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Shiqi
Li, CRMSE, July 21, 2008 Students from East Asian countries often top the list in international assessments of mathematics education. But classroom observation shows that mathematics teaching there is quite traditional and conservative. Some scholars have an impression of a “paradox” of mathematics education: traditional ways of teaching make excellent performance by students. It may be a misunderstanding. A distinctive and effective teaching strategy, variation, as a case of practical teaching in China, will be shown in a videotaped lesson. Based on four episodes in the lesson, the characteristics of variation and their underlying beliefs are analyzed. Dan
Lanier, SDSU, July 8, 2008 Nowadays, with the computational power of the home computer, you can create pretty pictures of fractal, utilizing Matlab, in as fast as 23 seconds. This talk will explore the complex function behind the escape-time algorithm to create the Julia set and the Mandelbrot set. It will also discuss the Matlab codes responsible for creating such art. Peter
Salamon, SDSU, July 1, 2008 The talk will begin with motivation expounding why phage and metagenomes are interesting. It will then describe some mathematical tools we have created in San Diego for the comparison and characterization of phage metagenomes. Finally it will conclude with some future directions for research in this area. Vadim
Ponomarenko, SDSU, June 24, 2008 Hojin
Moon, CSULB, May 2, 2008 Florin
Vaida, UCSD, April 25, 2008 An interesting feature
of DIC is that it depends on the model focus, or subset of parameters
of interest, with different focuses leading to different DIC values.
However, only one particular such focus is easy to compute and reported
when using MCMC (or in WinBUGS), which is the one conditional on all
model parameters. We show that for other model focuses more complex
computations are necessary. We show how to compute DIC for a general
model focus, based on the MCMC output, and we illustrate the methods
on several examples. Farshid
Arjomandi, SDSU, April 24, 2008 The original Kalman
filter is modeled on a Markov chain built on linear operators which
are perturbed by Gaussian noise. It can be shown that among all filters,
it's the one that minimizes the variance of the estimation error. In
this talk, I plan to present the theory and algorithms behind the construction
of this important control systems gadget. A couple of examples encompassing
applications will also be presented. Jo
Hardin, Pomona College, Apr. 18, 2008 We propose a robust
similarity metric based on Tukey's biweight estimation of multivariate
scale and location. The robust metric, the biweight correlation, is
simply the correlation obtained from a robust covariance matrix of scale.
We provide results demonstrating the robustness and improvement of the
correlation method. As well, our method gives an outlier identification
procedure which is valuable when dealing with such massive amounts of
data. Used in clustering algorithms, it is clear that the biweight correlation
gives more meaningful clusters of genes. Werner
Balser, Institute for Applied Analysis, University of Ulm, Mar.
24, 2008 Power series with radius of convergence equal to zero frequently occur as solutions of ordinary as well as partial differential equations. Several such examples shall be presented, and it shall be shown that one can still use them to compute a true solution of the corresponding equation. Zhaoxia
Yu, UC Irvine, Mar. 21, 2008 Goong
Chen, Texas A&M University, Mar. 7, 2008 In this talk, the speaker will introduce PDE models for a rigorous mathematical study aiming at problems directly or intimately related to these greenhouse effects. He will first introduce the Schrödinger equation from laser physics as a basic model. The symmetries of the molecular structures will then be presented. Numerical results will be illustrated. Important issues such as spectral broadening and interesting problems for research will be discussed. Vanamamalai
Seshadri, McGill University, Feb. 29, 2008 We begin with a short explanation of the term "inverse" appearing in the name of this distribution. This adjective was originally proposed by Tweedie who introduced this distribution to the statistical world as early as 1957. However even as early as 1915 this distribution appears to have been quite well known among the physicists and probabilists as the first passage time distribution of Brownian motion with positive drift . But Tweedie's justification has merit as will be explained in the talk. Among the many results obtained by Tweedie about this distribution there is one which stands out uniquely that has a lot of resemblance to a parallel result for the Gaussian distribution. We will use the notation IG ( at , at^2) to denote the inverse Gaussian distribution with parameters (at) and (at^2), the first denoting the mean of the distribution, where a > 0 and t > 0. Suppose that we have a random sample of n observations Y_i from IG ( at_i , a t_i^2 ) then Tweedie showed that Q = a[ { (t_1^2) / y_1 +.... +(t_n^2) /y_n } - ( T^2 / S ) ] has a distribution
which is independent of S = y_1 +....+ y_n (T is the sum of the t_i's).
He also showed that Q has a chi-squared distribution with (n-1) degrees
of freedom. In this talk we will propose a prior distribution for the
parameter t and see what happens. Daniel
Pick, Pick Data Mining, Feb. 22, 2008 Roger
Barnard, Texas Tech University, Feb. 8, 2008 We will discuss how we apply variational techniques and special function theory to verify some conjectures of C. Pommerenke and D. Minda on the sharp bound for the Schwarzian derivative of hyperbolically convex maps. This completes the classification of the extremal domains for the Schwarzian in all three classical geometries, hence answering the question first posed in the 50's as to how far one can distort a disk under a convex map in Euclidean, spherical and hyperbolic geometries. We will mention how these ideas are used to verify a number of other conjectures by Pommerenke. Vitaly
Skachek, University College, Dublin, Ireland, Jan. 30, 2008 A framework for
linear-programming (LP) decoding of non-binary linear codes over quasi-Frobenius
rings is developed. It is proved that the resulting LP decoder has the
maximum likelihood certificate property. It is also shown that the decoder
output is the lowest cost pseudocodeword. Equivalence between pseudocodewords
of the linear program and pseudocodewords of graph covers is proved.
Different polytopes for use with linear-programming decoding are studied,
and it is shown that for many classes of codes these polytopes yield
a complexity advantage for decoding. These representations lead to polynomial-time
decoders for a wide variety of classical non-binary linear codes. LP decoding performance
is illustrated for the $(11,6,5)$ ternary Golay code with ternary PSK
modulation over AWGN, and in this case it is shown that the LP decoder
performance is comparable to codeword-error-rate-optimum hard-decision
based decoding. Douglas
Nychka, National Center for Atmospheric Research, Jan. 25, 2008 Don
Lutz, SDSU, Jan. 25, 2008 R. Agarwal and M.
Pituk have recently considered some scalar linear difference equations
with coefficients that are asymptotically constant with exponentially
small perturbations. Using the method of generating functions and elementary
methods from complex analysis, they derived an asymptotic representation
for solutions, which was then applied to study the behavior of some
nonlinear autonomous scalar difference equations near a hyperbolic equilibrium.
Here, we (S. Bodine and D. A. L.) show that using standard methods of
asymptotic matrix analysis, their results can not only be modestly generalized
to systems, but the error estimates can also be made more precise. An
analogous result can also be applied to nonlinear autonomous systems.
We report on measurements and simulation results of time-reversal in the 2.4\,GHz regime. The measurements were made in indoor environments using wide angle directional antenna arrays; and the corresponding numerical simulations computed using a full 3D-waveguide propagation code. John
Brevik, CSU Long Beach, Nov. 30, 2007 In studying algebraic surfaces in projective 3-dimensional space, one wishes to classify the curves lying on a particular surface. I will first discuss the background necessary to frame the issue precisely and give relatively complete results for surfaces of low degree. A good general solution to the problem is provided by the Noether-Lefschetz Theorem, stated by Noether in the late 19th century and proved by Lefschetz in the 1920s. Griffiths and Harris gave a different proof of the theorem in the 1980s; their approach has allowed generalizations in a number of directions. I will discuss some of these generalizations, my current work with Scott Nollet (TCU) on related problems, and topics for future work. Colleen
Kelly, Exponent, Nov. 19, 2007 Colleen Kelly will talk about how Exponent, a leading engineering and scientific consulting firm, uses statistics to help their clients solve technical problems. Examples of statistical problems encountered will be given as well as a discussion of technical and personal skills required to be successful in consulting. A question and answer period will be held following the presentation. Changxuan
Mao, UC Riverside, Nov. 16, 2007 The Rasch model is adopted to estimate the unknown population size in multi-list disease surveillance studies. It takes both the list effectiveness and case heterogeneity into account. A stepwise approach is proposed in which optimization problems are solved conveniently. The sharpest lower bound to the odds that a case is unseen is introduced, which can be calculated by linear programming. There are also some less sharp lower bounds. Estimating a lower bound leads to an estimator for the population size. Real examples are investigated for the purpose of illustration. Mark
Dunster, SDSU, Nov. 16, 2007 We look at the classical modal expansion for the scattered field of a plane wave from a circular dielectric cylinder. Using classical WKBJ approximations for Bessel functions, a new uniform asymptotic approximation is presented for the late coefficients in this expansion, valid for the entire region exterior to the cylinder. These approximations predict the location of a certain critical Regge pole, which can lead to at least one dramatic resonant modal term at certain critical values. We also show that the mean square measure, over all space, of the difference of the scattered field from two distinct values of the dielectric constant of the cylinder can sometimes be very small; this can have consequences in inverse scattering, and we analyze this phenomenon, again using properties of Bessel functions. Serkan
Hosten, SFSU, Nov. 9, 2007 This will be a gentle introduction to the applications of algebraic geometry to statistics. The main goal of the talk is to present statistical models, i.e. sets of probability distributions (defined parametrically most of the time), as algebraic varieties. I will give examples where defining equations of such statistical model varieties have been successfully computed: various graphical models and models for DNA sequence evolution. I will also talk about the algebraic degree of maximum likelihood estimation with old and new examples. Peter
Salamon, SDSU, Nov., 2, 2007 Cooling physical systems to extremely low temperatures is important for quantum computing, for improved MRI, and for producing new states of matter known as Bose-Einstein condensates. The talk will present several simple mathematical problems posed by such cooling. Oh
Nam Kwon, Seoul National University, Nov. 1, 2007 Research on the relationship between different teaching methods and students’ understanding of mathematics at the university level is essential for cumulative improvement in mathematics. However, a number of researchers have reported that there is the gap between what is taught and what is learned in mathematics in traditional modes of teaching. This talk explores more effective teaching method at the university level. An example of inquiry-oriented mathematics teaching at the university will be discussed and illustrated how to enhance students’ authentic understanding in an ordinary differential equations course. Todd
Coffey, Amylin Pharmaceuticals, Oct. 30, 2007 Many students in statistics or biostatistics have heard of professional opportunities in the pharmaceutical industry to design and analyze clinical studies. Most students, however, are unaware of the wide variety of opportunities for statisticians in the nonclinical areas of drug discovery and nonclinical development. In this talk I will discuss the process of drug discovery, show examples of how statisticians can provide value, and give advice on the preparation needed while in school to succeed as a nonclinical statistician. Gerald
R. North, Texas A&M University, Oct. 18, 2007 Estimates of climate change over the last millennium indicate that the Earth’s temperature has increased dramatically over the last century and the pace of the warming is increasing as well. There are several ways of assessing the state of the science, including surveys, expert panel assessments and finally the Intergovernmental Panel on Climate Change. The scientific consensus is that the climate of the last few decades has been warming in an unusually rapid manner and that most of the warming is attributable to humans. The primary reason of this consensus is the emergence of several revolutionary approaches to the problem: Global Observing Systems and Analysis Techniques (satellites, routine weather observations, special field programs, etc.), Integrated Studies Across Disciplines (coupling model components, etc.), and finally the Development of Computer Intensive Simulations Systems (global climate models). While the climate system is incredibly complicated perhaps comparable to a biological system, there has been a steady accumulation of evidence supporting the hypothesis that excess anthropogenic emissions of greenhouse gases and other materials into the air are the primary drivers of recent climate change. The lecture will include some results of recent studies on future climates we might expect for the Earth and in particular the contiguous United States. Andre
Kundgen, CSU San Marcos, Oct. 12, 2007 We consider the problem of sending a message from a sender S to a receiver R through an unreliable network (given by a graph G) in which edges may fail, but cannot recover. Our aim is to design a protocol that ensures that a message sent by Swill be received by R as long as some SR-path remains (even if we don't know what path it is) without generating an infinite number of message traffic in the process. We explicitly characterize the family of networks in which this is possible in terms of forbidden rooted minors, and we give the protocol. We also show that there is a forbidden rooted minor characterization fort he case when we can attach a header (containing routing information) of fixed length to the message, and we discuss the algorithmic consequences of these characterizations. We also discuss the case when we can assume that at most k edges can fail. Xin
Lu, UCSD, Oct. 12, 2007 I'll discuss two statistical issues in microarray based gene selections, the False Discovery Rate (FDR) control and the reproducibility of selection procedures. To control the FDR and maintain a better power in gene selection, we need to estimate the proportion of true null hypothesis (PI0) based on the pooled statistics of all genes. Current methods usually assume genes are independent with each other or only weakly correlated. We showed that when strong correlation exists among the data, which is common in microarray datasets, the estimation of the proportion of null hypotheses could be highly variable resulting in a high level of variation in the FDR control. Therefore, we developed a re-sampling strategy to reduce the variation by breaking the correlations between gene expression values, then using a conservative strategy of using the upper quartile of the re-sampling estimates to obtain a strong control of FDR. With simulation studies and perturbations on actual microarray datasets, our method, compared to competing methods such as q-value, generated slightly biased estimates on the proportion of null hypotheses but with lower mean square errors. When selecting genes with controlling the same FDR level, our methods have on average a significantly lower false discovery rate at the price of a minor reduction in the power. Another related problem is to evaluate the gene selection procedures based on their reproducibility. We proposed a non-parametric Re-Discovery Curve (RDCurve) method, to estimate the probability of re-discovery of genes selected from a microarray data set. Given a selection procedure and a data set, the RDCurve method applies the selection procedure repeatedly to bootstrapped data, select the important genes, and then estimate the expected frequency of re-discovery of the selected subset of genes. We also proposed a permutation method to estimate the confidence band of RDCurve under null hypothesis to test the significance of the RDCurve. The method we proposed is a complement to traditional FDR method. It is non-parametric and model independent. With the RDCurve method, we can evaluate the signal-noise ratio of a give data set, compare the performance between selection procedures in term of them expected reproducibility, or select the number of genes to be reported. Farshid
Arjomandi, SDSU, Oct. 5, 2007 In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an underdetermined system of first-order homogeneous linear partial differential equations. Frobenius' original version of the theorem was stated in terms of Pfaffian systems, however today it can be restated more economically in the modern language of differential forms and vector fields. This nice geometric result can be utilized to yield a criterion for determining whether a given control system is nonholonomic, i.e., whether the constraints of the system depend on parameters other than the coordinates of the system and time (such as the velocity or momentum). In this talk we will introduce the mathematical machinery, and then describe and explore the usage of this theorem to a few problems from the area of nonlinear geometric control theory. Scott
Nelson, SDSU, Oct. 2, 2007 Statistical forecasting methods play a vital role in the electric power industry. In this talk I will give an introduction to the electric power industry, and discuss some of its unique characteristics. Specific, real world examples of short-term, long-term and financial forecasting problems will be presented, along with innovative methodology and software designed to address these problems. Persons who are interested in pursuing careers in the energy industry are encouraged to attend. The talk will be aimed at undergraduate and graduate statistics, math, and business majors. Subir
Ghosh, UC Riverside, Sept. 27, 2007 In fractional factorial experiments, we run a fraction of treatments for generating the data and assume that some or all factors do not interact with each other. For example, in a Resolution 3 plan we assume that the factors do not interact at all and in a Resolution 4 or a Resolution 5 plan we assume that the 3-factor and higher order interactions are negligible. Such assumptions may or may not be true in reality in the sense that a few of such interactions assumed to be negligible may in fact be non-negligible. We consider a class of models for 2m factorial experiments with the common parameters being the general mean, the main effects and the uncommon parameters in any two models being two 2-factor interactions one from each model. We want to identify all the models within the class, discriminate between any two models within the class, and search for the best model for describing the data. Both design and inference issues are discussed for this purpose. Rich
Levine, SDSU, Sept. 21, 2007 Over the past few months, the United Nations Fourth Intergovernmental Panel on Climate Change (IPCC) reorted that "the observed increase in globally averaged temperatures since the mid-20th century is very likely due to the observed increase in anthropogenic greenhouse gas concentrations," a statement strengthening previous IPCC assessment reports, but leaving policymakers with tough decisions due to the uncertainties involved. In this talk, we will present the statistical issues and research underlying and influencing the IPCC assessment of global warming and the future public health policy implications. David
Whitman, SDSU, Sept. 14, 2007 The concept of simultaneity has an interesting history from Newton until now. We present an anstraction of space time defined axiomatically by principles of simultaneity. Kung-Jong
Lui, SDSU, May 2, 2007 In a randomized clinical trial (RCT), we often come across the situations in which there are patients who do not comply with their assigned treatments or whose outcomes are missing due to their refusal or loss to follow-up. Because noncompliance and missing outcomes do not generally occur completely at random, analyzing data as treated or excluding patients with missing outcomes from our analysis can produce a biased estimate a treatment effect. In this paper, we consider estimation of the risk difference (RD) in the presence of both noncompliance and missing outcomes under a RCT. On the basis of a constant risk additive model proposed elsewhere, we derive the maximum likelihood estimator (MLE) and develop three asymptotic interval estimators in closed form for the RD. We apply Monte Carlo simulation to evaluate and compare the performance of these estimators in a variety of situations. We note that all interval estimators developed here can perform well with respect to the coverage probability in all the situations considered here. We find that the interval estimator using tanh -1 (x) transformation is generally more precise than the other estimators with respect to the average length. Finally, we use the data taken from a randomized trial studying the association between flu vaccine and the risk of flu-related hospitalization to illustrate the practical use of these interval estimators. Valdimir
Rotar, SDSU, April 6, 2007 Usually,
a limit theorem of Probability Theory is a theorem that concerns convergence
of a sequence of distributions P_n to a distribution P.
However, there is a number of works where the traditional setup is modified,
and the object of study is two sequences of distributions, P_n and
Q_n, and the goal consists in establishing conditions implying
the convergence Vadim
Ponomarenko, SDSU, April 5, 2007 Democracy's most fundamental ideal is for society to make choices that reflect the desires of the individuals living in it. Many voting mechanisms have been proposed to achieve this. All are deficient, due to a Nobel-prize-winning theorem by Kenneth Arrow -- those designing the election can manipulate the outcome. Furthermore, due to a theorem of Gibbard and Satterthwaite, individual voters can also manipulate the outcome by voting dishonestly. Kristin
Duncan, SDSU, April 2, 2007 Item response theory is a body of research directed at the assessment of an underlying trait or ability. In its simplest form, it allows one to use the results of a multiple choice exam or questionnaire both to rank-order a batch of subjects and to decide which subjects exceed a threshold level of the trait or ability. In this talk, we give an introduction to the most commonly used item response models and present a nonparametric Bayesian approach to item response theory. Under this approach, a Dirichlet process prior distribution is placed on each item characteristic curve. The resulting model has full support among models for which there is a one-dimensional trait underlying exam response. Features of the model will be described. Results from fitting the new model and traditional, parametric models to responses from an undergraduate statistics exam will be presented and contrasted. Steve
Baer, Arizona State U, March 23, 2007 In many biological, chemical and physical systems modeled mathematically as bifurcation problems, the bifurcation parameter may vary naturally and slowly with time or the parameter may be slowly varied by the experimenter. Mathematically, these are called slow passage or ramp problems. Of particular interest is when a parameter passes slowly through a Hopf bifurcation and the system's response changes from a slowly varying steady state to slowly varying oscillations. The interesting phenomenon is that the transition may not occur until the parameter is considerably beyond the value predicted from a static bifurcation analysis, no matter how slow the parameter is varied, and the delay in onset is dependent on the initial state of the system (memory effect). Previous studies have focused on linear or constant speed ramps [Baer, Erneux & Rinzel (1988,1989), Su (1991)]. In this talk I will introduce the problem of slow accelerating and de-accelerating ramps, obtain new results using numerical and asymptotic methods, and apply the results to problems in nerve membrane accommodation and neuronal bursting. Sigrun
Bodine, U of Puget Sound, March 15, 2007 This talk will concern “almost diagonal” systems of non-autonomous linear differential equations and the asymptotic behavior of their solutions. In order to achieve a so-called “asymptotic integration” of the system, a certain balance is needed between a kind of separation (dichotomy) condition on the diagonal terms and a growth condition on the perturbation. An overview of some classical methods will be presented along with some new results. A parallel theory also exists for linear difference equations, but in this talk differential equations will be the main focus. Martin
Haenggi, U of Notre Dame, March 14, 2007 One basic application of wireless sensor networks is the surveillance or monitoring of large areas: Assuming n sensor nodes are randomly deployed and each sensor can cover a circular area of a certain radius r, what fraction of the total area of interest can be expected to be covered (as a function of n and r)? This question has been answered for certain cases. In this talk a related problem, the so-called sentry selection problem, and a recent result will be presented. In practical applications, it is desirable to turn most of the sensor nodes off to conserve energy and only have a subset of nodes active acting as sentries. After a certain period of time, the sentry duty is moved to a new, disjoint set of nodes, and so on. Mathematically, it can be described as: Find the minimum radius r such that (with high probability) there exists a partition of the node set into k subsets that each provide a cover of the area. Gilbert
Walter, U of Wisconsin, Milwaukee, March 8, 2007 The prolate spheroidal wave functions go back to the 19th century. Their use in signal processing goes back almost 50 years. But the optimization problem to which they are the solution is finding new applications in sampling and imaging. In this talk we review some of their unique properties which make them useful in these applications. We also discuss wavelets based on them which have many nice properties lacking in other wavelets. Adolfo
J. Rumbos, Pomona College, March 1, 2007 In this talk we survey existence results for a general class of boundary value problems of the form Q(u) -λ a(x,u)u = g(u) + h(x) x in Ω where Ωis a domain in N-dimensional Euclidean space; u is a real valued function defined on Ω and lying in an appropriate function space; Q(u) is a second order elliptic differential operator (linear or nonlinear); λ is a real parameter; a and g are continuous functions; and h is measurable function lying in some Lp class. We focus on what has been traditionally called a resonance problem; that is, the situation in which the parameter λ is an eigenvalue of the differential operator Q(u); or λ is a value for which Q(u) -λ a(x,u)u=0 has a non-zero solution. Prototypes for the differential operator Q(u) are the Laplacian, Δu, in the semi-linear case, and the p-Laplacian, Δpu, in the quasi-linear case. Andres
Valloud, Cincon Systems, Feb. 23, 2007 The
pattern describes a way to make explicit a model by which one can explain
how the interaction between observers and their environments occurs.
The pattern applies to a complex system, or information manifold,
under observation and a player interacting with it. A game is an
example of such an information manifold. A program playing the game
is an example of a player. An adaptive compiler (player) observing
the execution of a program (information manifold) to modify the
performance of the program is another example. Kristin
Lauter, Microsoft Research, February 15, 2007 In this talk I will explain the importance of collision-resistant hash functions for cryptography and survey some important new developments. Next I will explain the central role of expander graphs in various branches of mathematics. Finally I will connect the two by presenting a new construction of provable collision resistant hash functions from expander graphs. As examples, I will
give two specific families of optimal expander graphs for hash function
constructions: the families of Ramanujan graphs constructed by Lubotzky-Phillips-Sarnak
and Pizer respectively. When the hash function is constructed from one
of Pizer's Ramanujan graphs, (the set of supersingular elliptic curves
in characteristic p with l-isogenies, l a prime different from p), then
collision resistance follows from the hardness of computing isogenies
between supersingular elliptic curves. This is joint work with Denis
Charles and Eyal Goren. This lecture gives an introduction to a recent book with this title. It concerns interactions between algebra and statistics and their emerging applications to computational biology. Statistical models of independence and sequence alignment will be illustrated by means of a fictional character, DiaNA, who rolls tetrahedral dice with face labels "A", "C", "G" and "T". Mark
Dunster, SDSU, February 2, 2007 No abstract provided for this talk. Bob
Grone, SDSU, January 26, 2007 Julia Robinson was a mathematics major at SDSU for 3 years, from 1936 to 1939. She transferred to UC Berkeley to obtain her BA degree in 1940. She worked in Mathematical Logic and earned her Ph.D. at Berkeley as well. Her later work was instrumental in solving Hilbert’s Tenth Problem, and she was the first woman mathematician elected to the National Academy of Sciences, as well as the first woman President of the American Mathematical Society. |