Homotopical Minimal Measures for Geodesic flows on Surfaces of Higher Genus

We study the homotopical minimal measures for positive definite autonomous Lagrangian systems. Homotopical minimal measures are action-minimizers in their homotopy classes, while the classical minimal measures (Mather measures) are action-minimizers in homology classes. Homotopical minimal measures are much more general, they are not necessarily homological action-minimizers. However, some of them can be obtained from the classical ones by lifting them to finite-fold covering spaces. We apply this idea of finite covering to the geodesic flows on surfaces of higher genus. Let $(M,G)$ be a compact closed surface with genus $g>1$, where $G$ is a complete Riemannian metric on $M$. Consider the positive definite autonomous Lagrangian $L(x,v)=G_x(v,v)$, whose Lagrangian system $\phi_t: TM\rightarrow TM$ is exactly the complete geodesic flow on $TM$. We show that for each homotopical minimal ergodic measure $\mu$ that is supported on a nontrivial simple closed periodic trajectory, there is a finite-fold covering space $M'$ such that each ergodic preimage of $\mu$ on $TM'$ is a minimal measure in the classic Mather theory for the Lagrangian system on $TM'$

Fractional matching preclusion for butterfly derived networks

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu [18] recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number (FMP number) of G, denoted by fmp(G), is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number (FSMP number) of G, denoted by fsmp(G), is the minimum number of vertices and edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we study the fractional matching preclusion number and the fractional strong matching preclusion number for butterfly network, augmented butterfly network and enhanced butterfly network

The effect of beta-blockers on mortality in patients with heart failure and atrial fibrillation: A meta-analysis of observational cohort and randomized controlled studies

Background: Beta-blockers (BB) are the cornerstone of therapy for heart failure (HF); however, theeffects of these drugs on the prognosis of patients with concomitant atrial fibrillation (AF) remaincontroversial. The objective of this meta-analysis was to evaluate the efficacy of BB on mortality in HFcoexisting with AF.Methods: A systematic search of PubMed, Embase and the Cochrane Library databases wasconducted. Observational cohort studies and randomized controlled trials reporting outcomes ofmortality or HF hospitalizations for patients with HF and AF, being assigned to BB treatment.A non-BB group was also included.Results: A total of 8 clinical studies (5 randomized controlled trials and 3 observational cohort studies)involving 34197 patients were included in the analysis. The pooled analysis demonstrated that BBtreatment was associated with a 22% reduction in relative risk of all-cause mortality in patients withHF and AF (RR: 0.78; 95% CI 0.71–0.86; p < 0.00001; I2 = 27%). The pooled analysis of 5 studiesreported the outcome of HF hospitalization (2774 patients) which showed that BB therapy was not associatedwith a reduction of HF hospitalizations (RR: 0.94; 95% CI 0.79–1.11; p = 0.46; I2 = 38%).Conclusions: Meta-analysis suggests the potential mortality benefit of BB in patients with HF and AF.It was concluded herein that it is premature to deny patients with AF and HF to receive BB therapyconsidering current evidence

GIFD: A Generative Gradient Inversion Method with Feature Domain Optimization

Federated Learning (FL) has recently emerged as a promising distributed machine learning framework to preserve clients' privacy, by allowing multiple clients to upload the gradients calculated from their local data to a central server. Recent studies find that the exchanged gradients also take the risk of privacy leakage, e.g., an attacker can invert the shared gradients and recover sensitive data against an FL system by leveraging pre-trained generative adversarial networks (GAN) as prior knowledge. However, performing gradient inversion attacks in the latent space of the GAN model limits their expression ability and generalizability. To tackle these challenges, we propose \textbf{G}radient \textbf{I}nversion over \textbf{F}eature \textbf{D}omains (GIFD), which disassembles the GAN model and searches the feature domains of the intermediate layers. Instead of optimizing only over the initial latent code, we progressively change the optimized layer, from the initial latent space to intermediate layers closer to the output images. In addition, we design a regularizer to avoid unreal image generation by adding a small ${l_1}$ ball constraint to the searching range. We also extend GIFD to the out-of-distribution (OOD) setting, which weakens the assumption that the training sets of GANs and FL tasks obey the same data distribution. Extensive experiments demonstrate that our method can achieve pixel-level reconstruction and is superior to the existing methods. Notably, GIFD also shows great generalizability under different defense strategy settings and batch sizes.Comment: ICCV 202

2-Amino-4-(2-chloro­phen­yl)-7,7-di­methyl-5-oxo-5,6,7,8-tetra­hydro-4H-chromene-3-carbonitrile hemihydrate

The asymmetric unit of the title compound, C18H17ClN2O2·0.5H2O, contains two organic mol­ecules and one solvent water mol­ecule. In each organic mol­ecule, the cyclo­hexene ring adopts an envelope conformation with the C atom connecting the two methyl groups on the flap; the 4H-pyran ring is nearly planar [maximum deviation = 0.113 (3) Å in one mol­ecule and 0.089 (3) Å in the other mol­ecule] and is approximately perpendicular to the chloro­phenyl ring [dihedral angle = 86.43 (15)° in one mol­ecule and 89.73 (15)° in the other mol­ecule]. Inter­molecular N—H⋯N, N—H⋯O, O—H⋯O and O—H⋯Cl hydrogen bonding is present in the crystal