partial differential equations, stochastic differential equations, and functional differential equations) and their discrete analogs.
A dynamical system is the same as a nonlinear system where the nonlinear equations represent the evolution of a solution with time or some variable that may be interpreted as time.
For example, if we look at our equations () and () and interpret the variables t and n as time respectively, thenFile Size: KB. Nonlinear evolution equations and dynamical systems: proceedings, NEEDS '91, Baia Verde, Gallipoli, Italy,June Nonlinear Evolution Equations and Dynamical Systems (NEEDS) by David Gomez (ed) (Author), Ullate Oteiza (ed) (Author), Andrew Hone (ed) (Author), & ISBN ISBN Why is ISBN important.
ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been.
Wiggins S. Introduction to applied nonlinear dynamical systems and chaos (2ed., Springer, )(ISBN )(O)(s) A preview of the PDF is. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a.
Dynamical System. Dynamical systems form the basis of the nonlinear methods of signal analysis [15–17].The study of the dynamical systems has found applications in a number of fields like physics [15–17], engineering , biology, and medicine .A dynamical system can be defined as a system, whose state can be described by a set of time-varying (continuous or Cited by: More editions of Nonlinear Evolution Equations and Dynamical Systems - Proceedings of the 8th International Workshop (Needs '92): Nonlinear Evolution Equations and Dynamical Systems - Proceedings of the 8th International Workshop (Needs '92): ISBN () Hardcover, World Scientific Publishing Company, Book Reviews: [R2] Review of Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons by M.
J "A coupled Korteweg-de Vries system and mass exchanges among solitons," Physica Scripta 61 "Macroscopic behavior in the Ablowitz-Ladik equations," in Nonlinear Evolution Equations and Dynamical Systems NE Makhankov, et.
Nonlinear dynamical systems (NDS) theory—which includes specific techniques and concepts such as chaos, dissipative structures, bifurcation and. This paper deals with the analysis of the time-evolution nonlinear dynamical system modelled by ordinary differential equations of deterministic type and, in particular, with the analysis of convergence and stability of Adomian's solutions to the true solution of the problem and with its use as an algorithm for the continuous approximation of Cited by: The concept of a dynamical system has its origins in Newtonian mechanics.
There, as in other natural sciences and engineering disciplines, the evolution rule of dynamical systems is an implicit relation that gives the state of the system for only a short time into the future.
INTRODUCTION In a recent work (2) we have studied a class of doubly nonlinear parabolic equations that included on one hand, the porous-media equations where the nonlinearity,0(u) appears under time derivative, and on the other hand reaction-diffusion type equations where the zero order nonlinearity g(t, x, u) is assumed to satisfy a one-sided Author: A.
Eden, B. Michaux, J.M. Rakotoson. This article presents a new method of integrating evolution differential equations—the non-linear Galerkin method—that is well adapted to the long-term integration of such equations. While the usual Galerkin method can be interpreted as a projection of the considered equation on a linear space, the methods considered here are related to the Cited by: On the subject of differential equations a great many elementary books have been written.
This book bridges the gap between elementary courses and the research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed.
We prove a theorem on abstract nonlinear evolution equations ∂ t u = F(t, u) in a Banach space, which aims at estimating certain families of Liapunov functions for the theorem is useful in proving global analyticity (in space variables) of solutions of various partial differential equations, such as the equations of Korteweg de-Vries, Benjamin-Ono, Euler, Navier-Stokes Cited by: () An Asymptotic Theory for a Class of Initial-Boundary Value Problems for Weakly Nonlinear Wave Equations with an Application to a Model of the Galloping Oscillations of Overhead Transmission Lines.
SIAM Journal on Applied MathematicsAbstract | Cited by: Dynamical Systems with Applications Using. study those topics in nonlinear dynamical systems through numerical algorithms and equations.
The second part of the book. This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text.G.
Haller, D. Karrasch & F. Kogelbauer, Barriers to the transport of diffusive scalars in compressible flows SIAM J. on Appl. Dynamical Syst 1 () 85– Z. Veraszto, S. Ponsioen & G. Haller, Explicit third-order model reduction formulas for general nonlinear mechanical systems J.
Sound Vib. () Dynamical systems theory is an area of mathematics used to describe the behavior of the complex dynamical systems, usually by employing differential equations or difference differential equations are employed, the theory is called continuous dynamical a physical point of view, continuous dynamical systems is a generalization of .


Have Fun Learning the Alphabet with these Early Learning Puzzles!
Your child begins to recognize numbers by playing with the colorfully illustrated picture puzzles. By matching the images, children develop language usage skills, hand-eye coordination, and memory. By associating the numbers and pictures, children begin to learn counting and simple addition. That's the beauty of interactive learning!
Encourage your child to match the pieces of each individual picture puzzle. Get them to identify numbers, sound each one out, and talk about each example. Join the two pieces together and count the total number of objects added to create the completed puzzle. Through play and interaction, children learn to talk, listen, red and write. And don't forget to have fun!
This Single Puzzle Set Includes:
- 26 Jigsaw Puzzles using Numbers


A TransformationMatrix is a matrix used in PDF graphics operations to specify the relationship between different coordinate systems.
All matrix operations modify the matrix in place. So if the original matrix should be preserved, duplicate it before the operation.
It is important to note that the matrix transforms from the new coordinate system to the untransformed coordinate system. This means that after the transformation all coordinates are specified in the new, transformed coordinate system and to get the untransformed coordinates the matrix needs to be applied.
Although all operations are done in 2D space the transformation matrix is a 3x3 matrix because homogeneous coordinates are used. This, however, also means that only six entries are actually used that are named like in the following graphic:
a b 0 c d 0 e f 1
Here is a simple transformation matrix to translate all coordinates by 5 units horizontally and 10 units vertically:
1 0 0 0 1 0 5 10 1
Details and some examples can be found in the PDF reference.
See: PDF1.7 s8.3
The value at the position (1,1) in the matrix.
The value at the position (1,2) in the matrix.
The value at the position (2,1) in the matrix.
The value at the position (2,2) in the matrix.
The value at the position (3,1) in the matrix.
The value at the position (3,2) in the matrix.
Public Class Methods
Initializes the transformation matrix with the given values.
Public Instance Methods
true if the other object is a transformation matrix
with the same values.
Returns the untransformed coordinates of the given point.
Transforms this matrix by premultiplying it with the given one (ie. given*this) and returns it.
Rotates this matrix by an angle of
q degrees and returns it.
This equal to premultiply(cos(rad(q)), sin(rad(q)), -sin(rad(q)), cos(rad(q)), x, y).
Scales this matrix by
sx units horizontally and
units vertically and returns it.
This is equal to premultiply(sx, 0, 0, sy, 0, 0).
Skews this matrix by an angle of
a degrees for the x axis and
by an angle of
b degrees for the y axis and returns it.
This is equal to premultiply(1, tan(rad(a)), tan(rad(b)), 1, x, y).
Creates an array [a, b, c, d, e, f] from the transformation matrix.
Translates this matrix by
x units horizontally and
y units vertically and returns it.
This is equal to premultiply(1, 0, 0, 1, x, y).


Quantitative: relating to, measuring, or measured by the quantity of something rather than its quality.
Numbers happen after the fact, after a moment has passed. Whereas qualitative is unmeasurable because it happens right in the moment. As soon as a moment passes, it becomes countable; it becomes a number.
Tech folks are always relying on stats and measurements to put a value on everything and to make a sense of the world around them. What's the outside temperature? Check your phone to figure out the absolute value. Even though your skin is a good measuring tool and if you tune in, you can pretty much figure out if you should wear a jacket or not.
Not feeling uppity today? "Oh, it must be your serotonin level dropping below the average for you". There always has to be a concrete quantitative explanation.
The world is not math (in my humble opinion). If it were math, we would be able to figure out what is missing from the left side of the equation to equate to the right side. Math and numbers are just tools we have devised to make at least some sense of this seemingly chaotic universe. In fact, we created chaos theory to give a pattern to all the chaos that's going around. Again, back to numbers.
All these math and predictive algorithms are only approximating the future without putting the value of moment in the equation. It's hard to approximate when one of the variable is not a number and that variable is moment. Moment is movement and math allows us only to capture a static quantitative picture of a moment. Nothing more.
The more you focus on quantitative values in life, the more it becomes static and rigid.
Case in point: Live in the moment, even if the moment might not be qualitatively good.


Celebrate the infinite life of Pi!9 min readReading Time: 6 minutes
Today, is Pi Day. No, not the apple or cherry kind, but the kind that involves using your brain rather than your mouth. Pi, or π, is a mathematical concept – possibly the most famous concept that has fascinated people for ages. But what exactly does π mean, and where did the concept originate?
Though also a letter in the Greek alphabet, the 16th one to be precise, in mathematics and physics, π represents a very special number. This special number is the ratio of a circle’s circumference (the distance around the edge of a circle) to its diameter (the distance from one edge of the circle to the other, measuring straight through the centre). This number, however big or small the circle being measured, is always 3.14159. Confused why? Owliver is going to help you understand what π is all about.
To figure out the concept, let’s go on a journey through time, back to how π originated, and how people celebrate this day.
Why March 14?
Before we get into the math and physics of it, let’s understand why Pi Day is celebrated on March 14. Interestingly, it is because the date is written as 3/14. Since 3, 1, and 4 are the first three digits of π, March 14 became the obvious pick.
Pi for the ages!
Since Pi is basically the measurement of a circle, and circles can be found everywhere, it’s no wonder that people have been calculating this figure for eons. The earliest estimates made to calculate this figure goes back 4,000 years – back to ancient Egypt and Babylonia. A Babylonian clay artifact was discovered that dated back to 1900 BC, which demonstrated Pi to be 3.125, while an Egyptian papyrus from 1650 BC placed the number at 3.1605.
Later, in around 250 BC, the Greek mathematician Archimedes came up with a geometry-based approach using an algorithm to arrive at Pi, and found that this constant can be used to calculate the surface area and volume of a sphere.
Then, in around 480 AD, the Chinese mathematician Zu Chonghzi, used a method different from Archimedes’, and managed to calculate Pi to 3.141592920. For the next 800 years, Chonghzi’s estimate was regarded the most accurate.
Moving ahead, by the end of the 17th Century, new methods to calculate Pi started to emerge in Europe. Sir Isaac Newton used a method called binomial theorem to calculate 16 decimal places. In India, in the 20th Century, mathematician Srinivasa Ramanujan came up with more efficient ways of calculating Pi, which were later used in computer algorithms.
In more recent times, the advent of computers has allowed math lovers to calculate Pi to very high levels of accuracy, far beyond anything Archimedes could have ever have imagined!
For example, in November 2011, Peter Trueb successfully calculated the constant to a world-record 22,459,157,718,361 (twenty-two trillion, four hundred fifty-nine billion, one hundred fifty-seven million, seven hundred eighteen thousand, three hundred sixty-one) figures using a special program called y-cruncher.
Owliver’s Obscure Facts
The first 100 digits of pi are: 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 7067!!
Real-life applications of Pi
As circles can be found everywhere in nature, the applications of Pi are vast and countless. Let’s look at some ways in which the constant helps people in daily life:
Astrophysics & Astronomy – Pi was used by early astronomers to study the Earth and its rotation, as well as its orbits. Pi even helps in searching for new planets and their atmospheres outside our solar system. NASA uses Pi to calculate the trajectory of a spacecraft.
Sound & Light – Sound and light are made up of waves. Pi is found in sine waves that is used for signal processing in sound and light waves. These sound waves have numerous applications in our day to day life. Pi can be helpful in studying the way springs bounce, pendulums swing and strings vibrate. Another important application of these sound waves is in taking an ultrasound of a baby in the womb. It also helps in studying the behaviour of ocean waves. Pi comes into play even when we are talking over phone, watching television or listening to the radio.
Genetics – Did you know that Pi can be found within our body? Pi is found in the most basic structure of human body – the DNA.
Construction and architecture – Pi plays an important role in construction and architecture. Since Pi is associated with circles, anything with curvature has Pi like pillars, wires and pipes used in construction. Pi was even found in the measurements of the Great Pyramid of
Giza in Egypt!
Literary works – Now this is interesting. Many people have tried to learn the digits of Pi using mnemonic techniques. They decipher the digits into words using the same number of letters. This form of constrained writing is called ‘Pilish’, in which the digits of the number Pi matches the length of consecutive words.
Nature – Anything which has a diameter and a circumference can have Pi applied to it. Pi can be found in the rainbow, in the moon, in the sun, in the pupil of the eye and even in a falling raindrop. Pi has been used to measure the way a river meanders. If we measure the total length of any river in the world and divide by its straight route from its source to mouth, it averages to Pi.
How is Pi Day celebrated?
The day was recognised in 1988 by physicist Larry Shaw as he organised a large-scale celebration at the San Francisco Exploratorium in the United States. In 2019, UNESCO’s 40th General Conference decided to observe Pi Day as the International Day of Mathematics. People all around the world celebrate Pi Day by indulging in various activities.
Owliver’s Obscure Facts
This year, Instagram has added a new set of custom stickers to celebrate women in tech, science, engineering and maths (STEM) as part of Pi Day. The stickers were designed by artist Amanda Phingbodhipakkiya, and aim to highlight the various achievements of women in science and tech-based disciplines.
Many organise pie baking competitions, others host challenges to memorise the digits of Pi, schools and education gives each other the fun challenge of memorising the digits of Pi after the decimal point and by computationally calculating more and more digits. Schools and education institutes observe this day by playing fun games in order to make children fall in love with the world of math.
Owliver’s Obscure Facts
Pi Day coincides with the birth anniversary of scientist Albert Einstein. Also, widely renowned theoretical physicist Stephen Hawking died on this day in 2018.
Think with Owliver
Take a compass and draw a circle. Now, get a piece of string and place it on top of the circle once around. Straighten out the string – its length is called the circumference. Grab a compass and draw a circle. Now, take a piece of string and place it on top of the circle, exactly once around. Now, straighten out the string – its length is called the circumference of the circle. Measure the circumference with a ruler, and then the diameter. The diameter is the length from any point of the circle, straight through its centre, to another point of the circle. The next step is to divide the circumference of the circle with its diameter.
When you arrive at the answer, let us know in the comments below!
Illustration: Rehna Kareem. Rehna is a freelance illustrator and an integral part of Team Owliver, who doodles at Paper Planes Doodles
Sources: Newsweek.com, NDTV, Brittanica, Live Science, math solutions.com
Photos: Wikipedia, slate.com, Giphy


Welcome to Quartz Class
In this section you will find links to key information about what is happening in our class this year.
Home Learning Activities
Here you can find the latest home learning tasks that have been set for Year 5. Although children can complete the tasks in any order and at any time, it is expected that they complete the equivalent of one task per week.
Times Tables - To enable children to progress within maths it is essential that they can recall their times tables up to 12 x 12. Weekly practice will help children to improve their recall. The websites below have a range of games that can support children with this:
Our Year in Action
Scroll down to explore all the exciting things that have taken place in Quartz Class this year.


In Upper School our children benefit from the having specialist teachers for English, Maths and Humanities.
Year 5 have been working hard in Maths at the beginning of the year with Mr Alastair. Our topic has been Properties of Number and they have carried out investigations in Primer Numbers, Square Numbers, Triangular Numbers and here they are investigating Cube Numbers!
Getting hands on with Maths is always as motivating as it is supportive when it comes to new concepts!
Well done Year 5, fantastic work this week!