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Articles 1 - 30 of 434
Full-Text Articles in Statistics and Probability
Revisiting Ulam Stability For Boundary Value Problems, Martin Bohner, Snezhana Hristova, Agnieszka B. Malinowska, Ewa Girejko
Revisiting Ulam Stability For Boundary Value Problems, Martin Bohner, Snezhana Hristova, Agnieszka B. Malinowska, Ewa Girejko
Mathematics and Statistics Faculty Research & Creative Works
The main goal of this paper is to apply Ulam stability theory to boundary value problems for dynamic equations, while addressing several common misconceptions found in the existing literature. We identify the key issues that arise when applying Ulam stability to such problems and propose three distinct approaches to overcome them. To enhance clarity and accessibility, we begin with nonlinear ordinary differential equations and subsequently extend the analysis to nonlinear dynamic equations on time scales. Since a time scale is defined as any nonempty closed subset of the real numbers, our results are applicable to dynamic equations on continuous, discrete, …
Laplace Factor Models In High-Dimensional Data, Siqi Liu, Xuerong Meggie Wen, Akim Adekpedjou, Guangbao Guo
Laplace Factor Models In High-Dimensional Data, Siqi Liu, Xuerong Meggie Wen, Akim Adekpedjou, Guangbao Guo
Mathematics and Statistics Faculty Research & Creative Works
Laplace factor models (LFMs) provide a heavy-tailed alternative to Gaussian factor models by representing high-dimensional observations through a low-rank common component and Laplace-distributed idiosyncratic errors. This paper develops an assumption-consistent finite-sample analysis of matrix concentration, covariance estimation, and Monte Carlo integration under this model. We first formulate the model with explicit dimensional, independence, covariance, and identifiability conditions. Standard matrix Laplace-transform and matrix Bernstein inequalities are then recalled with their precise applicability conditions. Because untruncated Laplace variables are neither almost surely bounded nor strongly log-concave, these standard results cannot be applied directly in the forms commonly used for bounded or Gaussian-like …
Existence And Uniqueness Of Positive Solutions For Hilfer–Hadamard-Type Fractional Differential Equations With Γ-Concave And Sub-Homogeneous Operators, Hasan Rasouli, Hojjat Afshari, Martin Bohner
Existence And Uniqueness Of Positive Solutions For Hilfer–Hadamard-Type Fractional Differential Equations With Γ-Concave And Sub-Homogeneous Operators, Hasan Rasouli, Hojjat Afshari, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
In this research, we present necessary and sufficient conditions for the existence and uniqueness of positive solutions for a class of Hilfer–Hadamard-type fractional differential equations with boundary value problems, including those with integral boundary conditions. The obtained results are conditional on a specific set of strong assumptions, which substantially narrow the class of admissible nonlinearities, coefficients, and boundary data. Thus, the present work extends the Hadamard-type framework to the Hilfer–Hadamard setting only within this restrictive regime, rather than providing a full extension to all Hilfer–Hadamard systems. We utilize the properties of (Formula presented.) -concave and sub-homogeneous operators along with two …
Genetic Analysis Of Triplicated Genes Affecting Sex-Specific Skeletal Deficits In Down Syndrome Model Mice, Kourtney Sloan, Kristina M. Piner, Pathum Randunu Nawarathna Kandedura Arachchige, Charles R. Goodlett, Yann Herault, Gayla R. Olbricht, Joseph M. Wallace, Randall J. Roper
Genetic Analysis Of Triplicated Genes Affecting Sex-Specific Skeletal Deficits In Down Syndrome Model Mice, Kourtney Sloan, Kristina M. Piner, Pathum Randunu Nawarathna Kandedura Arachchige, Charles R. Goodlett, Yann Herault, Gayla R. Olbricht, Joseph M. Wallace, Randall J. Roper
Mathematics and Statistics Faculty Research & Creative Works
Down syndrome (DS) is caused by the triplication of human chromosome 21 (Hsa21), resulting in skeletal insufficiency (low bone mineral density) and altered bone development. DS mouse models recapitulate these deficits, including sexual dimorphism in long bone alterations. Historically, Ts65Dn mice provided much of the insight behind DS-related skeletal deficits with ∼100 trisomic orthologous genes, but there are concerns about the genetic fidelity in this model due to the included triplication of genes not homologous to Hsa21. A new DS model, Ts66Yah, subtracted the non-Hsa21 homologous trisomic genes from Ts65Dn but has not been evaluated for long bone deficits. Comparing …
Multi-Population Sufficient Dimension Reduction, Xuerong Meggie Wen, Yuexiao Dong, Li Xing Zhu
Multi-Population Sufficient Dimension Reduction, Xuerong Meggie Wen, Yuexiao Dong, Li Xing Zhu
Mathematics and Statistics Faculty Research & Creative Works
A novel dimension-reduction method is introduced for multi-population data. The approach conducts a joint analysis that exploits information shared across populations while accommodating population-specific effects. Unlike partial dimension reduction methods, which identify related directions across all populations, or conditional analyses conducted independently within each population, the proposed two-step procedure leverages cross-population information to enhance estimation accuracy. The methodology is demonstrated through simulations and two real-data applications.
The Kaczmarz Algorithm In Hilbert C∗-Modules, Daniel Alpay, Chad Berner, Eric S. Weber
The Kaczmarz Algorithm In Hilbert C∗-Modules, Daniel Alpay, Chad Berner, Eric S. Weber
Mathematics and Statistics Faculty Research & Creative Works
The Kaczmarz algorithm in Hilbert spaces is a classical iterative method for stably recovering vectors from inner product data. In this paper, we extend the algorithm to the setting of Hilbert C∗-modules and establish analogues of its effectiveness in both finite-dimensional and stationary cases. Consequently, we demonstrate that continuous families of elements in a Hilbert space can be uniformly recovered using the Kaczmarz algorithm. Additionally, we develop a normalized Cauchy transform for continuous families of measures and use it to provide sufficient conditions under which standard frames in Hilbert C(X)-modules can be generated by the Kaczmarz algorithm and …
Sequences That Do Frame Reconstruction, Chad Berner
Sequences That Do Frame Reconstruction, Chad Berner
Mathematics and Statistics Faculty Research & Creative Works
Frames allow all elements of a Hilbert space to be reconstructed by inner product data in a stable manner. Recently, there is interest in relaxing the definition of frames to understand the implications for stable signal recovery. In this paper, we relax the definition of a frame by allowing the operator in the frame decomposition formula to not be invertible. We provide a complete classification of sequences that allow this decomposition via a type of frame operator. In addition, we provide several examples of sequences that allow this reconstruction property that are not frames and illustrate in which ways they …
Averaging Principle For A General Class Of Periodic Functions In Discrete Spaces, Martin Bohner, Jaqueline G. Mesquita, Sabrina Streipert
Averaging Principle For A General Class Of Periodic Functions In Discrete Spaces, Martin Bohner, Jaqueline G. Mesquita, Sabrina Streipert
Mathematics and Statistics Faculty Research & Creative Works
In this work, we develop a periodic averaging principle for arbitrary discrete time domains, leveraging a novel definition of periodicity. This definition does not rely on the classical requirement for the time domain itself to be periodic. We implement this averaging principle across diverse discrete time domains and explore a range of periodic functions within this extended context. The paper contains several examples with numerical simulations, providing visual demonstrations of our results. This highlights the versatility of our averaging principle and its potential to understand dynamics of nonautonomous recurrences with complex temporal patterns.
Controllability Of The Semilinear Benjamin–Bona–Mahony Dynamic Equation On Homogeneous Time Scales, Martin Bohner, Cosme Duque, Hugo Leiva
Controllability Of The Semilinear Benjamin–Bona–Mahony Dynamic Equation On Homogeneous Time Scales, Martin Bohner, Cosme Duque, Hugo Leiva
Mathematics and Statistics Faculty Research & Creative Works
This work investigates the approximate controllability and free-time approximate controllability of a generalized semi linear Benjamin–Bona–Mahony type dynamic equation defined on homogeneous time scales, subject to homogeneous Dirichlet boundary conditions. To accomplish this, the problem is framed within an abstract setting, employing the -semigroup theory on time scales. Moreover, we apply a technique introduced by Bashirov et al. [1, 2], which enables us to avoid relying on fixed point theorems.
An Seir Model On Time Scales With Discrete Applications To Tuberculosis, E. Akın, G. Yeni, D. Konur, S. R. Işık, M. R. Işık
An Seir Model On Time Scales With Discrete Applications To Tuberculosis, E. Akın, G. Yeni, D. Konur, S. R. Işık, M. R. Işık
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we propose a novel dynamical model on time scales consisting of new parameters to investigate the transmission dynamics of tuberculosis (TB), one of the deadliest infectious diseases worldwide, characterized by a long latency stage. The dynamical TB model, governed by the Susceptible–Exposed–Infected–Recovered (SEIR) framework within a unified form, yields a continuous model with a non-saturated incidence rate on the real numbers and discrete models with saturated incidence rates when different time domains are chosen. We analyze the stability of the equilibrium points of both the continuous TB model on the set of real numbers and the discrete …
Pointwise Self-Homeomorphic Generalized Inverse Limits, Ali H. Ali, Faruq A. Mena, Robert Paul Roe
Pointwise Self-Homeomorphic Generalized Inverse Limits, Ali H. Ali, Faruq A. Mena, Robert Paul Roe
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we find uncountable families of generalized inverse sequences on intervals, where the bonding functions consist of a finite number of line segments, such that the inverse limit spaces of these sequences are pointwise self-homeomorphic continua. We give several examples of pointwise self-homeomorphic continua obtained in this manner including the dendrite D3 and a dendrite containing Dω. The dendrite D3 was obtained previously, by others, as a generalized inverse limit but the bonding function in that example contained infinitely many line segments. We show that the techniques we use on intervals can be extended to inverse limits where …
Positive Solutions Of Semipositone Singular Three-Points Boundary Value Problems For Nonlinear Fractional Differential Equations, Xueyan Zhang, Zhaocai Hao, Martin Bohner
Positive Solutions Of Semipositone Singular Three-Points Boundary Value Problems For Nonlinear Fractional Differential Equations, Xueyan Zhang, Zhaocai Hao, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
This study introduces the existence of one positive solution for a specific category of semipositive singular three-point boundary value problems associated with Caputo fractional differential equations. The proof relies on the application of the Guo–Krasnosel'skii fixed point theorem. In the end, we provide an illustrative example.
A Note On Sufficient Dimension Folding For Regression Mean Function With Categorical Predictors, Bilin Zeng, Akim Adekpedjou, Xuerong Meggie Wen
A Note On Sufficient Dimension Folding For Regression Mean Function With Categorical Predictors, Bilin Zeng, Akim Adekpedjou, Xuerong Meggie Wen
Mathematics and Statistics Faculty Research & Creative Works
Multi-dimensional arrays are referred to as tensors. Tensor-valued predictors are commonly encountered in modern biomedical applications, such as electroencephalogram (EEG), magnetic resonance imaging (MRI), functional MRI (fMRI), diffusion-weighted MRI, and longitudinal health data. In survival analysis, it is both important and challenging to integrate clinically relevant information, such as gender, age, and disease state along with medical imaging tensor data or longitudinal health data to predict disease outcomes. Most existing higher-order sufficient dimension reduction regressions for matrix- or array-valued data focus solely on tensor data, often neglecting established clinical covariates that are readily available and known to have predictive value. …
Meshless Collocation Methods For Time-Dependent Nonlocal Problems Based On Radial Basis Functions, Qiao Zhuang, Yanzhi Zhang, Zhongqiang Zhang
Meshless Collocation Methods For Time-Dependent Nonlocal Problems Based On Radial Basis Functions, Qiao Zhuang, Yanzhi Zhang, Zhongqiang Zhang
Mathematics and Statistics Faculty Research & Creative Works
We present radial basis function (RBF) collocation methods for time-dependent space fractional problems on general bounded domains. Building on a recently developed approach for accurately computing the integral fractional Laplacian of any RBF, we design collocation schemes for fractional heat and Stokes equations using extended-domain techniques. In particular, we propose a numerical Leray projection method for fractional Stokes problems, where both the discrete projection operator and the collocation scheme are formulated on extended domains to handle complex domains. Numerical results demonstrate the effectiveness of the proposed methods in solving time-dependent nonlocal problems on complex domains.
Fourier Pseudospectral Methods For The Variable-Order Space Fractional Wave Equations, Yanzhi Zhang, Xiaofei Zhao, Shiping Zhou
Fourier Pseudospectral Methods For The Variable-Order Space Fractional Wave Equations, Yanzhi Zhang, Xiaofei Zhao, Shiping Zhou
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we propose Fourier pseudospectral methods to solve the variable-order space fractional wave equation and develop an accelerated matrix-free approach for its effective implementation. In constant-order cases, fast algorithms can be designed via the fast Fourier transforms (FFTs), and the computational cost at each time step is O(NlogN) with N the total number of spatial points. In variable-order cases, however, the spatial dependence in the power s(x) leads to the failure of inverse FFTs. While the direct matrix-vector multiplication approach becomes impractical due to excessive memory requirements. Hence, we propose an accelerated matrix-free approach for effective implementation in …
Serum Biomarker Trajectory Clusters Predict Functional Outcome And Quality Of Life For Traumatic Brain Injury, Thanh Son Do, Chantal Carnes, Zhihui Yang, Firas Kobeissy, Hamad Yadikar, Gayla R. Olbricht, Olli Tenovuo, Jussi P. Posti, Ewout W. Steyerberg, Lindsay Wilson, Nicole Von Steinbüchel, Endre Czeiter, Andras Buki, David K. Menon
Serum Biomarker Trajectory Clusters Predict Functional Outcome And Quality Of Life For Traumatic Brain Injury, Thanh Son Do, Chantal Carnes, Zhihui Yang, Firas Kobeissy, Hamad Yadikar, Gayla R. Olbricht, Olli Tenovuo, Jussi P. Posti, Ewout W. Steyerberg, Lindsay Wilson, Nicole Von Steinbüchel, Endre Czeiter, Andras Buki, David K. Menon
Mathematics and Statistics Faculty Research & Creative Works
Serum brain-enriched biomarkers are increasingly employed in the clinical evaluation of traumatic brain injury (TBI) to assist with triage, neuroimaging decisions, and prognostication. However, the potential of temporal biomarker trajectories to inform disease monitoring and long-term outcomes remains underexplored. We aim to identify distinct biomarker trajectory (TRAJ) profiles in traumatic brain injury patients and to examine their associations with long-term clinical outcomes. The study included 373, CT-positive Intensive Care Unit (ICU) traumatic brain injury patients (256 with initial Glasgow Coma Scale 3–12) from the Collaborative European Neurotrauma Effectiveness Research in TBI (CENTER-TBI) core study who had at least two serum …
Equilibrium Stability Under Nuclear Confrontation, Martin Bohner, A. A. Martynyuk
Equilibrium Stability Under Nuclear Confrontation, Martin Bohner, A. A. Martynyuk
Mathematics and Statistics Faculty Research & Creative Works
This article proposes and analyzes mathematical models of confrontation between two and n countries, including countries with nuclear weapons. The proposed models are based on a generalization of Richardson's well-known mathematical model of the arms race. Namely, the factor of hostility is filled with expanded content, including public opinion and the armed forces of the opposing countries. Qualitative analysis of confrontation models is carried out by the method of Lyapunov functions and by applying nonlinear integral inequalities. As a result of the analysis, the conditions for the stability of the equilibrium state of the opposing countries are established, and the …
Threshold Asymmetric Conditional Autoregressive Range (Tacarr) Model, Isuru Ratnayake, V. A. Samaranayake
Threshold Asymmetric Conditional Autoregressive Range (Tacarr) Model, Isuru Ratnayake, V. A. Samaranayake
Mathematics and Statistics Faculty Research & Creative Works
This paper introduces a Threshold Asymmetric Conditional Autoregressive Range (TACARR) model for analyzing the daily price ranges of financial assets. The proposed formulation assumes that the conditional expected range switches between two regimes, representing upward and downward market states, with the disturbance distribution also allowed to vary across regimes. A self-adjusting threshold component, determined by past values of the series, is used to identify the prevailing market regime. In this way, the model is able to capture asymmetric and heteroscedastic volatility behavior in financial markets. The TACARR model is designed to address several limitations of existing price range models, including …
Infimum Dimension Nash Embeddings For 2d Projective Shape Analysis, Robert L. Paige, Vic Patrangenaru
Infimum Dimension Nash Embeddings For 2d Projective Shape Analysis, Robert L. Paige, Vic Patrangenaru
Mathematics and Statistics Faculty Research & Creative Works
Vector embeddings make complicated data extracted from networks, words and images, more amendable to data science applications. At the present time, the Veronese-Whitney (VW) matrix embedding of the real projective space is the state of the art for making inference about digital images from an uncalibrated camera, such as a cell phone or security camera. In this work we consider vector embeddings for the projective shape data and in particular determine the minimum dimension isometric (distance-preserving or Nash) vector embedding for a projective space. We determine such an embedding for the projective plane in closed-form. From this embedding we determine …
Wacsaw: An Adaptive, Statistical Method To Classify Movement Into Sleep And Wakefulness States, Austin Vandegriffe, V. A. Samaranayake, Matthew S. Thimgan
Wacsaw: An Adaptive, Statistical Method To Classify Movement Into Sleep And Wakefulness States, Austin Vandegriffe, V. A. Samaranayake, Matthew S. Thimgan
Mathematics and Statistics Faculty Research & Creative Works
Wearable actimeters can improve our understanding of sleep in the natural environments. Current algorithms may produce inaccuracies in specific individuals and circumstances, such as quiet wakefulness. New hardware allows data collection at higher frequencies enabling sophisticated analytical methods. We have developed a novel statistical algorithm, the Wasserstein Algorithm for Classifying Sleep and Wakefulness (WACSAW), to identify behavioral states from recordings of everyday movement. WACSAW employs optimal transport techniques to identify segments with differing activity variability. Functions characterizing the segments' movement distributions were clustered into two groups using a k-nearest neighbors and labeled as sleep or wake based on their proximity …
Generalized Transversality Conditions For Fuzzy Quantum-Symmetric Variational Problems Via Granular Approach, Martin Bohner, Ewa Girejko, Agnieszka B. Malinowska, Linh Nguyen, Baruch Schneider, Tri Truong
Generalized Transversality Conditions For Fuzzy Quantum-Symmetric Variational Problems Via Granular Approach, Martin Bohner, Ewa Girejko, Agnieszka B. Malinowska, Linh Nguyen, Baruch Schneider, Tri Truong
Mathematics and Statistics Faculty Research & Creative Works
This paper investigates fuzzy q-symmetric variational problems with natural boundary conditions. Based on the relative distance measure fuzzy arithmetic and horizontal membership functions (HMFs), we propose novel concepts of differentiability and integrability for fuzzy functions on quantum geometric subsets of real numbers. Then, fundamental foundations of q-symmetric calculus of variations based on HMFs are provided. With the help of HMFs and granular q-symmetric differentiability, we derive necessary optimality conditions for fuzzy q-symmetric variational problems that depend on free endpoints. Moreover, sufficient conditions for minimizers of q-symmetric variational problems are obtained. Some numerical examples illustrating the proposed approach are presented.
Novel Statistical And Topological Data Analyses Of 2d Electronic Images, Robert L. Paige, Vic Patrangenaru
Novel Statistical And Topological Data Analyses Of 2d Electronic Images, Robert L. Paige, Vic Patrangenaru
Mathematics and Statistics Faculty Research & Creative Works
In this paper, novel statistical and topological data analyses of 2D images are developed. One considers methodologies based on the Region Covariance Descriptor (RCD) and Topological Data Analysis (TDA) rooted in the simplicial as well as cubical persistent homologies. These methods provide statistical methods for data from populations of complex data objects that are elements of non-Euclidean spaces. The 2D image data considered consist of pictures of two leaves—A and B—from the same tree, twenty of each leaf, from different perspectives. The novel statistical procedures developed are used for correctly determining that leaf A images and leaf B images are …
Ceno: Non-Uniform, Segment And Parallel Zero-Knowledge Virtual Machine, Tianyi Liu, Zhenfei Zhang, Yuncong Zhang, Wenqing Hu, Ye Zhang
Ceno: Non-Uniform, Segment And Parallel Zero-Knowledge Virtual Machine, Tianyi Liu, Zhenfei Zhang, Yuncong Zhang, Wenqing Hu, Ye Zhang
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we explore a novel Zero-knowledge Virtual Machine (zkVM) framework leveraging succinct, non-interactive zero-knowledge proofs for verifiable computation over any code. Our approach divides the proof of program execution into two stages. In the first stage, the process breaks down program execution into segments, identifying and grouping identical sections. These segments are then proved through data-parallel circuits that allow for varying amounts of duplication. In the subsequent stage, the verifier examines these segment proofs, reconstructing the program's control and data flow based on the segments' duplication number and the original program. The second stage can be further attested …
Variable Selection In Mixture Cure Models Using Elastic Net Penalty: Application To Covid-19 Data, Aluwani Ramalata, Akim Adekpedjou, Maseka Lesaoana
Variable Selection In Mixture Cure Models Using Elastic Net Penalty: Application To Covid-19 Data, Aluwani Ramalata, Akim Adekpedjou, Maseka Lesaoana
Mathematics and Statistics Faculty Research & Creative Works
In survival analysis, it is often assumed that all individuals will eventually experience the event of interest if followed long enough. However, in many real-world scenarios, a subset of individuals remains event-free indefinitely. For instance, in clinical studies, some patients never relapse and are considered cured rather than censored. Traditional survival models are inadequate for capturing this heterogeneity. Mixture cure models address this limitation by distinguishing between cured and susceptible individuals while modeling the survival of the latter. A key challenge in mixture cure modeling is selecting relevant covariates, particularly when dealing with time-varying effects. This study develops a penalized …
Some New Hardy-Type Inequalities With Negative Parameters On Time Scales, Martin Bohner, Irena Jadlovská, Ahmed I. Saied
Some New Hardy-Type Inequalities With Negative Parameters On Time Scales, Martin Bohner, Irena Jadlovská, Ahmed I. Saied
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we present new Hardy-type inequalities with negative parameters on a time scale T. The adopted approach draws upon the use of a reversed Hölder dynamic inequality, a chain rule, and the integration by parts rule on time scales. In the continuous case, our results contain integral inequalities due to Benaissa and Budak, while in the discrete case, the obtained inequalities are essentially new. Additionally, we demonstrate the applicability of our results in the quantum case.
Fourier Series For Singular Measures In Higher Dimensions, Chad Berner, John E. Herr, Palle E.T. Jorgensen, Eric S. Weber
Fourier Series For Singular Measures In Higher Dimensions, Chad Berner, John E. Herr, Palle E.T. Jorgensen, Eric S. Weber
Mathematics and Statistics Faculty Research & Creative Works
For multi-variable finite measure spaces, we present in this paper a new framework for non-orthogonal L2 Fourier expansions. Our results hold for probability measures μ with finite support in Rd that satisfy a certain disintegration condition that we refer to as "slice-singular". In this general framework, we present explicit L2(μ)-Fourier expansions, with Fourier exponentials having positive Fourier frequencies in each of the d coordinates. Our Fourier representations apply to every f∈L2(μ), are based on an extended Kaczmarz algorithm, and use a new recursive μ Rokhlin disintegration representation. In detail, our Fourier series expansion for f is in terms of the …
Massera’S Theorem On Arbitrary Discrete Time Domains, Martin Bohner, Jaqueline G. Mesquita, Sabrina Streipert
Massera’S Theorem On Arbitrary Discrete Time Domains, Martin Bohner, Jaqueline G. Mesquita, Sabrina Streipert
Mathematics and Statistics Faculty Research & Creative Works
We present a general version of Massera's theorems for arbitrary discrete domains, based on a newly introduced definition for both linear and nonlinear equations. For scalar nonlinear equations, we identify sufficient conditions that ensure each µ-bounded solution approaches a periodic solution asymptotically. In the case of linear systems, we prove that the presence of a µ-bounded solution necessarily leads to a periodic solution. We also provide some examples to show the practical implications of our findings.
Estimation And Model Misspecification For Recurrent Event Data With Covariates Under Measurement Errors, Ravinath Alahakoon, Gideon K.D. Zamba, Xuerong Meggie Wen, Akim Adekpedjou
Estimation And Model Misspecification For Recurrent Event Data With Covariates Under Measurement Errors, Ravinath Alahakoon, Gideon K.D. Zamba, Xuerong Meggie Wen, Akim Adekpedjou
Mathematics and Statistics Faculty Research & Creative Works
For subject i, we monitor an event that can occur multiple times over a random observation window [0, (Formula presented.)). At each recurrence, p concomitant variables, (Formula presented.), associated to the event recurrence are recorded—a subset ((Formula presented.)) of which is measured with errors. To circumvent the problem of bias and consistency associated with parameter estimation in the presence of measurement errors, we propose inference for corrected estimating equations with well-behaved roots under an additive measurement errors model. We show that estimation is essentially unbiased under the corrected profile likelihood for recurrent events, in comparison to biased estimations under a …
Multi-Valued Variational Inequalities For Variable Exponent Double Phase Problems: Comparison And Extremality Results, Siegfried Carl, Vy Khoi Le, Patrick Winkert
Multi-Valued Variational Inequalities For Variable Exponent Double Phase Problems: Comparison And Extremality Results, Siegfried Carl, Vy Khoi Le, Patrick Winkert
Mathematics and Statistics Faculty Research & Creative Works
We prove existence and comparison results for multi-valued variational inequalities in a bounded domain Ω of the form (Formula presented.) where A:W1,H(Ω)→W1,H(Ω)∗ given by (Formula presented.) for u∈W1,H(Ω), is the double phase operator with variable exponents and W1,H(Ω) is the associated Musielak–Orlicz Sobolev space. First, an existence result is proved under some weak coercivity condition. Our main focus aims at the treatment of the problem under consideration when coercivity fails. To this end we establish the method of sub–super-solution for the multi-valued variational inequality in the space W1, H(Ω) based on appropriately defined sub- and super-solutions, which yields the existence …
Existence Results For A Discrete Fractional Boundary Value Problem, David Barilla, Martin Bohner, Giuseppe Caristi, Shapour Heidarkhani, Shahin Moradi
Existence Results For A Discrete Fractional Boundary Value Problem, David Barilla, Martin Bohner, Giuseppe Caristi, Shapour Heidarkhani, Shahin Moradi
Mathematics and Statistics Faculty Research & Creative Works
In this study, we investigate the existence of at least one solution and the existence of an infinite number of solutions for a discrete fractional boundary value problem. Requiring an algebraic condition on the nonlinear term for small values of the parameter and requiring an additional asymptotical behavior of the potential at zero, we investigate the existence of at least one nontrivial solution for the problem. Moreover, under suitable assumptions on the oscillatory behavior of the nonlinearity at infinity, for exact collections of the parameter, we discuss the existence of a sequence of solutions for the problem. We also present …