2 edition of On the generic nonconvergence of Bayesian actions and beliefs found in the catalog.
1990 by College of Commerce and Business Administration, Bureau of Economic and Business Research, University of Illinois at Urbana-Champaign in Urbana, Ill .
Written in English
Includes bibliographical references (p.-25).
|Series||BEBR faculty working paper -- no. 90-1659, BEBR faculty working paper -- no. 90-1659.|
|Contributions||University of Illinois at Urbana-Champaign. Bureau of Economic and Business Research|
Philosophy. Classical statistics is a bucket of assorted methods; different "methods" may give different answers for whether, e.g., an experimental result is "statistically significant". In contrast, as the famous Bayesian E. T. Jaynes emphasized, probability theory is math and its results are theorems, every theorem consistent with every other theorem; you cannot get two different . An Initiate of the Bayesian Conspiracy. An Intuitive Explanation of Bayesian Reasoning is an extraordinary piece on Bayes' theorem that starts with this simple puzzle: 1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. Bayesian networks (BNs) are a type of graphical model that encode the conditional probability between different learning variables in a directed acyclic graph. There are benefits to using BNs compared to other unsupervised machine learning techniques. A few of these benefits are:It is easy to exploit expert knowledge in BN models. BN models have been found to be very robust .
Currach requires no harbours
How to restore and decorate chairs in early American styles
remote sampling of radioactively and chemically contaminated materials by laser ablation.
heritage of Indian art
Cass Timberlane novel of husbands and wives
Sigmund Freud, his exploration of the mind of man.
Ireland must never be united.
The white slave
University of Ghana.
Foundations of Dance/Movement Therapy
Hoare logic for GOLOG programs.
The Management of change
Corrections. All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:vyipSee general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its. Summary. SupposeY n is a sequence of i.i.d.
random variables taking values in Y, a complete, separable, non-finite metric space. The probability law indexed byθεΘ, is unknown to a Bayesian statistician with priorμ, observing this lizing Freedman , we show that “generically” (i.e., for a residual family of (θ,μ) pairs) the posterior beliefs do not weakly Cited by: Bayesian Learning, Shutdown and Convergence.
On the generic nonconvergence of Bayesian actions and beliefs for a residual family of (,) pairs) the posterior beliefs do not weakly converge. Volume 1, Issue 4, ISSN: (Print) On the generic nonconvergence of Bayesian actions and beliefs.
Feldman Pages Research Articles. Optimal contract mechanisms for principal-agent problems with moral hazard and adverse selection. Page Jr Pages Book Series; Protocols; Reference Works; Proceedings; Other. Bayesian Networks A Practical Guide to Applications. Bayesian Networks, the result of the convergence of artificial intelligence with statistics, are growing in popularity.
Their versatility and modelling power is now employed across a variety of fields for the purposes of analysis, simulation, prediction and diagnosis/5(2). I would suggest Modeling and Reasoning with Bayesian Networks: Adnan Darwiche.
This is an excellent book on Bayesian Network and it is very easy to follow. This book takes a much more rigorous approach to Bayesian statistics than Bayesian Data Analysis.
Robert develops both the decision theoretic background of Bayesian statistics up to the level of The Theory of Point Estimation by Lehmann and MCMC computation including practical implementation by: Thomas Bayes (/beɪz/; c. – ) was an English statistician, philosopher, and Presbyterian minister.
Bayesian (/ˈbeɪziən/) refers to a range of concepts and approaches that are ultimately based on a degree-of-belief interpretation of probability, the first item listed below. Bayesian probability, the degree-of-belief interpretation. Bayesian Theory book. Read reviews from world’s largest community for readers.
This highly acclaimed text, now available in paperback, provides a thoroug /5(15). The use of simulation modelling techniques in studies of technological innovation dates back to Nelson and Winter''s book "An Evolutionary Theory of Economic Change" and is an area which has been steadily expanding ever since.
Four main issues are identified in reviewing the key contributions that have been made to this burgeoning literature. Firstly, a key driver in the. For understanding the mathematics behind Bayesian networks, the Judea Pearl texts ,  are a good place to start.
I also enjoyed Learning Bayesian Networks . There's also a free text by David MacKay  that's not really a great introduct. Bayesian Belief Networks for dummies 1.
Bayesian Belief Networks for Dummies Weather Lawn Sprinkler 2. Bayesian Belief Networks for Dummies 0 Probabilistic Graphical Model 0 Bayesian Inference 3. Bayesian Belief Networks (BBN) BBN is a probabilistic graphical model (PGM) Weather Lawn Sprinkler 4.
Complexity of Bayesian belief exchange over a network where they receive private information and act based on that information while also observing other people's beliefs or actions. ^ In the. Convergence of Beliefs in Bayesian Network Games Willemien Kets∗ Octo This version: December 7, Abstract In many contexts, players.
"On the Generic Nonconvergence of Bayesian Actions and Beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(4), pagesOctober. Gilboa, Itzhak & Postlewaite, Andrew & Schmeidler, David, of Bayesian decision makers are identiﬁable, that is, unique prior and posterior subjective probabilities that represent the beliefs of a Bayesian decision maker.
Moreover, because the deﬁnition of beliefs is choice based, this claim is testable (that is, subject to refutation) within the realm of the revealed preference methodology.
Whether to interpret subjective beliefs as probabilities 2. Whether to interpret probabilities as subjective beliefs (as opposed to asymptotic frequencies) 3.
Whether a Bayesian or frequentist algorithm is better suited to solving a particular problem. Given my own research interests, I will add a fourth argument: Size: KB.
Other articles where Bayesian network is discussed: Judea Pearl: Pearl created the Bayesian network, which used graph theory (and often, but not always, Bayesian statistics) to allow machines to make plausible hypotheses when given uncertain or fragmentary information.
He described this work in his book Probabilistic Reasoning in Intelligent Systems: Networks of. Modeling Causal Learning Using Bayesian Generic Priors on Generative and Preventive Powers Hongjing Lu ([email protected]) beliefs to be updated by integrating prior beliefs with new observations.
Bayesian inference involves two basic that generic priors will favor necessary and sufficient causes. Bayesian Data Analysis by Gelman et.
al (Lots of interesting applications, a good amount of theory) I've also heard good things about Peter Hoff's "A first course in Bayesian Statistical Methods" which apparently spends a bit more time building the Bayesian framework.
We cast such tasks as Bayesian Games. As in the standard formulation , players know their own types but not those of their opponents; dyads are thus playing games of incomplete information. A player also has prior beliefs about their opponent that are updated in a Bayesian manner after observing the opponent’s actions.
Bayesian, we claim that Bayesian models can elucidate diverse aspects of scientiﬁc reasoning, increasing our understanding of how science works and why it is so successful.
The book is written a cycle of variations on this theme; it applies Bayesian inference to eleven different aspects of scientiﬁc Size: 1MB. The basic concepts of Bayesian inference and decision covered in this book have not really changed since the first edition of this book was published.
As a result, the changes from the First Edition are quite minor, and the preceding comments from the Preface to that edition still apply to the Second Edition. Bayesian decision theory It is a statistical system that tries to quantify the tradeoff between various decisions, making use of probabilities and costs.
An agent operating under such a decision theory uses the concepts of Bayesian statistics to estimate the expected value of its actions, and update its expectations based on new information.
A Bayesian network, Bayes network, belief network, decision network, Bayes(ian) model or probabilistic directed acyclic graphical model is a probabilistic graphical model (a type of statistical model) that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG).
Bayesian networks are ideal for taking an event that occurred and predicting the. BAYESIAN BELIEF NETWORK. BAYESIAN BELIEF NETWORK. N., Pam M.S. - April 7, n. a statistical model which illustrates random variables and conditional dependencies via a simple directed acyclic graph (DAG).
There is an assumption of causal factors and situations which contribute to and are responsible for resulting states. Pythonic Bayesian Belief Network Package, supporting creation of and exact inference on Bayesian Belief Networks specified as pure python functions.
- eBay/bayesian. Bayesian Belief Networks are a powerful tool for combining different knowledge sources with various degrees of uncertainty in a mathematically sound and computationally efficient way. A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest.
When used in conjunction with statistical techniques, the graphical model has several. Book Description. Understand the Foundations of Bayesian Networks—Core Properties and Definitions Explained. Bayesian Networks: With Examples in R introduces Bayesian networks using a hands-on approach.
Simple yet meaningful examples in R illustrate each step of the modeling process. Statistics and the Bayesian mind Thomas L. Griffiths Department of Psychology University of California, Berkeley Joshua B. Tenenbaum Department of Brain and Cognitive Sciences Massachusetts Institute of Technology When people mention statistics and human cognition in the same sentence, it is usually toFile Size: KB.
Using Bayesian belief networks in adaptive management1 J. Brian Nyberg, Bruce G. Marcot, and Randy Sulyma Abstract: Bayesian belief and decision networks are modelling techniques that are well suited to adaptive-management applications, but they appear not to have been widely used in adaptive management to date.
A theory of Bayesian groups Franz Dietrich1 preprint version Abstract A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through aver-aging.
In their celebrated \Groupthink", Russell et al. () require group credencesFile Size: KB. Pythonic Bayesian Belief Network Package, supporting creation of and exact inference on Bayesian Belief Networks specified as pure python functions. - eBay/bayesian-belief-networks.
A non complete list: The Bayesian Brain hypothesis (a brain is basically doing Bayesian stats), Bayesian philosophy of science, Bayesian statistics, Bayesian view of probability, Computational methods for doing Bayesian statistics, etc.
Surely many of these are related (say Bayes. probability and Bayes. stats), but you don't have to buy them all. Dynamic Bayesian Networks Beyond Graphical Models – Carlos Guestrin Carnegie Mellon University December 1st, Readings: K&F:, Dynamic Bayesian network (DBN) beliefs Compute t+1.
The Application of Bayesian Belief Networks Barbara Krumay WU, Vienna University of Economics and Business, Austria @ Roman Brandtweiner WU, Vienna University of Economics and Business, Austria [email protected] Abstract The analysis of nominal data is often reduced to accumulation and description.
Using Bayesian belief networks in adaptive management1 J. Brian Nyberg, Bruce G. Marcot, and Randy Sulyma Abstract: Bayesian belief and decision networks are modelling techniques that are well suited to adaptive-management applications, but they appear not to have been widely used in adaptive management to by: Correctness of Belief Propagation in Bayesian Networks with Loops Bayesian networks represent statistical dependencies of variables by a graph.
For example, in the figure, the "y" variables may be image values, and the "x" variables may be quantities to estimate by computer vision. Bayesian networks are used in many machine learning Size: 88KB.
Probabilistic models based on directed acyclic graphs have a long and rich tradition, beginning with the work of geneticist Sewall Wright in the s. Variants have appeared in many fields. Within statistics, such models are known as directed. If your question is "Is the only library for performing computations on Bayesian Networks?" Then the answer is no, there are several.
A quick google search turns up a list of Bayesian Network software. – Bayesian belief networks • Give solutions to the space, acquisition bottlenecks • Significant improvements in the time cost of inferences CS Bayesian belief networks Bayesian belief networks (BBNs) Bayesian belief networks.
• Represent the full joint distribution more compactly with smaller number of parameters.Knowledge Engineering and Maintenance [Druzdzel 95] Druzdzel, Marek J. and van der Gaag, Linda C., "Elicitation of Probabilities for Belief Networks: Combining Qualitative and Quantitative Information," Proceedings of the Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann, San Francisco, CA, ppData Mining and Knowledge Discovery KLHeckerman Febru BAYESIAN NETWORKS FOR DATA MINING 81 an introduction to the Bayesian approach for those readers familiar only with the classical view.
In a nutshell, the Bayesian probability of an event x is a person’sdegree of belief in that by:


Seeing what-causes-what is missing. Yesterday I said 99.99% of humanity lacks it… I wasn’t exaggerating. It’s really 99.999%… ten times more that lack it.
In essence one in 100,000 people, or ten in a million have it even partially, in one area of life.
It’s an intellectual capacity, fundamentally essential to success in the world
This is why Mathematics, Physics, and Geometry is so hard for people. Continue reading “Connecting the dots in the right order… seeing cause and effect accurately”


We see the strange mystic simplicity of the circle; we see the maddening complexity of the endless numbers: 3.14159265358979323846264338327950288419716939937510… off into the great yawning infinite.
The mathematical constant Π (that is, “pi”) is a Transcendental (there is no polynomial with rational coefficients of which Π is a root) and an Irrational (it cannot be written as the ratio of two integers) Real Number; the ratio of a circle`s circumference to its diameter in Euclidean geometry.
Also known as “Archimedes Constant” it has manifold uses in mathematics, physics, and engineering… and its irreducible complexity has provoked human imagination and wonder for centuries.
Today is the fourteenth day of the third month (3/14 in American date format) and it is currently 1:59 in the afternoon = 3.14159… and so forth. It is also the 128th birthday of Albert Einstein.


Entering the Third Dimension
Colon definitions typically contain both control flow operators and stack flow operators. In order to represent both these aspects of a program graphically we need to move from two dimensional flowcharts to three dimensions. This is illustrated here with two examples.
In his seminal work "The Art of Computer Programming" D E Knuth devotes a great deal of space to analysing this algorithm. In volume 1, page 2 he describes it thus;
Algorithm E. (Euclid's algorithm). given two positive integers m and n , find their greatest common divisor, i.e., the largest positive integer which evenly divides both m and n.
E1. [Find remainder.] Divide m by n and let r
be the remainder. (We will have 0<=r<n.)
And here is the Forth code to do this; (the test for zero has been placed before the division, so that it handles an argument of zero predictably).
: GCD ( n n--n) BEGIN DUP WHILE TUCK MOD REPEAT DROP ;
There are many possible algorithms to find the number of combinations of r items from n objects ( nCr). The two most commonly quoted are
and Vandermonde's theorem;
nCr = nC(r-1) + (n-1)Cr
The former has a problem in that very large intermediate results can occur, even when the result is very small. The latter does not suffer from this, but is computationally very inefficient.
Therefore we choose to use the following recurrance, which suffers from neither of those setbacks;
r=0 --> nCr = 1 r>0 --> nCr = nC(r-1)(n-r+1)/r
This translates in Forth into;
: (COMBS) ( n r--c) DUP IF 2DUP 1- RECURSE -ROT TUCK - 1+ SWAP */ ELSE 2DROP 1 THEN ;
Where the word RECURSE indicates that the definition is called recursively.
One refinement we can make to this is to note that the function is symmetrical, i.e. that nCr=nC(n-r), so we can reduce the amount of work that the word may do by choosing to compute the smaller of r and (n-r). To do this we can call (COMBS)from another word that does the test. (Having interactively tested (COMBS) first, naturally.)
: COMBS ( n r--c) 2DUP - MIN (COMBS) ;
This concludes the body of this introduction to Forth. In the last section we will mention some of the aspects of Forth not covered here, and give some pointers to other information about Forth.
Or, if you prefer, you may return to the contents page.


What they do[edit | edit source]
Beakers are the foundation of making your civilization strong. While your hammers let you build and construct buildings, beakers let you research new technologies to expand your civilizations horizons. These techs can expand your trade, military, and productive opportunities.
Where to get them[edit | edit source]
Beakers are found on every chunk of the world, a simple '/t survey' will let you know where to get the best ones.
How to Win with them[edit | edit source]
In order to win the Scientific Victory, you must have Enlightenment researched. You don't NEED to research armor techs to achieve this, but all other civilizations will war you in an attempt to stop you.
Researching[edit | edit source]
A single Beaker is worth 1 hour of research time, that means if you have 1 beaker and the tech you require has 60, it will take you 60 hours to Research that tech. An equation to solve for this would be:
((T / [P+C]) - T) / B
In order to make this work, you must add the percents 1st, then move the decimal once to the left, then solve. And ignore the negative, I'm to dumb to make this work any other way. Variables: T = Time, B = Beakers, P = Policy, C = Buildings Ex: Say you need a tech worth 5000 beakers researched and have a 10% Policy buff and 20% Building Buff along with 1000 base beakers.
((5000 / [.10 + .20]) - 5000) / 1000
First you would add the .10 and .20 to get .3 and you'd move the decimal making it 3. Then you would do 5000 / 3 which is 1666. Next you would do 1666 - 5000 and get a negative number. Then you divide that number by 1000 to get your time.


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ILP Statistical Analysis
Quantitative experimental data will generally need to be analysed using some form of statistics. There are a large number of different statistical tests that can be used depending upon your data, how it was collected and the types of comparisons you intend to make.
The information shown below is extracted from the "information for authors" for Nature Cell Biology submissions.
Nature Cell Biology - Guide to Authors and Referees
The description of all reported data that includes statistical testing must state the name of the statistical test used to generate error bars and P values, the number ( n ) of independent experiments underlying each data point (not replicate measures of one sample), and the actual P value for each test (not merely 'significant' or 'P < .05').
Descriptive statistics should include:
- clearly labeled measure of center (such as the mean or the median)
- clearly labeled measure of variability (such as standard deviation or range)
- Ranges are more appropriate than standard deviations or standard errors for small data sets. Standard error or confidence interval is appropriate to compare data to a control.
- Graphs should include clearly labeled error bars.
- Authors must state whether a number that follows the ± sign is a standard error (s.e.m.) or a standard deviation (s.d.).
Since for complex biological experiments the number of independent repeats of a measurement often has to be limited for practical reasons, statistical measures with a very small n are commonplace.
- Statistical measures applied to too small a sample size are not significant and they can suggest a false level of significance.
- Error bars should not be provided for n < 3. Instead, the actual individual data from each experiment should be plotted
- If n < 5 individual data should be plotted alongside an error bar.
- In cases where n is small, a justification for the use of the statistical test employed has to be provided.
It is admissible to present a single 'typical result' of n experiments.
- If n is not based on independent experiments (that is n merely represents replicates of a measurement), it may still be meaningful to present statistics, but a detailed description of the repeated measurement is required.
A basic description of n, P and the test applied should be provided in the figure legends, and a further discussion of statistical methodology should be provided in the methods section.
Authors must justify the use of a particular test and explain whether their data conform to the assumptions of the tests.
When making multiple statistical comparisons on a single data set, authors should explain how they adjusted the alpha level to avoid an inflated Type I error rate, or they should select statistical tests appropriate for multiple groups (such as ANOVA rather than a series of t-tests).
Many statistical tests require that the data be approximately normally distributed; when using these tests, authors should explain how they tested their data for normality. If the data do not meet the assumptions of the test, then a non-parametric alternative should be used instead.
Small Sample Size
When the sample size is small (less than about 10), authors should use tests appropriate to small samples or justify their use of large-sample tests.
Text extract source: Nature Cell Biology - Guide to Authors and Referees


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Jens LorenzUniversity of New Mexico
Abstract: In this talk I consider the blow-up question for the solutions of the Navier-Stokes equations, one of the millennium problems. After reviewing blow-up conditions for some simpler models, I will focus on the particular difficulties posed by the Navier-Stokes equations.
To analyze the equations, it is common to first eliminate the pressure by applying the Helmholtz projector. However, since pressure differences drive the flow, the pressure term is essential for understanding blow-up conditions. In this lecture, I will describe properties of the pressure, assuming that blow-up does occur.
Laszlo LempertPurdue University
Abstract: Originally, complex approximation was about approximating a holomorphic function, defined on an open subset of the complex plane, by polynomials. Subsequently one was led to consider more general problems: the function to be approximated had several, perhaps infinitely many variables, and the approximating functions could come from classes of functions other than polynomials.
In my talk I will describe one line of research, starting with Carl Runge's discovery from 1885 and leading up to recent results. I will also explain why approximations are in a sense inevitable in complex analysis/geometry.
Steven CoxRice University
Abstract: One may elicit the qth tone of a string by applying the 'correct touch' at one of its q-1 nodes during a simul-taneous pluck or bow. This effect was first scored for violin by Mondonville in 1735. Though it captured the attention of the 19th century masters, Chladni, Tyndall, Helmholtz and Rayleigh, it remained for Bamberger, Rauch and Taylor in 1982 to develop and analyze the first mathematical model of harmonics Their 'touch' is a damper of magnitude b concentrated at the node p/q. The `correct touch' is that b for which the modes, that do not vanish at p/q, are maximally damped. We here examine the associated spectral problem. We find the spectrum to be periodic and determined by a polynomial of degree q-1. We establish lower and upper bounds on the spectral abscissa and show that the set of associated root vectors constitutes a Riesz basis in the natural energy space and so identify 'correct touch' with the b that minimizes the spectral abscissa.
Constantin GeorgescuTulane University
Abstract: Improved estimates of a survey population parameter can be obtained by using information about co-related auxiliary variable. There is a huge literature on such methods for estimating the mean. In this talk we explore some median-versions of these mean-based methods.
Following a brief overview on quantile regression, the new quantile based estimator is introduced and some of its properties are examined. A proof for consistency of the marginal quantile estimator and for Bahadur-Expansion validity of the conditional quantile estimator is included. Then, a look by means of the conditional double exponential likelihood model reveals the quantile base estimator connections to some of the already classical estimators.
Some simulation results exploring the performance of the new estimator concludes the presentation.
Chris JonesUniversity of North Carolina
Abstract: The Lagrangian (fluid particle) trajectories of a steady Euler flow in 2D are determined by an integrable system and hence exhibit no chaotic motion. The question then naturally arises as to whether a perturbed flow, which incorporates the physical effects of viscosity and forcing, can be chaotic. This problem is non-trivial since the perturbation is added at the level of the full partial differential equation but the potential chaos is at the level of the particle trajectories. It brings up many issues including long-time existence for 2D Navier-Stokes and finite-time Melnikov theory.
Dan BurnsUniversity of Michigan
Abstract: Renormalized Chern forms are invariants of a complex manifold with strongly pseudoconvex boundary M. They give rise to numerical invariants because though X may have infinite (invariant) volume, the characteristic numbers are given by convergent integrals. Prompted by numerous examples in two complex dimensions, JS Ryu and the speaker have shown that if the boundary M is locally spherical (CR equivalent to the sphere), then these forms give rational cohomology classes. The methods of proof are analytic continuation and showing that monodromy eigenvalues are roots of unity, and a residue calculaton. Speculations on the real analogue, and analytic applications will also be discussed, as well as further applications of the analytic continuation technique.
John MayerUniversity of Alabama at Birmingham
Abstract: A simply-connected open set U in the plane R² can have a "nice" boundary (a circle, or homeomorphic image thereof) or a "nasty" one—with lots of interesting possibilities (to a topologist) for "nasty". There is a theory, useful in plane topology and in dynamics of the complex plane, that views even nasty boundaries from the point of view of the nicest one, a circle. Imagine that you have a map of U with polar coordinates provided by the Riemann Mapping Theorem. That is, there is a complex analytic homeomorphism h from the open unit disk D (with nice radial rays and concentric circles as its coordinates) onto U (with images of those rays and circles to provide coordinates). You stand at the image h(0) in U of the center 0 of D and walk along an image of a radial ray toward the boundary of U. Assume the sun is at h(0) and its illuminating rays follow the radial coordinates that h imposes on U. You are thicker than a ray, so you cast a shadow on the boundary. Suppose this shadow gets narrower as you get further from the sun and closer to the boundary. If the boundary is "nice" (like a circle, say), then your limiting shadow is a point on the boundary—surely a trivial impression! What is your limiting shadow if the boundary is "nasty" in the direction you are walking? Further progress on understanding the connected Julia sets of certain polynomials requires understanding shadows that leave nasty impressions.
Graeme MiltonUniversity of Utah
Abstract: Composite materials have been studied for centuries, and have attracted the interest of reknown scientists such as Poisson, Faraday, Maxwell, Rayleigh, and Einstein. Their properties are usually not just a linear average of the properties of the constituent materials and can sometimes be strikingly different. The beautiful red glass one sees in old church windows is a suspension of small gold particles in glass. Sound waves travel slower in bubbly water than in either water or air. In the last few decades composites have been found to have some surprising properties. Most materials, such as rubber, get thinner when they are stretched, but it is possible to design composites which get fatter as they are stretched. Electromagnetic signals can travel faster in a composite than in the constituent phases. It is possible to combine materials which expand when heated to obtain a material which contracts when heated. It is still an open question as to what properties can be achieved when one mixes two or more materials with known properties. This lecture will survey some of the progress which has been made.
Lex OversteegenVigreUniversity of Alabama, Birmingham
Abstract: A dynamical system is a function ƒ : Χ → Χ from a space Χ to itself. In dynamics one is interested in understanding the behavior of points under iteration (i.e., the behavior of the sequence ƒⁿ ( x ) as n → ∞). Even in very simple cases a complete description of the behavior of all points is not possible.
Much progress has been made in case Χ = C is the complex plane and ƒ : C → ℂ is a complex polynomial but important problems remain. In this case, it is well known that it suffices to consider polynomials of the form ƒ ( z ) = zd + ad-2 zd-2 + ⋅⋅⋅ +a₁ z + a₀. Hence the space of all relevant polynomials of degree d can be parameterized by C d-1.
For any polynomial ƒ, C + J ∪ F with J ∩ F = ∅, where J is perfect and compact (the Julia set) and F is open and dense (the Fatou set). For all z ∈ F, ƒⁿ ( z ) converges to either a periodic point, infinity, or a periodic circle (on which the polynomial is an irrational rotation). Hence all interesting dynamics occurs in the Julia set.
In an unpublished preprint W.P. Thurston outlined a method by which questions of the behavior of ƒ on J can be translated to the study of very simple geometric objects in the unit disk invariant under the map z → zd. Moreover this method can also be used to obtain information on subsets of the parameter space ℂd-1. Thurston's preprint is now 20 years old and left many questions unresolved. In this talk we will present Thurston's approach and answer one of his questions.
Randy LeVequeUniversity of Washington, Seattle
Abstract: Hyperbolic systems of partial differential equations often arise when modeling phenomena involving wave propagation or advective flow. Finite volume methods are a natural approach for conservation laws of this form since they are based directly on integral formulations and are applicable to problems involving shock waves and other discontinuities. High-resolution shock-capturing methods developed originally for compressible gas dynamics can also be applied to many other hyperbolic systems. A general formulation of these methods has been developed in the CLAWPACK software that allows application of these methods, with adaptive mesh refinement, to a variety of problems in fluid and solid dynamics.
I will describe these methods in the context of some recent work on modeling geophysical flow problems, particularly in the study of volcanos and tsunamis. Volcanos generate many challenging flow problems, and accurate simulation is required both to further scientific understanding and to aid in hazard assessment and mitigation. The initial blast wave can cause devastation in a large region around the volcano, the continuing eruption leads to lava flows or pyroclastic flows on the flanks of the volcano and ash plumes that are a danger to aircraft far away. Melting glaciers on snow-capped volcanos can lead to debris flows endangering nearby cities. Tsunamis generated by earthquakes or underwater landslides can cause damage and loss of life far away from the source, and accurate prediction of their propagation through the ocean and interaction with coastal topography is essential in issuing early warnings.
Edward B. BurgerWilliams College
Abstract: Here we will come to understand the "personality" of real numbers. Along the way we will encounter some beautiful ideas from number theory and develop an appreciation for an area known as "diophantine approximation". Results of both the ancient and recent variety will be offered. No number theory background is required beyond a desire to explore the alluring notion of number.
David LevinUniversity of Utah & MSRI
Abstract: I will describe research on recent models involving random walks. The first topic concerns the statistical problem of reconstructing the labeling of a graph from data generated by an unobservable random walker on the graph. (Joint work with Y. Peres, and Y. Peres and R. Pemantle.) I will also discuss work on dynamical random walk. This is a walk-valued stationary stochastic process whose equilibrium measure is the law (on sequence space) of an ordinary random walk. Of particular interest are the "exceptional times" for the dynamical random walk—times at which events of zero probability for the ordinary random walks occur in the dynamical version. (Joint work with D. Khoshnevisan and P. Mendez.)
Noel J. WalkingtonCarnegie Mellon University
Abstract: Given a collection of points, edges, and faces, in a bounded two or three dimensional region, the meshing problem is to construct a triangulation which (i) conforms to the given region, (ii) the triangles or tetrahedra have bounded aspect ratio, and (iii) is as coarse as possible. These requirements can lead to very complicated algorithms; so much so that it can be difficult to verify correctness. I will give an overview of the ideas and issues that arise when constructing algorithms to solve the meshing problem, and will indicate how the mesh generation problem touches on many areas of mathematics and computer science such as approximation/interpolation theory, computational geometry, sphere packing, graph theory, and algorithm design.
Laura GhezziFlorida International University
Abstract: This is an introduction to valuation theory and the role it plays in Algebraic Geometry.
After giving the necessary background and definitions we discuss Zariski's theorem of local uniformization and we give examples of valuations that arise naturally in Algebraic Geometry.
This is joint work with S.D. Cutkosky.
Wei-Ming NiUniversity of Minnesota
Abstract: "Diffusion-driven instability" was first formulated in the celebrated work of Turing (1952) in an attempt to model the regeneration phenomenon of hydra which is one of the earliest example observed in morphogenesis (Trombley, 1744). In this talk, I will describe recent mathematical progress on the Gierer-Meinhardt system (1972), which was derived based on Turing's original idea. The strikingly nontrivial patterns, namely, spike-layer steady states, exhibited by this system will be discussed mathematically. Other related concentration phenomena (such as the CIMA reaction in chemistry) will be mentioned as well.
Giovanni ForniNorthwestern University
Abstract: A flow is called parabolic if nearby orbits diverge with at most polynomial speed with time. Examples of such flows include billiards in polygons, conservative flows with saddle singularities on surfaces (related to interval exchange transformations), horocycle flows and nilflows. For the typical parabolic flow all trajectories tend to equidistribution and for applications, for instance to number theory, it is important to know the equidistribution speed (for smooth functions). In this talk we will describe an approach to this questions based on the introduction of an appropriate renormalization dynamics and on the study of the cohomological equation and of invariant distributions of the flow. The renormalization dynamics is hyperbolic and can be studied with tools of hyperbolic theory such as Lyapunov exponents. For instance, in the case of conservative flows on surfaces the renormalization is given by the Teichmueller flow on the moduli space of holomorphic differentials and for horocycle flows by the corresponding geodesic flow. The cohomological equation can be studied by tools of Fourier analysis/representation theory, although in some cases a dynamical approach is also possible. Interesting applications to number theory come from the study of nilflows.
Prakash PanangadenMcGill University
Abstract: The idea of using the phenomenon of quantum entanglement for more efficient implementation of algorithms is now 20 years old. In this talk I consider a relatively new variation on this theme: solving tasks in distributed systems using quantum resources. The task that we consider is the problem of a fully connected network of processors selecting a leader. This is an abstraction of a key step in many tasks involving distributed decision making. When the network is anonymous (no processor can be named and each processor runs the same protocol) the task is known to be unsolvable: essentially because there is no way to break the symmetry. If the system can use probabilistic resources then it can break the symmetry - with high probability - and elect a leader. With entangled states however one can break the symmetry and get a solution that works always and always with a fixed number of steps. In fact we show that there is one very special state - called the W state - that must be used, no other entangled state will work. This state thus embodies very different properties from the usual "Bell" states used in quantum algorithms. The arguments are essentially based on symmetry breaking. This talk will include an introduction to the background material needed to understand the results; in particular, I will not assume familiarity with quantum computing. This is joint work with Ellie D'Hondt.
Ginger DavisRice University
Abstract: Financial data are heavily analyzed due to the potential payoff of useful models. Many models exist for the joint analysis of several financial instruments such as securities due to the fact that they are not independent. These models often assume some type of constant behavior between the instruments over the time period of analysis. Instead of imposing that assumption for our system of securities, we are interested in modeling the dynamics of the overall system. Specifically, we model individual stock data that belong to one of three market sectors and examine the behavior of the market as a whole and the behavior of the sectors. Our aim is detecting and forecasting unusual changes in the system, such as market crashes and outliers.
Luc TartarCarnegie-Mellon University
Abstract: Problems in Mechanics and Physics have played an important role in the past for inducing mathematicians to create new mathematical tools. Nowadays, most mathematicians have no serious knowledge in Mechanics or Physics, which explains why so many fall prey to fashions, whose leaders play with terms from Mechanics or Physics but show a poor understanding of these fields. Even for those with enough critical judgment for avoiding some traps, learning Mechanics or Physics is difficult, as it is not easy to guess what one should believe from all that is said about the real world and about the mathematical models which are used for describing it.
Classical Mechanics is a 18th Century point of view, studied with Ordinary Differential Equations. Continuum Mechanics is a 19th Century point of view, studied with Partial Differential Equations, at least for the linear effects. Because the mathematical tools which existed in the late 1960s were only adapted to linear problems, part of my research work looked at the difficulties posed by nonlinear effects. I first developed Homogenization and Compensated Compactness (partly with François Murat), and then H-measures for a few particular questions (also introduced by Patrick Gérard for another question). I will describe why I consider all this as a (small) part of a new theory, which lies Beyond Partial Differential Equations, and should be adapted to 20th Century problems in Continuum Mechanics, like Plasticity or Turbulence, and 20th Century Physics, i.e. quantum effects.
Anyone who has understood Continuum Mechanics knows that Turbulence has nothing to do with letting time tend to infinity, a game which is one of the deluded fashions alluded to. Turbulence is a problem of Homogenization in the general framework that I had introduced in the late 1970s, which has little to do with -convergence, a game which has transformed in another deluded fashion (because it is played with entirely wrong topologies for being useful for Continuum Mechanics); however, the corresponding Homogenization problems have not been solved yet in general situations, but the simplified examples which have been understood explain why physicists have been misled in their use of probabilities in the laws of Physics.
Alejandro AcevesUniversity of New Mexico
Abstract: An area of intense research is that of photonics, where light propagation features are controlled by clever engineering of periodic optical structures. For example, the fiber bragg grating where an additional intensity dependent nonlinear index of refraction allows soliton like propagation with tunable velocities. In this work we consider nonlinear periodic geometries. We show that the additional transverse dimension allows for a richer dynamics of light trapping, bending and switching, provided stable gap soliton-like bullets exist.
Dale CutkoskyUniversity of Missouri
Abstract: A vector of m polynomials in n-variables gives an algebraic mapping of complex spaces Cⁿ to Cm. This is an example of an algebraic mapping of algebraic varieties. The simplest mappings are the locally monomial or toroidal mappings. The toroidal mappings from Cⁿ to Cm are given by polynomials which are monomials is the coordinate variables. We discuss the problem of toroidalization of mappings, and discuss our proof that algebraic mappings of 3-dimensional varieties can be toroidalized.
Hema SrinivasanUniversity of Missouri
Abstract: If R is a polynomial ring and I is a homogeneous ideal, then the invariant multiplicity of R/I can be easily computed from any homogenous free resolution of R/I over R. For this reason, it seems reasonable to bound the multiplicity by the shifts in a free resolution. The conjectured bounds in terms of the shifts in the minimal resolution of R/I are still open in general. In this talk we will survey various bounds for the multiplicity conjectured by Herzog-Huneke-Srinivasan and discuss the current status of these conjectures.
Philippe TondeurVigreUniversity of Illinois and former Director of Division of Mathematical Sciences at NSF
Samson AbramskyOxford University
Abstract: The new fields of quantum information and quantum computation are causing a re-examination of basic ideas in both Physics and Computer Science. One of the key ideas which has emerged is that quantum entanglement—Einstein's "spooky action at a distance"—can be seen as a computational resource. Entanglement arises because the state of a compound (e.g. two-particle) quantum system can encode correlations between the components, even when they are spatially separated, so that measuring one component has an instantaneous effect on the other. This receives a spectacular application in the teleportation protocol, which uses just two classical bits to transport an unknown qubit q from one site to another. Teleportation is simply the most basic of a family of quantum protocols, including logic-gate teleportation, entanglement swapping, and quantum key exchange, which form the basis for novel and potentially very important applications to secure and fault-tolerant communication and computation.
The current tools available for developing quantum algorithms and protocols are deficient on two main levels: Firstly, they are too low-level, because quantum algorithms are currently mainly described using the 'network model' corresponding to circuits in classical computation. One finds a plethora of ad hoc calculations with 'bras' and 'kets', normalizing constants, matrices etc.
At a more fundamental level, the standard mathematical framework for quantum mechanics (which is essentially due to von Neumann) is actually insufficiently comprehensive for informatic purposes. In describing a protocol such as teleportation, or any quantum process in which the outcome of a measurement is used to determine subsequent actions, the von Neumann formalism leaves feedback of information from the classical or macroscopic level back to the quantum implicit and informal, and hence not subject to rigorous analysis and proof.
In this talk I'll describe recent work with Bob Coecke, in which we recast the von Neumann formalism at a more abstract and conceptual level, and then use the extra structure made available by the category-theoretic framework to remedy the deficiencies in the standard approach noted above. This enables a high-level but effective approach to modelling and reasoning about all the key features of quantum information processing. The effectiveness of these methods is demonstrated by a detailed treatment of three of the main quantum protocols: teleportation, logic-gate teleportation (which is universal for quantum computation), and entanglement swapping. Because of the explicit treatment of 'classical communication'—i.e., the use of measurement outcomes to determine subsequent actions, possibly at other sites in a compound system than the site at which the measurement was performed—it can reasonably be claimed that these are the first completely formal descriptions and proofs of correctness of these protocols. From some very practical considerations we are led to a new fundamental axiomatization of quantum mechanics which can be cast in an essentially logical form, where the calculations to derive the information flow inherent in an entangled quantum system are performed diagrammatically, and correspond to the logical notion of Cut-elimination. Thus we find a new kind of "Categorical Quantum Logic", radically different from the Birkhoff-von Neumann quantum logic.
Proessor Abramsky holds the Christopher Strachey Chair of Computer Science at Oxford University, UK and recently was elected a Fellow of the Royal Society.
David EisenbudVigreDirector, MSRI and UC Berkeley
Abstract: Any algebraic curve in projective 3-space that is not contained in a plane has degree at least 3 -- that is, it meets any plane in at least 3 points. Moreover, any curve of degree 3, can be parametrised (in suitable coordinates) by t → (t, t², t³).
This was known 150 years ago, and since that time many mathematicians have used and generalized the result. I will describe some of the ideas involved, including recent work of mine with Mark Green, Klaus Hulek, and Sorin Popescu.
Eduardo CattaniUniversity of Massachusetts
Abstract: The modeling of cancer provides an enormous mathematical challenge because of its inherent multi-scale nature. For example, in vascular tumours, nutrient is transported by the vascular system, which operates on a tissue level. However, it affects processes occurring on a molecular level. Molecular and intra-cellular events in turn affect the vascular network and therefore the nutrient dynamics. Our modeling approach is to model, using partial differential equations, processes on the tissue level and couple these to the intercellular events (modeled by ordinary differential equations) via cells modeled as automaton units. Thus far, within this framework we have modeled structural adaptation at the vessel level and we have modeled the cell cycle in order to account for the effects of p27 during hypoxia. These results will be presented.
Phillip MainiOxford University, UK
Abstract: A binomial ideal in a polynomial ring is an ideal generated by binomials. They are quite ubiquitous in various contexts such as toric geometry, semigroup algebras, and hyper-geometric equations. Although binomial ideals are very amenable to Gröbner and standard bases techniques, they also provide some of the "worst-case" examples in computational algebra.
In this talk I will discuss some joint work with Alicia Dickenstein (U. of Buenos Aires), where we attempt to obtain properties of a binomial ideal such as characterization of complete intersections, number of "solutions" in the zero-dimensional case, etc. purely in terms of the monomials appearing in a set of generators of the ideal.
Brent D. StrunkPurdue University
Abstract: "Suppose G is a standard graded ring over an infinite field. From the minimal graded free resolution of G, it is possible to derive several invariants, among them the multiplicity, the Castelnuovo Mumford regularity, the Hilbert series, and the postulation number. I discuss a sharp lower bound for the regularity of G in terms of the postulation number, depth, and dimension. I also present a class of examples in dimension 1 where the postulation number is 0 and the regularity of G can take on any value between 1 and the embedding codimension of G."
Bill DukeUniversity of California at Los Angeles
Abstract: In this mostly expository talk I will show the connection between Ramanujan's work on the special values of certain continued fractions and Klein's theory of the icosahedron. In addition to explaining some of Ramanujan's identities, this observation opens some avenues for the study of special values of certain modular functions defined by continued fractions and generalizations.
Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 firstname.lastname@example.org


At Elmsleigh Infant and Nursery School, we have adopted a mastery approach to deliver the three aims of the National Curriculum, fluency, reasoning, and problem solving. Underpinning this pedagogy is a belief that all children can achieve in maths. We believe in promoting sustained and deepening understanding by employing a variety of mastery strategies, with teaching conceptual understanding at the heart of everything we do. Our approach aims to provide all children with full access to the curriculum, enabling them to develop independence, confidence, and competence- ‘mastery’ in mathematics in order to be independent mathematicians who are well equipped to apply their learning to the wider world and be ready for the next phase of their mathematical education
White Rose Maths 1 Minute App
White Rose have launched a fantastic app called 1-Minute Maths. It has been designed by Maths experts to help children learn number confidence and fluency using a method they can enjoy. With easy-to-follow tasks delivered in engaging, bite-sized chunks, it is simple for children to use independently at home. The app is totally free and it’s available for use on Apple, Android and Kindle devices.
The app has been designed for infant aged children. There are games for Reception, Year 1 and 2.
- Reception children: We suggest Reception children begin with tasks about subitising. It’s one of the most critical number skills a young child develops, recognising number groups without counting, making it a perfect place for Reception children to start.
- Year 1 children: If your child has mastered subitising, we recommend moving onto tasks focused on adding and subtracting (focusing on number bonds to 10). The moving onto multiplication and division (focusing on counting in 2s, 5s and 10s)
- Year 2 children: We suggest trying tasks focused on adding and subtracting (number bonds to 20. Then moving onto multiplication and division (2x, 5x, and 10x table).


Christina Eubanks-Turner, Associate Professor of Mathematics.
Christina Eubanks -Turner Discussion Guide Questions:
Do you enjoy puzzles and number games? Do you think you have a “mathematical mind?”
Christina describes her love of working on math problems as “getting her hands dirty.” What do you think she means by this?
Christina says her mother encouraged her math abilities with games and puzzles, so that Christina began to understand her mathematically creative way of thinking was an advantage she could apply to a future career. Is there something you do for fun today that you could imagine might lead to a career later? How?
Several studies show that girls often think boys are naturally smarter at math. Do you think this is true? Why do you think this idea is so widespread?
Christina describes graduate school as a very challenging time in her life that she got through with the support of her ‘tribe’ of fellow women mathematicians. Do you have a group of friends that help you study difficult subjects? How do you help each other?
Have you ever had what Christina calls a “Picasso Moment” solving a math problem? Does math feel like a creative form of expression to you? What does Christina mean when she says there can be different creative paths to solving the same math problem?
How important is an understanding of mathematics to the jobs of the future? What are some of the careers that require good math skills?


This module on gravity equations is composed of a literature review summarizing the key points and references you have to know when interested to estimate a gravity equation and a set of illustrative STATA program used to perform such estimations.
The code provided in this module will give you several examples of hands-on estimation to familiarize yourself with the gravity equation methodological choices highlighted in the literature review. We provide an illustrative dataset with alternative Stata codes presenting the different possible estimation strategies. As you read this guide, you can use STATA to carry out estimations designed to familiarize you with the software and, more importantly, the gravity model.
STATA is a statistical software program and we assume that you have a recent version of STATA (version 11.2 or later).
The literature review, written by Prof. Luca Salvatici is available as AGRODEP TN-04 "The Gravity Model in International Trade"
The user guide for the STATA code is the AGRODEP TN-05 "Hands-on gravity estimation with STATA" written by Prof. Luca Salvatici and Maria Cipollina.
The Stata codes of GRAVITY model are available to AGRODEP members.


Second Order Elementary Cellular Automata
Cellular automata are very interesting things. These are elementary
cellular automata, starting from a random seed. You can try out
different automata rules by typing a new number in the box and hitting
Enter (some favorites to try are 18, 30, and 184). If you select the
"Second order" box you will see that same rule rendered in second order.
For more information on what that means, check out this wikipedia


Virtually all students enrolled in a certificate or degree program at Wenatchee Valley College take at least one math course, since mathematical problem-solving skills are valuable in most areas of life. As part of the registration process, new WVC students seeking a degree or certificate can use multiple measures (including accuplacer, EdReady, transcript placement, or an SBAC or AP score) to determine if they are ready for 100-level and above college classes in math. If their scores indicate a need for developmental courses to strengthen their skills, they may enroll in basic math and algebra courses (MATH 090, 093, 098, 099).
College-level mathematics courses at WVC include math in society, precalculus (algebra and trigonometry), calculus and analytical geometry, business precalculus and business calculus, finite mathematics, statistics, linear algebra, and differential equations. Special topics and independent study courses are also available for varying credits.
The associate of arts and sciences (transfer) degree requires at least 5 credits of quantitative skills classes, taken from either mathematics or computer science, and up to 10 credits of non-lab math or science classes--plus additional electives. Students earning an associate of technical sciences degree need at least intermediate algebra. Most workforce education (professional/technical programs) at WVC have other math requirements as well.
Students who complete developmental math courses will be able to:
- Perform arithmetic calculations without the use of a calculator.
- Interpret and verbalize the language of beginning and intermediate algebra.
- Apply arithmetic and basic algebra to real-world problems.
- Gain enough mathematical skills and confidence to be successful in a college level math course.
Students who complete the quantitative skills requirement will be able to:
- Approach problem solving using critical thinking, mathematical skills, and efficiency.
- Interpret and verbalize the language of mathematics.
- Apply mathematics to real-world problems.
- Gain enough mathematical skills and confidence to be successful in additional college level courses, such as math, business, science, nursing, etc.


Why use Excel for Forecasting and Predictive Analytics?
In today’s rapidly evolving business landscape, utilizing advanced tools like Microsoft’s powerhouse Excel is essential not only for basic number crunching but also as an advanced analytical toolset that helps solve complex problems through forecasting and predictive analytics. By analyzing large amounts of diverse data with ease – Excel has adequately evolved as a preferred partner in making informed decisions across industries worldwide. In this article we explore various ways which users can leverage the versatile application to derive meaningful insights from incomplete or scattered input sets through accurate forecasts based on logical predictions refined over time using intuitive templates provided by the application itself!
Predictive analytics involves analyzing historical data to predict future trends or outcomes. Forecasting, a significant component of predictive analytics, deals specifically with estimating future values based on patterns and trends observed in past data.
Excel offers a number of built-in functions that allow for sophisticated forecasting and predictive analyticsIn numerous sectors like retail, finance and marketing alike,a crucial skillset that separates esteemed decision-makers from the rest is accurately forecasting the future.Taking into account historical data can help them scrutinize potential future trends; thereby enabling these individuals to make informed decisions.The applications of this skill are varied; ranging from strategic budget planning to efficient resource distribution.However,this understanding proves most critical while analyzing financial performance or predicting sales volume with some level of certainty .
What are various Ways to Use Excel for Forecasting and Predictive Analytics
Approach 1: Linear Forecasting using FORECAST function.
Approach 2: Non-Linear Forecasting using Trendline function.
Approach 3: Advanced Predictive Analytics using Data Analysis ToolPak.
Linear Forecasting using FORECAST function.
The first and simplest method is linear forecasting. This involves predicting a future value along a linear trend line, essentially assuming that the relationship between the variable you’re trying to predict and the time period you’re forecasting is a straight line.
The FORECAST function in Excel is a straightforward yet powerful tool for predicting a future point along a linear trend. Here are the steps to perform linear forecasting:
Step 1: Prepare your dataset with known X’s and Y’s.
Step 2: Identify the Known and Future X Values.
Step 3: In the cell next to your future X value, type =FORECAST(X, Known_Y’s, Known_X’s).
- Type “=FORCAST.LINEAR() “ selct the cell that we want to predict the future.
2. Now select the 2nd column all values (here we selected B2:B9)
3. Now select the 1st columns all vales (here we selected from A2:A9)
Step 4: Press Enter to get the predicted future Y value.
Non-Linear Forecasting using Trendline function.
Sometimes, trends are not linear but follow polynomial, logarithmic, or other types of curves. In these cases, Excel’s trendline function can be a useful tool. In scenarios where data follows a more complex, non-linear trend, Excel’s trendline function is highly useful. Excel provides several types of trendlines, such as linear, polynomial, logarithmic, and exponential, allowing for flexibility based on the data trend.
Step 1: Highlight your dataset
Step 2 : Insert a scatterplot via the Insert tab.
Step 3 : Click on a data point in the scatterplot, and click on the ‘Add Trendline’ option in the chart design tab.
Step 4: Make sure to click on Display Equation And Display R square equation.
Step 5 : Choose the type of trendline that fits your data trend (linear, logarithmic, polynomial, etc.). Check the ‘Display Equation on chart’ option.
Step 6: Use equation for Predicting the Future value select the instead of X in Y equation.
Step 7: Click enter to get the value of y at desired x.
Advanced Predictive Analytics using Data Analysis ToolPak.
Excel provides the Data Analysis ToolPak for more sophisticated predictive analytics. This includes performing regression analysis. For more complex predictive analytics, Excel offers the Data Analysis ToolPak. This add-on provides a variety of advanced statistical analysis tools, including Regression analysis.
Step 1: Click on File tab.
Step 2: Then Click on the Option Button.
Step 3: Now Click on the Add-ins option and then select the option Go in manage Excel add-ins
Step 4: Select the analysis toolpak option then press OK.
Step 5: Now the Data Analysis Option is available in Data Tab in Excel.
Step 6: Click on the ‘Data’ tab and select ‘Data Analysis’. Choose ‘Regression’ and click ‘OK’.
Step 7: Specify your input Y Range
Step 8: Specify your input X Range
Step 9: Check ‘Labels’, ‘Residuals’, ‘Residual Plots’, ‘Line Fit Plots’ options for a comprehensive analysis.
Step 10: Click ‘OK’. The output will give you various statistics and plots for your analysis.
This method is used for large data set to make analysis easy and give the output in proper format.
In conclusion, Microsoft Excel’s capabilities extend far beyond basic data entry and simple calculations. It serves as a powerful tool for forecasting and predictive analytics, empowering users with data-driven insights that aid in strategic decision-making. Excel’s various functions, such as the FORECAST function for linear forecasting, trendline functions for non-linear forecasting, and the sophisticated Data Analysis ToolPak for advanced predictive analytics, provide an array of methods to extract meaningful information from complex datasets.
The strategic application of these tools can significantly impact business outcomes, providing future-oriented insights that help organizations anticipate trends and make informed decisions. However, it’s essential to understand the data thoroughly and the assumptions underlying these methods to ensure accurate and meaningful predictions. Therefore, while Excel simplifies complex analysis and makes forecasting more accessible, the responsibility lies with the user to apply these tools judiciously.
Finally, Excel’s role in forecasting and predictive analytics exemplifies how a widely used software can be leveraged beyond its conventional uses, effectively turning raw data into a powerful decision-making resource. Whether you’re in finance, sales, inventory management, or any other field dealing with large data sets and future predictions, Excel offers robust and versatile solutions to meet your forecasting needs. Excel, indeed, remains a cornerstone in the world of data analysis, offering a balance of simplicity, flexibility, and sophistication.


August 2014 // Re:GENERATE
In August of 2014, I participated in Re:GENERATE, a show featuring computer-generated art. I made, among other things, a generative series for the event, that I named Fractal Circles.
It’s a simple recursive algorithm over a region of the sketch:
This generates a surprisingly wide variety of shapes, some very natural-looking.
There are three open-ended questions:
If you decide to recurse every other time, and always draw a circle, and alternate the circles types, you get this image, which I made to help explain:
If you let yourself pick the type of circle randomly, you’re left with two questions: whether to recurse, and whether to draw a circle. Answering those questions randomly, and controlling their probability, can generate whole families of images.
Here are 144 tiny fractal circle images. The probability of recursing decreases as we move from left to right, and the probability of drawing a circle increases as we move from top to bottom.
Here’s a p5.js version of it, where the probabilty-to-recurse increases as the hour passes, and the probability-to-draw increases as the minute passes:


With this calculator, you can calculate the resistance of the cable, knowing the material it is made of. You can also calculate the length of the conductor and the conductor diameter or the conductor cross-section area.
This calculator helps us check whether the planned investment will be profitable and whether the project should be accepted or rejected.
Thanks to the calculator, we can calculate:
NPV (Net Present Value) - sum of discounted net cash flows
PI (Profitability Index) - investment profitability
IRR (Internal Rate of Return) - internal rate of return
DPP (Discounted Payback Period) - discounted payback period
Value of discounted net cash flow for each period.
With this calculator you can calculate voltage drops for single-phase and three-phase AC circuits calculated from the rated current. You will also calculate wire length, wire diameter, wire cross-sectional area, voltage or current.
With the Fractions Calculator, you can add any two mixed numbers or proper and improper fractions. Fractions Calculator will show you the result of operations on fractions step by step and will give you explanations of the operations performed to add fractions. You will learn how to simplify fractions, how to find a common denominator, how to find the least common multiple and the greatest common divisor.


[Lecture] CAM Seminar—Recent Developments in Numerical Methods for Fully Nonlinear PDEs
Title: CAM Seminar—Recent Developments in Numerical Methods for Fully Nonlinear PDEs
Time: January 3, 2020, 15:00-16:00
Venue: Room 1560, Sciences Building No. 1
Speaker: Feng Xiaobing (The University of Tennessee)
Abstract: In this talk, I shall first present a brief overview about recent advances in numerical fully nonlinear PDEs. I shall then discuss in details a newly developed narrow-stencil finite difference framework for approximating viscosity solutions of fully nonlinear second order PDEs (such as Hamilton-Jacobi-Bellman and Monge-Ampere equations). The focus of the talk will be on discussing how to compensate the loss of monotonicity of the schemes (due to the use of narrow stencils) in order to ensure the convergence of the schemes, and to explain some key new concepts such as generalized monotonicity, consistency and numerical moment. The connection between the proposed methods and some well-known finite difference methods for first order Hamilton-Jacobi equations will be explained. Finally I shall briefly explain how to extend these finite difference techniques to a (high order) discontinuous Galerkin setting.
Edited by: Qiu Tianjie
Source: School of Mathematical Sciences


FIFA's World Cup 2002 Organising Committee adopted a
complex formula to rank the 32 qualifying teams for purpose of seeding for the
the Committee used the ranking only to
choose the five top-seeded teams that joined reigning champion
France and host nations South Korea and Japan atop the eight first round
groups. It did not use the ranking to assign the remaining teams to the
pots used in the final draw, but, instead made those assignments on the basis
of confederation affiliation.
The teams were ranked on both their previous World Cup performances and
their standing in FIFA's world rankings of national teams, and equal weight
was given to these two measures in calculating the ranking.
The Committee examined the 32 qualifying teams'
performances in the last three World Cup final tournaments, those of 1990,
1994 and 1998. First place in one of those final tournaments earned 32
points, second place 31 points, third 30 points and so on down to 16th place,
which earned 17 points. Teams eliminated at the group phase of those
tournaments received either 9 points (for 17th through 20th at the 1990 and
1994 tournaments and 17th through 24th at the 1998 tournament) or 8 points
(for 21st through 24th at the earlier two tournaments and for 25th through
32nd at the 1998 tournament).
The Committee decided the more recent the tournament, the
more weight it deserved, and so it scaled the points earned at the three
tournaments to give them a 3:2:1 ratio. Points given for the 1998
tournament were multiplied by 3, points awarded for the 1994 tournament by 2
and points awarded for the 1990 tournament by 1. The resulting numbers
were added and the total was divided by 6 (the total of the multipliers) to
give a World Cup final tournament points average.
For example, England finished 4th at the 1990 tournament
and earned 29 points, which was given a multiplier of 1, resulting in a 1990
total of 29 points. England did not qualify for the 1994 tournament and
so earned 0 points, which was given a multiplier of 2, producing a 1994 total
of 0 points. England finished 9th at the 1998 tournament, earning 24
points, which was given a multiplier of 3, producing a 1998 total of 72
points. The points for the three tournaments were added together,
producing a total of 101 World Cup points (29+0+72=101). That total was
divided by 6, producing a World Cup final tournament points average of 17 for
The Committee also examined the 32 qualifying teams'
standings in FIFA's national team rankings for the past three years. In
particular, it looked at the December end-of-year rankings for 1999 and 2000
and the latest available ranking for 2001, which was November's. The
team with the highest ranking among the 32 qualifying teams was awarded 32
points, the team with the second highest ranking was awarded 31, and so on,
down to the team with the 32nd highest ranking (the lowest among the 32
qualifying teams), which was given 1 point. The points earned for each
ranking were given equal weight and so no multipliers were involved in this
calculation. The points earned for all three ranking periods were
added together, and the resulting total was divided by 3 to give a world
rankings points average.
For example, England were 12th in the December, 1999
ranking, and since that was the 9th highest ranking among the 32 teams
qualifying for the World Cup 2002 final tournament,
England were awarded 24 points. England were 17th in the December, 2000
ranking, and because that was the 11th highest ranking among the 32 World Cup
2002 teams, 22
points were awarded. England were 10th in the November, 2001 ranking,
which was the 8th highest ranking among the 32 teams, earning 25 points.
The points for the three rankings were added together, producing a total of 71
world rankings points (24+22+25=71). That total was divided by 3,
producing a world rankings points average of 24 for England.
The Committee added together each team's World Cup final
tournament points average and world rankings points average, producing a
combined total, which was used to rank the teams.
For example, England had a World Cup points average of 17
and a world rankings points average of 24, which produced a combined total of
41. That total was the 8th highest among the 32 teams qualifying for the
World Cup 2002 tournament.
We have not checked the FIFA entries
for accuracy, but a few errors were apparent on the face of the ranking table
FIFA published. It gave Belgium no credit for their 19th place finish at World
Cup 1998, thus depriving them of five points in the combined point totals, and
we have adjusted Belgium's total points from 26 to 31. The FIFA table
also erred in adding the World Cup points average and the world ranking points
average for a few teams. Brazil\s combined points total is 62, not 61,
as FIFA had it, the U.S.A.'s is 32, not 31, Sweden's is 31, not 32, and South
Africa's is 20, not 19. As a result of these corrections, Belgium ranks
14th, not 15th, and Portugal 15th, not 14th, the U.S.A. occupies 12th place,
not 13th, and Sweden lies 13th, not 12th.


Conference “Subject Week: Traditions, Innovations, Competencies”Conference “Subject Week: Traditions, Innovations, Competencies”
on Mar 26, 2021 On March 22-26, the conference “Subject Week: Traditions, Innovations, Competencies” is being held online, during which topical issues of modern science are discussed with participants from 85 regions of the Russian Federation, knowledge, understanding, depth and scope of application of which are necessary for successful work teachers. 3rd and 4th year students of the Institute of Mathematics and Information Technologies of the “Pedagogical Education” direction took part in the online conference. On the first day of the conference, the Day of the Teacher of Mathematics took place. The online event was dedicated to the following issues: the real goals of teaching mathematics in school, methods, and resources to achieve these goals; the use of materials from textbooks and teaching aids for the effective preparation of schoolchildren for the state final certification: updating school mathematics education in line with digitalization trends and ensuring functional literacy; geometry in school education: from the first geometric constructions to solving complex problems; online resources to help teacher and student. Read: Middle schoolers use comic strips to share their pandemic stories The presenters of the Teacher’s Day were: E. D. Zubkova, leading methodologist of the Prosveshchenie Group of Companies; M.S. Yakir, math teacher, author of textbooks and teaching aids; T.F. Sergeeva, Doctor of Pedagogical Sciences, Professor of Moscow State Pedagogical University, author of textbooks; A.V. Shklover, teacher of mathematics, methodologist in the “Teacher for Russia” program; I.V. Soboleva, senior methodologist of the general education department of the Karelian Institute for the Development of Education; T.A. Burmistrova, member of the expert council of JSC “Publishing House” Education “. 3rd year students, under the guidance of a senior teacher of the Department of Theory and Methods of Teaching Mathematics and ICT in Education, senior teacher S.I. Markova, connected to the conference broadcast via the Zoom platform. The students listened to T.A. Burmistrova “The combination of traditions and innovations in the textbooks of mathematics by N. Ya. Vilenkin is the key to successful learning.” Textbook of mathematics by N.Ya. Vilenkina is one of the most famous and popular textbooks among Russian teachers. Within the framework of this report, the changes made to the textbook by N.Ya. Vilenkin, which reflect the requirements for the modern level of teaching mathematics, as well as the possibility of implementing continuity with the lines of primary school textbooks. 4th year students of the IMIT direction “Pedagogical Education” under the guidance of Associate Professor of the Department of Theory and Methods of Teaching Mathematics and Information and Communication Technologies in Education T.V. Bezhanu was connected to the broadcast of the conference from the audience of PetrSU. The students listened to the speech of M.S. Yakir on the topic “Function is the head of everything.” In this report, the equations were considered, for which the properties of functions are the key to their solution. Source: https://indiaeducationdiary.in/
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The standard deviation is the key indicator of how a specific market is going to respond in the future. There are two things dispersion and variance, which are going to determine what future response of a marketplace. The Standard Deviation Calculator determines that there is a proportional relationship between the standard deviation and its diversified response provided by calculator-online.net. If the standard deviation is larger it means the market is going to respond in a more diversified way. Businesses do find it quite critical to find the response of certain marketplaces.
The SD calculator makes the task easy for us businesses to find the perfect response to the marketplace and its dynamics. Calculate the standard deviation and find the response of the whole marketplace. You can simply able to find the mean and the mode of the whole sample by the mean and standard deviation calculator. Most organizations do extract a sample from the population and utilize the sample standard deviation calculator. It can also be possible to extract all the calculations from the population by the population standard deviation calculator.
Consider a sample and its standard deviation:
10, 12, 23, 23, 16, 23, 21, 16
Standard Deviation, σ: 4.8989794855664
Count, N: 8
Sum, Σx: 144
Mean, μ: 18
Variance, σ 2: 24
From the above data, it is possible for us to find the future prediction of the data and the appropriate response of the market place.We know the market can deviate around 4.88, and all the respective responses and what are the mean and the mode of the marketplace. In this data, the mean value is 18 and the mode is 23, which is also an indication of the market mode. The Standard Deviation Calculator makes the task much easier for us, and then we can predict how the market is going to place in the future.
There are many online apps and Standard Deviation Calculator, we are presenting 5 top tools and apps for the standard deviation
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It is a famous app for finding the Standard deviation of a dataset. You find the graphical representation and also a complete analysis of the dataset values. Making it possible for a business to have a complete analysis of the marketplace and its response. The Standard Deviation Calculator generates the result at a certain speed and the fast calculations may be remarkable when finding the standard deviation.
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If you are fond of color and graphical representation then MathisFun.com is a place to be and you are not going to feel boring when visiting. The concepts like the Standard Deviation by presented by MathisFun.com are simple and self-explanatory. The Standard Deviation Calculator by this forum is quite distinguishable.
Scribbr.com presents the stepwise demonstration of the concepts like the standard deviation. Each step of the Standard Deviation Calculator by Scribbr.com is self-explanatory and students can learn only to see the concepts.
Online apps and tools make the task much easier for students. The Standard Deviation Calculator presented by the top-notch brands has evaluated various features of the concepts. The tabular and the graphical representations make the task much easier for the stdetnds and you can learn the concepts easily as compared to the class learning.


Mastery of mathematics is not a fixed state but a continuum. At each stage of learning, pupils should acquire and demonstrate sufficient grasp of the mathematics relevant to their year group, so that their learning is sustainable over time and can be built upon in subsequent years.
This requires development of depth through looking at concepts in detail using a variety of representations and contexts and committing key facts, such as number bonds and times tables, to memory.
(Teaching for Mastery, NCETM 2015)
Our curriculum aims to embed the principles of a teaching for mastery approach underpinned with the belief that ‘every child can achieve in maths’.
Research informed curriculum and pedagogical choices:
- https://content.ncetm.org.uk/mastery/NCETM_Primary_Teachingformastery_Report_July2019.pdf report carried out by the NCETM to record progress made by Teaching for Mastery schools in England.
The Essence of Maths Teaching for Mastery NCETM
- Mathematics Mastery
- Jerome Bruner (1915 – 2016) Cognitive development research.
- Richard Skemp (1919-1995) Relational Understanding and Instrumental Understanding. 1976
- Zoltan Dienes (1916-2014) Systematic Variation
- EEF: Mastery Learning + 5 months
Mastery learning | EEF (educationendowmentfoundation.org.uk)
- EEF Guidance Improving Mathematics (2020):
The 5 Big Ideas of Teaching for Mastery
Our curriculum and pedagogical choices are underpinned by the five big ideas of teaching for mastery:
(Taken from NCETM March 2017)
Lessons are broken down into small connected steps that gradually unfold the concept, providing access for all children and leading to a generalisation of the concept and the ability to apply the concept to a range of contexts.
- Representation and Structure
Representations used in lessons expose the mathematical structure being taught, the aim being that students can do the maths without recourse to the representation
- Mathematical Thinking
If taught ideas are to be understood deeply, they must not merely be passively received but must be worked on by the student: thought about, reasoned with and discussed with others
Quick and efficient recall of facts and procedures and the flexibility to move between different contexts and representations of mathematics
Variation is twofold. It is firstly about how the teacher represents the concept being taught, often in more than one way, to draw attention to critical aspects, and to develop deep and holistic understanding. It is also about the sequencing of the episodes, activities and exercises used within a lesson and follow up practice, paying attention to what is kept the same and what changes, to connect the mathematics and draw attention to mathematical relationships and structure.
Mastery of Mathematics at Lansbury Lawrence
At Lansbury Lawrence, our maths curriculum has been designed to coherently sequence learning across EYFS to KS2. In response to the Pandemic, our curriculum was adapted and prioritised to meet the needs of all children in our school, which was supported through our partnerships with the NCETM, London North & South East Maths Hub and White Rose Maths.
Through our curriculum, we aim to develop mathematicians who:
- have a strong number sense
- can see patterns and make generalisations
- are articulate in their books and out loud
- make reasoned decisions and justify them
- think critically about their own and other’s strategies
- are equipped to solve unfamiliar problems in a range of contexts.
To achieve this our curriculum has:
- a consistent set of concrete and pictorial representations from EYFS to Year 6
- ensures all children experience coherent and progressive models throughout the school to support deep and sustained learning.
- ensures lessons plan opportunities for children to make connections. For example:
- Additive reasoning
- Multiplicative reasoning
- Fractions with ratio
- Links to prior learning
- takes a problem-solving approach to modelled, guided, and independent work
- provides daily opportunities for children to meaningfully rehearse their number facts to develop fluency and confidence:
- Number Sense Maths Programme EYFS & KS1
- Multiplication Table facts in LKS2
- Arithmetic and Recapping KS2
- ensures that explicitly explaining and justifying process is critical when working as a class, in a group or independently.
- provides challenge and scaffolds so that all children move through the curriculum broadly at the same pace
- focuses on conceptual understanding
- Provides a framework of vocabulary, key terms and phrases.
For this to happen, our teachers are supported to:
- understand the fundamentals of number
- understand the progression from concrete to visual to abstract is not linear and each stage should be revisited as needed.
- use modelled and shared sessions to promote choice, critical thinking and a diversity of ideas.
- use a range of questioning that support all children to reflect on, explain and extend their thinking.
- scaffold work so all children reach the same goals
- explicitly model new learning using strategies such as the ‘silent teacher’ and worked example approach
- anticipate and teach away from misconceptions
- know potential sticking points in lessons and plan accordingly
- be precise in their use of vocabulary and expectation of children’s vocabulary
- know progression within each unit to assess, intervene and know when all children are ready to move on.
- map the progression of models used throughout the year
- have updated working walls that support the unit being taught
- are fully equipped with a range of manipulatives accessible to all the children all of the time.
Response to the Pandemic:
We followed advice from the DfE Teaching Mathematics in Primary Schools guidance; Teaching mathematics in primary schools – GOV.UK (www.gov.uk) which offered support by:
- identifying the core concepts that are needed for pupils to progress in their study of mathematics
- demonstrating how pupils can build their understanding of these concepts from year 1 to year 6
This supported our decisions on what to prioritise to ensure children developed firm foundations before moving on to new content. Our planning and review process is exemplified in the flow chart below:
One notable gap in children’s knowledge upon returning to school was number facts and quick mental recall of these to perform formal algorithms. To address this, we have timetabled 15-minute daily fluency sessions in all year groups:
- EYFS – KS1 Number Sense Maths (Systematic number fact teaching | Number Sense Maths)
- LKS2: Number Sense Maths and Multiplication Tables
- UKS2: Multiplication Tables and Arithmetic
These are regularly assessed and reviewed to support progress of all children.
NCETM Curriculum Prioritisation in Primary Maths:
From September 2021, our curriculum map was supported by the NCETM prioritisation framework which:
‘… provides coherent sequencing for the primary maths curriculum. It draws together the DfE guidance on curriculum prioritisation, with the high quality professional development and classroom resources provided by the NCETM Primary Mastery PD materials.’
We supplement this with White Rose Maths and online tools such as Learning by Questions.


I am now a quarter of the way to 100 now.
When you are the age I will be in 4 days, if I were still alive, you would be half as old as me! How old am I?
Uh, I really have no idea. Except I cheat by already seeing your birthday on my bulletin board. So 66. :D But, I know you’re trying to get me to think about that mathmatically. However, I was only just above average and I couldn’t figure out word problems for the life of me. Wanna show me how to calculate your answer?