Digital Commons Network^™

Immune Classification Of Clear Cell Renal Cell Carcinoma, Sumeyye Su, Shaya Akbarinejad, Leili Shahriyari

Mathematics and Statistics Department Faculty Publication Series

Since the outcome of treatments, particularly immunotherapeutic interventions, depends on the tumor immune micro-environment (TIM), several experimental and computational tools such as flow cytometry, immunohistochemistry, and digital cytometry have been developed and utilized to classify TIM variations. In this project, we identify immune pattern of clear cell renal cell carcinomas (ccRCC) by estimating the percentage of each immune cell type in 526 renal tumors using the new powerful technique of digital cytometry. The results, which are in agreement with the results of a large-scale mass cytometry analysis, show that the most frequent immune cell types in ccRCC tumors are CD8+ …

Data-Driven Mathematical Model Of Osteosarcoma, Trang Le, Sumeyye Su, Arkadz Kirshtein, Leili Shahriyari

Mathematics and Statistics Department Faculty Publication Series

As the immune system has a significant role in tumor progression, in this paper, we develop a data-driven mathematical model to study the interactions between immune cells and the osteosarcoma microenvironment. Osteosarcoma tumors are divided into three clusters based on their relative abundance of immune cells as estimated from their gene expression profiles. We then analyze the tumor progression and effects of the immune system on cancer growth in each cluster. Cluster 3, which had approximately the same number of naive and M2 macrophages, had the slowest tumor growth, and cluster 2, with the highest population of naive macrophages, had …

A Mathematical Model Of Breast Tumor Progression Based On Immune Infiltration, Navi Mohammad Mirzaei, Sumeyye Su, Dilruba Sofia, Maura Hegarty, Mohamed H. Abel-Rahman, Alireza Asadpoure, Colleen M. Cebulla, Young Hwan Chang, Wenrui Hao, Pamela R. Jackson, Adrian V. Lee, Daniel G. Stover, Zuzana Tatarova, Ioannis K. Zervantonakis, Leili Shahriyari

Mathematics and Statistics Department Faculty Publication Series

Breast cancer is the most prominent type of cancer among women. Understanding the microenvironment of breast cancer and the interactions between cells and cytokines will lead to better treatment approaches for patients. In this study, we developed a data-driven mathematical model to investigate the dynamics of key cells and cytokines involved in breast cancer development. We used gene expression profiles of tumors to estimate the relative abundance of each immune cell and group patients based on their immune patterns. Dynamical results show the complex interplay between cells and molecules, and sensitivity analysis emphasizes the direct effects of macrophages and adipocytes …

Generalized Catalan Numbers From Hypergraphs, Paul E. Gunnells

Mathematics and Statistics Department Faculty Publication Series

The Catalan numbers C_n ∈ {1,1,2,5,14,42,…} form one of the most venerable sequences in combinatorics. They have many combinatorial interpretations, from counting bracketings of products in non-associative algebra to counting plane trees and noncrossing set partitions. They also arise in the GUE matrix model as the leading coefficient of certain polynomials, a connection closely related to the plane trees and noncrossing set partitions interpretations. In this paper we defi ne a generalization of the Catalan numbers. In fact we defi ne an infinite collection of generalizations C_n^(m) , m >= 1, with m = 1 giving the …

Data Driven Mathematical Model Of Folfiri Treatment For Colon Cancer, Aparajita Budithi, Sumeyye Su, Arkadz Kirshtein, Leili Shahriyari

Mathematics and Statistics Department Faculty Publication Series

Many colon cancer patients show resistance to their treatments. Therefore, it is important to consider unique characteristic of each tumor to find the best treatment options for each patient. In this study, we develop a data driven mathematical model for interaction between the tumor microenvironment and FOLFIRI drug agents in colon cancer. Patients are divided into five distinct clusters based on their estimated immune cell fractions obtained from their primary tumors’ gene expression data. We then analyze the effects of drugs on cancer cells and immune cells in each group, and we observe different responses to the FOLFIRI drugs between …

Unraveling The Mechanisms Of Surround Suppression In Early Visual Processing, Yao Li, Lai-Sang Young

Mathematics and Statistics Department Faculty Publication Series

This paper uses mathematical modeling to study the mechanisms of surround suppression in the primate visual cortex. We present a large-scale neural circuit alistic modeling work are used. The remaining parameters are chosen to produce model outputs that emulate experimentally observed size-tuning curves. Our two main results are: (i) we discovered the character of the long-range connections in Layer 6 responsible for surround effects in the input layers; and (ii) we showed that a net-inhibitory feedback, i.e., feedback that excites I-cells more than E-cells, from Layer 6 to Layer 4 is conducive to producing surround properties consistent with experimental data. …

Immune Classification Of Osteosarcoma, Trang Le, Sumeyye Su, Leili Shahriyari

Mathematics and Statistics Department Faculty Publication Series

Tumor immune microenvironment has been shown to be important in predicting the tumor progression and the outcome of treatments. This work aims to identify different immune patterns in osteosarcoma and their clinical characteristics. We use the latest and best performing deconvolution method, CIBERSORTx, to obtain the relative abundance of 22 immune cells. Then we cluster patients based on their estimated immune abundance and study the characteristics of these clusters, along with the relationship between immune infiltration and outcome of patients. We find that abundance of CD8 T cells, NK cells and M1 Macrophages have a positive association with prognosis, while …

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

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

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

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

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

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

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

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.

The Bullet Problem With Discrete Speeds, Brittany Dygert, Christoph Kinzel, Matthew Junge, Annie Raymond, Erik Slivken, Jennifer Zhu

Mathematics and Statistics Department Faculty Publication Series

Bullets are fired from the origin of the positive real line, one per second, with independent speeds sampled uniformly from a discrete set. Collisions result in mutual annihilation. We show that a bullet with the second largest speed survives with positive probability, while a bullet with the smallest speed does not. This also holds for exponential spacings between firing times. Our results imply that the middle-velocity particle survives with positive probability in a two-sided version of the bullet process with three speeds known to physicists as ballistic annihiliation.

Alignment Strength And Correlation For Graphs, Donniell E. Fishkind, Lingyao Meng, Ao Sun, Carey E. Priebe, Vince Lyzinski

Mathematics and Statistics Department Faculty Publication Series

When two graphs have a correlated Bernoulli distribution, we prove that the alignment strength of their natural bijection strongly converges to a novel measure of graph correlation ϱ_T that neatly combines intergraph with intragraph distribution parameters. Within broad families of the random graph parameter settings, we illustrate that exact graph matching runtime and also matchability are both functions of ϱ_T, with thresholding behavior starkly illustrated in matchability.

Dynamics Of Dirac Solitons In Networks, K K Sabirov, D B Babajanov, D U Matrasulov, P G Kevrekidis

Mathematics and Statistics Department Faculty Publication Series

We study dynamics of Dirac solitons in prototypical networks modeling them by the nonlinear Dirac equation on metric graphs. Stationary soliton solutions of the nonlinear Dirac equation on simple metric graphs are obtained. It is shown that these solutions provide reflectionless vertex transmission of the Dirac solitons under suitable conditions. The constraints for bond nonlinearity coefficients, conjectured to represent necessary conditions for allowing reflectionless transmission over a Y-junction are derived. The Y-junction considerations are also generalized to a tree and triangle network. The analytical results are confirmed by direct numerical simulations. Keywords: nonlinear Dirac equation, metric graphs, Lorentz transformation, Gross–Neveu …

Reduced Models Of Point Vortex Systems, Jonathan Maack, Bruce Turkington

Mathematics and Statistics Department Faculty Publication Series

Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler equations, as well as the quasi-geostrophic equations for either single-layer or two-layer flows. Optimal closure refers to a general method of reduction for Hamiltonian systems, in which macroscopic states are required to belong to a parametric family of distributions on phase space. In the case of point vortex ensembles, the macroscopic variables describe the spatially coarse-grained vorticity. Dynamical closure in terms of those macrostates is obtained by optimizing …

The Turán Polytope, Annie Raymond

Mathematics and Statistics Department Faculty Publication Series

The Turán hypergraph problem asks to find the maximum number of r-edges in a r-uniform hypergraph on n vertices that does not contain a clique of size a. When r=2, i.e., for graphs, the answer is well-known and can be found in Turán's theorem. However, when r ≥ 3, the problem remains open. We model the problem as an integer program and call the underlying polytope the Turán polytope. We draw parallels between the latter and the stable set polytope: we show that generalized and transformed versions of the web and wheel inequalities are also facet-defining …

Conditional Genetic Screen In Physcomitrella Patens Reveals A Novel Microtubule Depolymerizing-End-Tracking Protein, Xinxin Ding, Leah M. Pervere, Carl Bascom Jr., Jeffrey P. Bibeau, Sakshi Khurana, Allison M. Butt, Roger G. Orr, Patrick Flaherty, Magdalena Bezanilla, Luis Vidali

Mathematics and Statistics Department Faculty Publication Series

Our ability to identify genes that participate in cell growth and division is limited because their loss often leads to lethality. A solution to this is to isolate conditional mutants where the phenotype is visible under restrictive conditions. Here, we capitalize on the haploid growth-phase of the moss Physcomitrella patens to identify conditional loss-of-growth (CLoG) mutants with impaired growth at high temperature. We used whole-genome sequencing of pooled segregants to pinpoint the lesion of one of these mutants (clog1) and validated the identified mutation by rescuing the conditional phenotype by homologous recombination. We found that CLoG1 is a …

Stability Of Periodic Orbits In No-Slip Billiards, C. Cox, R. Feres, Hongkun Zhang

Mathematics and Statistics Department Faculty Publication Series

Rigid bodies collision maps in dimension-two, under a natural set of physical requirements, can be classified into two types: the standard specular reflection map and a second which we call, after Broomhead and Gutkin, no-slip. This leads to the study of no-slip billiards—planar billiard systems in which the moving particle is a disc (with rotationally symmetric mass distribution) whose translational and rotational velocities can both change after collisions with the boundary of the billiard domain.

This paper, which continues the investigation initiated in Cox and Feres (2017 Dynamical Systems, Ergodic Theory, and Probability: in Memory of Chernov (Providence, …

Existence, Stability And Dynamics Of Nonlinear Modes In A 2d Partiallypt Symmetric Potential, Jennie D’Ambroise, Panayotis G. Kevrekidis

Mathematics and Statistics Department Faculty Publication Series

It is known that multidimensional complex potentials obeying parity-time(PT)symmetry may possess all real spectra and continuous families of solitons. Recently, it was shown that for multi-dimensional systems, these features can persist when the parity symmetry condition is relaxed so that the potential is invariant under reflection in only a single spatial direction. We examine the existence, stability and dynamical properties of localized modes within the cubic nonlinear Schrödinger equation in such a scenario of partiallyPT-symmetric potential.

Discrete Solitons And Vortices In Anisotropic Hexagonal And Honeycomb Lattices, Q E. Hoq, Panayotis G. Kevrekidis, A R. Bishop

Mathematics and Statistics Department Faculty Publication Series

In the present work, we consider the self-focusing discrete nonlinear Schrödinger equation on hexagonal and honeycomb lattice geometries. Our emphasis is on the study of the effects of anisotropy, motivated by the tunability afforded in recent optical and atomic physics experiments. We find that multi-soliton and discrete vortex states undergo destabilizing bifurcations as the relevant anisotropy control parameter is varied. We quantify these bifurcations by means of explicit analytical calculations of the solutions, as well as of their spectral linearization eigenvalues. Finally, we corroborate the relevant stability picture through direct numerical computations. In the latter, we observe the prototypical manifestation …

Scattering Of Waves By Impurities In Precompressed Granular Chains, Panos Kevrekidis, Alejandro Martinez, Hiromi Yasuda, Eunho Kim, Mason Porter, Jinkyu Yang

Mathematics and Statistics Department Faculty Publication Series

We study scattering of waves by impurities in strongly precompressed granular chains. We explore the linear scattering of plane waves and identify a closed-form expression for the re ection and transmission coefficients for the scattering of the waves from both a single impurity and a double impurity. For single-impurity chains, we show that, within the transmission band of the host granular chain, high-frequency waves are strongly attenuated (such that the transmission coefficient vanishes as the wavenumber k → ± π), whereas low-frequency waves are well-transmitted through the impurity. For double-impurity chains, we identify a resonance—enabling full transmission at a particular …

Energy Criterion For The Spectral Stability Of Discrete Breathers, Panos Kevrekidis, Jesus Cuevas-Maraver, Dmitry Pelinovsky

Mathematics and Statistics Department Faculty Publication Series

No abstract provided.

Dark-Bright Soliton Interactions Beyond The Integrable Limit, G. Katsimiga, J. Stockhofe, Panos Kevrekidis, P. Schmelcher

Mathematics and Statistics Department Faculty Publication Series

In this work we present a systematic theoretical analysis regarding dark-bright solitons and their interactions, motivated by recent advances in atomic two-component repulsively interacting Bose-Einstein condensates. In particular, we study analytically via a two-soliton ansatz adopted within a variational formulation the interaction between two dark-bright solitons in a homogeneous environment beyond the integrable regime, by considering general inter/intra-atomic interaction coefficients. We retrieve the possibility of a fixed point in the case where the bright solitons are out of phase. As the inter-component interaction is increased, we also identify an exponential instability of the two-soliton state, associated with a subcritical pitchfork …

A Pt-Symmetric Dual-Core System With The Sine-Gordon Nonlinearity And Derivative Coupling, Jesus Cuevas-Maraver, Boris Malomed, Panos Kevrekidis

Mathematics and Statistics Department Faculty Publication Series

As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from local interaction between adjacent particles in coupled Frenkel-Kontorova (FK) chains, while the cross-derivative coupling, which was not considered before, is induced by three-particle interactions, provided that the particles in the parallel FK chains move in different directions. Nonlinear modes are then studied in this system. In particular, kink-kink (KK) and kink-antikink (KA) complexes are explored …

Performing Hong-Ou-Mandel-Type Numerical Experiments With Repulsive Condensates: The Case Of Dark And Dark-Bright Solitons, Panos Kevrekidis, Zhi-Yuan Sun, Peter Kruger

Mathematics and Statistics Department Faculty Publication Series

The Hong-Ou-Mandel experiment leads indistinguishable photons simultaneously reach-ing a 50:50 beam splitter to emerge on the same port through two-photon interference.Motivated by this phenomenon, we consider numerical experiments of the same flavor forclassical, wave objects in the setting of repulsive condensates. We examine dark solitonsinteracting with a repulsive barrier, a case in which we find no significant asymmetries inthe emerging waves after the collision, presumably due to their topological nature. We alsoconsider case examples of two-component systems, where the dark solitons trap a brightstructure in the second-component (dark-bright solitary waves). For these, pronouncedasymmetries upon collision are possible for the non-topological …

Reverse Chemical Genetics: Comprehensive Fitness Profiling Reveals The Spectrum Of Drug Target Interactions, Lai H. Wong, Sunita Sinha, Julian R. Bergeron, Joseph C. Mellor, Guri Giaever, Patrick Flaherty, Corey Nislow

Mathematics and Statistics Department Faculty Publication Series

The emergence and prevalence of drug resistance demands streamlined strategies to identify drug resistant variants in a fast, systematic and cost-effective way. Methods commonly used to understand and predict drug resistance rely on limited clinical studies from patients who are refractory to drugs or on laborious evolution experiments with poor coverage of the gene variants. Here, we report an integrative functional variomics methodology combining deep sequencing and a Bayesian statistical model to provide a comprehensive list of drug resistance alleles from complex variant populations. Dihydrofolate reductase, the target of methotrexate chemotherapy drug, was used as a model to identify functional …