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Articles 31 - 60 of 288
Full-Text Articles in Mathematics
On A Prior Based On The Wasserstein Information Matrix, Wuchen Li, F. J. Rubio
On A Prior Based On The Wasserstein Information Matrix, Wuchen Li, F. J. Rubio
Faculty Publications
We introduce a prior for the parameters of univariate continuous distributions, based on the Wasserstein information matrix, which is invariant under reparameterisations. We discuss the links between the proposed prior with information geometry. We present sufficient conditions for the propriety of the posterior distribution for general classes of models. We present a simulation study that shows that the induced posteriors have good frequentist properties.
Innovation Transition Success: Practice Doesn't Make Perfect, Kaitlyn Ryan, Amy M. Cox, Ethan Blake, Clay Koschnick, Alfred E. Thal Jr.
Innovation Transition Success: Practice Doesn't Make Perfect, Kaitlyn Ryan, Amy M. Cox, Ethan Blake, Clay Koschnick, Alfred E. Thal Jr.
Faculty Publications
The authors of this research examine and evaluate organizational factors associated with commercialization under the Air Force Small Business Innovation Research (SBIR) program. Their objective is to improve return on investment. The data set used was the SBIR Phase II program data set, which contains information on 433 SBIR topics with closed contracts reported during Department of Defense (DoD) fiscal years (FYs) 2015 to 2018. Each data point contained characteristics of the topic, including commercialization. Military capability or topic areas were hypothesized to have varying commercialization rates. Incumbency was theorized to be a characteristic of successful programs, while increased company …
Applications Of The Harary-Sachs Theorem For Hypergraphs, Gregory J. Clark, Joshua N. Cooper
Applications Of The Harary-Sachs Theorem For Hypergraphs, Gregory J. Clark, Joshua N. Cooper
Faculty Publications
The Harary-Sachs theorem for k-uniform hypergraphs equates the codegree-d coefficient of the adjacency characteristic polynomial of a uniform hypergraph with a weighted sum of subgraph counts over certain multi-hypergraphs with d edges. We begin by showing that the classical Harary-Sachs theorem for graphs is indeed a special case of this general theorem. To this end we apply the generalized Harary-Sachs theorem to the leading coefficients of the characteristic polynomial of various hypergraphs. In particular, we provide explicit and asymptotic formulas for the contribution of the k-uniform simplex to the codegree-d coefficient. Moreover, we provide an explicit formula for the leading …
Solving Inverse Conductivity Problems In Doubly Connected Domains By The Homogenization Functions Of Two Parameters, Jun Lu, Lianpeng Shi, Chein-Shan Liu, C.S. Chen
Solving Inverse Conductivity Problems In Doubly Connected Domains By The Homogenization Functions Of Two Parameters, Jun Lu, Lianpeng Shi, Chein-Shan Liu, C.S. Chen
Faculty Publications
In the paper, we make the first attempt to derive a family of two-parameter homogenization functions in the doubly connected domain, which is then applied as the bases of trial solutions for the inverse conductivity problems. The expansion coefficients are obtained by imposing an extra boundary condition on the inner boundary, which results in a linear system for the interpolation of the solution in a weighted Sobolev space. Then, we retrieve the spatial- or temperature-dependent conductivity function by solving a linear system, which is obtained from the collocation method applied to the nonlinear elliptic equation after inserting the solution. Although …
On Uniqueness And Stability For The Boltzmann-Enskog Equation, Martin Friesen, Barbara Ruediger, Padmanabhan Subdar
On Uniqueness And Stability For The Boltzmann-Enskog Equation, Martin Friesen, Barbara Ruediger, Padmanabhan Subdar
Faculty Publications
The time-evolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the Boltzmann-Enskog equation. Based on a McKean-Vlasov equation with jumps, the associated stochastic process was recently constructed by modified Picard iterations with the mean-field interactions, and more generally, by a system of interacting particles. By the introduction of a shifted distance that exactly compensates for the free transport term that accrues in the spatially inhomogeneous setting, we prove in this work an inequality on the Wasserstein distance for any two measure-valued solutions to the Boltzmann-Enskog equation. As a …
State Estimation—The Role Of Reduced Models, Albert Cohen, Wolfgang Dahmen, Ron Devore
State Estimation—The Role Of Reduced Models, Albert Cohen, Wolfgang Dahmen, Ron Devore
Faculty Publications
The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations and (ii) data provided by measurement devices or sensors. The amount of sensors is typically limited and data acquisition may be expensive and in some cases even harmful. This article reviews some recent developments for this “small-data” scenario where inversion is strongly aggravated by the typically large parametric dimensionality. The proposed concepts may be viewed as exploring alternatives to Bayesian inversion in favor of more deterministic accuracy quantification related …
A Bayesian Phase I/Ii Biomarker-Based Design For Identifying Subgroup-Specific Optimal Dose For Immunotherapy, Beibei Guo, Yong Zang
A Bayesian Phase I/Ii Biomarker-Based Design For Identifying Subgroup-Specific Optimal Dose For Immunotherapy, Beibei Guo, Yong Zang
Faculty Publications
Immunotherapy is an innovative treatment that enlists the patient's immune system to battle tumors. The optimal dose for treating patients with an immunotherapeutic agent may differ according to their biomarker status. In this article, we propose a biomarker-based phase I/II dose-finding design for identifying subgroup-specific optimal dose for immunotherapy (BSOI) that jointly models the immune response, toxicity, and efficacy outcomes. We propose parsimonious yet flexible models to borrow information across different types of outcomes and subgroups. We quantify the desirability of the dose using a utility function and adopt a two-stage dose-finding algorithm to find the optimal dose for each …
Strict Lyapunov Functions And Feedback Controls For Sir Models With Quarantine And Vaccination, Hiroshi Ito, Michael Malisoff, Frederic Mazenc
Strict Lyapunov Functions And Feedback Controls For Sir Models With Quarantine And Vaccination, Hiroshi Ito, Michael Malisoff, Frederic Mazenc
Faculty Publications
We provide a new global strict Lyapunov function construction for a susceptible, infected, and recovered (or SIR) disease dynamics that includes quarantine of infected individuals and mass vaccination. We use the Lyapunov function to design feedback controls to asymptotically stabilize a desired endemic equilibrium, and to prove input-to-state stability for the dynamics with a suitable restriction on the disturbances. Our simulations illustrate the potential of our feedback controls to reduce peak levels of infected individuals.
A New Matroid Lift Construction And An Application To Group-Labeled Graphs, Zach Walsh
A New Matroid Lift Construction And An Application To Group-Labeled Graphs, Zach Walsh
Faculty Publications
A well-known result of Brylawski constructs an elementary lift of a matroid M from a linear class of circuits of M. We generalize this result by constructing a rank-k lift of M from a rank-k matroid on the set of circuits of M. We conjecture that every lift of M arises via this construction. We then apply this result to group-labeled graphs, generalizing a construction of Zaslavsky. Given a graph G with edges labeled by a group, Zaslavsky's lift matroid K is an elementary lift of the graphic matroid M(G) that respects the group-labeling; specifically, the cycles of G that …
Ca Special Issue On Neural Network Approximation, Wolfgang Dahmen, Ronald A. Devore, Philipp Grohs
Ca Special Issue On Neural Network Approximation, Wolfgang Dahmen, Ronald A. Devore, Philipp Grohs
Faculty Publications
No abstract provided.
Maximal Spacelike Surfaces In A Certain Homogeneous Lorentzian 3-Manifold, Sungwook Lee
Maximal Spacelike Surfaces In A Certain Homogeneous Lorentzian 3-Manifold, Sungwook Lee
Faculty Publications
The 2-parameter family of certain homogeneous Lorentzian 3-manifolds, which includes Minkowski 3-space and anti-de Sitter 3-space, is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a solvable Lie group structure with left invariant metric. A generalized integral representation formula for maximal spacelike surfaces in the homogeneous Lorentzian 3-manifolds is obtained. The normal Gauß map of maximal spacelike surfaces and its harmonicity are discussed.
Node Generation For Rbf-Fd Methods By Qr Factorization, Tony Liu, Rodrigo B. Platte
Node Generation For Rbf-Fd Methods By Qr Factorization, Tony Liu, Rodrigo B. Platte
Faculty Publications
Polyharmonic spline (PHS) radial basis functions (RBFs) have been used in conjunction with polynomials to create RBF finite-difference (RBF-FD) methods. In 2D, these methods are usually implemented with Cartesian nodes, hexagonal nodes, or most commonly, quasi-uniformly distributed nodes generated through fast algorithms. We explore novel strategies for computing the placement of sampling points for RBF-FD methods in both 1D and 2D while investigating the benefits of using these points. The optimality of sampling points is determined by a novel piecewise-defined Lebesgue constant. Points are then sampled by modifying a simple, robust, column-pivoting QR algorithm previously implemented to find sets of …
Estimating Turbulence Distribution Over A Heterogeneous Path Using Time‐Lapse Imagery From Dual Cameras, Benjamin Wilson, Santasri Bose-Pillai, Jack E. Mccrae, Kevin J. Keefer, Steven T. Fiorino
Estimating Turbulence Distribution Over A Heterogeneous Path Using Time‐Lapse Imagery From Dual Cameras, Benjamin Wilson, Santasri Bose-Pillai, Jack E. Mccrae, Kevin J. Keefer, Steven T. Fiorino
Faculty Publications
Knowledge of turbulence distribution along an experimental path can help in effective turbulence compensation and mitigation. Although scintillometers are traditionally used to measure the strength of turbulence, they provide a path-integrated measurement and have limited operational ranges. A technique to profile turbulence using time-lapse imagery of a distant target from spatially separated cameras is presented here. The method uses the turbulence induced differential motion between pairs of point features on a target, sensed at a single camera and between cameras to extract turbulence distribution along the path. The method is successfully demonstrated on a 511 m almost horizontal path going …
2-Adic Valuations Of Quadratic Sequences, Will Boultinghouse, Jane H. Long, Olena Kozhushkina, Justin Trulen
2-Adic Valuations Of Quadratic Sequences, Will Boultinghouse, Jane H. Long, Olena Kozhushkina, Justin Trulen
Faculty Publications
We determine properties of the 2-adic valuation sequences for general quadratic polynomials with integer coefficients directly from the coefficients. These properties include boundedness or unboundedness, periodicity, and valuations at terminating nodes. We completely describe the periodic sequences in the bounded case. Throughout, we frame results in terms of trees and sequences.
Defect Detection In Atomic Resolution Transmission Electron Microscopy Images Using Machine Learning, Philip Cho, Aihua W. Wood, Krishnamurthy Mahalingam, Kurt Eyink
Defect Detection In Atomic Resolution Transmission Electron Microscopy Images Using Machine Learning, Philip Cho, Aihua W. Wood, Krishnamurthy Mahalingam, Kurt Eyink
Faculty Publications
Point defects play a fundamental role in the discovery of new materials due to their strong influence on material properties and behavior. At present, imaging techniques based on transmission electron microscopy (TEM) are widely employed for characterizing point defects in materials. However, current methods for defect detection predominantly involve visual inspection of TEM images, which is laborious and poses difficulties in materials where defect related contrast is weak or ambiguous. Recent efforts to develop machine learning methods for the detection of point defects in TEM images have focused on supervised methods that require labeled training data that is generated via …
Meta-Heuristic Optimization Methods For Quaternion-Valued Neural Networks, Jeremiah Bill, Lance E. Champagne, Bruce Cox, Trevor J. Bihl
Meta-Heuristic Optimization Methods For Quaternion-Valued Neural Networks, Jeremiah Bill, Lance E. Champagne, Bruce Cox, Trevor J. Bihl
Faculty Publications
In recent years, real-valued neural networks have demonstrated promising, and often striking, results across a broad range of domains. This has driven a surge of applications utilizing high-dimensional datasets. While many techniques exist to alleviate issues of high-dimensionality, they all induce a cost in terms of network size or computational runtime. This work examines the use of quaternions, a form of hypercomplex numbers, in neural networks. The constructed networks demonstrate the ability of quaternions to encode high-dimensional data in an efficient neural network structure, showing that hypercomplex neural networks reduce the number of total trainable parameters compared to their real-valued …
Quantum Statistical Learning Via Quantum Wasserstein Natural Gradient, Simon Becker, Wuchen Li
Quantum Statistical Learning Via Quantum Wasserstein Natural Gradient, Simon Becker, Wuchen Li
Faculty Publications
In this article, we introduce a new approach towards the statistical learning problem argminρ(θ )∈Pθ W2 Q(ρ*, ρ(θ )) to approximate a target quantum state ρ* by a set of parametrized quantum states ρ(θ ) in a quantum L2-Wasserstein metric. We solve this estimation problem by considering Wasserstein natural gradient flows for density operators on finite-dimensional C∗ algebras. For continuous parametric models of density operators, we pull back the quantum Wasserstein metric such that the parameter space becomes a Riemannian manifold with quantum Wasserstein information matrix. Using a quantum analogue …
Commuting Perturbations Of Operator Equations, Xue Xu, Jiu Ding
Commuting Perturbations Of Operator Equations, Xue Xu, Jiu Ding
Faculty Publications
Let X be a Banach space and let T: X →X be a bounded linear operator with closed range. We study a class of commuting perturbations of the corresponding operator equation, using the concept of the spectral radius of a bounded linear operator. Our results extend the classic perturbation theorem for invertible operators and its generalization for arbitrary operators under the commutability assumption.
Spectral Extremal Results For Hypergraphs, Yuan Hou, An Chang, Joshua Cooper
Spectral Extremal Results For Hypergraphs, Yuan Hou, An Chang, Joshua Cooper
Faculty Publications
Let F be a graph. A hypergraph is called Berge F if it can be obtained by replacing each edge in F by a hyperedge containing it. Given a family of graphs F, we say that a hypergraph H is Berge F-free if for every F ∈ F, the hypergraph H does not contain a Berge F as a subhypergraph. In this paper we investigate on the connections between spectral radius of the adjacency tensor and structural properties of a linear hypergraph. In particular, we obtain a spectral version of Turán-type problems over linear k-uniform hypergraphs by using spectral methods.
Acceleration Of Boltzmann Collision Integral Calculation Using Machine Learning, Ian Holloway, Aihua W. Wood, Alexander Alekseenko
Acceleration Of Boltzmann Collision Integral Calculation Using Machine Learning, Ian Holloway, Aihua W. Wood, Alexander Alekseenko
Faculty Publications
The Boltzmann equation is essential to the accurate modeling of rarefied gases. Unfortunately, traditional numerical solvers for this equation are too computationally expensive for many practical applications. With modern interest in hypersonic flight and plasma flows, to which the Boltzmann equation is relevant, there would be immediate value in an efficient simulation method. The collision integral component of the equation is the main contributor of the large complexity. A plethora of new mathematical and numerical approaches have been proposed in an effort to reduce the computational cost of solving the Boltzmann collision integral, yet it still remains prohibitively expensive for …
A Radial Basis Function Finite Difference Scheme For The Benjamin–Ono Equation, Benjamin F. Akers, Tony Liu, Jonah A. Reeger
A Radial Basis Function Finite Difference Scheme For The Benjamin–Ono Equation, Benjamin F. Akers, Tony Liu, Jonah A. Reeger
Faculty Publications
A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on ℝ, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed.
Legendre G-Array Pairs And The Theoretical Unification Of Several G-Array Families, K. T. Arasu, Dursun A. Bulutoglu, J. R. Hollon
Legendre G-Array Pairs And The Theoretical Unification Of Several G-Array Families, K. T. Arasu, Dursun A. Bulutoglu, J. R. Hollon
Faculty Publications
We investigate how Legendre G-array pairs are related to several different perfect binary G-array families. In particular we study the relations between Legendre G-array pairs, Sidelnikov-Lempel-Cohn-Eastman ℤq−1-arrays, Yamada-Pott G-array pairs, Ding-Helleseth-Martinsen ℤ2×ℤmp-arrays, Yamada ℤ(q−1)/2-arrays, Szekeres ℤmp-array pairs, Paley ℤmp-array pairs, and Baumert ℤm1p1×ℤm2p2-array pairs. Our work also solves one of the two open problems posed in Ding~[J. Combin. Des. 16 (2008), 164-171]. Moreover, we provide several computer search based existence and non-existence results regarding Legendre ℤn-array pairs. …
A Fictitious Points One-Step Mps-Mfs Technique, Xiaomin Zhu, Fangfang Dou, Andreas Karageorghis, C. S. Chen
A Fictitious Points One-Step Mps-Mfs Technique, Xiaomin Zhu, Fangfang Dou, Andreas Karageorghis, C. S. Chen
Faculty Publications
© 2020 The method of fundamental solutions (MFS) is a simple and efficient numerical technique for solving certain homogenous partial differential equations (PDEs) which can be extended to solving inhomogeneous equations through the method of particular solutions (MPS). In this paper, radial basis functions (RBFs) are considered as the basis functions for the construction of a particular solution of the inhomogeneous equation. A hybrid method coupling these two methods using both fundamental solutions and RBFs as basis functions has been effective for solving a large class of PDEs. In this paper, we propose an improved fictitious points method in which …
Small Gaps Between Almost Primes, The Parity Problem, And Some Conjectures Of Erdős On Consecutive Integers Ii, Daniel A. Goldston, Sidney W. Graham, Apoorva Panidapu, Janos Pintz, Jordan Schettler, Cem Y. Yıldırım
Small Gaps Between Almost Primes, The Parity Problem, And Some Conjectures Of Erdős On Consecutive Integers Ii, Daniel A. Goldston, Sidney W. Graham, Apoorva Panidapu, Janos Pintz, Jordan Schettler, Cem Y. Yıldırım
Faculty Publications
We show that for any positive integer n, there is some fixed A such that d(x) = d(x +n) = A infinitely often where d(x) denotes the number of divisors of x. In fact, we establish the stronger result that both x and x +n have the same fixed exponent pattern for infinitely many x. Here the exponent pattern of an integer x > 1is the multiset of nonzero exponents which appear in the prime factorization of x.
Shake Slice And Shake Concordant Links, Anthony Bosman
Shake Slice And Shake Concordant Links, Anthony Bosman
Faculty Publications
© 2020 World Scientific Publishing Company. We can construct a 4-manifold by attaching 2-handles to a 4-ball with framing r along the components of a link in the boundary of the 4-ball. We define a link as r-shake slice if there exists embedded spheres that represent the generators of the second homology of the 4-manifold. This naturally extends r-shake slice, a generalization of slice that has previously only been studied for knots, to links of more than one component. We also define a relative notion of shaker-concordance for links and versions with stricter conditions on the embedded spheres that we …
Legendrian Dga Representations And The Colored Kauffman Polynomial, Justin Murray, Dan Rutherford
Legendrian Dga Representations And The Colored Kauffman Polynomial, Justin Murray, Dan Rutherford
Faculty Publications
For any Legendrian knot K in standard contact R-3 we relate counts of ungraded (1-graded) representations of the Legendrian contact homology DG-algebra (A(K), partial derivative) with the n-colored Kauffman polynomial. To do this, we introduce an ungraded n-colored ru-ling polynomial, R-n,K(1)(q), as a linear combination of reduced ruling polynomials of positive permutation braids and show that (i) R-n,K(1)(q) arises as a specialization F-n,F-K(a, q)vertical bar(a-1) = 0 of the n-colored Kauffman polynomial and (ii) when q is a power of two R-n,K(1)(q) agrees with the total ungraded representation number, Rep(1) (K, F-q(n)), which is a normalized count of n-dimensional representations …
Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Matthew C. Fickus, Courtney A. Schmitt
Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Matthew C. Fickus, Courtney A. Schmitt
Faculty Publications
An equiangular tight frame (ETF) is a sequence of unit-norm vectors in a Euclidean space whose coherence achieves equality in the Welch bound, and thus yields an optimal packing in a projective space. A regular simplex is a simple type of ETF in which the number of vectors is one more than the dimension of the underlying space. More sophisticated examples include harmonic ETFs which equate to difference sets in finite abelian groups. Recently, it was shown that some harmonic ETFs are comprised of regular simplices. In this paper, we continue the investigation into these special harmonic ETFs. We begin …
Cell Velocity Is Asymptotically Independent Of Force: A Differential Equation Model With Random Switching., J. C. Dallon, Emily J. Evans, Christopher P. Grant, William V. Smith
Cell Velocity Is Asymptotically Independent Of Force: A Differential Equation Model With Random Switching., J. C. Dallon, Emily J. Evans, Christopher P. Grant, William V. Smith
Faculty Publications
Numerical simulations suggest that average velocity of a biological cell depends largely on attachment dynamics and less on the forces exerted by the cell. We determine the relationship between two models of cell motion, one based on finite spring constants modeling attachment properties (a randomly switched differential equation) and a limiting case (a centroid model-a generalized random walk) where spring constants are infinite. We prove the main result of this paper, the Expected Velocity Relationship theorem. This result shows that the expected value of the difference between cell locations in the differential equation model at the initial time and at …
A Comparison Of The Trojan Y Chromosome Strategy To Harvesting Models For Eradication Of Non-Native Species, Jingjing Lyu, Pamela J. Schofield, Kristen M. Reaver, Matthew Beauregard, Rana D. Parshad
A Comparison Of The Trojan Y Chromosome Strategy To Harvesting Models For Eradication Of Non-Native Species, Jingjing Lyu, Pamela J. Schofield, Kristen M. Reaver, Matthew Beauregard, Rana D. Parshad
Faculty Publications
The Trojan Y Chromosome Strategy (TYC) is a promising eradication method for biological control of non-native species. The strategy works by manipulating the sex ratio of a population through the introduction of supermales that guarantee male offspring. In the current manuscript, we compare the TYC method with a pure harvesting strategy. We also analyze a hybrid harvesting model that mirrors the TYC strategy. The dynamic analysis leads to results on stability of solutions and bifurcations of the model. Several conclusions about the different strategies are established via optimal control methods. In particular, the results affirm that either a pure harvesting …
Periodic Traveling Interfacial Hydroelastic Waves With Or Without Mass Ii: Multiple Bifurcations And Ripples, Benjamin F. Akers, David M. Ambrose, David W. Sulon
Periodic Traveling Interfacial Hydroelastic Waves With Or Without Mass Ii: Multiple Bifurcations And Ripples, Benjamin F. Akers, David M. Ambrose, David W. Sulon
Faculty Publications
In a prior work, the authors proved a global bifurcation theorem for spatially periodic interfacial hydroelastic traveling waves on infinite depth, and computed such traveling waves. The formulation of the traveling wave problem used both analytically and numerically allows for waves with multi-valued height. The global bifurcation theorem required a one-dimensional kernel in the linearization of the relevant mapping, but for some parameter values, the kernel is instead two-dimensional. In the present work, we study these cases with two-dimensional kernels, which occur in resonant and non-resonant variants. We apply an implicit function theorem argument to prove existence of traveling waves …