Small data global regularity for simplified 3-D Ericksen-Leslie's compressible hyperbolic liquid crystal model

In this article, we consider the Ericksen-Leslie's hyperbolic system for compressible liquid crystal model in three spatial dimensions. Global regularity for small and smooth initial data near equilibrium is proved for the case that the system is a nonlinear coupling of compressible Navier-Stokes equations with wave map to $\mathbb{S}^2$. Our argument is a combination of vector field method and Fourier analysis. The main strategy to prove global regularity relies on an interplay between the control of high order energies and decay estimates, which is based on the idea inspired by the method of space-time resonances. In particular the different behaviors of the decay properties of the density and velocity field for compressible fluids at different frequencies play a key role.Comment: 61 pages; all comments wellcom

Scaling Limits of the Wasserstein information matrix on Gaussian Mixture Models

We consider the Wasserstein metric on the Gaussian mixture models (GMMs), which is defined as the pullback of the full Wasserstein metric on the space of smooth probability distributions with finite second moment. It derives a class of Wasserstein metrics on probability simplices over one-dimensional bounded homogeneous lattices via a scaling limit of the Wasserstein metric on GMMs. Specifically, for a sequence of GMMs whose variances tend to zero, we prove that the limit of the Wasserstein metric exists after certain renormalization. Generalizations of this metric in general GMMs are established, including inhomogeneous lattice models whose lattice gaps are not the same, extended GMMs whose mean parameters of Gaussian components can also change, and the second-order metric containing high-order information of the scaling limit. We further study the Wasserstein gradient flows on GMMs for three typical functionals: potential, internal, and interaction energies. Numerical examples demonstrate the effectiveness of the proposed GMM models for approximating Wasserstein gradient flows.Comment: 32 pages, 3 figure

Cosmological Fisher forecasts for next-generation spectroscopic surveys

Next-generation spectroscopic surveys such as the MegaMapper, MUltiplexed Survey Telescope (MUST), MaunaKea Spectroscopic Explorer (MSE), and Wide Spectroscopic Telescope (WST) are foreseen to increase the number of galaxy/quasar redshifts by an order of magnitude, with hundred millions of spectra that will be measured at $z>2$. We perform a Fisher matrix analysis for these surveys on the baryonic acoustic oscillation (BAO), the redshift-space distortion (RSD) measurement, the non-Gaussianity amplitude $f_{\rm NL}$, and the total neutrino mass $M_\nu$. For BAO and RSD parameters, these surveys may achieve precision at sub-percent level (<0.5 per cent), representing an improvement of factor 10 w.r.t. the latest database. For NG, these surveys may reach an accuracy of $\sigma(f_{\rm NL})\sim 1$. They can also put a tight constraint on $M_\nu$ with $\sigma(M_\nu) \sim 0.02\,\rm eV$ if we do joint analysis with Planck and even $0.01\,\rm eV$ if combined with other data. In addition, we introduce a general survey model, to derive the cosmic volume and number density of tracers, given instrumental facilities and survey strategy. Using our Fisher formalism, we can explore (continuously) a wide range of survey observational parameters, and propose different survey strategies that optimise the cosmological constraints. Fixing the fibre number and survey duration, we show that the best strategy for $f_{\rm NL}$ and $M_\nu$ measurement is to observe large volumes, despite the noise increase. However, the strategy differs for the apparent magnitude limit. Finally, we prove that increasing the fibre number improves $M_{\nu}$ measurement but not significantly $f_{\rm NL}$.Comment: 15 pages, 9 figure

Self‐Healable and Recyclable Tactile Force Sensors with Post‐Tunable Sensitivity

It is challenging to post‐tune the sensitivity of a tactile force sensor. Herein, a facile method is reported to tailor the sensing properties of conductive polymer composites by utilizing the liquid‐like property of dynamic polymer matrix at low strain rates. The idea is demonstrated using dynamic polymer composites (CB/dPDMS) made via evaporation‐induced gelation of the suspending toluene solution of carbon black (CB) and acid‐catalyzed dynamic polydimethylsiloxane (dPDMS). The dPDMS matrices allow CB to redistribute to change the sensitivity of materials at the liquid‐like state, but exhibit typical solid‐like behavior and thus can be used as strain sensors at normal strain rates. It is shown that the gauge factor of the polymer composites can be easily post‐tuned from 1.4 to 51.5. In addition, the dynamic polymer matrices also endow the composites with interesting self‐healing ability and recyclability. Therefore, it is envisioned that this method can be useful in the design of various novel tactile sensing materials for many applications

Federated Learning Incentive Mechanism under Buyers' Auction Market

Auction-based Federated Learning (AFL) enables open collaboration among self-interested data consumers and data owners. Existing AFL approaches are commonly under the assumption of sellers' market in that the service clients as sellers are treated as scarce resources so that the aggregation servers as buyers need to compete the bids. Yet, as the technology progresses, an increasing number of qualified clients are now capable of performing federated learning tasks, leading to shift from sellers' market to a buyers' market. In this paper, we shift the angle by adapting the procurement auction framework, aiming to explain the pricing behavior under buyers' market. Our modeling starts with basic setting under complete information, then move further to the scenario where sellers' information are not fully observable. In order to select clients with high reliability and data quality, and to prevent from external attacks, we utilize a blockchain-based reputation mechanism. The experimental results validate the effectiveness of our approach

Portfolio-Based Incentive Mechanism Design for Cross-Device Federated Learning

In recent years, there has been a significant increase in attention towards designing incentive mechanisms for federated learning (FL). Tremendous existing studies attempt to design the solutions using various approaches (e.g., game theory, reinforcement learning) under different settings. Yet the design of incentive mechanism could be significantly biased in that clients' performance in many applications is stochastic and hard to estimate. Properly handling this stochasticity motivates this research, as it is not well addressed in pioneering literature. In this paper, we focus on cross-device FL and propose a multi-level FL architecture under the real scenarios. Considering the two properties of clients' situations: uncertainty, correlation, we propose FL Incentive Mechanism based on Portfolio theory (FL-IMP). As far as we are aware, this is the pioneering application of portfolio theory to incentive mechanism design aimed at resolving FL resource allocation problem. In order to more accurately reflect practical FL scenarios, we introduce the Federated Learning Agent-Based Model (FL-ABM) as a means of simulating autonomous clients. FL-ABM enables us to gain a deeper understanding of the factors that influence the system's outcomes. Experimental evaluations of our approach have extensively validated its effectiveness and superior performance in comparison to the benchmark methods

A matter of time: Using dynamics and theory to uncover mechanisms of transcriptional bursting

Eukaryotic transcription generally occurs in bursts of activity lasting minutes to hours; however, state-of-the-art measurements have revealed that many of the molecular processes that underlie bursting, such as transcription factor binding to DNA, unfold on timescales of seconds. This temporal disconnect lies at the heart of a broader challenge in physical biology of predicting transcriptional outcomes and cellular decision-making from the dynamics of underlying molecular processes. Here, we review how new dynamical information about the processes underlying transcriptional control can be combined with theoretical models that predict not only averaged transcriptional dynamics, but also their variability, to formulate testable hypotheses about the molecular mechanisms underlying transcriptional bursting and control.Comment: 41 pages, 4 figures, review articl