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Events This Week





Week of March 29 - March 25


Friday, March 29

Applied and Computational

Topic


Jose Castillo - Computational Science Research Center - San Diego State University


Abstract: TBA


Location: Gibson Hall 126


Time:  3:30



Thursday, March 28

Colloquium

Stability in the homology of configuration spaces


Jennifer Wilson - University of Michigan Host (Mentor Stafa)


Abstract:

This talk will illustrate some patterns in the homology of the configuration space F_k(M), the space of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in joint work with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.


Location:  Dinwiddie 102


Time:  3:30



Thursday, March 28

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Wednesday, March 27

Probability & Statistics

Application of large deviations to genetic evolution of bacterial populations


Ilya Timofeyev - University of Houston


Abstract:

Radical shifts in the genetic composition of large cell populations are rare events with quite low probabilities, which direct numerical simulations generally fail to evaluate accurately. We develop an applicable large deviations framework for a class of Markov chains used to model genetic evolution of bacterial populations. We illustrate this framework by computing the most likely evolutionary paths describing emergence of genotypes with lower fitness in realistic parameter settings.


Location:  Dinwiddie 102


Time:  3:00



Wednesday, March 27

Algebra & Combinatorics

The Group Algebra of a Compact  Group in the Category of Weakly Complete Vector Spaces


Karl Hofmann - TU Darmstadt


Abstract: Gibson Hall 310


Location: 

 

 Karl Hofmann


Time:  3:00



Tuesday, March 26

Graduate Colloquium


Towards a dynamic theory of ontologies


Nathan Bedell - Tulane University


Abstract:


In this talk, I will introduce the notion of an "Olog" (short for ontology log), as popularized by David Spivak in his book "Category Theory for the Sciences". An Olog is a natural format for knowledge representation given (usually) by a free category generated by a directed graph, quotiented by some domain-specific relationships expressed as equalities between morphisms in the category. A functor from this category to some other category is interpreted as an implementation, or model of the Olog. I then discuss some of the latest findings in my theory of graded categories, and discuss how this framework might prove useful in extending Spivak's Ologs to a "dynamic" theory of ontologies, what I am tentatively calling a theory of "meta-ontologies", with an eye towards applications in both metamathematics and artificial intelligence, as well as potentially in fields such as biology, psychology, and the social sciences, where a study of such "dynamic ontologies" might yield interesting results which would not otherwise be obvious.


Location:  Stanley Thomas 316


Time:  4:30



Monday, March 25

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Week of March 22 - March 18


Friday, March 22

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Thursday, March 21

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Thursday, March 21

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Wednesday, March 20

Algebra & Combinatorics

On ideals defining products of affine schemes


Robert Walker - University of Michigan


Abstract:

This is joint work with Irena Swanson found on arXiv:1806.03545. Given a polynomial ring C over a field and proper ideals I and J whose generating sets involve disjoint variables, we determine how to embed the associated primes of each power of I+J into a collection of primes described in terms of the associated primes of select powers of I and of J. We discuss applications to constructing primary decompositions for powers of I+J, and to attacking the persistence problem for associated primes of powers of an ideal.


Location:  Gibson Hall 310


Time:  3:00



Wednesday, March 20

Probability & Statistics

Recent issues and discoveries on stochatically modeled reaction networks


Jinsu Kim - UC Irvine


Abstract:

A reaction network is a graphical configuration that describes an interaction between species (molecules). If the abundances of the network system is small, then the randomness inherent in the molecular interactions is important to the system dynamics, and the abundances are modeled stochastically as a jump by jump fashion continuous-time Markov chain. One of challenging issues facing researchers who study biological systems is the often extraordinarily complicated structure of their interaction networks. Thus, how to characterize network structures that induce characteristic behaviors of the system dynamics is one of the major open questions in this literature. In this talk, I will provide recent issues and discoveries on stochastically modeled reaction networks. Specifically, we will focus on existence of stationary distributions and the convergence rate for the process to its stationary distribution.


Location:  Dinwiddie 102


Time:  3:00



Tuesday, March 19

Graduate Colloquium

p-adic numbers... WHY?


Vaishavi Sharma - Tulane University


Abstract:

In this talk, I will start from scratch and introduce the p-adic numbers and discuss the field Qp.  I'll go over some examples and applications and then finally talk a little about the problems we're working on.


Location:  Stanley Thomas 316


Time: 4:30



Monday, March 18

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Week of March 15 - March 11


Friday, March 15

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Thursday, March 14

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Thursday, March 14

AMS/AWM

A mathematician's link to art in the profesional environment


Karl Hofmann - Tulane/TU Darmstadt


Abstract:

One of the drawings of mine, produced for a book on topological semigroups and exhibited in our Common Room, gave rise to the "Tulane Mathematics Coffee Mug"—which in turn suggested that I give a talk meandering through my encounters with the arts when they become applied in the professional life of mathematicians. So I hope to present a picture book of examples created when I was called upon to provide illustrations to journals and books–a few more at any rate than are exhibited in the Mathematics Common Room and the Mathematics Library.

I studied studio arts in the graphic domain at the University of Tübingen (Germany) on the side of my academic training in Mathematics prior to my joining the Tulane Mathematics Department in 1960.


Location:  Tilton Hall 305


Time:  1:00pm


Wednesday, March 13

Algebra & Combinatorics

Strongly robust toric ideals


Marius Vladoiu - Purdue University and the University of Bucharest


Abstract:

Naturally,  most famous classes of toric ideals come equipped with a rich algebraic and homological structure, but they also have a common combinatorial feature, namely, equality of various special combinatorial subsets. In particular, one such class is represented by strongly robust toric ideals, for which the Graver basis is a minimal generating set. In this talk we aim to discuss a few open questions related to strongly robust toric ideals, arising from combinatorial commutative algebra, algebraic geometry, and a surprising connection to combinatorics.  The talk is based on joint works with Sonja Petrovic and Apostolos Thoma, and on an ongoing project with Apostolos Thoma.


Location: Gibson Hall 310


Time: 3:00



Wednesday, March 13

Probability and Statistics

A non-central limit theorem on heavy-tailed chaos


Ray Bai - Institution


Abstract:

We introduce the partial-sum limit theorems for a class of stationary sequences exhibiting both heavy tails and long-range dependence. The stationary sequences are constructed using heavy-tailed multiple stochastic integrals and conservative null dynamical systems. The limits are represented by multiple stables integrals, where the integrands involve the local times of the intersections of stationary stable regenerative sets. This is a joint work with Takashi Owada and Yizao Wang.


Location: Dinwiddie 102


Time: 3:00



Tuesday, March 12

CCS

Fluid-structure interaction at low Reynolds numbers


Olivia du Roure - PMMH, ESPCI Paris, France


Abstract:

The dynamics of an individual flexible objects in viscous flows is key to deciphering the rheological behavior of many complex fluids and soft materials. It also underlies a wealth of biophysical processes from flagellar propulsion to intracellular streaming. The interaction between an elongated object and a given flow depends strongly on the properties of the object - flexibility, aspect ratio and dimensions - and the flow geometry. This interaction is governed by the elasto-viscous number that compares elastic and viscous forces. In this seminar I will discuss dome of the configurations of this problem we have studied ,during the last years, by combining microfluidics, microfabrication and microscopy.


Location:  Stanley Thomas 316


Time:  3:00



Monday, March 11

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Week of March 8 - March 3


Friday, March 8

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Thursday, March 7

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Wednesday, March 6

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Tuesday, March 5

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Monday, March 4

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Week of March 1 - February 25


Friday, March 1

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Thursday, February 28

AWM/AMS

Consideration of Pedagogy:  Developing Equitable Teaching Practices for Mathematics Instruction


Cynthia Anhalt - University of Arizona


Abstract:

This presentation will engage participants in considering ways to develop pedagogical strategies and ways of thinking for actively and purposefully engaging students in mathematics classrooms.  We will examine research-based recommendations recently highlighted in the mathematical Association of America (MAA) publication,  Instructional Practices Guide (2017). These strategies call for inclusion of multiple ways to express and represent mathematical ideas in order to develop connections for learning.  Diversifying ways to represent the mathematical ideas during instruction translates into access to mathematics for more students.



Location:  Tilton Hall 305


Time: 1:00



Thursday, February 28

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Wednesday, February 27

Algebra & Combinatorics

What is WZ?


Tewodros Amdeberhan - Tulane University


Abstract:

WZ stands for Wilf-Zeilberger. We will explain the ideas behind this meta-mathematics and explore further implications, including some of our own work.


Location:
  Gibson Hall 310

Time:
3:00


Tuesday, February 26

Grad Colloquium

Combinatorics of Feynman diagrams


Diego Villamizar - Tulane University


Abstract:

We will discuss the combinatorial definition and some properties of Feynman diagrams based on the book "A combinatorial perspective of Quantum field theory" of Karen Yeats. Also, we will show some connections with Stirling numbers.


Location: Stanley Thomas 316


Time:  4:30



Monday, February 25

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Week of February 22 - February 18


Friday, February 22

Applied and Computational

Modeling Within-Vector Viral Kinetics in a Multi-Scale Vector-Host Model


Hayriye Gulbudak - University of Louisiana at Lafayette


Abstract: 


A current challenge for disease modeling and public health is understanding pathogen dynamics across scales since their ecology and evolution ultimately operate on several coupled scales. This is particularly true for vector-borne diseases, where within-vector, within-host, and between vector-host populations all play crucial roles in diversity and distribution of the pathogen. Despite recent modeling efforts to determine the effect of within-host virus-immune response dynamics on between-host transmission, the role of within-vector viral dynamics on disease spread is overlooked. Here we formulate an age-since-infection structured model where epidemic model parameters are governed by ODE systems describing within-host immune-pathogen dynamics and within-vector viral kinetics. We define the basic reproduction number, R0 and study the threshold dynamics of the system. Numerical results suggest that within-vector-viral kinetics may play a substantial role in epidemics. Finally, we address how the model can be utilized to better predict the success of control strategies such as vaccination, or Wolbachia-based biocontrol.

Location:  Gibson Hall 126


Time: 3:30



Thursday, February 21

Colloquium

Real-time forecasting using computational dynamic ensembles based on differential equation models: Application to epidemic forecasting


Gerardo Chowell - Georgia State (Host: James Hyman and Zhuolin Qu)


Abstract:


Forecasting the trajectory of social dynamic processes such as the spread of infectious diseases poses significant challenges that call for methods that account for data and model uncertainty. Here we introduce a frequentist computational bootstrap approach that weights the uncertainty derived from a set of plausible models to build an ensemble model for sequential forecasting. The power and transparency of this approach is illustrated in the context of simple dynamic differential-equation models, which we confront against the trajectory of real and simulated outbreak data. For illustration, we generate sequential short-term ensemble forecasts of epidemic outbreaks by combining the strengths of phenomenological models that incorporate flexible epidemic growth scaling namely the Generalized-Growth Model (GGM) and the Generalized Logistic Model (GLM). With our ensemble approach, we also addressed prior lessons of the Ebola forecasting challenge particularly with a focus at improving short-term forecasts of outbreaks which may involve a temporary downturn in case incidence.

Location: Dinwiddie 102


Time: 3:30



Thursday, February 21

AWM/AMS STUDENT

Outreach Activities at the Local and National Levels: Reflection and Discussion


Ricardo Cortez - Tulane University


Abstract:

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Location:  Gibson Hall 400D


Time:  11:00


Wednesday, February 20

Algebra & Combinatorics

Topic


Aram Bingham - Tulane University


Abstract: 


Location:  Gibson Hall 310


Time:  3:00



Tuesday, February 19

Graduate Student Colloquium

Resurgence number and  Fiber Product of Projective Schemes


Sankhaneel Bisui - Tulane University


Abstract: 


I am going to present our joint work with Dr. Tai Huy Ha, Dr.  A.V. Jayanthan and Abu C. Thomas. Our interest is to investigate the resurgence number of fiber product of projective schemes.  In this talk, we will also see how resurgence number corresponding to the ideal of the fiber product of the schemes depends on that of the original schemes. While considering the asymptotic resurgence the resurgence number of the fiber product follows a nice relation with the resurgence of the original schemes. We will also see the relationship and we will also see how there is a possibility of the resurgence number becoming arbitrarily large.

Location:  Stanley Thomas 316


Time:  4:30



Monday, February 18

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Week of February 15 - February 11



Saturday, February 16

SCALA WORKSHOP



Friday, February 15

SCALA WORKSHOP



Friday, February 15

Applied and Computational

Dynamically constrained interpolation of large data sets in oceanography: computational aspects


Max Yaremchuk - Navy Research Laboratory


Abstract:

Improving the quality of global ocean weather forecasts is a primary task of oceanographic research. The problem is currently treated as a statistically and dynamically consistent synthesis of the data streams arriving from satellites and autonomous observational platforms. Due to the immense size of the ocean state vector (10^8-10^9), operational algorithms combine variational optimization techniques with limited-size (10^2-10^3) ensembles simulating statistical properties of the error fields. A brief overview of current situation in operational state estimation/forcasting is presented with a special focus on selected problems requiring applied math research. These include efficient linearization and transposition of the operators describing evolution of the ocean state, sparse approximation of the inverse correlation matrices and consistent treatment of the state vector components with non-gaussian error statistics.


Location:  Gibson Hall


Time:  10:00



Thursday, February 14

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Thursday, February 14

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Wednesday, February 13

Probability and Statistics

Diffusive search for diffusing receptors


Chris Miles - NYU


Abstract:

Cells send and receive signals in the form of diffusing particles that search for target sites called receptors. This mechanism has received great theoretical interest for over 40 years, but a more recent fact that receptors themselves diffuse along a surface has largely been neglected. This raises the natural question: does the target diffusing help or hurt the ability of a diffusing particle to locate it? We'll modify a classical PDE model into a PDE with stochastic boundary conditions, which we'll study using matched asymptotic analysis and Monte Carlo simulations.


Location: Dinwiddie 102


Time: 3:00



Tuesday, February 12

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Monday, February 11

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Week of February 9 - January 28





Friday, February 8

Applied and Computational

Results on some local energy solutions to the Navier-Stokes equations


Zach Bradshaw - University of Arkansas

Abstract:

Local energy solutions to the Navier-Stokes equations, that is, weak solutions which are uniformly locally square integrable, but not necessarily globally square integrable, have proven a useful class for studying regularity and uniqueness. In this talk we survey several recent results concerning the existence and properties of local energy solutions, including applications to self-similar solutions.


Location: 
Greenbaum House – GR – MacLaren Room
Time:  3:30


Thursday, February 7

AWM

Distance Measures for Embedded Graphs


Carola Wenk - Tulane University


Abstract: 


We introduce new distance measures for comparing embedded graphs based on the Fréchet distance and the weak Fréchet distance. These distances take the combinatorial structure as well as the geometric embeddings of the graphs into account. Our distance measures are motivated by the comparison of road networks, for instance, to evaluate the quality of a map construction algorithm, a task for which suitable distance measures are currently missing. We present a general algorithmic approach for computing these distances, which yields polynomial time algorithms if the graphs are trees and, if the weak Fréchet distance is used, if the graphs are plane. For general embedded graphs, however, deciding the distances is NP-complete. This work has been conducted in collaboration with Hugo A. Akitaya, Maike Buchin, Bernhard Kilgus, and Stef Sijben. The preprint is available at https://arxiv.org/abs/1812.09095 .

Location:  Hebert Hall


Time:




Wednesday, February 6

Algebra & Combinatorics

Chudnowsky's Conjecture for a general set of points in PNk


Abu Thomas - Tulane University


Abstract:

Thomas A



Location:  Gibson Hall 310


Time: 3:00



Tuesday, February 5

Colloquium

Limit theorems for eigenvectors of adjacency and normalized Laplacian for random graphs


Speaker - Institution


Abstract:

We prove a central limit theorem for the components of the eigenvectors corresponding to the d largest eigenvalues of the normalized Laplacian matrix of a finite dimensional random dot product graph. As a corollary, we show that for stochastic blockmodel graphs, the rows of the spectral embedding of the normalized Laplacian converge to multivariate normals and furthermore the mean and the covariance matrix of each row are functions of the associated vertex's block membership. Together with prior results for the eigenvectors of the adjacency matrix, we then compare, via the Chernoff information between multivariate normal distributions, how the choice of embedding method impacts subsequent inference. We demonstrate that neither embedding method dominates with respect to the inference task of recovering the latent block assignments.


Location: Gibson Hall 126A


Time: 3:30



Tuesday, February 5

Graduate Student Colloquium

SOME COMBINATORIAL IDENTITIES INVOLVING A FAMILY OF GENERALIZED EULERIAN NUMBERS AND POLYNOMIALS


Villamarin Gomez, Sergio Nicolas - Tulane University


Abstract:

The Eulerian polynomials were introduced by Euler when studying the sum of alternating consecutive numbers with a fix exponent. Afterwards he introduced its coefficients as the Eulerian numbers and gave many interesting combinatorial identities, some of which relate to the Riemann Zeta function. In our talk I’ll introduce them and present some of its properties and also some generalizations along with generalizations of the Stirling numbers of the second kind.


Location:
Stanley Thomas 3:16

Time: 4:30



Monday, February 4

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Week of February 1 - January 28
Friday, February 1

Applied and Computational Mathematics


Existence, continuation, and lower mass bounds for the Landau equation


Andrei Tarfulea - University of Chicago


Abstract:

Kinetic equations model gas and particle dynamics, specifically focusing on the interactions between the micro-, meso-, and macroscopic scales.  Mathematically, they demonstrate a rich variety of nonlinear phenomena,  such as hypoellipticity through velocity-averaging and Landau damping. The question of well-posedness remains an active area of research.

In this talk, we look at the Landau equation, a mathematical model for plasma physics arising from the Boltzmann equation as so-called grazing collisions dominate. Previous results are in the perturbative regime, or in the homogeneous setting, or rely on strong a priori control of the solution (the most crucial assumption being a lower bound on the density, as this prevents the elliptic terms from becoming degenerate).

We prove that the Landau equation has local-in-time solutions with no additional a priori assumptions; the initial data is even allowed to contain regions of vacuum. We then prove a "mass spreading" result via a probabilistic approach. This is the first proof that a density lower bound is generated dynamically from collisions. From the lower bound, it follows that the local solution is smooth, and we establish the mildest (to date) continuation criteria for the solution to exist for all time.


Location:  Greenbaum House – GR – MacLaren Room


Time: 3:30



Thursday, January 31

Colloquium


The normal scores estimator for the high-dimensional Gaussian copula model


Yue Zhao - Leuven (Host: Gustavo Didier)


Abstract:


The (semiparametric) Gaussian copula model consists of distributions that have dependence structure described by Gaussian copulas but that have arbitrary marginals.  A Gaussian copula is in turn determined by an Euclidean parameter $R$ called the copula correlation matrix.  In this talk we study the normal scores (rank correlation coefficient) estimator, also known as the van der Waerden coefficient, of $R$ in high dimensions.  It is well known that in fixed dimensions, the normal scores estimator is the optimal estimator of $R$, i.e., it has the smallest asymptotic covariance.  Curiously though, in high dimensions, nowadays the preferred estimators of $R$ are usually based on Kendall's tau or Spearman's rho.  We show that the normal scores estimator in fact remains the optimal estimator of $R$ in high dimensions.  More specifically, we show that the approximate linearity of the normal scores estimator in the efficient influence function, which in fixed dimensions implies the optimality of the normal scores estimator, holds in high dimensions as well.


Location:  Dinwiddie 102


Time: 3:30




Wednesday, January 30

Algebra & Combinatorics

 

Resurgence number and  Fiber Product of Projective Schemes


Sankhaneel Bisui - Tulane University


Abstract:

The symbolic powers of a homogeneous ideal  are a well-studied object. In the study of symbolic power it is natural to ask when these symbolic powers contain ordinary powers and vice versa. We can easily check that for any, n I^n \subset I^{(n)}. It is a subtle and generally open problem to determine for which positive integers m,r we have  $I^{(m)} \subset I^r  $. It is now known that for $m > Nr $ that containment holds. Now, what can be said about the bounds for a specific ideal? This question leads to the definition of resurgence number and the asymptotic versions of this number. In this talk, I will introduce the resurgence number and the asymptotic versions of the number.

Our interest is to investigate the resurgence number of fiber product of projective schemes.  We will also see how resurgence number corresponding to the ideal of the fiber product of the schemes depends on that of the original schemes. While considering the asymptotic resurgence the resurgence number of the fiber product follows a nice relation with the resurgence of the original schemes.  I am going to present the relation and we will also see how there is a possibility of the resurgence number becoming arbitrarily large.


Location: Gibson Hall 310


Time:  3:00



Tuesday, January 29

Graduate Student Colloquium

Discrete Morse Theory and its Applications in Topological Data Analysis (TDA)


Sushovan Majhi - Tulane University


Abstract:

We eat pizza and talk about Topological Data Analysis (TDA). TDA is an emerging subfield of applied mathematics. Various topological concepts such as homology, persistent homology, discrete Morse theory are becoming widely useful in analyzing and visualizing data. Applications include reconstruction of shapes, 3D printing, feature detection, medical imaging etc. We briefly touch upon Morse theory and its discrete analog. Also, we discuss some of its major applications in TDA.


Location:  Stanley Thomas 316


Time: 4:30



Monday, January 28

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Week of January 25 - January 21


Friday, January 25

Clifford Lectures



Thursday, January 24

Clifford Lectures



Thursday, January 24

Colloquium

A theoretical framework of the scaled Gaussian stochastic process for calibrating imperfect mathematical models


Mengyang Gu - Johns Hopkins (Host: Gustavo Didier)


Abstract:


Model calibration or data inversion involves using experimental or field data to estimate the unknown parameters of a mathematical model. This task is complicated by the discrepancy between the model and reality, and by possible bias in field data. The model discrepancy is often modeled by a Gaussian stochastic process (GaSP), but it was observed in many studies that the calibrated mathematical model can be far from the reality. Here we show that modeling the discrepancy function via a GaSP often leads to an inconsistent estimation of the calibration parameters even if one has an infinite number of repeated experiments and an infinite number of observations in each experiment. In this work, we develop the scaled Gaussian stochastic process (S-GaSP), a new stochastic process to model the discrepancy function in calibration. We establish the explicit connection between the GaSP and S-GaSP through the orthogonal series representation. We show the predictive mean estimator in the S-GaSP calibration model converges to the reality at the same rate as the one by the GaSP model, and the calibrated mathematical model in the S-GaSP calibration converges to the one that minimizes the L2 loss between the reality and mathematical model, whereas the GaSP calibration model does not have this property. The scientific goal of this work is to use multiple interferometric synthetic-aperture radar (InSAR) interferograms to calibrate a geophysical model for Kilauea Volcano, Hawaii. Analysis of both simulated and real data confirms that our approach is better than other approaches in prediction and calibration. Both the GaSP and S-GaSP calibration models are implemented in the "RobustCalibration" R Package on CRAN.


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Wednesday, January 23

Clifford Lectures



Tuesday, January 22

Graduate Student Colloquium

Error Correcting Codes


Victor Bankston - Institution


Abstract: 


That which is physical decays, but that which is mathematical persists. Since computation bridges the corporeal and the ideal, schemes of "error correcting codes" are needed. Beyond solving this necessary engineering problem, error correcting codes serve as examples of extremal combinatorial objects. We will discuss the Hamming Code, linear codes, convolutional codes and theoretical bounds.

Location:  Stanley Thomas, 316


Time: 4:30



Monday, January 21

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Tuesday, January 15

Colloquium


A moment-based approach to estimating molecular heterogeneity


Timothy Daley - Stanford  (HOST: Michelle Lacey)


Abstract:

In modern applications of high-throughput sequencing technologies researchers may be interested in quantifying the molecular diversity of a sample (e.g. T-Cell repertoire, transcriptional diversity, or microbial species diversity).  In these sampling-based technologies there is an important detail that is often overlooked in the analysis of the data and the design of the experiments, specifically that the sampled observations often do not give a fully representative picture of the underlying population. This has long been a recognized problem in statistical ecology and in the broader statistics literature, and is commonly known as the missing species problem.

 

In classical settings, the size of the sample is usually small. New technologies such as high-throughput sequencing have allowed for the sampling of extremely large and heterogeneous populations at scales not previously attainable or even considered. New algorithms are required that take advantage of the scale of the data to account for heterogeneity, but are also sufficiently fast and scale well with the size of the data.  I will discuss a moment-based approach for estimating the missing species based on an extension of Chao's moment-based lower bound (Chao, 1984).  We apply results from the classical moment problem to show that solutions can be obtained efficiently, allowing for estimators that are simultaneously conservative and use more information. By connecting the rich theory of the classical moment problem to the missing species problem we can also clear up issues in the identifiability of the missing species.

Location:  Stanley Thomas


Time:  3:30



Friday, January 11

Influence of Receptor Recharge on the Statistics of Captured Particles

Greg Handy - University of Utah

Abstract: 


We consider a setup where particles are released into a domain and diffuse freely. Part of the boundary is absorbing, where the particles can escape the domain, another part is reflecting. The rest of boundary consists of capture regions that switch between being reflecting and absorbing. After capturing a particle, the capture region becomes reflecting for an exponentially distributed amount of time. This non-zero recharge time correlates the particles' paths, complicating the mathematical analysis of this system. We are interested in the distribution of the number of particles that are captured before they escape.

Our results are derived from considering our system in several ways: as a full spatial diffusion process with recharging traps on the boundary; as a continuous-time Markov process approximating the original system; and lastly as a system of ODEs in a mean-field approximation. Considering the full spatial diffusion process, we prove that the total expected number of the captured particles has an upper-bound of the order of log n.  We then apply our approximations to investigate time courses for the expected number and higher ordered statistics of captured particles. We find that the amount of variation observed in the total number of captured particles varies non-monotonically with the mean recharge time. Lastly, we combine these results together to predict stochastic properties of intracellular signals resulting from receptor activation.

Location:  TBA

Time:  3:00




Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 math@math.tulane.edu