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Dec 24, 2014
General Finance
Dynamical Systems

Inflation and speculation in a dynamic macroeconomic model

We study a monetary version of the Keen model by merging two alternative extensions, namely the addition of a dynamic price level and the introductio…
Sep 18, 2010
Group Theory

Relative Quasiconvexity using Fine Hyperbolic Graphs

We provide a new and elegant approach to relative quasiconvexity for relatively hyperbolic groups in the context of Bowditch's approach to relative h…
Jan 24, 2015
Analysis of PDEs
Dynamical Systems

Part of this work was was carried out while R.C. was a Visiting Assistant Professor at the School of Mathematics in the Georgia Institute of Technology. R.C. would also like to thank G. Flores for useful discussions and for sharing a preprint versio…

Response solutions for quasi-periodically forced, dissipative wave …

We consider several models of nonlinear wave equations subject to very strong damping and quasi-periodic external forcing. This is a singular perturb…
Dec 23, 2012
Methodology
Computation
Machine Learning

Mixture Model Averaging for Clustering

In mixture model-based clustering applications, it is common to fit several models from a family and report clustering results from only the `best' o…
Nov 07, 2017
Pattern Formation and Solitons
Dynamical Systems
Mathematical Physics

Krein Signature in Hamiltonian and $\mathcal{PT}$-symmetric Systems

We explain the concept of Krein signature in Hamiltonian and $\mathcal{PT}$-symmetric systems on the case study of the one-dimensional Gross-Pitaevsk…
Nov 03, 2014
Computation
Methodology
Machine Learning

Multivariate response and parsimony for Gaussian cluster-weighted mod…

A family of parsimonious Gaussian cluster-weighted models is presented. This family concerns a multivariate extension to cluster-weighted modelling t…
Jul 11, 2011
Optimization and Control
Systems and Control
Portfolio Management

On Investment-Consumption with Regime-Switching

In a continuous time stochastic economy, this paper considers the problem of consumption and investment in a financial market in which the representa…
Aug 06, 2015
Analysis of PDEs

Sharp interface limit of an energy modelling nanoparticle-polymer ble…

We identify the $\Gamma$-limit of a nanoparticle-polymer model as the number of particles goes to infinity and as the size of the particles and the p…
Oct 14, 2015
Representation Theory

Let F∙ be a p-adic field of odd residual characteristic p. Let F/F∙ be the unramified quadratic extension. We denote by oF∙ and pF∙ (resp. oF and pF) the ring of integers and its maximal ideal of F∙ (resp. F). We choose a uniformizer ϖ such that ϖoF…

Endoscopic classification of very cuspidal representations of quasi…

Let $\mathbf{G}$ be an unramified quasi-split unitary group over a p-adic field of odd residual characteristic. The goal of this paper is to describe…
Oct 08, 2015
Algebraic Geometry
Representation Theory

In this section, we use the restriction maps

Hessenberg varieties for the minimal nilpotent orbit

For a connected, simply-connected complex simple algebraic group $G$, we examine a class of Hessenberg varieties associated with the minimal nilpoten…
Jul 13, 2013
Methodology
Applications
Computation
Machine Learning

Fractionally-Supervised Classification

Traditionally, there are three species of classification: unsupervised, supervised, and semi-supervised. Supervised and semi-supervised classificatio…
Apr 11, 2018
Analysis of PDEs
Mathematical Physics
Pattern Formation and Solitons
Fluid Dynamics

Linear instability and uniqueness of the peaked periodic wave in the …

Stability of the peaked periodic waves in the reduced Ostrovsky equation has remained an open problem for a long time. In order to solve this problem…
Jan 08, 2018
Classical Analysis and ODEs

Number and Stability of Relaxation Oscillations for Predator-Prey S…

We consider planar systems of predator-prey models with small predator death rate $\epsilon>0$. Using geometric singular perturbation theory and Floq…
Mar 17, 2015
Analysis of PDEs

Convergence of regularized nonlocal interaction energies

Inspired by numerical studies of the aggregation equation, we study the effect of regularization on nonlocal interaction energies. We consider energi…
Mar 04, 2019
Quantitative Methods

Global analysis of a simplified model of anaerobic digestion and a ne…

A. Bornh\"oft, R. Hanke-Rauschenbach, and K. Sundmacher, [Nonlinear Dyn., 73 (2013), pp. 535-549] introduced a qualitative simplification to the ADM1…
Sep 04, 2014
Geometric Topology

Alexander invariants for virtual knots

Given a virtual knot $K$, we construct a group $VG_K$ called the virtual knot group, and we use the elementary ideals of $VG_K$ to define invariants …
Jun 23, 2013
Methodology
Computation
Machine Learning

A Variational Approximations-DIC Rubric for Parameter Estimation and …

Mixture model-based clustering has become an increasingly popular data analysis technique since its introduction fifty years ago, and is now commonly…
Nov 02, 2014
Analysis of PDEs

A KAM result on compact Lie groups

We describe some recent results on existence of quasi-periodic solutions of Hamiltonian PDEs on compact manifolds. We prove a linear stability result…
Jan 25, 2013
Fluid Dynamics
Optimization and Control
Computational Physics

Optimal Reconstruction of Material Properties in Complex Multiphysics…

We develop an optimization-based approach to the problem of reconstructing temperature-dependent material properties in complex thermo-fluid systems …
Dec 18, 2014
Geometric Topology
Algebraic Topology

Cyclic Group Actions on Contractible 4-Manifolds

There are known infinite families of Brieskorn homology 3-spheres which can be realized as boundaries of smooth contractible 4-manifolds. In this pap…
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