Digital Commons Network^™

Nonparametric Collective Spectral Density Estimation With An Application To Clustering The Brain Signals, Mehdi Maadooliat, Ying Sun, Tianbo Chen

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log‐SDF can be represented using a common set of basis functions. The basis shared by the collection of the log‐SDFs is estimated as a low‐dimensional manifold of a large space spanned by a prespecified rich basis. A collective estimation approach pools information and borrows strength across the SDFs to achieve better estimation efficiency. Moreover, each estimated spectral density has a concise representation using the …

Lozenge Tilings Of A Halved Hexagon With An Array Of Triangles Removed From The Boundary, Part Ii, Tri Lai

Department of Mathematics: Faculty Publications

Proctor's work on staircase plane partitions yields an exact enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi later ex- tended this tiling enumeration to a halved hexagon with a triangle cut o from the boundary. In his previous paper, the author proved a common generalization of Proctor's and Rohatgi's results by enumerating lozenge tilings of a halved hexagon in the case an array of an arbitrary number of triangles has been removed from a non-staircase side. In this paper we consider the other case when the array of tri- angles has been removed from the …

Power In Pairs: Assessing The Statistical Value Of Paired Samples In Tests For Differential Expression, John R. Stevens, Jennifer S. Herrick, Roger K. Wolff, Martha L. Slattery

Mathematics and Statistics Faculty Publications

Background: When genomics researchers design a high-throughput study to test for differential expression, some biological systems and research questions provide opportunities to use paired samples from subjects, and researchers can plan for a certain proportion of subjects to have paired samples. We consider the effect of this paired samples proportion on the statistical power of the study, using characteristics of both count (RNA-Seq) and continuous (microarray) expression data from a colorectal cancer study.

Results: We demonstrate that a higher proportion of subjects with paired samples yields higher statistical power, for various total numbers of samples, and for various strengths of …

Logarithmic Hennings Invariants For Restricted Quantum Sl (2), Anna Beliakova, Christian Blanchet, Alexandra Tebbs

Mathematics and Statistics Faculty Publications

We construct a Hennings-type logarithmic invariant for restricted quantum sl (2) at a 2p^th root of unity. This quantum group U is not quasitriangular and hence not ribbon, but factorizable. The invariant is defined for a pair: a 3–manifold M and a colored link L inside M. The link L is split into two parts colored by central elements and by trace classes, or elements in the 0^th Hochschild homology of U, respectively. The two main ingredients of our construction are the universal invariant of a string link with values in tensor powers of U, and the modified …

Equilibrium Analysis For An Epidemic Model With A Reservoir For Infection, Istvan Lauko, Gabriella Pinter, Rachel Elizabeth Tewinkel

Mathematical Sciences Student Articles

We consider a system of non-linear differential equations describing the spread of an epidemic in two interacting populations. The model assumes that the epidemic spreads within the first population, which in turn acts as a reservoir of infection for the second population. Weexplore the conditions under which the epidemic is endemic in both populations and discuss the global asymptotic stability of the endemic equilibrium using a Lyapunov function and results established for asymptotically autonomous systems. We discuss monkeypox as an example of an emerging disease that can be modelled in this way and present some numerical results representing the model …

On Nonnegatively Curved Hypersurfaces In Hyperbolic Space, Vincent Bonini, Shiguang Ma, Jie Qing

Mathematics

In this paper we prove a conjecture of Alexander and Currier that states, except for covering maps of equidistant surfaces in hyperbolic 3-space, a complete, nonnegatively curved immersed hypersurface in hyperbolic space is necessarily properly embedded.

Larval Food Limitation In A Speyeria Butterfly (Nymphalidae): How Many Butterflies Can Be Supported?, Ryan I. Hill, Cassidi E. Rush, John Mayberry

College of the Pacific Faculty Articles

For herbivorous insects the importance of larval food plants is obvious, yet the role of host abundance and density in conservation are relatively understudied. Populations of Speyeria butterflies across North America have declined and Speyeria adiaste is an imperiled species endemic to the southern California Coast Ranges. In this paper, we study the link between the food plant Viola purpurea quercetorum and abundance of its herbivore Speyeria adiaste clemencei to better understand the butterfly’s decline and aid in restoration of this and other Speyeria species. To assess the degree to which the larval food plant limits adult abundance of S. …

Almost Periodic Functions In Quantum Calculus, Martin Bohner, Jaqueline Godoy Mesquita

Mathematics and Statistics Faculty Research & Creative Works

In this article, we introduce the concepts of Bochner and Bohr almost periodic functions in quantum calculus and show that both concepts are equivalent. Also, we present a correspondence between almost periodic functions defined in quantum calculus and N₀, proving several important properties for this class of functions. We investigate the existence of almost periodic solutions of linear and nonlinear q-difference equations. Finally, we provide some examples of almost periodic functions in quantum calculus.

Some New Nonlinear Second-Order Boundary Value Problems On An Arbitrary Domain, Ahmed Alsaedi, Mona Alsulami, Ravi P. Agarwal, Bashir Ahmad

Mathematics and System Engineering Faculty Publications

In this paper, we develop the existence theory for nonlinear second-order ordinary differential equations equipped with new kinds of nonlocal non-separated type integral multi-point boundary conditions on an arbitrary domain. Existence results are proved with the aid of fixed point theorems due to Schaefer, Krasnoselskii, and Leray–Schauder, while the uniqueness of solutions for the given problem is established by means of contraction mapping principle. Examples are constructed for the illustration of the obtained results. Ulam-stability is also discussed for the given problem. A variant of the problem involving different boundary data is also discussed. Finally, we introduce an associated boundary …

The Evolution Of Psychological Altruism, Gualtiero Piccinini, Armin Schulz

Philosophy Faculty Works

We argue that there are two different kinds of altruistic motivation: classical psychological altruism, which generates ultimate desires to help other organisms at least partly for those organisms’ sake, and nonclassical psychological altruism, which generates ultimate desires to help other organisms for the sake of the organism providing the help. We then argue that classical psychological altruism is adaptive if the desire to help others is intergenerationally reliable and, thus, need not be learned. Nonclassical psychological altruism is adaptive when the desire to help others is adaptively learnable. This theory opens new avenues for the interdisciplinary study of psychological altruism.

Conjugacy Of Embeddings Of Alternating Groups In Exceptional Lie Groups, Darrin D. Frey, Alex Ryba

Science and Mathematics Faculty Publications

We discuss conjugacy classes of embeddings of Alternating groups in Exceptional Lie groups. We settle the count of classes of embeddings in E8 of a subgroup Alt10 and its double cover. This involves computation and the reduction of the problems to relative eigenvector problems. We update previously published tables of embeddings. We comment on the improvements present in our table and on the remaining unsettled conjugacy questions.

Dispersion Analysis Of Hdg Methods, Jay Gopalakrishnan, Manuel Solano, Felipe Vargas

Mathematics and Statistics Faculty Publications and Presentations

This work presents a dispersion analysis of the Hybrid Discontinuous Galerkin (HDG) method. Considering the Helmholtz system, we quantify the discrepancies between the exact and discrete wavenumbers. In particular, we obtain an analytic expansion for the wavenumber error for the lowest order Single Face HDG (SFH) method. The expansion shows that the SFH method exhibits convergence rates of the wavenumber errors comparable to that of the mixed hybrid Raviart–Thomas method. In addition, we observe the same behavior for the higher order cases in numerical experiments.

A Plausible Resolution To Hilbert’S Failed Attempt To Unify Gravitation & Electromagnetism, Florentin Smarandache, Victor Christianto, Robert Neil Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we explore the reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed and outline a plausible resolution of this problem. The latter is based on Gödel’s incompleteness theorem and Newton’s aether stream model.

Markov Chains And Generalized Wavelet Multiresolutions, Myung-Sin Song, Palle Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We develop some new results for a general class of transfer operators, as they are used in a construction of multi-resolutions. We then proceed to give explicit and concrete applications. We further discuss the need for such a constructive harmonic analysis/dynamical systems approach to fractals.

Vacuum Polarization For Varying Quantum Scalar Field Parameters In Schwarzschild–Anti–De Sitter Spacetime, Cormac Breen, Peter Taylor

Articles

Equipped with new powerful and efficient methods for computing quantum expectation values in static-spherically symmetric spacetimes in arbitrary dimensions, we perform an in-depth investigation of how the quantum vacuum polarization varies with the parameters in the theory. In particular, we compute and compare the vacuum polarization for a quantum scalar field in the Schwarzschild–anti–de Sitter black hole spacetime for a range of values of the field mass and field coupling constant as well as the black hole mass and number of spacetime dimensions. In addition, a new approximation for the vacuum polarization in asymptotically anti–de Sitter black hole spacetimes is …

Enhancing Value-Based Healthcare With Reconstructability Analysis: Predicting Cost Of Care In Total Hip Replacement, Cecily Corrine Froemke, Martin Zwick

Systems Science Faculty Publications and Presentations

Legislative reforms aimed at slowing growth of US healthcare costs are focused on achieving greater value per dollar. To increase value healthcare providers must not only provide high quality care, but deliver this care at a sustainable cost. Predicting risks that may lead to poor outcomes and higher costs enable providers to augment decision making for optimizing patient care and inform the risk stratification necessary in emerging reimbursement models. Healthcare delivery systems are looking at their high volume service lines and identifying variation in cost and outcomes in order to determine the patient factors that are driving this variation and …

Not So Many Non-Disjoint Translations, Andrzej Roslanowski, Vyacheslav V. Rykov

Mathematics Faculty Publications

We show that, consistently, there is a Borel set which has uncountably many pairwise very non-disjoint translations, but does not allow a perfect set of such translations.

An Introduction To Psychological Statistics, Garett C. Foster, David Lane, David Scott, Mikki Hebl, Rudy Guerra, Dan Osherson, Heidi Zimmer

Open Educational Resources Collection

This work has been superseded by Introduction to Statistics in the Psychological Sciences available from https://irl.umsl.edu/oer/25/.

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We are constantly bombarded by information, and finding a way to filter that information in an objective way is crucial to surviving this onslaught with your sanity intact. This is what statistics, and logic we use in it, enables us to do. Through the lens of statistics, we learn to find the signal hidden in the noise when it is there and to know when an apparent trend or pattern is really just randomness. The study of statistics involves math and relies …

How Hilbert’S Attempt To Unify Gravitation And Electromagnetism Failed Completely, And A Plausible Resolution, Victor Christianto, Florentin Smarandache, Robert N. Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

In the present paper, these authors argue on actual reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed completely. An outline of plausible resolution of this problem is given here, based on: a) Gödel’s incompleteness theorem, b) Newton’s aether stream model. And in another paper we will present our calculation of receding Moon from Earth based on such a matter creation hypothesis. More experiments and observations are called to verify this new hypothesis, albeit it is inspired from Newton’s theory himself.

Translation Theorems For The Fourier-Feynman Transform On The Product Function Space C2 A,B, [0,T], Seung Jun Chang, Jae Gil Choi, David Skoug

Department of Mathematics: Faculty Publications

In this article, we establish the Cameron{Martin translation theo- rems for the analytic Fourier{Feynman transform of functionals on the product function space C2 a;b[0; T]. The function space Ca;b[0; T] is induced by the gener- alized Brownian motion process associated with continuous functions a(t) and b(t) on the time interval [0; T]. The process used here is nonstationary in time and is subject to a drift a(t). To study our translation theorem, we introduce a Fresnel-type class Fa;b A1;A2 of functionals on C2 a;b[0; T], which is a generaliza- tion of the Kallianpur and Bromley{Fresnel class FA1;A2 . We then …

Developmental Parameters Of A Southern Mountain Pine Beetle (Coleoptera: Curculionidae) Population Reveal Potential Source Of Latitudinal Differences In Generation Time, Anne E. Mcmanis, James A. Powell, Barbara J. Bentz

Mathematics and Statistics Faculty Publications

Mountain pine beetle (Dendroctonus ponderosae, Hopkins) is a major disturbance agent in pine ecosystems of western North America. Adaptation to local climates has resulted in primarily univoltine generation time across a thermally diverse latitudinal gradient. We hypothesized that voltinism patterns have been shaped by selection for slower developmental rates in southern populations inhabiting warmer climates. To investigate traits responsible for latitudinal differences we measured lifestage-specific development of southern mountain pine beetle eggs, larvae and pupae across a range of temperatures. Developmental rate curves were fit using maximum posterior likelihood estimation with a Bayesian prior to improve fit stability. …

The Dpg-Star Method, Leszek Demkowicz, Jay Gopalakrishnan, Brendan Keith

Portland Institute for Computational Science Publications

This article introduces the DPG-star (from now on, denoted DPG*) finite element method. It is a method that is in some sense dual to the discontinuous Petrov– Galerkin (DPG) method. The DPG methodology can be viewed as a means to solve an overdetermined discretization of a boundary value problem. In the same vein, the DPG* methodology is a means to solve an underdetermined discretization. These two viewpoints are developed by embedding the same operator equation into two different saddle-point problems. The analyses of the two problems have many common elements. Comparison to othermethods in the literature round out the newly …

Efficient Blind Image Deblurring Using Nonparametric Regression And Local Pixel Clustering, Yicheng Kang, Partha Sarathi Mukherjee, Peihua Qiu

Mathematics Faculty Publications and Presentations

Blind image deblurring is a challenging ill-posed problem. It would have an infinite number of solutions even in cases when an observed image contains no noise. In reality, however, observed images almost always contain noise. The presence of noise would make the image deblurring problem even more challenging because the noise can cause numerical instability in many existing image deblurring procedures. In this paper, a novel blind image deblurring approach is proposed, which can remove both pointwise noise and spatial blur efficiently without imposing restrictive assumptions on either the point spread function (psf) or the true image. It even allows …

Why Early Galaxies Were Pickle-Shaped: A Geometric Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The vast majority of currently observed geometric shapes of celestial bodies can be explained by a simple symmetry idea: the initial distribution of matter is invariant with respect to shifts, rotations, and scaling, but this distribution is unstable, so we have spontaneous symmetry breaking. According to statistical physics, among all possible transitions, the most probable are the ones that retain the largest number of symmetries. This explains the currently observed shapes and -- on the qualitative level -- their relative frequency. According to this idea, the most probable first transition is into a planar (pancake) shape, then into …

Translating Discrete Estimates Into A Less Detailed Scale: An Optimal Approach, Thongchai Dumrongpokaphan, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we use estimates that experts make on a 0-to-n scale. For example, to estimate the quality of a lecturer, we ask each student to evaluate this quality by selecting an integer from 0 to n. Each such estimate may be subjective; so, to increase the estimates' reliability, it is desirable to combine several estimates of the corresponding quality. Sometimes, different estimators use slightly different scales: e.g., one estimator uses a scale from 0 to n+1, and another estimator uses a scale from 0 to n. In such situations, it is desirable to translate these estimates to …

Relativistic Effects Can Be Used To Achieve A Universal Square-Root (Or Even Faster) Computation Speedup, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we show that special relativity phenomenon can be used to reduce computation time of any algorithm from T to square root of T. For this purpose, we keep computers where they are, but the whole civilization starts moving around the computer -- at an increasing speed, reaching speeds close to the speed of light. A similar square-root speedup can be achieved if we place ourselves near a growing black hole. Combining the two schemes can lead to an even faster speedup: from time T to the 4-th order root of T.

Bhutan Landscape Anomaly: Possible Effect On Himalayan Economy (In View Of Optimal Description Of Elevation Profiles), Thach N. Nguyen, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

Economies of countries located in seismic zones are strongly effected by this seismicity. If we underestimate the seismic activity, then a reasonably routine earthquake can severely damage the existing structures and thus, lead to huge economic losses. On the other hand, if we overestimate the seismic activity, we waste a lot of resources on unnecessarily fortifying all the buildings -- and this too harms the economies. From this viewpoint, it is desirable to have estimations of regional seismic activities which are as accurate as possible. Current predictions are mostly based on the standard geophysical understanding of earthquakes as being largely …

Modeling Association In Microbial Communities With Clique Loginear Models, Adrian Dobra, Camilo Valdes, Dragana Ajdic, Bertrand S. Clarke, Jennifer Clarke

Department of Mathematics: Faculty Publications

There is a growing awareness of the important roles that microbial communities play in complex biological processes. Modern investigation of these often uses next generation sequencing of metagenomic samples to determine community composition. We propose a statistical technique based on clique loglinear models and Bayes model averaging to identify microbial components in a metagenomic sample at various taxonomic levels that have significant associations. We describe the model class, a stochastic search technique for model selection, and the calculation of estimates of posterior probabilities of interest. We demonstrate our approach using data from the Human Microbiome Project and from a study …

On The Origin Of Crystallinity: A Lower Bound For The Regularity Radius Of Delone Sets, Igor A. Baburin, Mikhail M. Bouniaev, Nikolay Dolbilin, Nikolay Yu. Erokhovets, Alexey Garber, Sergey V. Krivovichev, Egon Schulte

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The mathematical conditions for the origin of long-range order or crystallinity in ideal crystals are one of the very fundamental problems of modern crystallography. It is widely believed that the (global) regularity of crystals is a consequence of `local order', in particular the repetition of local fragments, but the exact mathematical theory of this phenomenon is poorly known. In particular, most mathematical models for quasicrystals, for example Penrose tiling, have repetitive local fragments, but are not (globally) regular. The universal abstract models of any atomic arrangements are Delone sets, which are uniformly distributed discrete point sets in Euclidean d space. …

Isar Autofocus Imaging Algorithm For Maneuvering Targets Based On Phase Retrieval And Gabor Wavelet Transform, Hongyin Shi, Ting Yang, Zhijun Qiao

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The imaging issue of a rotating maneuvering target with a large angle and a high translational speed has been a challenging problem in the area of inverse synthetic aperture radar (ISAR) autofocus imaging, in particular when the target has both radial and angular accelerations. In this paper, on the basis of the phase retrieval algorithm and the Gabor wavelet transform (GWT), we propose a new method for phase error correction. The approach first performs the range compression on ISAR raw data to obtain range profiles, and then carries out the GWT transform as the time-frequency analysis tool for the rotational …