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Day/Time/Room |
Speaker |
Title and abstract |
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Wed. Oct.12, 3pm Conference Room |
Yevgeniy Kovchegov
Oregon State University |
"On Mixing Times I" |
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Wed. Oct.19, 3pm Covell 221 |
Ed Waymire
Oregon State University |
"The anamolous diffusion problem for directed polymers" |
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Wed. Oct.26, 3pm Covell 221 |
Robert Burton
Oregon State University |
"Stationary Measures for Reinforcing Randomly Chosen Maps" |
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Tue. Nov.1, 1pm Kidder 364 |
David Levin
University of Oregon |
"A coupling, and conjectures of Darling and Erdos" |
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Wed. Nov.9, 3pm Covell 221 |
Yevgeniy Kovchegov
Oregon State University |
"On Mixing Times II" |
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Wed. Nov.16, 3pm Covell 221 |
Ben Morris
University of California, Davis |
"The spectral gap for the zero range process with constant rate" Abstract. The zero range process with constant rate can be described as follows. Particles are distributed over the vertices of the d-dimensional torus. Each vertex has a clock that rings at rate one. When the clock of a (nonempty) vertex rings, a particle moves from that vertex to a randomly chosen neighbor. We obtain a tight bound for the spectral gap of this process, solving an open problem. |
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Wed. Nov.23 NO SEMINAR |
NO SEMINAR | NO SEMINAR THIS WEEK |
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Wed. Nov.30, 3pm Covell 221 |
Ed Waymire
Oregon State University |
"The anamolous diffusion problem for directed polymers II" |
Day/Time/Room |
Speaker |
Title and abstract |
|
Wed. Jan.11, 3pm Kidder 280 |
Yevgeniy Kovchegov
Oregon State University |
"Subcritical percolation: cluster expansion and Brownian bridge asymptotics" Abstract. First,we will review basic facts about Bernoulli bond percolation model. Then,for a given point a in Z^d, we will show that a cluster in the d-dimensional subcritical Bernoulli bond percolation model conditioned on connecting points (0,...,0) and na if scaled by 1/(n||a||) along a and by 1/sqrt{n} in all orthogonal directions converges asymptotically to Time x (d-1)-dimensional Brownian bridge. |
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Wed. Jan.18, 3pm Kidder 280 |
Yevgeniy Kovchegov
Oregon State University |
"Critical percolation and Lorentz lattice gas model: an expository talk" Abstract. Critical probability p_c=1/2 in 2D. Lorentz lattice gas model. Increasing events, pivotal edges and Russo's formula. Exponential decay in subcritical phase. Russo's formula adapted to LLG model. |
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Wed. Jan.25 NO SEMINAR |
NO SEMINAR
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NO SEMINAR THIS WEEK |
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Wed. Feb.1, 3pm Kidder 280 |
Jorge Ramirez
Oregon State University |
"Skew Brownian motion and diffusion: a model for heterogeneity" Abstract. Solute transport in a medium with sharp discontinuities in the diffusion coefficient is studied via the identification of the associated stochastic process: skew diffusion. The model sheds light on the physical microscopic movement of solute particles in the presence of membranes, and connects back with the macroscopical PDE formulation via classic theory. Some interesting probabilistic properties and constructions of skew diffusion are discussed. The results are applied to a classic homogenization problem in layered medium. |
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Wed. Feb.8, 3pm Kidder 280 |
Ed Waymire
Oregon State University |
"An approach to unique invariant probabilities for Markov Processes" Abstract. This talk is based on prior work with Rabi Bhattacharya and concerns conditions for existence of unique invariant probabilities for Markov processes on general state spaces in the absence of irreducibility. |
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Tue. Feb.14, 3pm (Colloquium) Dearborn 118 |
Nathanael Berestycki
University of British Columbia |
" OF MICE AND MEN,... and random walks" Abstract. We will see how tools from probability theory can help us answer some questions arising in the study of genome rearrangement, which have the following flavor: given two species (say, mice and men), can we quantify how different or how similar they are? On a mathematical level, this will lead us to study the behavior of a certain random walk on the symmetric group and show that it exhibits a phase transition. Along the way we will discuss some connections with Erdos-Renyi random graphs (aka mean-field percolation) and hyperbolic geometry. Some familiarity with elementary probability notions (such as the Poisson process) is preferable but not essential. |
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Wed. Feb.15, 3pm BATCHELLER 250 |
Nathanael Berestycki
University of British Columbia |
"Gibbs fragmentations" Abstract. We study random partitions of 1,...,n where every cluster of size j can be in any of w(j) possible internal states. A Gibbs distribution is obtained by sampling uniformly among all possible configurations. Gibbs distributions arise naturally as equilibrium distributions of reversible coagulation - fragmentation processes. In this work we characterize irreversible processes where this microscopical equilibrium is moving towards a more fragmented state as time evolves. In particular we show that after reversing the direction of time they are the Marcus-Lushnikov coalescent process with affine collision rate K(x,y)=a+b(x+y) for some real numbers a and b. This is joint work with Jim Pitman (U.C. Berkeley). |
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Wed. Feb.22, 3pm Kidder 280 |
Mina Ossiander
Oregon State University |
"Random multiplicative cascade measures. Part I" Abstract. The distribution of random cascade measures depends implicitly on that of an underlying cascade generator along with a branching number. This pair of talks will give some basic background and then discuss some interesting convergence and estimation issues. The material covered represents joint work with R. Keim, D. Rupp, and E. Waymire. |
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Wed. Mar.1, 3pm Kidder 280 |
Mina Ossiander
Oregon State University |
"Random multiplicative cascade measures. Part II" Abstract. The distribution of random cascade measures depends implicitly on that of an underlying cascade generator along with a branching number. This pair of talks will give some basic background and then discuss some interesting convergence and estimation issues. The material covered represents joint work with R. Keim, D. Rupp, and E. Waymire. |
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Mon. Mar.6, 3pm TBA |
Jesus Rodriguez
North Carolina State University |
"Recent Topics in Math Finance" Abstract. With traditional financial derivatives having been so well studied, investment banks are looking for new areas to exploit market participants. This has led to a rush to study new areas. We will discuss possible directions for some of these areas. In particular we will discuss some probabilistic issues in credit derivatives and how ideas from energy derivatives can be used to tackle pricing issues in other areas. |
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Wed. Mar.15, 3pm Kidder 280 |
Robert T. Smythe
Department of Statistics, Oregon State University |
"Yet Another Interval-Division Problem" Abstract. |
Day/Time/Room |
Speaker |
Title and abstract |
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Tue. Apr.11, 3pm (Colloquium) Kidder 364 |
Krzysztof Burdzy
University of Washington |
"On the Robin problem in fractal domains" Abstract. The Robin boundary conditions represent the flow of a substance or heat through a semi-permeable membrane. Let u be a non-negative solution to the heat equation in a bounded domain with Robin boundary conditions. I will address the question of whether the infimum of u over the whole domain is equal to 0. I will stress the use of probabilistic techniques in the investigation of this purely analytic problem. The talk will be accessible to a broad mathematical audience and graduate students. Joint work with R. Bass and Z.-Q. Chen. |
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Wed. Apr.19, 4pm Kidder 364 POSTPONED |
Larry Pierce
Oregon State University |
POSTPONED |
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Wed. Apr.26, 4pm Kidder 364 (Probability Seminar and Colloquium) |
Anthony Quas
University of Victoria |
"Maximal rates of divergence of ergodic averages along subsequences" Abstract. Given a measure-preserving transformation T, there has been interest in the study of ergodic averages of the form 1/N[f(T^{a_1}x)+f(T^{a_2}x)+....+f(T^{a_N}x)]. For some sequences (a_n), these averages can be shown to converge pointwise for all measure preserving transformations, whereas for other sequences they diverge. In this talk, I'll describe the maximal rate of divergence and will apply the methods to review the negative solution to an old conjecture of Khinchine's (the original conjecture was as follows: given an integrable function g on the unit circle (written additively), the averages 1/N[g(x)+g(2x)+...+g(Nx)] converge almost everywhere to the integral of g) (joint work with Mate Wierdl) |
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Wed. May 3, 4pm Kidder 364 |
Larry Pierce
Oregon State University |
"Computing entropy for Z^d-actions." Abstract. We will explore new methods for the numerical approximation of entropy for Z^d-actions. |
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Wed. May 10, 4pm Kidder 364 |
Stanley C. Williams
Utah State University |
"Vector generated multiplicative cascades" Abstract. (To be posted) |
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Wed. May 17, 4pm NO SEMINAR |
No seminar this week |
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Wed. May 24, 4pm Kidder 364 |
Weng-Keen Wong
Computer Science, Oregon State University |
"What's Strange About Recent Events: An Algorithm For the Early Detection of Disease Outbreaks" Abstract. Syndromic surveillance is a new field with the goal of detecting disease outbreaks as early as possible using health-care data that precede diagnosis. Traditional outbreak detection algorithms detect disease outbreaks by looking for peaks in a univariate time series of health-care data. Current health-care surveillance data, however, are no longer simply univariate data streams. Instead, a wealth of spatial, temporal, demographic and symptomatic information is available. I will present a disease outbreak detection algorithm called What's Strange About Recent Events (WSARE), which uses a multivariate approach to improve detection time and accuracy. The algorithm itself incorporates a wide range of ideas, including association rules, Bayesian networks, hypothesis testing and permutation tests to produce a detection algorithm that is careful to evaluate the significance of the alarms that it raises. |
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Tue. May 30, 3pm (Colloquium) Kidder 364 |
Christopher Hoffman
University of Washington |
"Uses of the Ergodic Theorem in Probability" Abstract. The ergodic theorem is a powerful tool in probability. Its use involves considering a probabilistic model as a dynamical system. The ergodic theorem has been particularly useful in studying percolation, where it has been used to construct simple geometric proofs to a number of difficult problems. In this talk I will discuss three such applications: 1) Burton and Keane's proof that there is a unique infinite supercritical percolation cluster, 2) Berger and Biskup's proof that simple random walk on the infinite percolation cluster converges to Brownian motion, and 3) A proof that coexistence is possible in Richardson's growth model. |
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Wed. May 31, 4pm Kidder 364 |
Christopher Hoffman
University of Washington |
"Random Simplicial Complexes" |
Day/Time/Room |
Speaker |
Title and abstract |
|
Thursday, Oct 5, 2pm Covell 221 |
Yevgeniy Kovchegov
Oregon State University |
"Mixing times via coupling method" Abstract. An introduction into computing mixing times bounds and asymptotics with coupling techniques. |
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Thursday, Oct 12, 2pm Covell 221 |
Yevgeniy Kovchegov
Oregon State University |
"Mixing times via super-fast coupling" Abstract. We provide a coupling proof that the transposition shuffle on a deck of n cards is mixing of rate $n\log(n)$ with a moderate constant. This has already been shown by Diaconis and Shahshahani but no natural coupling proof has been demonstrated to date. We also enlarge the methodology of coupling to include intuitive but nonadapted coupling rules, for example, to take in account future events and to prepare for their occurrence. (Joint work with R.Burton) The paper for this talk can be found on Math ArXiv at http://front.math.ucdavis.edu/math.PR/0609568 |
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Thursday, Oct 19, 2pm Covell 221 |
Nick Meredith
Oregon State University |
"Computing occupation times with integral equations" Abstract. Consider a simple Markov process on [0,T]. The occupation times were extensively studied in the case of T increasing to infinity. Here we develop a method of computing the distribution for occupation times when T is small via integral equations and integral transforms. |
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Thursday, Oct 26, 2pm Covell 221 |
Corina Constantinescu
Oregon State University |
"Ordering of the Ruin Probabilities" Abstract. In a renewal risk model the inter-claim times form a sequence of independent, identically distributed random variables. If the inter-claim times are distributed as a sum of n exponentials then a comparison between the ruin probabilities may be established for different n's. If, additionally, the insurance company invests in an asset with a price modeled by a geometric Brownian motion, a similar comparison between the ruin probabilities is presented. These comparisons are derived using sample path-wise domination and coupling arguments. |
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Thursday, Nov 2, 2pm Covell 221 |
Robert Burton
Oregon State University |
"Learning about Learning: using coupling paths to construct joint distributions for a pair of Markov chains" Abstract. This should be an exposition that is fairly accessible. I will review coupling as a methodology for computing with Markov chains. This has had many payoff, from the understanding of mixing properties and then to the path Central Limit Theorems. It has been very useful in statistical physics and showing connectivity of random structures. It is also the natural tool for a looking at a Markov Chain with additional structure because they arise in a certain natural way: as the independent and identically distributed composition of random transformations. This object exploded fractals (and by association chaos theory) into the everyday realm of human consciousness. |
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Thursday, Nov 9, 2pm Covell 221 |
Stephen D. Scarborough
Oregon State University |
"Probability and Continued Fractions" Abstract. This material was created for use as a possible project in a Senior Seminar. This talk will be very accessible for undergraduates. The required background is calculus and Laplace transforms. The needed number theory will be given in the talk. Let x be a U(0,1) random variable. Express x as a continued fraction. x = [0;a(1),a(2),a(3),...]. We will find an expression for P(a(n)=k). Next we will closely examine P(a(2)=k). If time permits an expository discussion will be given for the asymptotic case. |
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Thursday, Nov 16, 2pm Covell 221 |
David Levin
University of Oregon |
"Glauber dynamics for Ising model on complete graph" Abstract. This talk is mostly expository -- I describe the phase transition from fast to slow mixing for the Glauber dynamics for Ising on complete graph. The upper bound uses path coupling, and the lower bound uses Cheeger's inequality. |
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Thursday, Nov 30, 2pm no seminar |
NO SEMINAR
|
no seminar this week |
Day/Time/Room |
Speaker |
Title and abstract |
|
Thursday, Jan 18, 2pm Kidder 364 |
Mina Ossiander
Oregon State University |
"Stein's Method: Part I" Abstract. This is the first of a pair of seminars on Stein's method. It will be expository in nature. The plan is to give a sketch of Stein's original idea of characterizing distributions via certain expectation properties along with an application to normal approximation for sums of iid r.v.'s. Some refinements due to Chen and Shao will be included. |
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Thursday, Jan 25, 2pm Kidder 364 |
Mina Ossiander
Oregon State University |
"Stein's Method: Part II" Abstract. This is the second of a pair of seminars on Stein's method. The plan is to indicate further applications of Stein's general approach to convergence of random variables. First we will see how his original idea can be used to characterize a variety of distributions. This will be followed by a new application of Stein's method to Polya's urn using a Stein characterization of the Beta distribution. |
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Thursday, Feb 1, 2pm Joint with University of Oregon, at University of Oregon, Deady 208 |
Davar Khoshnevisan
University of Utah |
"Potential theory for several Markov chains." Abstract. In 1989, P. Fitzsimmons and T. Salisbury solved the long-standing open problem of describing exactly when the trajectories of two (or more) independent Markov processes intersect. Although the proof has been greatly simplified in the setting of Markov chains (Salisbury, 1996), this is still considered a very difficult result. In this talk, I will present a completely self-contained proof [still in the context of denumerable chains], which is based on arguments that were originally designed to study the Brownian sheet (Khoshnevisan and Shi, 1999). |
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Friday, Feb 2, 3pm (Colloquium) Kidder 364 |
Davar Khoshnevisan
University of Utah |
"On the stochastic heat equation." Abstract. Consider the classical heat equation in dimension d, and formally replace the external forcing term by white noise. The resulting "stochastic PDE" (SPDE, for short) is the so-called stochastic heat equation. It has been known for some time that the stochastic heat equation suffers from a "curse of dimensionality": It has function solutions if and only if the ambient dimension is one. First we present a rigorous formulation of this SPDE, and explain why it has function solutions in only one dimension. Then, we discuss some newly-found connections between systems of solutions and classical notions from geometric measure theory [joint work with Robert Dalang and Eulalia Nualart]. Time permitting, we also address the mentioned curse of dimensionality, in greater length, by presenting an unexpected connection to classical probabilistic potential theory and the theory of local times [joint work with Mohammud Foondun and Eulalia Nualart]. |
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Thursday, Feb 8, 2pm NO SEMINAR |
No seminar this week
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Thursday, Feb 15, 2pm Kidder 364 |
Yan-Xia Ren
Peking University, visiting U.Oregon |
"Limit theorems for super-diffusions corresponding to the operator Lu+βu-ku2 " Abstract. |
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Thursday, Feb 22, 2pm Kidder 364 |
Yevgeniy Kovchegov
Oregon State University |
"On Stein-Chen coupling." Abstract. This will be an expository talk on the Stein-Chen method. We will provide examples of applying Stein-Chen method, such as providing error estimates for Poisson approximation. |
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Thursday, March 1, 2pm Kidder 364 |
Robert Burton
Oregon State University |
"Stuck in the Middle Between Determinism and Randomness: The Birth of Chaos" Abstract. This talk will be expository and will look at the origins of modern dynamical systems and the failure of the Newtonian program of determinism. This failure is implicit within Newtonian mechanics and does not rely on quantum effect. It turns out that under very general circumstances dynamical systems are observed as a finite events, for example, as on a computer monitor. This leads us to symbolic dynamics and formalism. From there Markov process arise naturally as do substitution like rules. These polar opposites are, in some sense, orthogonal. There will be no specific set of Differential Equations presented, rather we begin on one of the nicest and simplest objects, automorphisms of the torus. |
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Thursday, March 8, 2pm NO SEMINAR |
No seminar this week
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Thursday, March 15, 2pm NO SEMINAR |
No seminar this week
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Day/Time/Room |
Speaker |
Title and abstract |
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Wednesday, April 18, 12:00-12:50pm (Eco-IGERT Colloquium) Wilkinson 203 |
Serban Nacu
École Normale Supérieure, Paris |
"Probability with Ants" Abstract. Ants make an interesting subject for mathematicians. At the low level, an ant colony consists of a large number of similar individuals, performing fairly simple tasks, often with a random element. Yet at the high level, the colony is capable of complex and robust behavior, achieved without central control. Information is transmitted across the colony by interactions among ants, and the behavior of individuals is strongly influenced by these interactions. Ants are also very successful creatures; it is estimated they make up at least 10% of the terrestrial animal biomass. We discuss a series of experiments performed on a population of harvester ants living in the Arizona desert, that illustrate some of these points. Their analysis raises some interesting statistical and mathematical questions. We also mention some problems in (pure) probability theory that were inspired by the ants. No previous knowledge of ants will be assumed. This talk is based in part on joint work with Deborah Gordon and Susan Holmes |
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Thursday, April 19, 2pm Kidder 364 |
Serban Nacu
École Normale Supérieure, Paris |
"GENE EXPRESSION NETWORK ANALYSIS" Abstract. There is a strong genetic component in cancer and many other diseases. Often the disease involves, or is caused by, dysfunction in the cellular machinery: genes in normal and disease cells behave in different ways. Those differences in gene expression can be measured using microarray technology, which in the recent past has become a fundamental technique in biology and medicine. A typical microarray measures expression levels for 20,000 genes at the same time: this massive parallel power also raises important statistical and computational problems. After a brief introduction to the technology, we focus on the issue of gene interactions. Standard microarray analysis treats each gene separately, and ranks them according to some measure of differential expression. But in reality genes interact, they act in concert rather than alone; an analysis that accounts for those interactions has the potential to be more statistically accurate and biologically meaningful. We introduce a method called GXNA (Gene eXpression Network Analysis). GXNA uses a gene interaction graph to search for clusters of related genes that are differentially expressed. It has several desirable features, such as fast runtimes and the computation of objective, permutation-based significance levels, and it shows promising results when applied to data sets involving cancer and the human immune system. This is joint work with Rebecca Critchley-Thorne, Peter Lee, and Susan Holmes. |
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Friday, April 20, 3pm (Colloquium) Kidder 364 |
Serban Nacu
École Normale Supérieure, Paris |
"Fast Coin Simulation" Abstract. ou are given a coin with probability of heads p, where p is unknown. Can you use it to simulate a fair coin? How about a coin with probability of heads 2p? Or a coin with probability of heads f(p), where f is a known function? For a fair coin, the problem goes back to Von Neumann in the 1950s. In 1994, Keane and O'Brien obtained necessary and sufficient conditions for a function f to have such a simulation. We are looking at the problem of efficient simulation. Let N be the number of p-coin tosses required to simulate a f(p)-coin toss. Typically N will be random; we say the simulation is fast if N is small, in the sense that its distribution has exponential tails. When does a function have a fast simulation? Surprisingly, it turns out this happens if and only if the function is real analytic. This is an instance of a more general phenomenon: there is a connection between the computational and analytic/algebraic properties of certain systems. The proof is constructive, and leads to algorithms that can be implemented. We use tools from the theory of large deviations, approximation theory, and complex analysis. This is joint work with Yuval Peres. |
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Thursday, April 26, 2pm Kidder 364 |
Ioana Dumitriu
University of Washington |
"Tridiagonal matrix models for general β ensembles" Abstract. β-Hermite, -Laguerre, and -Jacobi ensembles are generalizations of the Gaussian, central Wishart, and MANOVA matrices, with applicability in fields like statistical mechanics and traffic pattern analysis. Matrix models for these β-ensembles have been discovered relatively recently, and the implications of this discovery for the study of the β-ensemble eigenstatistics cannot be understated. In this talk, we will show how these matrix models were discovered, and sketch the proof that the eigenvalues of the β-Hermite matrix have joint eigenvalue distribution given by the β-Hermite ensemble (which, for β=1,2, respectively 4, are the same as the eigenvalue distributions of the Gaussian Orthogonal, Unitary, respectively Symplectic ensembles). |
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Friday, April 27, 3pm (Colloquium) Kidder 364 |
Ioana Dumitriu
University of Washington |
"Classical ensembles of random matrices: from the threefold way to a β future" Abstract. In classical probability, the Gaussian, Chi-square, and Beta are three of the most studied distributions, with wide applicability. In the last century, matrix equivalents to these three distributions have emerged from nuclear physics (Gaussian ensembles) and multivariate statistics (Wishart and MANOVA ensembles). Their eigenvalue statistics have been studied in depth for three values of a parameter (β = 1, 2 and 4) which defines the "threefold way" and can be thought of as a counting tool for their real, complex, or quaternion entries. The re-examination of the Selberg integral formula, in the late `80s, has brought the advent of general β-ensembles, which subsume the classical cases, and for which the Boltzmann parameter β acts as an inverse temperature. Their eigenvalue statistics interpolate between the isolated instances 1, 2, and 4, offering a "behind the scenes" perspective. With the discovery of matrix models for the general β-ensembles in the early 00's, we have entered a new stage in the understanding of the complex phenomena that lie beneath the threefold way. While the β = 1,2 and 4 cases are and will always be special, we can now argue that the future of the classical ensembles is written in terms of a continuous β parameter. |
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Thursday, May 3, 2pm Kidder 364 |
Robert Burton
Oregon State University |
"Iterated Function Systems: The Fractal Nature of Discovery" Abstract. Iterated Function Systems are a given by a composition of randomly chosen transformations of a separable metric space (ok, sometimes complete also). They are natural objects that arising in modeling, and as a coordinatization for Markov Chains with stationary transition probabilities. They have been going in and out of style, but they are guaranteed to raise a smile, in the sense that they have been often rediscovered in all innocence with new terminology. Here, in this part of the talk, I will insert a list of famous people over the last century and some friends (non-empty intersection) who have thought about these models. Iterated Function Systems have seen a lot exposure lately because of Fractal Image Compression, using the idea that rough textures are often enough detail, and that this may be simulated with fast simple code. In fact, before they were used to produce detailed and attractive pictures, they were used as models of learning and adaptation. We give a very simple proof of the main idea, explore how they could model learning and give some results, with a hint at the methodology we used. If you just want the pictures go to www.electricsheep.org, itself a free open source downloadable software package and is an allusion to the greatest science fiction writer of all time. |
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Thursday, May 10, 2pm Kidder 364 |
Tom Dietterich
School of Electrical Engineering and Computer Science, Oregon State University |
"Experience with Slice Sampling in the CALO Probabilistic Constraint Engine" Abstract. This talk will present an overview of the CALO project and then discuss the Probabilistic Constraint Engine (PCE), which is the core inference engine in CALO. We have implemented a form of Slice Sampling (originally developed by Pedro Domingos at the University of Washington). This talk will describe the algorithm, our implementation, and initial experiments with it. |
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Thursday, May 17, 2pm Kidder 364 |
Ed Waymire
Oregon State University |
"Stochastic Particle Tracking and Skew Brownian Motion." Abstract. In recent years a variety of stochastic particle tracking methods have been proposed, developed and compared for efficient numerical mass transfer computations in the engineering literature. Particle tracking microscopy is also an essential method of observation of heterogeneous protein diffusion in cellular biology. In this talk a particular stochastic particle method recently proposed and and shown to be superior in laboratory tests is explained as an unexpected byproduct of our earlier work on dispersion rates. This is based on a recent paper with B. Chastenet, J. Ramirez, E. Thomann, and B. Wood. |
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Thursday, May 24, 2pm Kidder 364 |
Jorge M. Ramirez
Oregon State University |
"Multiple Skew Brownian motion (MSBM) and applications" Abstract. I construct MSBM as a generalization of skew Brownian motion to the case of infinitely many interfaces x_k, with k ranging over the integers. This process behaves like Brownian motion when away from the interfaces, and experiences a skewness (or localized drift) alpha_k at each x_k. The construction and most of the results are derived using the representation of MSBM as a scaling of Brownian motion under a random time change. Then the theory of Dirichlet forms is used to derive the L^2 semigroup of MSBM and connect it to a diffusion process with discontinuous coefficient. As an application, I give some results concerning advection-diffusion in a two dimensional layered medium, and an elementary proof of an arcsine law for skew Brownian motion. |
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Thursday, May 31, 2pm Kidder 364 |
David Plaehn
InsightsNow, Inc. |
"Mathematics in the Food Industry: Penalty Analysis" Abstract. As an example of mathematics in the food industry, a method called (traditional) penalty analysis is considered. With penalty analysis, product developers try to better understand product deficiencies by looking at consumer responses to overall liking vs. so-called "just-about-right" (JAR) questions. JAR variables are categorical with response categories ranging from some degree of "too little" to 'just-about-right' to some degree of "too much". By calculating the overall liking for those consumers answering, "too little", for example, compared to those that answered 'just-about-right', one can assign a "penalty" for being "too little". It is shown that traditional penalty analysis is equivalent to ordinary least squares (OLS) regression, allowing for standard methods of significance testing of the penalties. A distribution for testing the so-called "penalty weights" is proposed and compared to a non-parametric method on a real data set. |
Day/Time/Room |
Speaker |
Title and abstract |
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Thursday, October 4, 2pm Covell 221 |
Ed Waymire
Oregon State University |
"Size Biasing and Tree Polymer Models" Abstract. An important size bias change of measure was introduced in the context of multiplicative cascades by Jacques Peyriere, also referred to as the "Peyriere probability", for the purpose of analyzing the structure of random measures obtained in the supercritical regime in which non-trivial cascade limits can be determined from the seminal 1976 paper of Kahane and Peyriere. Size biasing was extended by Stanley Williams and the author in 1994 as another approach to the Kahane-Peyriere existence theory for multiplicative cascades. Certain problems arising in the analysis of tree polymers will be shown to involve the analysis of cascade limits in the critical and subcritical cases, to which size biasing can effectively be applied. Some improvements on present theory are possible by this approach which will be presented. Based on joint work with Stanley C Williams, and inspired by discussions with Harry Kesten during a sabbatical year at Cornell. |
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Thursday, October 11, 1:30pm Covell 221 |
Yevgeniy Kovchegov
Oregon State University |
"Occupation times and modified Bessel functions" Abstract. For a given state of a continuous time Markov process, we use a combination of Fourier and Laplace transforms to express the distribution of the time spent by the process at that state within [0,t] time interval. Based on joint work with N.Meredith. |
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Thursday, October 18, 1:30pm NO SENINAR |
No seminar this week.
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No seminar |
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Thursday, October 25, 1:30pm Covell 221 |
Larry Marple
School of Electrical Engineering and Computer Science Oregon State University |
"DOUBLY TOEPLITZ COVARIANCE STRUCTURES FOR 2-D SIGNAL PROCESSING APPLICATIONS" Abstract. Sophisticated multi-dimensional sensors are becoming more commonplace in radar, sonar, ultrasound medical imaging, and seismic signal collection systems. Statistical signal processing of acquired data from the sensors involves multi-dimensional and multi-channel (multivariate) covariance matrix structures for purposes of detection and target/feature classification. The size of matrices in actual sensor applications have dimensions of many thousands and require fast computational algorithms to make them feasible for real-time implementation. This presentation will show the some fast algorithm structures involving parametric means of estimating the covariances for the one-dimensional case to establish a baseline, and then will show some recent research efforts to develop the two-dimensional versions dealing with doubly Toeplitz (or Toeplitz-block-Toeplitz in some literature) structures. |
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Thursday, November 1, 1:30pm Covell 221 |
Robert Burton
Oregon State University |
"Shuffles, Couples, and Waffles" Abstract. There has been interest in how long it should take a set, often a set with an algebraic structure, to uniformly mix. This time is infinite on arithmetic grounds. It is similar to asking how long it will take a binary expansion to equal 1/3. Instead, we back up a little and ask for mixing times. The amount of time (length of expansion) it takes to be closer than \epsilon to 1/3 is -log(\epsilong) where the log is to base 2. This rate is uniform over all points in the interval, not just 1/3. In our context, we ask how long will it take for mixing to be uniform with at least a fixed probability, say prob = 1/2. (This value is not usually important for the rate at which mixing occurs as function of the size of the set.) We may not mix exactly but we can get uniformly close. The method that is often used is coupling as a way to estimate the total variation norm. Often, this method cannot obtain the best mixing time. By 'tunnelling' into the future, we show how to improve the estimate on the time until it is optimal in the limit. We apply this to some simple models of shuffling card, and to a form of mixing, which we call matrix mixing. |
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Thursday, November 8, 1:30pm NO SENINAR |
No seminar this week.
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No seminar |
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Thursday, November 15, 1:30pm Covell 221 |
Yaroslav Bulatov
Oregon State University |
"Belief Propagation in Graphical Models" Abstract. Suppose we have a hidden Markov model with a sequence of states Y1,...,Yn and observations X1,...,Xn. An important quantity, for signal processing, and inference is the probability of some state Yi given all the observations X1,...,Xk. For HMM, this quantity can be found by marginalizing out the variables, which in signal processing community is known as the Forward-Backward algorithm. There's a generalization of the Forward-Backward algorithm to compute an analogous quantity for a wider class of probabilistic models, where interactions are described by a general tree graph, known as the Sum-Product algorithm, Message Passing or Belief Propagation. In addition to estimating the probability of a variable conditioned on the evidence, versions of this algorithm are used for decoding error-correcting codes, computing free energy in Ising-like models and providing heuristics for various NP-hard problems such as Min-Cut. In this talk I will describe the algorithm and some applications, some known results, and associated open problems. |
Day/Time/Room |
Speaker |
Title and abstract |
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Thursday, January 24, 2:00pm Kidder 364 |
Yevgeniy Kovchegov
Oregon State University |
"Perfect coupling and tunneling to the future" Abstract. We will compare coupling methods in probability to Perron-Frobeniuous decomposition. We will discuss perfect coupling and the method of "tunneling to the future" as a non-Markovian coupling technique that can be used to produce correct mixing rate. |
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Thursday, January 31 NO SEMINAR |
No seminar today
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Thursday, Feb 7, 2:00pm Kidder 364 |
Robert Burton
Oregon State University |
"Plausible Reconstruction of Mixtures of Genetic Information from the Sargasso Sea." Abstract. We will talk about partial data from close to a decade's worth of data from a single location in the Sargasso Sea. Because of cost/time constraints, there is only partial information available. There are enzymes that cut the RNA at specific locations in specific finite patterns (like CCGG in the AGCT alphabet of nucleotides). We are then given estimates of the distance from an origin. Usually, one enzyme is used to estimate the percentage of certain bacteria. This experiment used three different enzymes in the hope of getting better estimates of the percentage of different organisms present, over months, depths, years. We show partial progress in solving this model in a meaningful way. There is a debate in the microbiology community as to whether the dominant method of evolution is from ancestor-derived genetic information or whether it is lateral organism-to-organism and organism-to-floating stuff. The answer is probably context and organism dependent. The difference is whether a tree model describes evolution (slow to adapt) or whether a network graph describes evolution (lots of variation and quicker to adapt). This data may show some surprising uniformity in the way that micro-organisms are constructed, giving support for the lateral method of adaptation. |
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Thursday, Feb 14, 2:00pm Kidder 364 |
No seminar. The faculty will meet to discuss probability classes for next year.
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No seminar. Probability offerings discussion. |
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Thursday, Feb 21, 2:00pm Kidder 364 |
Raviv Raich
Electrical Engineering and Computer Science Oregon State University |
"Flow Cytometry: Manifold Learning of High Dimensional Data" Abstract. The task of analyzing and processing high volumes of information poses a great challenge. We are interested in extracting a simple model that supports the complex data we observe to explain phenomena of interest. Geometry and more specifically manifolds offer means of explaining a low dimensional description of high dimensional data. One application of interest is Flow Cytometry, a technique that utilizes fluid dynamics to allow for individual identification of cells and statistical analysis of the sample as whole. In this presentation, we will demonstrate how learning Riemannian manifolds can be applied to Flow Cytometry for visualization, clustering, and classification of various cancer types. |
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Thursday, Feb 28, 2:00pm Kidder 364 |
Torrey Johnson
Oregon State University |
"Low-Dimensional Lattice Polymer Models." Abstract. Sharp results are rare for low-dimensional lattice polymers. We will consider some examples of low-dimensional lattice polymer models for which such results are possible. These models examine the tendency of the polymer to localize near an "interface" (for us this will be the x-axis). We will also consider a mapping from the lattice polymer to the tree polymer which may be useful in obtaining results about the lattice polymer, which are usually more difficult to obtain. |
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Thursday, March 6, 2:00pm CANCELED |
Qi-Man Shao
University of Oregon and Hong Kong University of Science and Technology |
"Stein's Method of Exchangeable Pairs with Application to the Curie-Weiss Model" Abstract. PDF file |
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Thursday, March 13, 2:00pm Kidder 364 |
Young Soo Seol
Oregon State University |
"ON WEAK CONVERGENCE OF SKEW RANDOM WALK" Abstract. The primary purpose of this presentation is to establish functional central limit theorem for skew random walks and to define skew Brownian motion as resulting weak limit. Since the skew random walk is just a symmetric random walk when away form the origin, the right scaling of space and time will be the same as in the functional central limit theorem for Brownian motion. Finally, we will show that skew Brownian motion is the weak limit of skew random walk proving the convergence of finite-dimentional distributions and tightness. |