# Baylor University

• Waco, TX, United States
Recent publications
A system of two partial differential equations with fractional diffusion is considered in this study. The system extends the conventional Zakharov system with unknowns being nonlinearly coupled complex- and real-valued functions. The diffusion is understood in the Riesz sense, and suitable initial–boundary conditions are imposed on an open and bounded domain of the real numbers. It is shown that the mass and Higgs’ free energy of the system are conserved. Moreover, the total energy is proven to be dissipated, and that both the free and the total energy are non-negative. As a corollary from the conservation of energy, we find that the solutions of the system are bounded throughout time. Motivated by these properties on the solutions of the system, we propose a numerical model to approximate the fractional Zakharov system via finite-difference approaches. Along with this numerical model for solving the continuous system, discrete analogues for the mass, the Higgs’ free energy and the total energy are we provided. Furthermore, utilizing Browder’s fixed-point theorem, we establish the solubility of the discrete model. It is shown that the discrete total mass and the discrete free energy are conserved, in agreement with the continuous case. The discrete energy functionals (both the discrete free energy and the discrete total energy) are proven to be non-negative functions of the discrete time thoroughly the boundedness of the numerical solutions. Properties of consistency, stability and convergence of the scheme are also studied rigorously. Numerical simulations illustrate some of the anticipated theoretical features of our finite-difference solution procedure.
Boundedness is an essential feature of the solutions for various mathematical and numerical models in the natural sciences, especially those systems in which linear or nonlinear preservation or stability features are fundamental. In those cases, boundedness of the solutions outside a set of zero measure is not enough to guarantee that the solutions are physically relevant. In this note, we will establish a criterion for the boundedness of integrable solutions of general continuous and numerical systems. More precisely, we establish a characterization of those measures over arbitrary spaces for which real-valued integrable functions are necessarily bounded at every point of the domain. The main result states that the collection of measures for which all integrable functions are everywhere bounded are exactly all of those measures for which the infimum of the measures for nonempy sets is a positive extended real number.
In this work, we propose an implicit finite-difference scheme to approximate the solutions of a generalization of the well-known Klein-Gordon-Zakharov system. More precisely, the system considered in this work is an extension to the spatially fractional case of the classical Klein-Gordon-Zakharov model, considering two different orders of differentiation and fractional derivatives of the Riesz type. The numerical model proposed in this work considers fractional-order centered differences to approximate the spatial fractional derivatives. The energy associated to this discrete system is a non-negative invariant, in agreement with the properties of the continuous fractional model. We establish rigorously the existence of solutions using fixed-point arguments and complex matrix properties. To that end, we use the fact that the two difference equations of the discretization are decoupled, which means that the computational implementation is easier that for other numerical models available in the literature. We prove that the method has square consistency in both time and space. In addition, we prove rigorously the stability and the quadratic convergence of the numerical model. As a corollary of stability, we are able to prove the uniqueness of numerical solutions. Finally, we provide some illustrative simulations with a computer implementation of our scheme.
This manuscript is devoted to studying approximations of a coupled Klein-Gordon-Zakharov system where different orders of fractional spatial derivatives are utilized. The fractional derivatives involved are in the Riesz sense. It is understood that such a modeling system possesses an energy functional which is conserved throughout the period of time considered, and that its solutions are uniformly bounded. Motivated by these facts, we propose two numerical models to approximate the underlying continuous system. While both approximations remain to be nonlinear, one of them is implicit and the other is explicit. For each of the discretized models, we introduce a proper discrete energy functional to estimate the total energy of the continuous system. We prove that such a discrete energy is conserved in both cases. The existence of solutions of the numerical models is established via fixed-point theorems. Continuing explorations of intrinsic properties of the numerical solutions are carried out. More specifically, we show rigorously that the two schemes constructed are capable of preserving the boundedness of the approximations and that they yield consistent estimates of the true solution. Numerical stability and convergence are likewise proved theoretically. As one of the consequences, the uniqueness of numerical solutions is shown rigorously for both discretized models. Finally, comparisons of the numerical solutions are provided, in order to evaluate the capabilities of these discrete methods to preserve the discrete energy of underlying systems.
Background Long-term balancing selection (LTBS) can maintain allelic variation at a locus over millions of years and through speciation events. Variants shared between species in the state of identity-by-descent, hereafter “trans-species polymorphisms”, can result from LTBS, often due to host–pathogen interactions. For instance, the major histocompatibility complex (MHC) locus contains TSPs present across primates. Several hundred candidate LTBS regions have been identified in humans and chimpanzees; however, because many are in non-protein-coding regions of the genome, the functions and potential adaptive roles for most remain unknown. Results We integrated diverse genomic annotations to explore the functions of 60 previously identified regions with multiple shared polymorphisms (SPs) between humans and chimpanzees, including 19 with strong evidence of LTBS. We analyzed genome-wide functional assays, expression quantitative trait loci (eQTL), genome-wide association studies (GWAS), and phenome-wide association studies (PheWAS) for all the regions. We identify functional annotations for 59 regions, including 58 with evidence of gene regulatory function from GTEx or functional genomics data and 19 with evidence of trait association from GWAS or PheWAS. As expected, the SPs associate in humans with many immune system phenotypes, including response to pathogens, but we also find associations with a range of other phenotypes, including body size, alcohol intake, cognitive performance, risk-taking behavior, and urate levels. Conclusions The diversity of traits associated with non-coding regions with multiple SPs support previous hypotheses that functions beyond the immune system are likely subject to LTBS. Furthermore, several of these trait associations provide support and candidate genetic loci for previous hypothesis about behavioral diversity in human and chimpanzee populations, such as the importance of variation in risk sensitivity.
Entrepreneurial intention plays a key role in entrepreneurship. Over the years, scholars have explained it using personality traits, cognitive models and, to a lesser extent, the role of social environment. Since this role has been underestimated, we build on trait activation theory to explore how social networks are especially relevant and can trigger the activation of individuals’ need for achievement to predict entrepreneurial intention. We test our hypotheses on a sample of 597 university students from Spain using partial least squares (PLS). Our results confirm that social network size positively influences the entrepreneurial information obtained in social networks, which in turn, positively impacts entrepreneurial intention. Additionally, we found that need for achievement is activated in the context of social networks, enhancing the influence of this information on entrepreneurial intention. Through fuzzy-set qualitative comparative analysis (fsQCA), we also identify alternative configurations of the previous variables that lead to greater entrepreneurial intention.
Optical fiber biosensors are receiving significant interest, as they allow real-time, low-limit, and high precision detection of biological analytes such as biomarkers, proteins, and small cells. Classical biosensor designs include gratings, interferometers, and plasmonic structures; however, these systems require a complex design, hard to manufacture on high volumes. Recently, several biosensors having a minimalistic design, rapid and suitable to be automated, have been proposed; the key asset is the scalability potential, in view of fabricating numerous devices for disposable use or for large parallel immunoassays. This new sensor class features reflector-less sensors, shallow tapers, and ball resonators; a pseudo-random spectrum characterizes all these biosensors. In this paper, we provide a bird-eye view of these minimalistic designs and a perspective of their use in advanced biosensing applications.
High temporal resolution, geostationary, thermal infrared data from the Advanced Baseline Imager combined with seismic data of La Soufrière Volcano, St. Vincent provide empirical insights into the volcanic processes and mechanisms that occurred from November 2020 until the explosive phase in April 2021. An overall increase in intensity of thermal output and seismicity are observed during the effusive phase; however, the intensity of the thermal data increased ∼20 days earlier than the seismicity. During the effusive phase, the daily radiant heat flux increased from 0.01 to >100 MW and the seismicity increased from 1 to 647 events. The climax of both records occurred during the explosive eruptions on April 9-14, 2021. Strong correlations are observed between these datasets in the weeks leading to the explosive eruptions. A significant (∼5 day) decrease in thermal and seismic activity is observed ∼12 days prior to the explosive phase, which could reveal a hiatus in magma migration prior to the eruption. Periods of decoupling between these datasets are also observed and are attributed to different mechanisms during the volcanic unrest. Occurrences with high seismicity and low heat flux may indicate deeper magmatic migration where no significant surface thermal response could be detected, for example. Recognizing correlations, or lack thereof, between high-temporal resolution thermal infrared and seismic data expands potential insights to subsurface volcanic processes by providing a second, complementary vantage. Such seismic-thermal analysis can improve our community's capability to monitor and evaluate new volcanic eruptions. Indeed, extensive seismic networks (local and regional) and multiple geostationary weather satellites now provide near global coverage. A similar analysis to our work at La Soufrière Volcano, St. Vincent is feasible, and should become routine, at other volcanoes worldwide using combined high-temporal, ground and orbital data where available. The 2022 eruption at Hunga-Tonga-Hunga-Ha'apai volcano, Tonga, illustrates the important potential for these high cadence data and subsequent analysis even at extremely remote volcanoes.
We study a mean field game system introduced by Chan and Sircar (Appl Math Optim 71:533–569, 2015) to model production of an exhaustible resource. In particular, we study the sensitivity of the solution with respect to a parameter ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document}, which measures the degree to which producers are interchangeable. We prove that on some interval [0,ε0]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[0,\varepsilon _0]$$\end{document}, where ε0>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon _0 > 0$$\end{document}, the solution is infinitely differentiable with respect to ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document}. The result is based on a set of new a priori estimates for forward-backward systems of linear partial differential equations.
We show that stimulated scattering of an isolated system of N Bose particles with initially broad energy distribution can yield condensation of particles into excited collective state in which most of the bosons occupy one or several modes. During condensation, the total particle number and energy are conserved, while the entropy of the system grows. Onset of condensation occurs at a critical particle occupation number when spectrum narrowing due to stimulated processes overcomes spectrum broadening due to diffusion. This differs from Bose–Einstein condensation in which particles undergo condensation into the equilibrium state due to thermalization processes.
The use of quantum optical/laser physics techniques yields interesting insights into Bose–Einstein condensation and Unruh–Hawking radiation.
We obtain a Mikhlin multiplier theory for the nonabelian free groups. Let F∞ be a free group on infinite many generators {g1,g2,⋯}. Given d≥1 and a bounded symbol m on Zd satisfying the classical Mikhlin condition, the linear map Mm:C[F∞]→C[F∞] defined by λ(g)↦m(k1,⋯,kd)λ(g) for g=gi1k1⋯ginkn∈F∞ in reduced form (with kl=0 in m(k1,⋯,kd) for l>n), extends to a completely bounded map on Lp(Fˆ∞) for all 1<p<∞, where Fˆ∞ is the group von Neumann algebra of F∞. In the process, we establish a platform to transfer Lp-completely bounded maps on tensor products of von Neumann algebras to Lp-completely bounded maps on the corresponding amalgamated free products. A similar result holds for any free product of discrete groups.
The charging of various airborne particles was investigated using single-particle levitation and charge-balance equations. Though radioactive decay and triboelectrification can induce charging, it is typically assumed that the aerosols in a radioactive plume will not carry significant charge at steady state since atmospheric particles can have their charge neutralized through the capture of adjacent counter-ions (i.e., diffusion charging). To assess this assumption, we directly measured the surface charge and charge density of various triboelectrically charged aerosols including radioactive uranium oxide (<1 μm), urban dust, Arizona desert dust, hydrophilic and hydrophobic silica nanoparticles, and graphene oxide powders using an electric field-assisted particle levitator in air. Of these particles, uranium oxide aerosols exhibited the highest surface charge density. Charge balance equations were employed to predict the average charge gained from radioactive decay as a function of time and to evaluate the effects of diffusion charging on triboelectrically charged radioactive and non-radioactive particles in the atmosphere. Simulation results show that particles, initially charged through triboelectrification, can be quickly discharged by diffusion charging in the absence of radioactive decay. Nevertheless, simulation results also indicate that particles can be strongly charged when they carry radionuclides. These experimental and simulation results suggest that radioactive decay can induce strong particle charging that may potentially affect atmospheric transport of airborne radionuclides.
Cities influence land use change on neighboring and distal areas through sociopolitical or infrastructural connections between urban and non-urban regions, termed teleconnections. While teleconnections are generally recognized as important to land cover dynamics, many land use and land cover change (LULCC) modeling efforts do not explicitly account for non-contiguous spatial urban-land relationships. Here, we quantify and map urban land teleconnections in the US using information theory in concert with graphical networks. Evidence of teleconnections relied on long-term (1950–2016) changes in urban land cover and urban population intensity in urban areas (census defined “urban area”) relative to land dynamics in other cities and rural lands (rural portions of counties), located both proximate and distal to each city. While there are numerous definitions of rural and urban (see Richter, 2021 for review), we rely on national census definitions in this study for replicability. We find that optimal urban-rural land network complexity and network size ranged dramatically and depended on the information theory measure and variables under consideration. City-city networks were very large, suggesting the complex and simultaneous effects of globalization on cities. However, we also find that proximate urban-rural networks are small and influenced directly by individual cities, though each city may, in turn, be influenced by complex teleconnections with other cities. Distal rural areas providing agricultural commodities were characterized by decreasing agriculture land use yet increasing agricultural production intensity. Hence, distal rural commodity areas may support multiple cities, incurring increased land stress in those areas. Our results suggest that changes in population intensity, rather than urban land cover alone, induce more numerous effects on proximate and distal rural lands, as well as other cities. Predictive models of teleconnection strength explained 4.5% to 98% of variation in teleconnection measures and suggested that rural land characteristics were equally, if not more, important than variables characterizing city land dynamics. This indicates that local dynamics in rural areas are potentially more important drivers of land change relative to teleconnections with cities. Ultimately, the methodological approach presented in this paper holds promise in incorporating teleconnections in LULCC modeling efforts, providing important considerations for later studies on emissions modeling, economic supply chains and future land-use planning.
Background: Leaks of the esophagus and stomach are difficult to manage and associated with significant morbidity and mortality. Endoscopic therapy can manage these leaks without surgical intervention. Our goal is to create a scoring tool to aid in predicting the success of endoscopic therapy in these patients. Study design: An IRB-approved prospectively maintained database was retrospectively reviewed for all patients treated for gastrointestinal leaks from July 2013 to January 2021, including patients treated for esophageal and stomach leaks. Endpoints include success of leak closure for patients treated solely by endoscopic therapy (ET) compared with surgical therapy as failed endoscopic therapy (FET). A multivariable logistic regression model was fitted to identify independent risk factors for predicting success of endoscopic therapy, and a scoring calculator was developed. Results: There were 80 patients (60 females) with a mean age of 50 years. The ET group included 59 patients (74%), whereas the FET group included 21 patients (26%). Patient demographics, comorbidities, surgical history, and timing of leak diagnosis were used. Multivariable analysis resulted in 4 variables associated with higher probability of successful endoscopic leak management without need for additional surgery. These included increased age, lower BMI, lack of previous bariatric surgery, and quicker identification of the leak. Consequently, a scoring nomogram was developed with values from 0 to 22. Conclusion: Our data show the development of a scoring calculator capable of quantifying the likelihood of success treating foregut and bariatric leaks with endoscopic therapies. This can be used clinically to guide treatment decisions.
Research on the impact of new technologies on American youth often fails to consider their impact on religious commitment, and research on adolescent religiosity often fails to consider how technology use may influence adolescents’ religious lives. But the copious amount of time adolescents spend in front of screens and on social media platforms may affect their religious commitment through a process of self-socialization or by outcompeting religion for adolescents’ time and attention. Using data from the National Survey of Moral Formation (N = 3,033), we examine whether adolescent screen time and social media use are associated with religious commitment. We find that screen time is related to diminished religious commitment, and, for private religious outcomes, the negative relationship is stronger among adolescents whose parents are more religious. There is no unique negative effect of social media use on religious commitment except on the scripture reading of adolescents with religious parents. Studies of adolescent religiosity should consider technology use to be an important agent in the religious socialization process. Although social media use appears to pose no major unique challenge to adolescent religious commitment, researchers should continue to explore the effects of new technological developments on youth religiosity.
Introduction: Current evidence supports the inclusion of directional preference exercises for a subgroup of patients with low back (LBP) and leg pain. Recent pain neuroscience strategies have suggested that cortical restructuring associated with movement activating the body map representation in the brain might account for the observed improvement with the directional preference approach. Objectives: To explore whether or not a motor imagery directional preference approach would result in any changes in patients with LBP and leg pain. Methods: A consecutive convenience sample of patients with LBP and leg pain were recruited at two outpatient physical therapy clinics. Measurements of LBP, leg pain, fear-avoidance beliefs (FABQ), pain catastrophizing (PCS), active lumbar flexion, and straight leg raise (SLR) were compared before and immediately after a virtual (motor imagery) directional preference exercise. Results: Statistically significant differences for LBP, FABQ, PCS, active lumbar flexion, and SLR were observed, but only SLR changes met or exceeded the minimally clinically important difference (MCID). Conclusions: A brief virtual motor imagery extension treatment yielded some immediate positive shifts in patients presenting to physical therapy with LBP and leg pain. Our results indicate that randomized comparison trials are needed to determine the effect of this intervention on the short- and longer-term outcomes in patients with LBP and leg pain.
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