Asymptotic Behavior of a Class of Evolution Variational Inequalities

We establish a new LaSalle's invariance principle and discuss the asymptotic behavior of a class of first-order evolution variational inequalities

An invariant set bifurcation theory for nonautonomous nonlinear evolution equations

In this paper we establish an invariant set bifurcation theory for the nonautonomous dynamical system (ϕλ, θ)X,H generated by the evolution equation ut + Au = λu + p(t, u), p ∈ H = H[ f(·, u)] (0.1) on a Hilbert space X, where A is a sectorial operator, λ is the bifurcation parameter, f(·, u) : R → X is translation compact, f(t, 0) ≡ 0 and H[ f ] is the hull of f(·, u). Denote by ϕλ := ϕλ(t, p)u the cocycle semiflow generated by the system. Under some other assumptions on f , we show that as the parameter λ crosses an eigenvalue λ0 ∈ R of A, the system bifurcates from 0 to a nonautonomous invariant set Bλ(·) on one-sided neighborhood of λ0. Moreover, lim λ→λ0 HXα (Bλ(p), 0) = 0, p ∈ P, where HXα (·, ·) denotes the Hausdorff semidistance in X (here X (α ≥ 0) defined below is the fractional power spaces associated with A). Our result is based on the pullback attractor bifurcation on the local central invariant manifolds Mλ loc(·)

An invariant set bifurcation theory for nonautonomous nonlinear evolution equations

In this paper we establish an invariant set bifurcation theory for the nonautonomous dynamical system $(\varphi_\lambda,\theta)_{X,\mathcal H}$ generated by the evolution equation \begin{equation}\label{e0}u_t+Au=\lambda u+p(t,u),\hspace{0.4cm} p\in \mathcal H=\mathcal H[f(\cdot,u)]\end{equation} on a Hilbert space $X$, where $A$ is a sectorial operator, $\lambda$ is the bifurcation parameter, $f(\cdot,u):\mathbb{R}\rightarrow X$ is translation compact, $f(t,0)\equiv0$ and $\mathcal H[f]$ is the hull of $f(\cdot,u)$. Denote by $\varphi_\lambda:=\varphi_\lambda(t,p)u$ the cocycle semiflow generated by the equation. Under some other assumptions on $f$, we show that as the parameter $\lambda$ crosses an eigenvalue $\lambda_0\in\mathbb{R}$ of $A$, the system bifurcates from $0$ to a nonautonomous invariant set $B_\lambda(\cdot)$ on one-sided neighborhood of $\lambda_0$. Moreover, $$\lim_{\lambda\rightarrow\lambda_0}H_{X^\alpha}\left(B_\lambda(p),0\right)=0,\hspace{0.4cm} p\in P,$$ where $H_{X^\alpha}(\cdot,\cdot)$ denotes the Hausdorff semidistance in $X^\alpha$ (here $X^\alpha$ ($\alpha\geq0$) defined below is the fractional power spaces associated with $A$). Our result is based on the pullback attractor bifurcation on the local central invariant manifolds $\mathcal {M}^\lambda_{\operatorname{loc}}(\cdot)$

Structural Controllability of Discrete-Time Linear Control Systems with Time-Delay: A Delay Node Inserting Approach

This paper is concerned with the structural controllability analysis for discrete-time linear control systems with time-delay. By adding virtual delay nodes, the linear systems with time-delay are transformed into corresponding linear systems without time-delay, and the structural controllability of them is equivalent. That is to say, the time-delay does not affect or change the controllability of the systems. Several examples are also presented to illustrate the theoretical results

detrex: Benchmarking Detection Transformers

The DEtection TRansformer (DETR) algorithm has received considerable attention in the research community and is gradually emerging as a mainstream approach for object detection and other perception tasks. However, the current field lacks a unified and comprehensive benchmark specifically tailored for DETR-based models. To address this issue, we develop a unified, highly modular, and lightweight codebase called detrex, which supports a majority of the mainstream DETR-based instance recognition algorithms, covering various fundamental tasks, including object detection, segmentation, and pose estimation. We conduct extensive experiments under detrex and perform a comprehensive benchmark for DETR-based models. Moreover, we enhance the performance of detection transformers through the refinement of training hyper-parameters, providing strong baselines for supported algorithms.We hope that detrex could offer research communities a standardized and unified platform to evaluate and compare different DETR-based models while fostering a deeper understanding and driving advancements in DETR-based instance recognition. Our code is available at https://github.com/IDEA-Research/detrex. The project is currently being actively developed. We encourage the community to use detrex codebase for further development and contributions.Comment: project link: https://github.com/IDEA-Research/detre

Targeting SALL4 by entinostat in lung cancer

The overall survival of lung cancer patients remains dismal despite the availability of targeted therapies. Oncofetal protein SALL4 is a novel cancer target. We herein report that SALL4 was aberrantly expressed in a subset of lung cancer patients with poor survival. SALL4 silencing by RNA interference or SALL4 peptide inhibitor treatment led to impaired lung cancer cell growth. Expression profiling of SALL4-knockdown cells demonstrated that both the EGFR and IGF1R signaling pathways were affected. Connectivity Map analysis revealed the HDAC inhibitor entinostat as a potential drug in treating SALL4-expressing cancers, and this was confirmed in 17 lung cancer cell lines. In summary, we report for the first time that entinostat can target SALL4-positive lung cancer. This lays the foundation for future clinical studies evaluating the therapeutic efficacy of entinostat in SALL4-positive lung cancer patients

Variant rs9939609 in the FTO gene is associated with body mass index among Chinese children

<p>Abstract</p> <p>Background</p> <p>Fat-mass and obesity-associated (<it>FTO</it>) gene is a gene located in chromosome region 16q12.2. Genetic variants in <it>FTO </it>are associated with the obesity phenotype in European and Hispanic populations. However, this association still remains controversial in Asian population. We aimed to test the association of <it>FTO </it>genetic variants with obesity and obesity-related metabolic traits among children living in Beijing, China.</p> <p>Methods</p> <p>We genotyped <it>FTO </it>variants rs9939609 in 670 children (332 girls and 338 boys) aged 8-11 years living in Beijing, and analyzed its association with obesity and obesity-related metabolic traits. Overweight and obesity were defined by age- and sex-specific BMI reference for Chinese children. Obesity-related metabolic traits included fasting plasma glucose, lipid profiles, leptin, ghrelin, adiponectin and blood pressures.</p> <p>Results</p> <p>The frequency of rs9939609 A allele was 12.2%, which was 21.9% for the heterozygote and 1.2% for the homozygote of the A allele. The obesity prevalence among the carriers of AA/AT genotypes was significantly higher than that among those with TT genotype (36.4% <it>vs</it>. 22.6%, <it>P </it>= 0.004). Compared to the carrier of TT genotype, the likelihood of obesity was 1.79 (95% confidence interval (95% CI) 1.20-2.67, <it>P </it>= 0.004) for the carrier of AA/AT genotype, after adjustment of sex, age and puberty stages. The BMI Z-score of children with AA/AT genotype were significantly higher than that of their counterparts with the TT genotype (1.1 ± 0.1 <it>vs</it>. 0.8 ± 0.1, <it>P </it>= 0.02). The concentration of triglyceride was 1.03 ± 0.52 mmol/L among TT carrier and 1.13 ± 0.68 mmol/L among AA/AT carrier (<it>P </it>= 0.045). While, the concentrations of adiponectin were 18.0 ± 0.4 μg/ml among carriers of TT and 16.2 ± 0.7 μg/ml among subjects with AA/AT genotype (<it>P </it>= 0.03). The level of glucose marginally increased in the AA/AT genotype subjects (4.67 ± 0.40 mmol/L <it>vs</it>. 4.60 ± 0.35 mmol/L, <it>P </it>= 0.08). The evidence of association was reduced after adjustment for BMI (<it>P </it>= 0.38 for triglyceride, <it>P </it>= 0.20 for adiponectin and glucose). There was weak evidence of association between rs9939609 and other obesity-related metabolic traits including total cholesterol (3.92 ± 0.03 mmol/L <it>vs</it>. 4.02 ± 0.05 mmol/L, <it>P </it>= 0.10), insulin (2.69 ± 1.77 ng/ml <it>vs</it>. 3.12 ± 2.91 ng/ml, <it>P </it>= 0.14), and insulin resistance (HOMA-IR 0.56 ± 0.03 <it>vs</it>. 0.66 ± 0.05, <it>P </it>= 0.10).</p> <p>Conclusions</p> <p>Genetic variation in the <it>FTO </it>gene associates with obesity in Chinese children.</p

Research on Operation Mode of the Yalong River Cascade Reservoirs Based on Improved Stochastic Fractal Search Algorithm

With the completion of the Lianghekou Reservoir, with a multiyear regulation capacity, the operation relationship of the cascade reservoirs in the Yalong River is becoming increasingly complex. In order to study an optimal operation mode of the cascade reservoirs in the Yalong River under different inflow frequencies, based on the shortcomings of the existing single reservoir operation mode and the local joint operation mode of the cascade reservoirs, this paper first proposed a global joint operation mode for the cascade reservoirs to develop the power generation potential of daily regulating reservoirs and then gave a solution method for the cascade reservoirs&rsquo; operational model based on an improved stochastic fractal search (ISFS) algorithm. Finally, taking the maximum power generation as the goal and the inflow data of five typical years as the model inputs, this paper analyzed the differences in the power generation and water abandonment results of the cascade reservoirs in the middle and lower reaches of the Yalong River under the above three operation modes. The results show that (1) compared with the stochastic fractal search (SFS) algorithm and the particle swarm optimization (PSO) algorithm, the ISFS algorithm had faster convergence speed and higher precision; (2) the global joint operation mode had a more significant optimization effect in the year with more inflow, followed by the local joint operation mode, and the single reservoir operation mode had the worst; however, the difference in the results of the three operation modes gradually decreased as the inflows gradually decreased

Research on Operation Mode of the Yalong River Cascade Reservoirs Based on Improved Stochastic Fractal Search Algorithm

With the completion of the Lianghekou Reservoir, with a multiyear regulation capacity, the operation relationship of the cascade reservoirs in the Yalong River is becoming increasingly complex. In order to study an optimal operation mode of the cascade reservoirs in the Yalong River under different inflow frequencies, based on the shortcomings of the existing single reservoir operation mode and the local joint operation mode of the cascade reservoirs, this paper first proposed a global joint operation mode for the cascade reservoirs to develop the power generation potential of daily regulating reservoirs and then gave a solution method for the cascade reservoirs’ operational model based on an improved stochastic fractal search (ISFS) algorithm. Finally, taking the maximum power generation as the goal and the inflow data of five typical years as the model inputs, this paper analyzed the differences in the power generation and water abandonment results of the cascade reservoirs in the middle and lower reaches of the Yalong River under the above three operation modes. The results show that (1) compared with the stochastic fractal search (SFS) algorithm and the particle swarm optimization (PSO) algorithm, the ISFS algorithm had faster convergence speed and higher precision; (2) the global joint operation mode had a more significant optimization effect in the year with more inflow, followed by the local joint operation mode, and the single reservoir operation mode had the worst; however, the difference in the results of the three operation modes gradually decreased as the inflows gradually decreased