The Mathematics Calendar
http://www.math.psu.edu/seminars/calendar.php
Seminars and special events the Pennsylvania State University Mathematics Department2014-10-22webmaster@math.psu.eduAlgebraic independence of derivatives of Carlitz periods
http://www.math.psu.edu/seminars/meeting.php?id=21887
Speaker(s): Dale Brownawell
2014-10-23T11:15:00Algebra and Number Theory Seminarrvaughan@math.psu.eduschwede@math.psu.edupapikian@math.psu.eduyee@math.psu.eduEvolution of resistance to white pine blister rust in high-elevation pines
http://www.math.psu.edu/seminars/meeting.php?id=24059
Speaker(s): Simon Tavener
Five-needle white pines play an important role in high-elevation ecosystems but are highly susceptible to white pine blister rust (WPBR) caused by a nonnative fungal pathogen. We construct a nonlinear, stage-structured infection model to investigate the effect of WPBR on the dynamics and stand structure of high-elevation five-needle white pines. Management decisions are by definition short-term perturbations that require analysis of transient behavior and we have developed a general software package to examine both transient and equilibrium sensitivities and elasticities. The presence in a population of a resistant genotype can modify both transient and equilibrium behaviors and suggest potential new control strategies. We extend our model to include a resistant allele at a single genetic locus and provide preliminary results. This work was conducted as part of an NSF sponsored undergraduate research program (FEScUE) at the intersection of mathematics and biology.2014-10-23T13:25:00MASS Colloquiumvxs137@math.psu.edudunlop@math.psu.eduA posteriori error analysis for multirate, multiphysics problems
http://www.math.psu.edu/seminars/meeting.php?id=22012
Speaker(s): Simon Tavener
Finite element methods are well-established and popular techniques for solving systems of partial differential equations. A priori analyses of finite element methods seek to establish error bounds in appropriate norms and to determine rates of convergence with mesh refinement. Adjoint-based a posteriori analyses seek to estimate the error in a functional of the solution (a “quantity of interest”) for a given numerical calculation. Computation plays an essential role in many areas of science and technology where we seek to understand complex systems involving multiple physical processes which often evolve on distinctly different time scales. Complicating matters, the model parameters and even computational domains may be uncertain. Further, specific numerical approaches such as finite volume methods or explicit time integration techniques may be entrenched within particular scientific communities. The goal of this work is to use mathematically appealing adjoint-based a posteriori ideas to develop accurate a posteriori error estimates for a range of computational problems encountered in practice and to use the insights gained in to the multiple sources of error to construct adaptive computational strategies.2014-10-23T15:30:00Department of Mathematics Colloquiumsaz11@math.psu.eduliu@math.psu.eduWhen does a mixture of products contain a product of mixtures?
http://www.math.psu.edu/seminars/meeting.php?id=22063
Speaker(s): Jason Morton
We derive relations between theoretical properties of restricted Boltzmann machines (RBMs), popular machine learning models which form the building blocks of deep learning models, and several natural notions from discrete mathematics and convex geometry. We give implications and equivalences relating RBM-representable probability distributions, perfectly reconstructible inputs, Hamming modes, zonotopes and zonosets, point configurations in hyperplane arrangements, linear threshold codes, and multi-covering numbers of hypercubes. As a motivating application, we prove results on the relative representational power of mixtures of product distributions and products of mixtures of pairs of product distributions (RBMs) that formally justify widely held intuitions about distributed representations. In particular, we show that an exponentially larger mixture of products, requiring an exponentially larger number of parameters, is required to represent the probability distributions represented as products of mixtures.2014-10-24T15:35:00Probability and Financial Mathematics Seminardenker@math.psu.edumazzucat@math.psu.eduroyer@math.psu.edunistor@math.psu.eduanovikov@math.psu.eduAdaptive Learning and Optimization for Machine Intelligence
http://www.math.psu.edu/seminars/meeting.php?id=22701
Speaker(s): Haibo He
With the recent development of brain research and modern technologies, scientists and engineers will hopefully find efficient ways to develop brain-
like intelligent systems that are highly robust, adaptive, scalable, and
fault tolerant to uncertain and unstructured environments. Yet, developing such truly intelligent systems requires significant research on both fundamental understanding of brain intelligence as well as complex engineering design. This talk aims to present the recent research developments in computational intelligence to advance the machine intelligence research and explore their wide applications across different critical engineering domains. Specifically, this talk covers numerous aspects of the foundations and architectures of adaptive learning and control. The key objective is to achieve cognitive‐alike optimization and prediction capability through learning. An essential component of this talk is a recent development of a new adaptive dynamic programing (ADP) architecture for improved learning and optimization capability over time. This architecture integrates a hierarchical goal generator network to provide the system a more informative and detailed goal representation to guide its decision-making. Various real-world applications including smart grid, robotics, cyber‐physical systems, and big data analysis, will be presented to demonstrate the broader and far‐reaching applications of our research.2014-10-27T12:20:00CCMA Luncheon Seminarshaffer@math.psu.eduliu@math.psu.eduDiscretization of time-dependent quantum systems: propagation of the evolution operator
http://www.math.psu.edu/seminars/meeting.php?id=22718
Speaker(s): Joseph Jerome
The talk represents joint work with Eric Polizzi and is based on a paper of similar title recently published online in Applicable Analysis. We discuss time-dependent quantum systems on bounded domains; these represent closed systems and are relevant for application to Carbon Nanotubes and molecules. Included in our framework are linear iterations involved in time-dependent density functional theory as well as the global nonlinear model which includes the Hartree potential. A key aspect of the analysis of the algorithms is the use of time-ordered evolution operators, which allow for both a well-posed problem and its approximation. The approximation theorems we obtain are operator extensions of classical quadrature theorems. The global existence theorem uses the Leray-Schauder fixed point theorem, coupled to a modified conservation of energy principle. The simulations were performed by Eric Polizzi using his algorithm FEAST. The evolution operators used in the talk are due to T. Kato and their properties will be summarized. Application areas make significant use of these operators, particularly chemical physics. In the mathematical literature, the Euclidean space problem has been studied by T. Cazenave and others, employing the Strichartz inequalities. These are ultimately based on semi-groups. Our results appear to be complementary to results of this type. The solutions we discuss are strong solutions. We are currently studying more general potentials via weak solutions. This work is in-progress.2014-10-27T14:30:00Computational and Applied Mathematics Colloquiumshaffer@math.psu.eduliu@math.psu.eduDynamical properties of conformally symplectic systems
http://www.math.psu.edu/seminars/meeting.php?id=22829
Speaker(s): Rafael de la Llave
When one considers the dynamics of mechanical systems with a friction
proportional to the velocity one obtains a system with the
remarkable property that a symplectic form is transformed into
a multiple of itself.
The same phenomenon happens when one minimizes
the action after discounting it by an exponential factor
(these models are very common in economics when one
minimizes the present cost and includes inflation).
We will present several results for this systems:
1) A KAM theory for these systems that leads to efficient algorithms.
2) Absence of Birkhoff invariants near Lagrangian tori.
3) Numerical experiments at the breakdown of tori
4) Analyticity domains of expansions for KAM tori.
All these works are in collaboration with R. Calleja and A. Celletti
(the numerical work reported is by R. Calleja, A. Celletti, J.L - Figueras)2014-10-27T15:35:00Dynamical systems seminarkatok_s@math.psu.edusaz11@math.psu.edukatok_a@math.psu.eduhertz@math.psu.eduMultiplicative properties of the number of $k$-regular partitions.
http://www.math.psu.edu/seminars/meeting.php?id=21922
Speaker(s): Olivia Beckwith
Earlier this year, Bessenrodt and Ono proved surprising multiplicative properties of the partition function. In this project, we deal with $k$-regular partitions. Extending the generating function for $k$-regular partitions multiplicatively to a function on $k$-regular partitions, we show that it takes its maximum at an explicitly described small number of partitions, and thus can be easily computed. The basis for this is an extension of a classical result of Lehmer, from which we prove an inequality for the number of $k$-regular partitions which seems not to have been noticed before.2014-10-28T11:15:00Combinatorics/Partitions Seminarkatz@math.psu.edusellersj@math.psu.edusaz11@math.psu.eduandrews@math.psu.eduGraph Limits and Dynamics of Large Networks
http://www.math.psu.edu/seminars/meeting.php?id=23666
Speaker(s): Georgi Medvedev
The continuum limit is an approximate procedure, by which coupled dynamical systems on large graphs are replaced by an evolution integral equation on a continuous spatial domain. This approach has been
instrumental for studying dynamics of diverse networks throughout physics and biology. We use the ideas and results from the theories of graph limits and nonlinear evolution equations to develop a rigorous justification for using the continuum limit in a variety of dynamical models on deterministic
and random graphs. As a specific application, we discuss synchronization in small-world networks of Kuramoto oscillators.
References: Georgi S. Medvedev, The nonlinear heat equation on dense graphs and graph limits, SIAM J. Math. Anal., 46(4), 2743-2766, 2014; Georgi S. Medvedev, The nonlinear heat equation on W-random graphs, Archive for Rational Mechanics and Analysis, 212(3), 781-803, 2014; Georgi S. Medvedev, Small-world networks of Kuramoto oscillators, Physica D, 266, 13-22, 2014.2014-10-28T13:00:00Theoretical Biology Seminarcpc16@math.psu.edutreluga@math.psu.eduContinuous Model Theory
http://www.math.psu.edu/seminars/meeting.php?id=22081
Speaker(s): Jan Reimann
While the basic framework of classical model theory is very suitable for algebraic structures, it is less so for metric structures, where the basic relation is not so much equality, but the distance between two objects.
One can extend classical model theory to better capture metric notions. One approach that has gained particular prominence is known as "continuous model theory". An essential feature of this approach is to replace the classical binary truth value by the continuous interval [0,1].
In this talk I will outline the basic features of continuous model theory, in particular how syntax and semantics work in this approach and how basic model theoretic notions such as elementary substructures are being recast. This will be followed by a number of talks over the next weeks that look at more advanced model theory from a continuous point of view.2014-10-28T14:30:00Logic Seminarreimann@math.psu.edusimpson@math.psu.edujmr71@math.psu.eduSome geometric mechanisms for Arnold Diffusion
http://www.math.psu.edu/seminars/meeting.php?id=23387
Speaker(s): Rafael de la Llave
We consider the problem whether small perturbations of integable mechanical systems
can have very large effects.
It is known that in many cases, the effcts of the perturbations average out, but there
are exceptional cases (resonances) where the perturbations do accumulate. It is a complicated
problem whether this can keep on happening because once the instability accumulates, the system
moves out of resonance.
V. Arnold discovered in 1964 some geometric structures that lead to accumulation in carefuly constructed
examples. We will present some other geometric structures that lead to the same effect in
more general systems and that can be verified in concrete systems. In particular, we will present an
application to the restricted 3 body problem. We show that, given some
conditions, for all sufficiently small
(but non-zero) values of the eccentricity, there are orbits near a Lagrange point that gain
a fixed amount of energy. These conditions (amount to the non-vanishing of an integral) are
verified numerically.
Joint work with M. Capinski, M. Gidea, T. M-Seara2014-10-28T14:30:00Center for Dynamics and Geometry Colloquiumkatok_s@math.psu.edusaz11@math.psu.edukatok_a@math.psu.eduhertz@math.psu.eduFiner structure of minimal systems, the Bohr problem and its higher version
http://www.math.psu.edu/seminars/meeting.php?id=22807
Speaker(s): Xiangdong Ye
In this talk first I will explain why the regionally proximal relation of order d is an equivalence relation and why the quotient space is a d-step nilsystem for minimal systems. Then we will discuss the Bohr problem, i.e. if the difference of a syndetic set conatains a Bohr_0 set, and its higher version.2014-10-28T15:30:00Working Seminar: Dynamics and its Working Toolskatok_a@math.psu.eduhertz@math.psu.edukalinin@math.psu.eduAlgebraic geometry of tree tensor networks 2
http://www.math.psu.edu/seminars/meeting.php?id=23164
Speaker(s): Sara Jamshidi
2014-10-29T14:30:00Applied Algebra and Network Theory Seminarmorton@math.psu.educpc16@math.psu.eduvui1@math.psu.eduPreparing Students for Calculus
http://www.math.psu.edu/seminars/meeting.php?id=23977
Speaker(s): Attendees
Last week, we considered ways of preparing calculus students for higher-level classes. This week, we consider what it takes to adequately prepare students for calculus.
<br>
Judd, April B., and Terry Crites. "Preparing students for calculus." <i>16TH Annual Conference on Research in Undergraduate Mathematics Education</i> 1 (n.d.): 96-105. Web. 20 Aug. 2014.2014-10-29T15:35:00Teaching Mathematics Discussion Group Seminarjamshidi@math.psu.edu