Study on the Effect of Repetitive Peripheral Magnetic Stimulation Combined with Conventional Rehabilitation Measures on Shoulder Dysfunction in Early Stroke

Objective:To study the effect of repetitive peripheral magnetic stimulation(rPMS)combined with conventional rehabilitation measures on shoulder dysfunction in early stroke.Methods:60 patients with shoulder dysfunction in early stroke were selected,and all of them were admitted to our hospital from August 2021 to August 2023.The patients were randomly grouped into a control group(conventional rehabilitation measures intervention,30 cases)and an intervention group(rPMS and conventional rehabilitation measures intervention,30 cases)according to the lottery method.The pain scores,shoulder mobility,and motor function scores of the two groups were compared.Results:The pain score was lower in the intervention group,and the shoulder mobility and motor function scores were higher in the intervention group(P<0.05)as compared to that of the control group.Conclusion:The effect of combining rPMS and conventional rehabilitation measures in treating shoulder dysfunction in early stroke was remarkable and should be popularized.

Multistability of delayed complex-valued recurrent neural networks with discontinuous real-imaginarytype activation functions

In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.

Functions of “Marriage” in Shakespeare's Measure for Measure

Marriage is usually associated with happiness and harmony. But in Shakespear's Measure for Measure, it seems it is infused with power of law. Is it a clear-cut punishment or reward? Its qualities revolve around the individual situations in which it occurs, which is interpreted and deployed by characters in the play in different ways.

The Exact Measure Functions of the Images for a Class of Self-Similar Processes

Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.

Determination of the degree 120 time-variable gravity field in the Sichuan-Yunnan region using Slepian functions and terrestrial measurements

The terrestrial time-variable gravity measurements are characterized by a high signal-to-noise ratio and sensitivity to the sources of mass change in the Earth's crust.These gravity data have many applications,such as surface deformation,groundwater storage changes,and mass migration before and after earthquakes.Based on repeated terrestrial gravity measurements at 198 gravity stations in the Sichuan-Yunnan region(SYR)from 2015 to 2017,we determine a time series of degree 120 gravity fields using the localized spherical harmonic(Slepian)basis functions.Our results show that adopting the first 6 Slepian basis functions is sufficient for effective localized Slepian modeling in the SYR.The differences between two gravity campaigns at the same time of year show an obvious correlation with tectonic features.The degree 120 timevariable gravity models presented in this paper will benefit the study of the regional mass migration inside the crust of the SYR and supplement the existing geophysical models for the China Seismic Experimental Site.

Scattering of Geometric Algebra Wave Functions and Collapse in Measurements

The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function.

Analytical Evaluation of Non-Elementary Integrals Involving Some Exponential, Hyperbolic and Trigonometric Elementary Functions and Derivation of New Probability Measures Generalizing the Gamma-Type and Gaussian-Type Distributions

The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, and where α,η and β are real or complex constants are evaluated in terms of the confluent hypergeometric function 1F1 and the hypergeometric function 1F2. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions 1F1 and 1F2. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (x2) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.

Beyond functional MRI signals:molecular and cellular modifiers of the functional connectome and cognition

Our brain is constantly active.Even at rest,the brain carries out essential functions such as maintenance of resting potentials,subthreshold synaptic activity,and spiking activity related to information processing.This resting activity can be assessed with several in vivo tools,such as resting-state functional magnetic resonance imaging.This technique measures subtle changes in blood flow,volume,and oxygenation that occur over time.Although vascular in nature,resting-state functional magnetic resonance imaging is considered a reliable proxy of neural activity and several studies have shown that the brain is functionally divided into interacting neural networks called the“functional connectome”.

CURRENTS CARRIED BY THE SUBGRADIENT GRAPHS OF SEMI-CONVEX FUNCTIONS AND APPLICATIONS TO HESSIAN MEASURES

In this paper we study integer multiplicity rectifiable currents carried by the subgradient （subdifferential） graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the structure theorem of the Lagrangian currents for semi-convex functions is given and the k-Hessian measures are calculated by a different method in terms of currents.

α-CARLESON MEASURE AND BLOCH FUNCTIONS ON BOUNDED SYMMETRIC DOMAINS OF C^n

In this paper we defineα-Carleson measure in the Bergman metric on bounded symmetric domains. Some necessary and sufficient conditions about it and Bloch functions on the domains are given.

Centrality Measures Based on Matrix Functions

Network is considered naturally as a wide range of different contexts, such as biological systems, social relationships as well as various technological scenarios. Investigation of the dynamic phenomena taking place in the network, determination of the structure of the network and community and description of the interactions between various elements of the network are the key issues in network analysis. One of the huge network structure challenges is the identification of the node(s) with an outstanding structural position within the network. The popular method for doing this is to calculate a measure of centrality. We examine node centrality measures such as degree, closeness, eigenvector, Katz and subgraph centrality for undirected networks. We show how the Katz centrality can be turned into degree and eigenvector centrality by considering limiting cases. Some existing centrality measures are linked to matrix functions. We extend this idea and examine the centrality measures based on general matrix functions and in particular, the logarithmic, cosine, sine, and hyperbolic functions. We also explore the concept of generalised Katz centrality. Various experiments are conducted for different networks generated by using random graph models. The results show that the logarithmic function in particular has potential as a centrality measure. Similar results were obtained for real-world networks.

The Lebesgue Measure of the Julia Sets of Permutable Transcendental Entire Functions

In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by the properties of permutable transcendental entire functions, we prove that if f and g are permutable transcendental entire functions, then mes (J(f)) = mes (J(g)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.

Algebraic Independence Measures for the Values of Mahler Type Functions

在这份报纸，我们分别地在复杂数字地和 p-adic 数字地里为 Mahler 类型函数的值给代数学的独立措施。

The Orthogonal Bases of Exponential Functions Based on Moran-Sierpinski Measures

Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1,0)^(t),(0,1)^(t)}is the Sierpinski digit.We prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1})if and only if 1/3(1,-1)A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).

MBIUS INVARIANT GRADIENT AND LITTLE α-BLOCH FUNCTIONS

In this paper, the authors get the characterizations of the integral and Car-leson type measure both associated with the invariant gradient for little a-Bloch functions in the unit ball of Cn. As a consequence, some results of Ouyang C H, Yang W S and Zhao R H in [4] and a result of Yang W S in [10] are extended.

Complex-Valued Neural Networks:A Comprehensive Survey

Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.

HIGHER RADIAL DERIVATIVE OF BLOCH TYPE FUNCTIONS

In this paper, The integral characterizations of alpha-Bloch (little alpha-Bloch) axe given in terms of higher radial derivative, and their characterizations of Caxleson type measure are obtained.

The pig as a preclinical traumatic brain injury model:current models,functional outcome measures,and translational detection strategies

Traumatic brain injury(TBI) is a major contributor of long-term disability and a leading cause of death worldwide. A series of secondary injury cascades can contribute to cell death, tissue loss, and ultimately to the development of functional impairments. However, there are currently no effective therapeutic interventions that improve brain outcomes following TBI. As a result, a number of experimental TBI models have been developed to recapitulate TBI injury mechanisms and to test the efficacy of potential therapeutics. The pig model has recently come to the forefront as the pig brain is closer in size, structure, and composition to the human brain compared to traditional rodent models, making it an ideal large animal model to study TBI pathophysiology and functional outcomes. This review will focus on the shared characteristics between humans and pigs that make them ideal for modeling TBI and will review the three most common pig TBI models–the diffuse axonal injury, the controlled cortical impact, and the fluid percussion models. It will also review current advances in functional outcome assessment measures and other non-invasive, translational TBI detection and measurement tools like biomarker analysis and magnetic resonance imaging. The use of pigs as TBI models and the continued development and improvement of translational assessment modalities have made significant contributions to unraveling the complex cascade of TBI sequela and provide an important means to study potential clinically relevant therapeutic interventions.

Nonlinear Measurement Function in the Ensemble Kalman Filter

ABSTRACT The optimal Kalman gain was analyzed in a rigorous statistical framework. Emphasis was placed on a comprehensive understanding and interpretation of the current algorithm, especially when the measurement function is nonlinear. It is argued that when the measurement function is nonlinear, the current ensemble Kalman Filter algorithm seems to contain implicit assumptions： the forecast of the measurement function is unbiased or the nonlinear measurement function is linearized. While the forecast of the model state is assumed to be unbiased, the two assumptions are actually equivalent. On the above basis, we present two modified Kalman gain algorithms. Compared to the current Kalman gain algorithm, the modified ones remove the above assumptions, thereby leading to smaller estimated errors. This outcome was confirmed experimentally, in which we used the simple Lorenz 3-component model as the test-bed. It was found that in such a simple nonlinear dynamical system, the modified Kalman gain can perform better than the current one. However, the application of the modified schemes to realistic models involving nonlinear measurement functions needs to be further investigated.