The traditional approaches to false discovery rate (FDR) control in multiple hypothesis testing are usually based on the null distribution of a test statistic. However, all types of null distributions, including the theoretical, permutation-based and empirical ones, have some inherent drawbacks. For example, the theoretical null might fail because of improper assumptions on the sample distribution. Here, we propose a null distribution-free approach to FDR control for multiple hypothesis testing in the case-control study. This approach, named target-decoy procedure, simply builds on the ordering of tests by some statistic or score, the null distribution of which is not required to be known. Competitive decoy tests are constructed from permutations of original samples and are used to estimate the false target discoveries. We prove that this approach controls the FDR when the score function is symmetric and the scores are independent between different tests. Simulation demonstrates that it is more stable and powerful than two popular traditional approaches, even in the existence of dependency. Evaluation is also made on two real datasets, including an arabidopsis genomics dataset and a COVID-19 proteomics dataset.

In this paper, we study the existence of positive solution for the $p$-Laplacian equations with fractional critical nonlinearity \[ \begin{cases} (-\Delta)^{s}_{p}u+V(x)|u|^{p-2}u=K(x)f(u)+P(x)|u|^{p^{*}_{s}-2}u, \qquad x\in \mathbb{R}^{N}, \\ u\in \mathcal {D}^{s,p}(\mathbb{R}^{N}), \end{cases} \] where $s\in(0,1), \ p^{*}_{s}=\frac{Np}{N-sp}, \ N>sp, \ p>1$ and $ V(x),K(x)$ are positive continuous functions which vanish at infinity, $f$ is a function with a subcritical growth, and $P(x)$ is bounded, nonnegative continuous function. By using variational method in the weighted spaces, we prove the above problem has at least one positive solution.

This paper proposes an approximate analytical solution method to calculate counterparty credit risk exposures. Compared with the Standard Approach for measuring Counterparty Credit Risk and the Internal Modeling Method provided by Basel Committee, the proposed method significantly improves the calculation efficiency based on sacrificing a little accuracy. Taking Forward Rate Agreement as an example, this article derives the exact expression for Expected Exposure. By approximating the distribution of Forward Rate Agreement’s future value to a normal distribution, the approximate analytical expression for Potential Future Exposure is derived. Numerical results show that this method is reliable and is robust under different parameters.

This paper considers an on-off fluid queue model. The on and off states of the system appear alternately, and the sojourn times at these two different states are independent, and each one follows an exponential distribution. The fluid flows into the system buffer with some strategies to wait for the system service under the first-come first-served discipline. Here the system can process the fluid in the buffer only when the system is on state. With given utility functions such as an expected average social profit, and an individual expected profit, the equilibrium strategies are characterized under both the fully unobservable case and the partially observable case.

The authors present some new criteria for oscillation and asymptotic behavior of solutions of third-order nonlinear differential equations with a sublinear neutral term of the form $$\left(r(t)(z''(t))^{\alpha}\right)'+\int^{d}_{c}q(t,\xi)f\left(x\left(\sigma(t,\xi)\right)\right)d\xi=0, \qquad t\geq t_{0}$$ where $z(t)=x(t)+\int^{b}_{a}p(t,\xi)x^{\gamma}\left(\tau(t,\xi)\right)d\xi,~0<\gamma\leq1.$ Under the conditions $\int^{\infty}_{t_{0}}r^{-\frac{1}{\alpha}}(t)dt=\infty$ or $\int^{\infty}_{t_{0}}r^{-\frac{1}{\alpha}}(t)dt<\infty.$ The results obtained here extend, improve and complement to some known results in the literature. Examples are provided to illustrate the theorems.

In this paper, we derive a time-dependent Ginzburg-Landau model for liquid ⁴He coupling with an applied magnetic field basing on the Le Châtlier principle.
We also obtain the existence and uniqueness of global weak solution for this model. In addition, by utilizing the regularity estimates for linear semigroup, we prove that the model possesses a global classical solution.

As biological studies become more expensive to conduct, it is a frequently encountered question that how to take advantage of the available auxiliary covariate information when the exposure variable is not measured. In this paper, we propose an induced cure rate mean residual life time regression model to accommodate the survival data with cure fraction and auxiliary covariate, in which the exposure variable is only assessed in a validation set, but a corresponding continuous auxiliary covariate is ascertained for all subjects in the study cohort. Simulation studies elucidate the practical performance of the proposed method under finite samples. As an illustration, we apply the proposed method to a heart disease data from the Study of Left Ventricular Dysfunction.

A tournament is an orientation of the complete graph. Tournaments form perhaps the most interesting class of digraphs and it has a great potential for application. Tournaments provide a model of the statistical technique called the method of paired comparisons and they have also been studied in connection with sociometric relations in small groups. In this paper, we investigate disjoint cycles of the same length in tournaments. In 2010, Lichiardopol conjectured that for given integers l ≥ 3 and k ≥ 1, any tournament with minimum out-degree at least (l - 1)k - 1 contains k disjoint l-cycles, where an l-cycle is a cycle of order l. Bang-Jensen et al. verified the conjecture for l = 3 and Ma et al. proved that it also holds for l ≥ 10. This paper provides a proof of the conjecture for the case of 9 ≥ l ≥ 4

n this paper, we deal with the nonlinear second-order differential equation with damped vibration term involving p-Laplacian operator. Of particular interest is the resolution of an open problem. An interesting outcome from our result is that we can obtain the fast homoclinic solution with general superlinear growth assumption in suitable Sobolev space. To our knowledge, our theorems appear to be the first such result about damped vibration problem with p-Laplacian operator.

In this paper, we study the well-posedness and the asymptotic stability of a one-dimensional thermoelastic microbeam system, where the heat conduction is given by Gurtin-Pipkin thermal law. We first establish the well-posedness of the system by using the semigroup arguments and Lumer-Phillips theorem. We then obtain an explicit and general formula for the energy decay rates through perturbed energy method and some properties of the convex functions.

A graph G is called a fractional [a, b]-covered graph if for each e ∈ E(G), G contains a fractional [a,b]-factor covering e. A graph G is called a fractional (a,b,k)-critical covered graph if for any W ⊆ V (G) with |W| = k, G - W is fractional [a, b]-covered, which was first defined and investigated by Zhou, Xu and Sun [S. Zhou, Y. Xu, Z. Sun, Degree conditions for fractional (a,b,k)-critical covered graphs, Information Processing Letters 152(2019)105838]. In this work, we proceed to study fractional (a,b,k)-critical covered graphs and derive a result on fractional (a,b,k)-critical covered graphs depending on minimum degree and neighborhoods of independent sets.

For some infectious diseases such as mumps, HBV, there is evidence showing that vaccinated individuals always lose their immunity at different rates depending on the inoculation time. In this paper, we propose an age-structured epidemic model using a step function to describe the rate at which vaccinated individuals lose immunity and reduce the age-structured epidemic model to the delay differential model. For the age-structured model, we consider the positivity, boundedness, and compactness of the semiflow and study global stability of equilibria by constructing appropriate Lyapunov functionals. Moreover, for the reduced delay differential equation model, we study the existence of the endemic equilibrium and prove the global stability of equilibria. Finally, some numerical simulations are provided to support our theoretical results and a brief discussion is given.

In this paper, we investigate dual problems for nonconvex set-valued vector optimization via abstract subdifferential. We first introduce a generalized augmented Lagrangian function induced by a coupling vector-valued function for set-valued vector optimization problem and construct related set-valued dual map and dual optimization problem on the basic of weak efficiency, which used by the concepts of supremum and infimum of a set. We then establish the weak and strong duality results under this augmented Lagrangian and present sufficient conditions for exact penalization via an abstract subdifferential of the object map. Finally, we define the sub-optimal path related to the dual problem and show that every cluster point of this sub-optimal path is a primal optimal solution of the object optimization problem. In addition, we consider a generalized vector variational inequality as an application of abstract subdifferential.

In this paper, we investigate a delayed HIV infection model that considers the homeostatic proliferation of CD4⁺ T cells. The existence and stability of uninfected equilibrium and infected equilibria (smaller and larger ones) are studied by analyzing the characteristic equation of the system. The intracellular delay does not affect the stability of uninfected equilibrium, but it can change the stability of larger positive equilibrium and Hopf bifurcation appears inducing stable limit cycles. Furthermore, direction and stability of Hopf bifurcation are well investigated by using the central manifold theorem and the normal form theory. The numerical simulation results show that the stability region of larger positive equilibrium becomes smaller as the increase of time delay. Moreover, when the maximum homeostatic growth rate is very small, the larger positive equilibrium is always stable. On the contrary, when the rate of supply of T cells is very small, the larger positive equilibrium is always unstable.

In this paper we first establish the uniform regularity of smooth solutions with respect to the viscosity coefficients to the isentropic compressible magnetohydrodynamic system in a periodic domain $\mathbb{T}^n$. We then apply our result to obtain the isentropic compressible magnetohydrodynamic system with zero viscosity.

Let $m$, $t$, $r$ and $k_i$ $(1\leq i\leq m)$ be positive integers with $k_i\geq\frac{(t+3)r}{2}$, and $G$ be a digraph with vertex set $V(G)$ and arc set $E(G)$. Let $H_1,H_2,\cdots,H_t$ be $t$ vertex-disjoint subdigraphs of $G$ with $mr$ arcs. In this article, it is verified that every $[0,k_1+k_2+\cdots+k_m-(m-1)r]$-digraph $G$ has a $[0,k_i]_1^{m}$-factorization $r$-orthogonal to every $H_i$ for $1\leq i\leq t$.

A bio-safe dengue control strategy is to use Wolbachia, which can induce incomplete cytoplasmic incompatibility (CI) and reduce the mating competitiveness of infected males. In this work, we formulate a delay differential equation model, including both the larval and adult stages of wild mosquitoes, to assess the impacts of CI intensity ξ and mating competitiveness θ of infected males on the suppression efficiency. Our analysis identifies a CI intensity threshold ξ^* below which a successful suppression is impossible. When ξ≥ξ^*, the wild population will be eliminated ultimately if the releasing level exceeds the release amount threshold R^* uniformly. The dependence of R^* on ξ and θ, and the impact of temperature on suppression are further exhibited through numerical examples. Our analyses indicate that a slight reduction of ξ is more devastating than significantly decrease of θ in the suppression efficiency. To suppress more than 95% wild mosquitoes during the peak season of dengue in Guangzhou, the optimal starting date for releasing is sensitive to ξ but almost independent of θ. One percent reduction of ξ from 1 requires at least one week earlier in the optimal releasing starting date from 7 weeks ahead of the peak season of dengue.

We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming. At each iteration, we solve a linear semidefinite programming to test whether the linearized constraints are consistent or not. The search direction is generated by a piecewise quadratic-linear model of the exact penalty function. The penalty parameter is only related to the information of the current iterate point. The line search strategy is a penalty-free one. Global and local convergence are analyzed under suitable conditions. We finally report some numerical experiments to illustrate the behavior of the algorithm on various degeneracy situations.

We consider non-autonomous ordinary differential equations in two cases. One is the one-dimensional case that admits a condition of hyperbolicity, and the other one is the higher-dimensional case that admits an exponential dichotomy. For differential equations of this kind, we give a rigorous treatment of the Harmonic Balance Method to look for almost periodic solutions.

In present work studied the new boundary value problem for semi linear (Power-type nonlinearities) system equations of mixed hyperbolic -elliptic Keldysh type in the multivariate dimension with the changing time direction. Considered problem and equation belongs to the modern level partial differential equations. Applying methods of functional analysis, topological methods, “ε” -regularizing. and continuation by the parameter at the same time with aid of a prior estimates, under assumptions conditions on coefficients of equations of system, the existence and uniqueness of generalized and regular solutions of a boundary problem are established in a weighted Sobolev’s space. In this work one of main idea consists of show that the new boundary value problem which investigated in case of linear system equations can be well-posed when added nonlinear terms to this linear system equations, moreover in this case constructed new weithged spaces, the identity between of strong and weak solutions is established.

In this paper, we consider a modification of the well-known logistic family using a family of fuzzy numbers. The dynamics of this modified logistic map is studied by computing its topological entropy with a given accuracy. This computation allows us to characterize when the dynamics of the modified family is chaotic. Besides, some attractors that appear in bifurcation diagrams are explained. Finally, we will show that the dynamics induced by the logistic family on the fuzzy numbers need not be complicated at all.

For a revised model of Caldentey and Stacchetti (Econometrica, 2010) in continuous-time insider trading with a random deadline which allows market makers to observe some information on a risky asset, a closed form of its market equilibrium consisting of optimal insider trading intensity and market liquidity is obtained by maximum principle method. It shows that in the equilibrium, (i) as time goes by, the optimal insider trading intensity is exponentially increasing even up to infinity while both the market liquidity and the residual information are exponentially decreasing even down to zero; (ii) the more accurate information observed by market makers, the stronger optimal insider trading intensity is such that the total expect profit of the insider is decreasing even go to zero while both the market liquidity and the residual information are decreasing; (iii) the longer the mean of random time, the weaker the optimal insider trading intensity is while the more both the residual information and the expected profit are, but there is a threshold of trading time, half of the mean of the random time, such that if and only if after it the market liquidity is increasing with the mean of random time increasing.

We study the Schwarzschild spacetime solutions to the Einstein-Euler equations. In our analysis, we aim to show local stability under small perturbations. To resolve this problem, we use the Nash-Moser (-Hamilton) theorem. The work was originally developed for the nonrelativistic Euler-Poisson equations.

In this paper, we study the global behavior of solutions to the spherically symmetric(it means that the problem is 2+2 framework)coupled Nonlinear-Einstein-Klein-Gordon (NLEKG) system in the presence of a negative cosmological constant. We prove the well posedness of the NLEKG system in the Schwarzschild-AdS spacetimes and that the Schwarzschild-AdS spacetimes (the trivial black hole solutions of the EKG system for which ϕ = 0 identically) are asymptotically stable. Small perturbations of Schwarzschild-AdS initial data again lead to regular black holes, with the metric on the black hole exterior approaching a SchwarzschildAdS spacetime. Bootstrap argument on the black hole exterior, with the redshift effect and weighted Hardy inequalities playing the fundamental role in the analysis. Both integrated decay and pointwise decay estimates are obtained.

In this paper, we consider the statistical inferences in a partially linear model when the model error follows an autoregressive process. A two-step procedure is proposed for estimating the unknown parameters by taking into account of the special structure in error. Since the asymptotic matrix of the estimator for the parametric part has a complex structure, an empirical likelihood function is also developed. We derive the asymptotic properties of the related statistics under mild conditions. Some simulations, as well as a real data example, are conducted to illustrate the finite sample performance.

The perfect matching polytope of a graph $G$ is the convex hull of the incidence vectors of all perfect matchings of $G$. A graph $G$ is PM-compact if the 1-skeleton graph of the prefect matching polytope of $G$ is complete. Equivalently, a matchable graph $G$ is PM-compact if and only if for each even cycle $C$ of $G$, $G-V(C)$ has at most one perfect matching. This paper considers the class of graphs from which deleting any two adjacent vertices or nonadjacent vertices, respectively, the resulting graph has a unique perfect matching. The PM-compact graphs in this class of graphs are presented.

Delta-matroid theory is often thought of as a generalization of topological graph theory. It is well-known that an orientable embedded graph is bipartite if and only if its Petrie dual is orientable. In this paper, we first introduce the concepts of Eulerian and bipartite delta-matroids and then extend the result from embedded graphs to arbitrary binary delta-matroids. The dual of any bipartite embedded graph is Eulerian. We also extend the result from embedded graphs to the class of delta-matroids that arise as twists of binary matroids. Several related results are also obtained.

In this paper, the bilinear formalism, bilinear Bäcklund transformations and Lax pair of the (2+1)-dimensional KdV equation are constructed by the Bell polynomials approach. The N-soliton solution is derived directly from the bilinear form. Especially, based on the two-soliton solution, the lump solution is given out analytically by taking special parameters and using Taylor expansion formula. With the help of the multidimensional Riemann theta function, multiperiodic (quasiperiodic) wave solutions for the (2+1)-dimensional KdV equation are obtained by employing the Hirota bilinear method. Moreover, the asymptotic properties of the one- and two-periodic wave solution, which reveal the relations with the single and two-soliton solution, are presented in detail.

A vertex-colored path $P$ is rainbow if its internal vertices have distinct colors; whereas $P$ is monochromatic if its internal vertices are colored the same. For a vertex-colored connected graph $G$, the rainbow vertex-connection number ${\rm rvc} (G)$ is the minimum number of colors used such that there is a rainbow path joining any two vertices of $G$; whereas the monochromatic vertex-connection number ${\rm mvc} (G)$ is the maximum number of colors used such that any two vertices of $G$ are connected by a monochromatic path. These two opposite concepts are the vertex-versions of rainbow connection number ${\rm rc} (G)$ and monochromatic connection number ${\rm mc} (G)$ respectively. The study on ${\rm rc} (G)$ and ${\rm mc} (G)$ of random graphs drew much attention, and there are few results on the rainbow and monochromatic vertex-connection numbers. In this paper, we consider these two vertex-connection numbers of random graphs and establish sharp threshold functions for them, respectively.

Let $K_{1,k}$ be a star of order $k+1$ and $K_n\sqcup K_{1,k}$ the graph obtained from a complete graph $K_n$ and an additional vertex $v$ by joining $v$ to $k$ vertices of $K_n$. For graphs $G$ and $H$, the star-critical Ramsey number $r_*(G,H)$ is the minimum integer $k$ such that any red/blue edge-coloring of $K_{r-1}\sqcup K_{1,k}$ contains a red copy of $G$ or a blue copy of $H$, where $r$ is the classical Ramsey number $R(G,H)$. Let $C_m$ denote a cycle of order $m$ and $W_n$ a wheel of order $n+1$. Hook (2010) proved that $r_*(W_n,C_3)=n+3$ for $n\geq6$. In this paper, we show that $r_*(W_n,C_m)=n+3$ for $m$ odd, $m\geq5$ and $n\geq 3(m-1)/2+2$.

In this paper, we analyze the existence, multiplicity and nonexistence of nontrivial radial convex solutions to the following system coupled by singular Monge-Ampère equations $$ \left \{ \begin{array}{l} \text{det}\ D^2u_1=\lambda h_1(|x|)f_1(-u_2), \qquad \text{in} \ \ \Omega,\\ \text{det}\ D^2u_2=\lambda h_2(|x|)f_2(-u_1), \qquad \text{in} \ \ \Omega,\\ u_1=u_2=0, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{on} \ \ \partial \Omega \end{array} \right. $$ for a certain range of $\lambda >0$, $h_i$ are weight functions, $f_i$ are continuous functions with possible singularity at $0$ and satisfy a combined $N$-superlinear growth at $\infty$, where $i\in \{1,2\}$, $\Omega$ is the unit ball in $\mathbb{R}^N$. We establish the existence of a nontrivial radial convex solution for small $\lambda$, multiplicity results of nontrivial radial convex solutions for certain ranges of $\lambda$, and nonexistence results of nontrivial radial solutions for the case $\lambda\gg 1$. The asymptotic behavior of nontrivial radial convex solutions is also considered.

It is difficult to characterize graphs which contain no a 2-connected graph as a minor in graph theory. Let V₈ be a graph constructed from an 8-cycle by connecting the antipodal vertices. There are thirteen 2-connected spanning subgraphs of V₈. In particular, one of them is obtained from the Petersen graph by deleting two vertices and it is also a hard problem to characterize Petersen-minor-free graphs. In this paper, we characterize internally 4-connected graphs which contain a 2-connected spanning subgraph of V₈ as a forbidden minor.

Joint analysis of multiple phenotypes can have better interpretation of complex diseases and increase statistical power to detect more significant single nucleotide polymorphisms (SNPs) compare to traditional single phenotype analysis in genome-wide association analysis. Principle component analysis (PCA), as a popular dimension reduction method, has been broadly used in the analysis of multiple phenotypes. Since PCA transforms the original phenotypes into principal components (PCs), it is natural to think that by analyzing these PCs, we can combine information across phenotypes. Existing PCA-based methods can be divided into two categories, either selecting one particular PC manually or combining information from all PCs. In this paper, we propose an adaptive principle component test (APCT) which selects and combines the PCs adaptively by using Cauchy combination method. Our proposed method can be seen as a generalization of traditional PCA based method since it contains two existing methods as special situation. Extensive simulation shows that our method is robust and can generate powerful result in various situations. The real data analysis of stock mice data also demonstrate that our proposed APCT can identify significant SNPs that are missed by traditional methods.