Efficacy of coping mechanisms used during COVID-19 as reported by parents of children with autism

The COVID-19 pandemic’s alterations to daily life have been especially challenging for families with Autism Spectrum Disorder (ASD), worsening the core features of ASD and overall mental health. With the increased need for effective coping, the current retrospective study used data from a survey regarding parent reports of how often their child with ASD used certain coping strategies (frequency), as well as the extent to which they felt their child benefitted from their use (efficacy) in mitigating stress during the pandemic. This retrospective study Repeated measures ANOVAs were conducted to evaluate whether there were significant differences in both frequency and efficacy ratings for each coping strategy, for the entire sample as well as for three children’s age groups. Using Spearman’s rank-order correlations, correlation coefficients between the frequency and efficacy of each coping strategy were explored. Results revealed that maladaptive strategies were used more frequently than adaptive strategies, while parent routine as the most frequently used and efficacious for all age groups. Additionally, for adaptive strategies, humor and focusing on the positive had the strongest correlations between frequency and efficacy ratings amongst all age groups. Of the maladaptive strategies, repetitive behaviors, rumination, and isolation had the strongest correlations for the youngest, middle, and oldest age groups, respectively. Further, for each age group, the adaptive coping strategies had stronger correlations between frequency and efficacy than the maladaptive ones. It is our hope that the results of this study will lay the foundation for developing adaptive coping strategies to alleviate stress in children with ASD. Further investigations using a larger cohort are warranted to determine effective coping strategies for individuals with ASD across a range of situations, including acute stressors (such as future public health emergencies and natural disasters), as well as common daily stressors

Reduction Operators of Linear Second-Order Parabolic Equations

The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1+1)-dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary differential ones are exhaustively described. This problem proves to be equivalent, in some sense, to solving the initial equations. The ``no-go'' result is extended to the investigation of point transformations (admissible transformations, equivalence transformations, Lie symmetries) and Lie reductions of the determining equations for the nonclassical symmetries. Transformations linearizing the determining equations are obtained in the general case and under different additional constraints. A nontrivial example illustrating applications of reduction operators to finding exact solutions of equations from the class under consideration is presented. An observed connection between reduction operators and Darboux transformations is discussed.Comment: 31 pages, minor misprints are correcte

Group classification of (1+1)-Dimensional Schr\"odinger Equations with Potentials and Power Nonlinearities

We perform the complete group classification in the class of nonlinear Schr\"odinger equations of the form $i\psi_t+\psi_{xx}+|\psi|^\gamma\psi+V(t,x)\psi=0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x,$ $\gamma$ is a real non-zero constant. We construct all the possible inequivalent potentials for which these equations have non-trivial Lie symmetries using a combination of algebraic and compatibility methods. The proposed approach can be applied to solving group classification problems for a number of important classes of differential equations arising in mathematical physics.Comment: 10 page

Multidimensional simple waves in fully relativistic fluids

A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for fully relativistic fluid and plasma flows. Three essential modes: vortex, entropy and sound modes are derived where each of them is different from its nonrelativistic analogue. Vortex and entropy modes are formally solved in both the laboratory frame and the wave frame (co-moving with the wave front) while the sound mode is formally solved only in the wave frame at ultra-relativistic temperatures. In addition, the surface which is the boundary between the permitted and forbidden regions of the solution is introduced and determined. Finally a symmetry analysis is performed for the vortex mode equation up to both point and contact transformations. Fundamental invariants and a form of general solutions of point transformations along with some specific examples are also derived.Comment: 21 page

Numerical study on load-bearing capabilities of beam-like lattice structures with three different unit cells

The design and analysis of lattice structures manufactured using Additive Manufacturing (AM) technique is a new approach to create lightweight high-strength components. However, it is difficult for engineers to choose the proper unit cell for a certain function structure and loading case. In this paper, three beam-like lattice structures with triangular prism, square prism and hexagonal prism were designed, manufactured by SLM process using AlSi10Mg and tested. The mechanical performances of lattice structures with equal relative density, equal base area and height, and equal length for all unit cells were conducted by Finite Element Analysis (FEA). It was found that effective Young’s modulus is proportional to relative density, but with different affecting levels. When the lattice structures are designed with the same relative density or the same side lengths, the effective Young’s modulus of lattice structure with triangular prism exhibits the maximum value for both cases. When the lattice structures are designed with the same base areas for all unit cells, the effective Young’s modulus of lattice structures with square prism presents the maximum. FEA results also show that the maximum stress of lattice structures with triangular prisms in each comparison is at the lowest level and the stiffness-to-mass ratio remains at the maximum value, showing the overwhelming advantages in terms of mechanical strength. The excellent agreements between numerical results and experimental tests reveal the validity of FEA methods applied. The results in this work provide an explicit guideline to fabricate beam-like lattice structures with the best tensile and bending capabilities

A parallel cellular automata Lattice Boltzmann Method for convection-driven solidification

This article presents a novel coupling of numerical techniques that enable three-dimensional convection-driven microstructure simulations to be con- ducted on practical time scales appropriate for small-size components or experiments. On the microstructure side, the cellular automata method is efficient for relatively large-scale simulations, while the lattice Boltzmann method provides one of the fastest transient computational fluid dynamics solvers. Both of these methods have been parallelized and coupled in a single code, allowing resolution of large-scale convection-driven solidification problems. The numerical model is validated against benchmark cases, extended to capture solute plumes in directional solidification and finally used to model alloy solidification of an entire differentially heated cavity capturing both microstructural and meso-/macroscale phenomena

An otoprotective role for the apoptosis inhibitor protein survivin

Hearing impairment caused by ototoxic insults, such as noise or gentamicin is a worldwide health problem. As the molecular circuitries involved are not yet resolved, current otoprotective therapies are rather empirical than rational. Here, immunohistochemistry and western blotting showed that the cytoprotective protein survivin is expressed in the human and guinea pig cochlea. In the guinea pig model, moderate noise exposure causing only a temporary hearing impairment transiently evoked survivin expression in the spiral ligament, nerve fibers and the organ of Corti. Mechanistically, survivin upregulation may involve nitric oxide (NO)-induced Akt signaling, as enhanced expression of the endothelial NO synthase and phosphorylated Akt were detectable in some surviving-positive cell types. In contrast, intratympanic gentamicin injection inducing cell damage and permanent hearing loss correlated with attenuated survivin levels in the cochlea. Subsequently, the protective activity of the human and the guinea pig survivin orthologs against the ototoxin gentamicin was demonstrated by ectopic overexpression and RNAi-mediated depletion studies in auditory cells in vitro. These data suggest that survivin represents an innate cytoprotective resistor against stress conditions in the auditory system. The pharmacogenetic modulation of survivin may thus provide the conceptual basis for the rational design of novel therapeutic otoprotective strategies