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Mathematics and Statistics Department Faculty Publication Series
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Separable Graph Hamiltonian Network: A Graph Deep Learning Model For Lattice Systems, Hong-Kun Zhang, Et. Al.
Separable Graph Hamiltonian Network: A Graph Deep Learning Model For Lattice Systems, Hong-Kun Zhang, Et. Al.
Mathematics and Statistics Department Faculty Publication Series
Addressing the challenges posed by nonlinear lattice models, which are vital across diverse scientific disciplines, we present a new deep learning approach that harnesses the power of graph neural networks. By representing the lattice system as a graph and leveraging the graph structures to identify complex nonlinear relationships, we have developed a flexible solution that outperforms traditional techniques. Our model not only offers precise trajectory predictions and energy conservation properties by incorporating separable Hamiltonians but also proves superior to existing top-tier models when tested on classic nonlinear oscillator lattice problems: a mixed Fermi-Pasta-Ulam Klein-Gordon, a Klein-Gordon system with long-range interactions, …
Patient-Specific Mathematical Model Of The Clear Cell Renal Cell Carcinoma Microenvironment, Dilruba Sofia, Navid Mohammad Mirzaei, Leili Shahriyari
Patient-Specific Mathematical Model Of The Clear Cell Renal Cell Carcinoma Microenvironment, Dilruba Sofia, Navid Mohammad Mirzaei, Leili Shahriyari
Mathematics and Statistics Department Faculty Publication Series
The interactions between cells and molecules in the tumor microenvironment can give insight into the initiation and progression of tumors and their optimal treatment options. In this paper, we developed an ordinary differential equation (ODE) mathematical model of the interaction network of key players in the clear cell renal cell carcinoma (ccRCC) microenvironment. We then performed a global gradient-based sensitivity analysis to investigate the effects of the most sensitive parameters of the model on the number of cancer cells. The results indicate that parameters related to IL-6 have high a impact on cancer cell growth, such that decreasing the level …
Nonparametric Inference Under A Monotone Hazard Ratio Order, Yujian Wu, Ted Westling
Nonparametric Inference Under A Monotone Hazard Ratio Order, Yujian Wu, Ted Westling
Mathematics and Statistics Department Faculty Publication Series
The ratio of the hazard functions of two populations or two strata of a single population plays an important role in time-to-event analysis. Cox regression is commonly used to estimate the hazard ratio under the assumption that it is constant in time, which is known as the proportional hazards assumption. However, this assumption is often violated in practice, and when it is violated, the parameter estimated by Cox regression is difficult to interpret. The hazard ratio can be estimated in a nonparametric manner using smoothing, but smoothing-based estimators are sensitive to the selection of tuning parameters, and it is often …
Dynamic Instability Of 3d Stationary And Traveling Planar Dark Solitons, Thudiyangal Mithun, A. R. Fritsch, I. B. Spielman, Panayotis G. Kevrekidis
Dynamic Instability Of 3d Stationary And Traveling Planar Dark Solitons, Thudiyangal Mithun, A. R. Fritsch, I. B. Spielman, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
Here we revisit the topic of stationary and propagating solitonic excitations in self-repulsive three-dimensional (3D) Bose–Einstein condensates by quantitatively comparing theoretical analysis and associated numerical computations with our experimental results. Motivated by numerous experimental efforts, including our own herein, we use fully 3D numerical simulations to explore the existence, stability, and evolution dynamics of planar dark solitons. This also allows us to examine their instability-induced decay products including solitonic vortices and vortex rings. In the trapped case and with no adjustable parameters, our numerical findings are in correspondence with experimentally observed coherent structures. Without a longitudinal trap, we identify numerically …
Dense Dark-Bright Soliton Arrays In A Two-Component Bose-Einstein Condensate, S. Mossman, G. C. Katsimiga, S. I. Mistakidis, A. Romero-Ros, T. M. Bersano, P. Schmelcher, Panayotis G. Kevrekidis, P. Engels
Dense Dark-Bright Soliton Arrays In A Two-Component Bose-Einstein Condensate, S. Mossman, G. C. Katsimiga, S. I. Mistakidis, A. Romero-Ros, T. M. Bersano, P. Schmelcher, Panayotis G. Kevrekidis, P. Engels
Mathematics and Statistics Department Faculty Publication Series
We present a combined experimental and theoretical study of regular dark-bright soliton arrays in a two-component atomic Bose-Einstein condensate. We demonstrate a microwave pulse-based winding technique which allows for a tunable number of solitary waves en route to observing their dynamics, quantified through Fourier analysis of the density. We characterize different winding density regimes by the observed dynamics including the decay and revival of the Fourier peaks, the emergence of dark-antidark solitons, and disordering of the soliton array. The experimental results are in good agreement with three-dimensional numerical computations of the underlying mean-field theory. These observations open a window into …
Discrete Breathers In A Mechanical Metamaterial, Henry Duran, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Anna Vainchtein
Discrete Breathers In A Mechanical Metamaterial, Henry Duran, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Anna Vainchtein
Mathematics and Statistics Department Faculty Publication Series
We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a chain of pairs of rigid units connected by flexible hinges. Upon analyzing the linear band structure of the model, we identify parameter regimes in which this system may possess discrete breather solutions with frequencies inside the gap between optical and acoustic dispersion bands. We compute numerically exact solutions of this type for several different parameter regimes and investigate their properties and stability. Our findings demonstrate that upon appropriate parameter tuning within experimentally tractable ranges, the system exhibits a plethora of discrete breathers, with multiple …
Discovering Governing Equations In Discrete Systems Using Pinns, Sheikh Saqlain, Wei Zhu, Efstathios G. Charalampidis, Panayotis G. Kevrekidis
Discovering Governing Equations In Discrete Systems Using Pinns, Sheikh Saqlain, Wei Zhu, Efstathios G. Charalampidis, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom. We illustrate the ability of a suitable adaptation of Physics-Informed Neural Networks (PINNs) to solve the inverse problem of parameter identification in such discrete, high-dimensional systems inspired by physical applications. The methodology is illustrated in a diverse array of examples including real-field ones (ϕ4 and sine-Gordon), as well as complex-field (discrete nonlinear Schr{ö}dinger equation) and going beyond Hamiltonian to dissipative cases (the discrete complex Ginzburg-Landau …
Dirac Solitons And Topological Edge States In The Β-Fermi-Pasta-Ulam-Tsingou Dimer Lattice, Rajesh Chaunsali, Panayotis G. Kevrekidis, Dimitri Frantzeskakis, Georgios Theocharis
Dirac Solitons And Topological Edge States In The Β-Fermi-Pasta-Ulam-Tsingou Dimer Lattice, Rajesh Chaunsali, Panayotis G. Kevrekidis, Dimitri Frantzeskakis, Georgios Theocharis
Mathematics and Statistics Department Faculty Publication Series
We consider a dimer lattice of the Fermi-Pasta-Ulam-Tsingou (FPUT) type, where alternating linear couplings have a controllably small difference, and the cubic nonlinearity (β-FPUT) is the same for all interaction pairs. We use a weakly nonlinear formal reduction within the lattice bandgap to obtain a continuum, nonlinear Dirac-type system. We derive the Dirac soliton profiles and the model's conservation laws analytically. We then examine the cases of the semi-infinite and the finite domains and illustrate how the soliton solutions of the bulk problem can be ``glued'' to the boundaries for different types of boundary conditions. We thus explain the existence …
An Ising Machine Based On Networks Of Subharmonic Electrical Resonators, L. Q. English, A. V. Zampetaki, K. P. Kalinin, N. G. Berloff, Panayotis G. Kevrekidis
An Ising Machine Based On Networks Of Subharmonic Electrical Resonators, L. Q. English, A. V. Zampetaki, K. P. Kalinin, N. G. Berloff, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We explore a case example of networks of classical electronic oscillators evolving towards the solution of complex optimization problems. We show that when driven into subharmonic response, a network of such nonlinear electrical resonators can minimize the Ising Hamiltonian on non-trivial graphs such as antiferromagnetically coupled rewired-M{ö}bius ladders. In this context, the spin-up and spin-down states of the Ising machine are represented by the oscillators' response at the even or odd driving cycles. Our experimental setting of driven nonlinear oscillators coupled via a programmable switch matrix leads to a unique energy minimizer when one such exists, and probes frustration where …
Revisiting Multi-Breathers In The Discrete Klein-Gordon Equation: A Spatial Dynamics Approach, Ross Parker, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Alejandro Aceves
Revisiting Multi-Breathers In The Discrete Klein-Gordon Equation: A Spatial Dynamics Approach, Ross Parker, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Alejandro Aceves
Mathematics and Statistics Department Faculty Publication Series
We consider the existence and spectral stability of multi-breather structures in the discrete Klein-Gordon equation, both for soft and hard symmetric potentials. To obtain analytical results, we project the system onto a finite-dimensional Hilbert space consisting of the first M Fourier modes, for arbitrary M. On this approximate system, we then take a spatial dynamics approach and use Lin's method to construct multi-breathers from a sequence of well-separated copies of the primary, single-site breather. We then locate the eigenmodes in the Floquet spectrum associated with the interaction between the individual breathers of such multi-breather states by reducing the spectral …
Efficient Manipulation Of Bose-Einstein Condensates In A Double-Well Potential, J. Adriazola, R. H. Goodman, Panayotis G. Kevrekidis
Efficient Manipulation Of Bose-Einstein Condensates In A Double-Well Potential, J. Adriazola, R. H. Goodman, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We pose the problem of transferring a Bose-Einstein Condensate (BEC) from one side of a double-well potential to the other as an optimal control problem for determining the time-dependent form of the potential. We derive a reduced dynamical system using a Galerkin truncation onto a finite set of eigenfunctions and find that including three modes suffices to effectively control the full dynamics, described by the Gross-Pitaevskii model of BEC. The functional form of the control is reduced to finite dimensions by using a Galerkin-type method called the chopped random basis (CRAB) method, which is then optimized by a genetic algorithm …
The Role Of Mobility In The Dynamics Of The Covid-19 Epidemic In Andalusia, Z. Rapti, Jesús Cuevas-Maraver, E. Kontou, S. Liu, Y. Drossinos, Panayotis G. Kevrekidis, G. A. Kevrekidis, M. Barmann, Q.-Y. Chen
The Role Of Mobility In The Dynamics Of The Covid-19 Epidemic In Andalusia, Z. Rapti, Jesús Cuevas-Maraver, E. Kontou, S. Liu, Y. Drossinos, Panayotis G. Kevrekidis, G. A. Kevrekidis, M. Barmann, Q.-Y. Chen
Mathematics and Statistics Department Faculty Publication Series
Metapopulation models have been a popular tool for the study of epidemic spread over a network of highly populated nodes (cities, provinces, countries) and have been extensively used in the context of the ongoing COVID-19 pandemic. In the present work, we revisit such a model, bearing a particular case example in mind, namely that of the region of Andalusia in Spain during the period of the summer-fall of 2020 (i.e., between the first and second pandemic waves). Our aim is to consider the possibility of incorporation of mobility across the province nodes focusing on mobile-phone time dependent data, but also …
Two-Component 3d Atomic Bose-Einstein Condensates Support Complex Stable Patterns, N. Boullé, I. Newell, P. E. Farrell, Panayotis G. Kevrekidis
Two-Component 3d Atomic Bose-Einstein Condensates Support Complex Stable Patterns, N. Boullé, I. Newell, P. E. Farrell, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multi-component nonlinear wave systems of nonlinear Schrödinger type. While our computations relate to two-component atomic Bose-Einstein condensates in parabolic traps, our methods can be broadly applied to high-dimensional, nonlinear systems of partial differential equations. The combination of the so-called deflation technique with a careful selection of initial guesses enables the computation of an unprecedented breadth of patterns, including ones combining vortex lines, rings, stars, and “vortex labyrinths”. Despite their complexity, they may be dynamically robust and amenable to experimental observation, as confirmed by Bogolyubov-de Gennes …
Characterization Of Elastic Topological States Using Dynamic Mode Decomposition, Shuaifeng Li, Panayotis G. Kevrekidis, Jinkyu Yang
Characterization Of Elastic Topological States Using Dynamic Mode Decomposition, Shuaifeng Li, Panayotis G. Kevrekidis, Jinkyu Yang
Mathematics and Statistics Department Faculty Publication Series
Elastic topological states have been receiving increased intention in numerous scientific and engineering fields due to their defect-immune nature, resulting in applications of vibration control and information processing. Here, we present the data-driven discovery of elastic topological states using dynamic mode decomposition (DMD). The DMD spectrum and DMD modes are retrieved from the propagation of the relevant states along the topological boundary, where their nature is learned by DMD. Applications such as classification and prediction can be achieved by the underlying characteristics from DMD. We demonstrate the classification between topological and traditional metamaterials using DMD modes. Moreover, the model enabled …
Dragging A Defect In A Droplet Bose-Einstein Condensate, Sheikh Saqlain, Thudiyangal Mithun, R. Carretero-González, Panayotis G. Kevrekidis
Dragging A Defect In A Droplet Bose-Einstein Condensate, Sheikh Saqlain, Thudiyangal Mithun, R. Carretero-González, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
In the present work we consider models of quantum droplets in the presence of a defect in the form of a laser beam moving through the respective condensates including the Lee-Huang-Yang correction. Our analysis features separately an exploration of the existence, stability, bifurcations and dynamics in 1D, 2D and 3D settings. In the absence of an analytical solution of the problem, we provide an analysis of the speed of sound and observe how the states traveling with the defect may feature a saddle-center bifurcation as the speed or the strength of the defect is modified. Relevant bifurcation diagrams are constructed …
How Close Are Integrable And Non-Integrable Models: A Parametric Case Study Based On The Salerno Model, Thudiyangal Mithun, Aleksandra Maluckov, Ana Mančić, Avinash Khare, Panayotis G. Kevrekidis
How Close Are Integrable And Non-Integrable Models: A Parametric Case Study Based On The Salerno Model, Thudiyangal Mithun, Aleksandra Maluckov, Ana Mančić, Avinash Khare, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
n the present work we revisit the Salerno model as a prototypical system that interpolates between a well-known integrable system (the Ablowitz-Ladik lattice) and an experimentally tractable non-integrable one (the discrete nonlinear Schrödinger model). The question we ask is: for "generic" initial data, how close are the integrable to the non-integrable models? Our more precise formulation of this question is: how well is the constancy of formerly conserved quantities preserved in the non-integrable case? Upon examining this, we find that even slight deviations from integrability can be sensitively felt by measuring these formerly conserved quantities in the case of the …
Breathers In Lattices With Alternating Strain-Hardening And Strain-Softening Interactions, Marisa M. Lee, Efstathios G. Charalampidis, Siyuan Xing, Christopher Chong, Panayotis G. Kevrekidis
Breathers In Lattices With Alternating Strain-Hardening And Strain-Softening Interactions, Marisa M. Lee, Efstathios G. Charalampidis, Siyuan Xing, Christopher Chong, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
This workfocuses onthe study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain-hardening and strain-softening. The existence, stability, and bifurcation structure of such solutions, as well as the system dynamics in the presence of damping and driving are studied systematically. It is found that the linear resonant peaks in the system bend toward the frequency gap in the presence of nonlinearity. The time-periodic solutions that lie within the frequency gap compare well to Hamiltonian breathers if the damping and driving are small. In the Hamiltonian limit of the problem, we use a …
Kink-Antikink Interaction Forces And Bound States In A Φ4 Model With Quadratic And Quartic Dispersion, G. A. Tsolias, Robert J. Decker, A. Demirkaya, T. J. Alexander, Ross Parker, Panayotis G. Kevrekidis
Kink-Antikink Interaction Forces And Bound States In A Φ4 Model With Quadratic And Quartic Dispersion, G. A. Tsolias, Robert J. Decker, A. Demirkaya, T. J. Alexander, Ross Parker, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
In the present work we explore the competition of quadratic and quartic dispersion in producing kink-like solitary waves in a model of the nonlinear Schrödinger type bearing cubic nonlinearity. We present the first 6 families of multikink solutions and explore their bifurcations as the strength of the quadratic dispersion is varied. We reveal a rich bifurcation structure for the system, connecting two-kink states with states involving 4-, as well as 6-kinks. The stability of all of these states is explored. For each family, we discuss a “lower branch” adhering to the energy landscape of the 2-kink states. We also, however, …
Control Of 164Dy Bose-Einstein Condensate Phases And Dynamics With Dipolar Anistropy, S. Halder, K. Mukherjee, S. I. Mistakidis, S. Das, Panayotis G. Kevrekidis, P. K. Panigrahi, S. Majumder, H. R. Sadeghpour
Control Of 164Dy Bose-Einstein Condensate Phases And Dynamics With Dipolar Anistropy, S. Halder, K. Mukherjee, S. I. Mistakidis, S. Das, Panayotis G. Kevrekidis, P. K. Panigrahi, S. Majumder, H. R. Sadeghpour
Mathematics and Statistics Department Faculty Publication Series
We investigate the quench dynamics of quasi-one and two dimensional dipolar Bose-Einstein condensates (dBEC) of 164Dy atoms under the influence of a fast rotating magnetic field. The magnetic field thus controls both the magnitude and sign of the dipolar potential. We account for quantum fluctuations, critical to formation of exotic quantum droplet and supersolid phases in the extended Gross-Pitaevskii formalism, which includes the so-called Lee-Huang-Yang (LHY) correction. An analytical variational ansatz allows us to obtain the phase diagrams of the superfluid and droplet phases. The crossover from the superfluid to the supersolid phase and to single and droplet arrays …
Asymptotic Dynamics Of Higher-Order Lumps In The Davey-Stewartson Ii Equation, Lijuan Guo, Panayotis G. Kevrekidis, Jingsong He
Asymptotic Dynamics Of Higher-Order Lumps In The Davey-Stewartson Ii Equation, Lijuan Guo, Panayotis G. Kevrekidis, Jingsong He
Mathematics and Statistics Department Faculty Publication Series
A family of higher-order rational lumps on non-zero constant background of Davey–Stewartson (DS) II equation are investigated. These solutions have multiple peaks whose heights and trajectories are approximately given by asymptotical analysis. It is found that the heights are time-dependent and for large time they approach the same constant height value of the first-order fundamental lump. The resulting trajectories are considered and it is found that the scattering angle can assume arbitrary values in the interval of which is markedly distinct from the necessary orthogonal scattering for the higher-order lumps on zero background. Additionally, it is illustrated that the higher-order …
Solitary Wave Billiards, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Hongkun Zhang
Solitary Wave Billiards, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Hongkun Zhang
Mathematics and Statistics Department Faculty Publication Series
In the present work we introduce the concept of solitary wave billiards. I.e., instead of a point particle, we consider a solitary wave in an enclosed region and explore its collision with the boundaries and the resulting trajectories in cases which for particle billiards are known to be integrable and for cases that are known to be chaotic. A principal conclusion is that solitary wave billiards are generically found to be chaotic even in cases where the classical particle billiards are integrable. However, the degree of resulting chaoticity depends on the particle speed and on the properties of the potential. …
Schwarzschild-Finsler-Randers Spacetime: Dynamical Analysis, Geodesics And Deflection Angle, E. Kapsabelis, Panayotis G. Kevrekidis, P. C. Stavrinos, A. Triantafyllopoulos
Schwarzschild-Finsler-Randers Spacetime: Dynamical Analysis, Geodesics And Deflection Angle, E. Kapsabelis, Panayotis G. Kevrekidis, P. C. Stavrinos, A. Triantafyllopoulos
Mathematics and Statistics Department Faculty Publication Series
In this work, we extend the study of Schwarzschild-Finsler-Randers (SFR) spacetime previously investigated by a subset of the present authors. We will examine the dynamical analysis of geodesics which provides the derivation of the energy and the angular momentum of a particle moving along a geodesic of SFR spacetime. This study allows us to compare our model with the corresponding of general relativity (GR). In addition, the effective potential of SFR model is examined and it is compared with the effective potential of GR. The phase portraits generated by these effective potentials are also compared. Finally, we deal with the …
Dispersive Shock Waves In Lattices: A Dimension Reduction Approach, Christopher Chong, Michael Herrman, Panayotis G. Kevrekidis
Dispersive Shock Waves In Lattices: A Dimension Reduction Approach, Christopher Chong, Michael Herrman, Panayotis G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
Dispersive shock waves (DSWs), which connect states of different amplitude via a modulated wave train, form generically in nonlinear dispersive media subjected to abrupt changes in state. The primary tool for the analytical study of DSWs is Whitham's modulation theory. While this framework has been successfully employed in many space-continuous settings to describe DSWs, the Whitham modulation equations are virtually intractable in most spatially discrete systems. In this article, we illustrate the relevance of the reduction of the DSW dynamics to a planar ODE in a broad class of lattice examples. Solutions of this low-dimensional ODE accurately describe the orbits …
Exploring Approaches For Predictive Cancer Patient Digital Twins: Opportunities For Collaboration And Innovation, Eric A. Stahlberg, Mohamed Abdel-Rahman, Boris Aguilar, Alireza Asadpoure, Robert A. Beckman, Lynn L. Borkon, Jeffrey N. Bryan, Colleen M. Cebulla, Young Hwan Chang, Ansu Chatterjee, Jun Deng, Sepideh Dolatshahi, Olivier Gevaert, Emily J. Greenspan, Wenrui Hao, Tina Hernandez-Boussard, Pamela R. Jackson, Marieke Kuijjer, Adrian Lee, Paul Macklin, Subha Madhavan, Matthew D. Mccoy, Navid Mohammad Mirzaei, Talayeh Razzaghi, Heber L. Rocha, Leili Shahriyari, Ilya Shmulevich, Daniel G. Stover, Yi Sun, Tanveer Syeda-Mahmood, Jinhua Wang, Qi Wang, Ioannis Zervantonakis
Exploring Approaches For Predictive Cancer Patient Digital Twins: Opportunities For Collaboration And Innovation, Eric A. Stahlberg, Mohamed Abdel-Rahman, Boris Aguilar, Alireza Asadpoure, Robert A. Beckman, Lynn L. Borkon, Jeffrey N. Bryan, Colleen M. Cebulla, Young Hwan Chang, Ansu Chatterjee, Jun Deng, Sepideh Dolatshahi, Olivier Gevaert, Emily J. Greenspan, Wenrui Hao, Tina Hernandez-Boussard, Pamela R. Jackson, Marieke Kuijjer, Adrian Lee, Paul Macklin, Subha Madhavan, Matthew D. Mccoy, Navid Mohammad Mirzaei, Talayeh Razzaghi, Heber L. Rocha, Leili Shahriyari, Ilya Shmulevich, Daniel G. Stover, Yi Sun, Tanveer Syeda-Mahmood, Jinhua Wang, Qi Wang, Ioannis Zervantonakis
Mathematics and Statistics Department Faculty Publication Series
We are rapidly approaching a future in which cancer patient digital twins will reach their potential to predict cancer prevention, diagnosis, and treatment in individual patients. This will be realized based on advances in high performance computing, computational modeling, and an expanding repertoire of observational data across multiple scales and modalities. In 2020, the US National Cancer Institute, and the US Department of Energy, through a trans-disciplinary research community at the intersection of advanced computing and cancer research, initiated team science collaborative projects to explore the development and implementation of predictive Cancer Patient Digital Twins. Several diverse pilot projects were …
Modelling Of Spatial Infection Spread Through Heterogeneous Population: From Lattice To Partial Differential Equation Models, Arvin Vaziry, T. Kolokolnikov, P. G. Kevrekidis
Modelling Of Spatial Infection Spread Through Heterogeneous Population: From Lattice To Partial Differential Equation Models, Arvin Vaziry, T. Kolokolnikov, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We present a simple model for the spread of an infection that incorporates spatial variability in population density. Starting from first-principle considerations, we explore how a novel partial differential equation with state-dependent diffusion can be obtained. This model exhibits higher infection rates in the areas of higher population density—a feature that we argue to be consistent with epidemiological observations. The model also exhibits an infection wave, the speed of which varies with population density. In addition, we demonstrate the possibility that an infection can ‘jump’ (i.e. tunnel) across areas of low population density towards areas of high population density. We …
Formation And Quench Of Homonuclear And Heteronuclear Quantum Droplets In One Dimension, Simeon I. Mistakadis, Mithun Thudiyangal, Panayotis Kevrekidis, H. R. Sadeghpour, Peter Schmelcher
Formation And Quench Of Homonuclear And Heteronuclear Quantum Droplets In One Dimension, Simeon I. Mistakadis, Mithun Thudiyangal, Panayotis Kevrekidis, H. R. Sadeghpour, Peter Schmelcher
Mathematics and Statistics Department Faculty Publication Series
We study the impact of beyond Lee-Huang-Yang (LHY) physics, especially due to intercomponent correlations, in the ground state and the quench dynamics of one-dimensional quantum droplets with an ab initio nonperturbative approach. It is found that the droplet Gaussian-shaped configuration arising for intercomponent attractive couplings becomes narrower for stronger intracomponent repulsion and transits towards a flat-top structure either for larger particle numbers or weaker intercomponent attraction. Additionally, a harmonic trap prevents the flat-top formation. At the balance point where mean-field interactions cancel out, we show that a correlation hole is present in the few-particle limit of LHY fluids as well …
Phase Diagram, Stability And Magnetic Properties Of Nonlinear Excitations In Spinor Bose–Einstein Condensates, G. C. Katsimiga, S. I. Mistakidis, P. Schmelcher, P. G. Kevrekidis
Phase Diagram, Stability And Magnetic Properties Of Nonlinear Excitations In Spinor Bose–Einstein Condensates, G. C. Katsimiga, S. I. Mistakidis, P. Schmelcher, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We present the phase diagram, the underlying stability and magnetic properties as well as the dynamics of nonlinear solitary wave excitations arising in the distinct phases of a harmonically confined spinor F = 1 Bose-Einstein condensate. Particularly, it is found that nonlinear excitations in the form of dark-dark-bright solitons exist in the antiferromagnetic and in the easy-axis phase of a spinor gas, being generally unstable in the former while possessing stability intervals in the latter phase. Dark-bright-bright solitons can be realized in the polar and the easy-plane phases as unstable and stable configurations respectively; the latter phase can also feature …
Refinements And Symmetries Of The Morris Identity For Volumes Of Flow Polytopes, Alejandro H. Borrero, William Shi
Refinements And Symmetries Of The Morris Identity For Volumes Of Flow Polytopes, Alejandro H. Borrero, William Shi
Mathematics and Statistics Department Faculty Publication Series
Flow polytopes are an important class of polytopes in combinatorics whose lattice points and volumes have interesting properties and relations. The Chan–Robbins–Yuen (CRY) polytope is a flow polytope with normalized volume equal to the product of consecutive Catalan numbers. Zeilberger proved this by evaluating the Morris constant term identity, but no combinatorial proof is known. There is a refinement of this formula that splits the largest Catalan number into Narayana numbers, which Mészáros gave an interpretation as the volume of a collection of flow polytopes. We introduce a new refinement of the Morris identity with combinatorial interpretations both in terms …
Investigating Optimal Chemotherapy Options For Osteosarcoma Patients Through A Mathematical Model, Trang M. Le, Sumeyye Su, Leili Shahriyari
Investigating Optimal Chemotherapy Options For Osteosarcoma Patients Through A Mathematical Model, Trang M. Le, Sumeyye Su, Leili Shahriyari
Mathematics and Statistics Department Faculty Publication Series
Since all tumors are unique, they may respond differently to the same treatments. Therefore, it is necessary to study their characteristics individually to find their best treatment options. We built a mathematical model for the interactions between the most common chemotherapy drugs and the osteosarcoma microenvironments of three clusters of tumors with unique immune profiles. We then investigated the effects of chemotherapy with different treatment regimens and various treatment start times on the behaviors of immune and cancer cells in each cluster. Saliently, we suggest the optimal drug dosages for the tumors in each cluster. The results show that abundances …
Easing Covid-19 Lockdown Measures While Protecting The Older Restricts The Deaths To The Level Of The Full Lockdown, A. S. Fokas, J. Cuevas-Maraver, P. G. Kevrekidis
Easing Covid-19 Lockdown Measures While Protecting The Older Restricts The Deaths To The Level Of The Full Lockdown, A. S. Fokas, J. Cuevas-Maraver, P. G. Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
Guided by a rigorous mathematical result, we have earlier introduced a numerical algorithm, which using as input the cumulative number of deaths caused by COVID-19, can estimate the effect of easing of the lockdown conditions. Applying this algorithm to data from Greece, we extend it to the case of two subpopulations, namely, those consisting of individuals below and above 40 years of age. After supplementing the Greek data for deaths with the data for the number of individuals reported to be infected by SARS-CoV-2, we estimated the effect on deaths and infections in the case that the easing of the …