Configuration space integrals and formal smooth structures

Watanabe disproved the 4-dimensional Smale conjecture by constructing topologically trivial $D^{4}$-bundles over spheres and showing that they are smoothly nontrivial using configuration space integrals. In this paper, we define a new version of configuration space integrals that only relies on a formal smooth structure on the $D^{4}$-bundle (i.e., a vector bundle structure on the vertical tangent microbundle). It coincides with Watanabe's definition when the $D^{4}$-bundle is smooth. We obtain several applications. First, we give a lower bound (in terms of the graph homology) on the dimension of the rational homotopy and homology groups of $\textrm{Top}(4)$ and $\textrm{Homeo}(S^4)$ (the homeomorphism group of $\mathbb{R}^4$ and $S^4$). In particular, this implies that $\textrm{Top}(4)$ and $\textrm{Homeo}(S^4)$ are not rationally equivalent to any finite-dimensional CW complexes. Second, we discover a generalized Miller-Morita-Mumford class $\kappa_{\theta}(\pi)\in H^{3}(B;\mathbf{Q})$, which is defined for any topological 4-manifold bundle $X\to E\to B$. This class obstructs the existence of a formal smooth structure on the bundle. Third, we show that for any compact, orientable, smooth 4-manifold $X$ (possibly with boundary), the inclusion map from its diffeomorphism group to its homeomorphism group is not rationally $2$-connected (hence not a weak homotopy equivalence). This implies that the space of smooth structures on $X$ has a nontrivial rational homotopy group in dimension 2.Comment: 79 pages, comments welcom

DYNAMICALLY MITIGATING BOTTLENECK EFFECT TO GUARANTEE QUALITY OF SERVICE IN LOW-POWER AND LOSSY NETWORKS

Techniques are described herein for providing an intelligent and dynamic routing policy for Quality of Service (QoS) based on Routing Protocol for Low-Power and Lossy Networks (RPL) Directed Acyclic Graph (DAG). This helps mitigate the bottleneck effect in a connected grid mesh by forecasting the capacity of the routing path. Each sender device may be able to forward packets based on QoS requirements to the proper next hop before RPL DAG updates by Expected Transmission Count (ETX) change. With this approach, the QoS of latency sensitive or low packet loss tolerance services can be better satisfied in the connected grid mesh network

Convergence of flow-based generative models via proximal gradient descent in Wasserstein space

Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance. Compared to the accumulating theoretical studies on related score-based diffusion models, analysis of flow-based models, which are deterministic in both forward (data-to-noise) and reverse (noise-to-data) directions, remain sparse. In this paper, we provide a theoretical guarantee of generating data distribution by a progressive flow model, the so-called JKO flow model, which implements the Jordan-Kinderleherer-Otto (JKO) scheme in a normalizing flow network. Leveraging the exponential convergence of the proximal gradient descent (GD) in Wasserstein space, we prove the Kullback-Leibler (KL) guarantee of data generation by a JKO flow model to be $O(\varepsilon^2)$ when using $N \lesssim \log (1/\varepsilon)$ many JKO steps ($N$ Residual Blocks in the flow) where $\varepsilon$ is the error in the per-step first-order condition. The assumption on data density is merely a finite second moment, and the theory extends to data distributions without density and when there are inversion errors in the reverse process where we obtain KL-$W_2$ mixed error guarantees. The non-asymptotic convergence rate of the JKO-type $W_2$-proximal GD is proved for a general class of convex objective functionals that includes the KL divergence as a special case, which can be of independent interest

Numerical simulation of fractal interface effect of mining-caused activation of fault

Mining-caused activation of fault is an important research subject in mining science. In the past, the influences of geometrical morphology of fault surface on the activation have not been revealed. In view of the fractal character of fault surface, the self-affine fractal curves and geological-mining models with these kinds of fractal fault surface are constructed in order to numerically simulate the mining-caused activation phenomenon of fractal fault surface, and the law of influence of fractal fault surface on mining subsidence is studied and summarized. Our study shows that the mining-cased activation of fault has remarkable fractal interface effect; the mechanical behavior of mining-caused shearing sliding of fault is correlated with its fractal dimension, and after mining-caused activation fault surface with different fractal dimensions will result in different stress fields and different displacement fields in the nearby rock mass

Immune dysregulation in sepsis: experiences, lessons and perspectives.

Sepsis is a life-threatening organ dysfunction syndrome caused by dysregulated host responses to infection. Not only does sepsis pose a serious hazard to human health, but it also imposes a substantial economic burden on the healthcare system. The cornerstones of current treatment for sepsis remain source control, fluid resuscitation, and rapid administration of antibiotics, etc. To date, no drugs have been approved for treating sepsis, and most clinical trials of potential therapies have failed to reduce mortality. The immune response caused by the pathogen is complex, resulting in a dysregulated innate and adaptive immune response that, if not promptly controlled, can lead to excessive inflammation, immunosuppression, and failure to re-establish immune homeostasis. The impaired immune response in patients with sepsis and the potential immunotherapy to modulate the immune response causing excessive inflammation or enhancing immunity suggest the importance of demonstrating individualized therapy. Here, we review the immune dysfunction caused by sepsis, where immune cell production, effector cell function, and survival are directly affected during sepsis. In addition, we discuss potential immunotherapy in septic patients and highlight the need for precise treatment according to clinical and immune stratification

Design and compressive behavior of controllable irregular porous scaffolds: based on Veronoi-tessellation and for additive manufacturing

Adjustment of the mechanical properties (apparent elastic modulus and compressive strength) in porous scaffolds is important for artificial implants and bone tissue engineering. In this study, a top-down design method based on Voronoi-Tessellation was proposed. This method was successful in obtaining the porous structures with specified and functionally graded porosity. The porous specimens were prepared by selective laser melting technology. Quasi-static compressive tests were conducted as well. The experiment results revealed that the mechanical properties were affected by both porosity and irregularity. The irregularity coefficient proposed in this study can achieve good accommodation and balance of “irregularity” and “controllability”. The method proposed in this study provides an efficient approach for the bionic design and topological optimization of scaffolds