The potential mechanism and clinical application value of remote ischemic conditioning in stroke

Some studies have confirmed the neuroprotective effect of remote ischemic conditioning against stroke. Although numerous animal researches have shown that the neuroprotective effect of remote ischemic conditioning may be related to neuroinflammation, cellular immunity, apoptosis, and autophagy, the exact underlying molecular mechanisms are unclear. This review summarizes the current status of different types of remote ischemic conditioning methods in animal and clinical studies and analyzes their commonalities and differences in neuroprotective mechanisms and signaling pathways. Remote ischemic conditioning has emerged as a potential therapeutic approach for improving stroke-induced brain injury owing to its simplicity, non-invasiveness, safety, and patient tolerability. Different forms of remote ischemic conditioning exhibit distinct intervention patterns, timing, and application range. Mechanistically, remote ischemic conditioning can exert neuroprotective effects by activating the Notch1/phosphatidylinositol 3-kinase/Akt signaling pathway, improving cerebral perfusion, suppressing neuroinflammation, inhibiting cell apoptosis, activating autophagy, and promoting neural regeneration. While remote ischemic conditioning has shown potential in improving stroke outcomes, its full clinical translation has not yet been achieved.

FedCLCC:A personalized federated learning algorithm for edge cloud collaboration based on contrastive learning and conditional computing

Federated learning(FL)is a distributed machine learning paradigm for edge cloud computing.FL can facilitate data-driven decision-making in tactical scenarios,effectively addressing both data volume and infrastructure challenges in edge environments.However,the diversity of clients in edge cloud computing presents significant challenges for FL.Personalized federated learning(pFL)received considerable attention in recent years.One example of pFL involves exploiting the global and local information in the local model.Current pFL algorithms experience limitations such as slow convergence speed,catastrophic forgetting,and poor performance in complex tasks,which still have significant shortcomings compared to the centralized learning.To achieve high pFL performance,we propose FedCLCC:Federated Contrastive Learning and Conditional Computing.The core of FedCLCC is the use of contrastive learning and conditional computing.Contrastive learning determines the feature representation similarity to adjust the local model.Conditional computing separates the global and local information and feeds it to their corresponding heads for global and local handling.Our comprehensive experiments demonstrate that FedCLCC outperforms other state-of-the-art FL algorithms.

Necessary and Sufficient Conditions in Smooth Programming with Generalized Convexity

Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.

ON THE NECESSARY AND SUFFICIENT CONDITIONS TO SOLVE A HEAT EQUATION WITH GENERAL ADDITIVE GAUSSIAN NOISE

In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.

Necessary and Sufficient Conditions for Reactive Azeotropes in Multi-reaction Mixtures in Terms of Elemental Composition

Necessary and sufficient conditions for azeotropy in reactive mixtures are derived in terms of elemental composition, which shows that in the space of elemental compositions, they take the same functional form as the conditions for azeotropy in non-reactive mixtures. The production of methyl tert-butyl ether (MTBE) is taken as an example. It is found that there are a 'pseudo' intermediate-boiling ternary reactive azeotrope at p = 101.325kPa and two 'real' ternary reactive azeotropes at p = 101.325 Pa. The introduced elemental compositions also reduce the dimensionality of the phase diagrams and provide a natural set of variables for visualization of phase behavior.

NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM

In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We prove that (1) possesses at most one limit cycle and give out the necessary and sufficient conditions of existence and uniqueness of limit cycles.

A NECESSARY AND A SUFFICIENT CONDITION FOR THE EXISTENCE OF THE POSITIVE RADIAL SOLUTIONS TO HESSIAN EQUATIONS AND SYSTEMS WITH WEIGHTS

In this article, we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation technique. Our results complete and improve a work published recently by Zhang and Zhou（existence of entire positive k-convex radial solutions to Hessian equations and systems with weights. Applied Mathematics Letters,Volume 50, December 2015, Pages 48–55）.

Necessary Optimality Conditions for Multi-Objective Semi-Infinite Variational Problem

In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.

SUFFICIENT AND NECESSARY CONDITIONS ON THE EXISTENCE AND ESTIMATES OF BOUNDARY BLOW-UP SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATIONS

Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.

ON A CLASS OF BESICOVITCH FUNCTIONS TO HAVE EXACT BOX DIMENSION: A NECESSARY AND SUFFICIENT CONDITION

This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given bywhere 1 < s < 2, λk> tends to infinity as k→∞ and λk satisfies λk+1/λk≥λ>1. The results show thatis a necessary and sufficient condition for Graph(B(t)) to have same upper and lower box dimensions. For the fractional Riemann-Liouvtlle differential operator Du and the fractional integral operator D-v, the results show that if A is sufficiently large, then a necessary and sufficient condition for box dimensionof Graph(D-v(B)), 0 < v < s - 1, to be s - v and box dimension of Graph(Du(B)), 0 < u < 2 - s, to bes + u is also lim.

The convergence rate and necessary-and-sufficient condition for the consistency of isogeometric collocation method

Although the isogeometric collocation(IGA-C)method has been successfully utilized in practical applications due to its simplicity and efficiency,only a little theoretical results have been established on the numerical analysis of the IGA-C method.In this paper,we deduce the convergence rate of the consistency of the IGA-C method.Moreover,based on the formula of the convergence rate,the necessary and sufficient condition for the consistency of the IGA-C method is developed.These results advance the numerical analysis of the IGA-C method.

A NECESSARY AND SUFFICIENT CONDITION FOR THEOSCILLATION OF SOLUTIONS OF LIENARD TYPE SYSTEM WITH MULTIPLE SINGULAR POINTS

In this paper, a necessary and sufficient condition for teh solution of Lienard typesystem with muliiple singular points to oscillation under the more general assumptionis given.Results of the papers [1-4] are also extended and improved in this paper.

Necessary Conditions for the Application of Moving Average Process of Order Three

Invertibility is one of the desirable properties of moving average processes. This study derives consequences of the invertibility condition on the parameters of a moving average process of order three. The study also establishes the intervals for the first three autocorrelation coefficients of the moving average process of order three for the purpose of distinguishing between the process and any other process (linear or nonlinear) with similar autocorrelation structure. For an invertible moving average process of order three, the intervals obtained are , -0.5ρ2ρ1<0.5.

Necessary Conditions and Situational Variables of Payments for Ecosystem Services

Clarifying the necessary conditions for the emergence of payments for ecosystem services (PES) and the situational variables that affect PES is the basis for their interpretation, prediction, and selection. This article proposes an analytical framework for the emergence of PES and argues that the key to determining whether PES can occur and whether a selected PES program is appropriate is to evaluate the net gain. When payers anticipate that a PES program will provide a satisfactory number of ES and a net gain over the opportunity cost and will cover all costs, it is assumed that the program will be implemented. When it is difficult to accurately evaluate the net gain of PES, the situational variables that affect the costs and benefits need to be examined. The group characteristics, ES characteristics, spatial and temporal contacts between the suppliers and demanders, correlation with private goods and additionality are important situational variables that affect the emergence and choice of PES.

Some Necessary and Sufficient Condition of Multivariate Random Variable Satisfy Normal Distribution

In this paper,we extended some results of article[1],obtain some sufficient and necessary condition which multivariate random variable satisfy normal distribution.

A necessary and sufficient condition for positive solutions of singular fourth order boundary value problems

This paper deals with the existence of positive solutions for the singular fourth order boundary value problem.A necessary and sufficient condition for the existence of C3 positive solution is given by means of the monotone iterative technique.Furthermore,the uniqueness of the C3 positive solution,and the iterative sequence of the C3 positive solution are also obtained.

ON NECESSARY CONDITIONS FOR RESONANCE IN TURNING POINT PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.

NECESSARY AND SUFFICIENT CONDITIONS FOR THE ABSOLUTE STABILITY OF DISCRETE TYPE LURIE CONTROL SYSTEM

In this paper. it is discussed that the absohue stability for zero solution of thediscrete type Lurie control systmin which the nonlinear function f(σ) satisfying conditions as followsIt gives the necessary and sufficent conditions for the absolute stability forystem (I) under conditions (2).We also obtain the sufficient criteria for absolutesiability of the simplified system of (I) under conditions (3) .

NECESSARY AND SUFFICIENT CONDITIONS FOR THE ABSOLUTE STABILITY OF DISCRETE TYPE LURIE CONTROL SYSTEM

In this paper. it is discussed that the absolute for zero solution of the discrete type Lurie control systemin which the nonlinear function f(σ)satisfying conditions followsIt gives the necessary and sufficient conditions for the absolute stability for system (1) under conditions (2).We also obtain the sufficient for absolute stability of the simplified system of (1) under conditions (3) .

A NECESSARY AND SUFFICIENT CONDITION FOR SINGULAR NONLINEAR SECOND-ORDER BOUNDARY VALUE PROBLEMS TO HAVE POSITIVE SOLUTIONS

In this paper the following result is obtained: Suppose f(x,u,v) is nonnegative, continuous in ( a, b)×R +×R +; f may be singular at x=a (and/or x=b ) and v=0; f is nondecreasing on u for each x,v, nonincreasing on v for each x,u; there exists a constant q∈(0,1) such that t qf(x,t -1 u,tu)f(x,u,u)λ qf(x,λ -1 u,λu),0<t<1<λ, u∈R +. Then a necessary and sufficient condition for the equation u″+f(x,u,u)=0 on the boundary condition αu(a)-βu′(a)=0, γ(b)+δu′(b)=0 to have C 1(I) nonzero solutions is that 0<∫ b af(x,e(x),e(x))dx<∞, where α,β,γ,δ are nonnegative real numbers, Δ=(b-a)αγ+αδ+βγ>0, e(x)=G(x,x), G(x,y) is Green's function of above mentioned boundary value problem (when f(x,u,v)≡0). Received September 9,1996. Revised March 31,1997. 1991 MR Subject Classification: 34B.