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University of Massachusetts Amherst
Mathematics and Statistics Department Faculty Publication Series
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Articles 1 - 8 of 8
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Casting Dissipative Compact States In Coherent Perfect Absorbers, Carlo Danieli, Mithun Thudiyangal
Casting Dissipative Compact States In Coherent Perfect Absorbers, Carlo Danieli, Mithun Thudiyangal
Mathematics and Statistics Department Faculty Publication Series
Coherent perfect absorption (CPA), also known as time-reversed laser, is a wave phenomenon resulting from the reciprocity of destructive interference of transmitted and reflected waves. In this work we consider quasi-one-dimensional lattice networks which posses at least one flat band and show that CPA and lasing can be induced in both linear and nonlinear regimes of this lattice by fine-tuning non-Hermitian defects (dissipative terms localized within one unit-cell). We show that local dissipations that yield CPA simultaneously yield novel dissipative compact solutions of the lattice, whose growth or decay in time can be fine-tuned via the dissipation parameter. The scheme …
Data Driven Mathematical Model Of Colon Cancer Progression, Arkadz Kirshtein, Shaya Akbarinejad, Wenrui Hao, Trang Le, Sumeyye Su, Rachel A. Aronow, Leili Shahriyari
Data Driven Mathematical Model Of Colon Cancer Progression, Arkadz Kirshtein, Shaya Akbarinejad, Wenrui Hao, Trang Le, Sumeyye Su, Rachel A. Aronow, Leili Shahriyari
Mathematics and Statistics Department Faculty Publication Series
Every colon cancer has its own unique characteristics, and therefore may respond differently to identical treatments. Here, we develop a data driven mathematical model for the interaction network of key components of immune microenvironment in colon cancer. We estimate the relative abundance of each immune cell from gene expression profiles of tumors, and group patients based on their immune patterns. Then we compare the tumor sensitivity and progression in each of these groups of patients, and observe differences in the patterns of tumor growth between the groups. For instance, in tumors with a smaller density of naive macrophages than activated …
Breather Stripes And Radial Breathers Of The Two-Dimensional Sine-Gordon Equation, Panayotis G. Kevrekidis, R. Carretero-González, J. Cuevas-Maraver, D. J. Frantzeskakis, J.-G. Caputo, B. A. Malomed
Breather Stripes And Radial Breathers Of The Two-Dimensional Sine-Gordon Equation, Panayotis G. Kevrekidis, R. Carretero-González, J. Cuevas-Maraver, D. J. Frantzeskakis, J.-G. Caputo, B. A. Malomed
Mathematics and Statistics Department Faculty Publication Series
We revisit the problem of transverse instability of a 2D breather stripe of the sine-Gordon (sG) equation. A numerically computed Floquet spectrum of the stripe is compared to analytical predictions developed by means of multiple-scale perturbation theory showing good agreement in the long-wavelength limit. By means of direct simulations, it is found that the instability leads to a breakup of the quasi-1D breather in a chain of interacting 2D radial breathers that appear to be fairly robust in the dynamics. The stability and dynamics of radial breathers in a finite domain are studied in detail by means of numerical methods. …
Relating Nets And Factorization Algebras Of Observables: Free Field Theories, Owen Gwilliam, Kasia Rejzner
Relating Nets And Factorization Algebras Of Observables: Free Field Theories, Owen Gwilliam, Kasia Rejzner
Mathematics and Statistics Department Faculty Publication Series
In this paper we relate two mathematical frameworks that make perturbative quantum field theory rigorous: perturbative algebraic quantum field theory (pAQFT) and the factorization algebras framework developed by Costello and Gwilliam. To make the comparison as explicit as possible, we use the free scalar field as our running example, while giving proofs that apply to any field theory whose equations of motion are Greenhyperbolic (which includes, for instance, free fermions). The main claim is that for such free theories, there is a natural transformation intertwining the two constructions. In fact, both approaches encode equivalent information if one assumes the time-slice …
Correcting An Estimator Of A Multivariate Monotone Function With Isotonic Regression, Ted Westling, Mark J. Van Der Laan, Marco Carone
Correcting An Estimator Of A Multivariate Monotone Function With Isotonic Regression, Ted Westling, Mark J. Van Der Laan, Marco Carone
Mathematics and Statistics Department Faculty Publication Series
In many problems, a sensible estimator of a possibly multivariate monotone function may fail to be monotone. We study the correction of such an estimator obtained via projection onto the space of functions monotone over a finite grid in the domain. We demonstrate that this corrected estimator has no worse supremal estimation error than the initial estimator, and that analogously corrected confidence bands contain the true function whenever the initial bands do, at no loss to band width. Additionally, we demonstrate that the corrected estimator is asymptotically equivalent to the initial estimator if the initial estimator satisfies a stochastic equicontinuity …
Correcting For Differential Recruitment In Respondent-Driven Sampling Data Using Ego-Network Information, Isabelle S. Beaudry, Krista J. Gile
Correcting For Differential Recruitment In Respondent-Driven Sampling Data Using Ego-Network Information, Isabelle S. Beaudry, Krista J. Gile
Mathematics and Statistics Department Faculty Publication Series
Respondent-Driven sampling (RDS) is a sampling method devised to overcome challenges with sampling hard-to-reach human populations. The sampling starts with a limited number of individuals who are asked to recruit a small number of their contacts. Every surveyed individual is subsequently given the same opportunity to recruit additional members of the target population until a pre-established sample size is achieved. The recruitment process consequently implies that the survey respondents are responsible for deciding who enters the study. Most RDS prevalence estimators assume that participants select among their contacts completely at random. The main objective of this work is to correct …
Systematic Coarse-Grained Models For Molecular Systems Using Entropy †, Evangelina Kalligiannaki, Vagelis Harmandaris, Markos Katsoulakis
Systematic Coarse-Grained Models For Molecular Systems Using Entropy †, Evangelina Kalligiannaki, Vagelis Harmandaris, Markos Katsoulakis
Mathematics and Statistics Department Faculty Publication Series
The development of systematic coarse-grained mesoscopic models for complex molecular systems is an intense research area. Here we first give an overview of different methods for obtaining optimal parametrized coarse-grained models, starting from detailed atomistic representation for high dimensional molecular systems. We focus on methods based on information theory, such as relative entropy, showing that they provide parameterizations of coarse-grained models at equilibrium by minimizing a fitting functional over a parameter space. We also connect them with structural-based (inverse Boltzmann) and force matching methods. All the methods mentioned in principle are employed to approximate a many-body potential, the (n-body) potential …
Modulational Instability, Inter-Component Asymmetry, And Formation Of Quantum Droplets In One-Dimensional Binary Bose Gases, Thudiyangal Mithun, Aleksandra Maluckov, Kenichi Kasamatsu, Boris A. Malomed, Avinash Khare
Modulational Instability, Inter-Component Asymmetry, And Formation Of Quantum Droplets In One-Dimensional Binary Bose Gases, Thudiyangal Mithun, Aleksandra Maluckov, Kenichi Kasamatsu, Boris A. Malomed, Avinash Khare
Mathematics and Statistics Department Faculty Publication Series
Quantum droplets are ultradilute liquid states that emerge from the competitive interplay of two Hamiltonian terms, the mean-field energy and beyond-mean-field correction, in a weakly interacting binary Bose gas. We relate the formation of droplets in symmetric and asymmetric two-component one-dimensional boson systems to the modulational instability of a spatially uniform state driven by the beyond-mean-field term. Asymmetry between the components may be caused by their unequal populations or unequal intra-component interaction strengths. Stability of both symmetric and asymmetric droplets is investigated. Robustness of the symmetric solutions against symmetry-breaking perturbations is confirmed.