Well-posedness and invariant measure for quasilinear parabolic SPDE on a bounded domain

We study quasilinear parabolic stochastic partial differential equations with general multiplicative noise on a bounded domain in $\mathbb{R}^{d}$, with homogeneous Dirichlet boundary condition. We establish the existence and uniqueness of solutions in a $L^{1}$ setting, and we prove a comparison result and an $L^{1}$-contraction property for the solutions. In addition, we show the existence of an invariant measure in case of non-degenerate diffusion. Finally, we show the uniqueness and ergodicity of the invariant measure in $L^{1}$, in case of bounded diffusion and additive noise

Spectral Radii of Products of Random Rectangular Matrices

We consider m independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables. Assume the product of the m rectangular matrices is an n by n square matrix. The maximum absolute values of the n eigenvalues of the product matrix is called spectral radius. In this paper, we study the limiting spectral radii of the product when m changes with n and can even diverge. We give a complete description for the limiting distribution of the spectral radius. Our results reduce to those in Jiang and Qi [26] when the rectangular matrices are square ones.Comment: 29 page

On the small-mass limit for stationary solutions of stochastic wave equations with state dependent friction

We investigate the convergence, in the small mass limit, of the stationary solutions of a class of stochastic damped wave equations, where the friction coefficient depends on the state and the noisy perturbation if of multiplicative type. We show that the Smoluchowski-Kramers approximation that has been previously shown to be true in any fixed time interval, is still valid in the long time regime. Namely we prove that the first marginals of any sequence of stationary solutions for the damped wave equation converge to the unique invariant measure of the limiting stochastic quasilinear parabolic equation. The convergence is proved with respect to the Wasserstein distance associated with the $H^{-1}$ norm

Across the great divides: Gender dynamics influence how intercultural conflict helps or hurts creative collaboration

Ministry of Education, Singapore, Social Science Research Thematic Gran

No-Regret Learning in Dynamic Competition with Reference Effects Under Logit Demand

This work is dedicated to the algorithm design in a competitive framework, with the primary goal of learning a stable equilibrium. We consider the dynamic price competition between two firms operating within an opaque marketplace, where each firm lacks information about its competitor. The demand follows the multinomial logit (MNL) choice model, which depends on the consumers' observed price and their reference price, and consecutive periods in the repeated games are connected by reference price updates. We use the notion of stationary Nash equilibrium (SNE), defined as the fixed point of the equilibrium pricing policy for the single-period game, to simultaneously capture the long-run market equilibrium and stability. We propose the online projected gradient ascent algorithm (OPGA), where the firms adjust prices using the first-order derivatives of their log-revenues that can be obtained from the market feedback mechanism. Despite the absence of typical properties required for the convergence of online games, such as strong monotonicity and variational stability, we demonstrate that under diminishing step-sizes, the price and reference price paths generated by OPGA converge to the unique SNE, thereby achieving the no-regret learning and a stable market. Moreover, with appropriate step-sizes, we prove that this convergence exhibits a rate of $\mathcal{O}(1/t)$

Probabilistic topic modelling in food spoilage analysis : a case study with Atlantic salmon (Salmo salar)

Probabilistic topic modelling is frequently used in machine learning and statistical analysis for extracting latent information from complex datasets. Despite being closely associated with natural language processing and text mining, these methods possess several properties that make them particularly attractive in metabolomics applications where the applicability of traditional multivariate statistics tends to be limited. The aim of the study was thus to introduce probabilistic topic modelling more specifically, Latent Dirichlet Allocation (LDA) in a novel experimental context: volatilome-based (sea) food spoilage characterization. This was realized as a case study, focusing on modelling the spoilage of Atlantic salmon (Salmo solar) at 4 degrees C under different gaseous atmospheres (% CO2/O-2/N-2): 0/0/100 (A), air (B), 60/0/40 (C) or 60/40/0 (D). First, an exploratory analysis was performed to optimize the model tunings and to consequently model salmon spoilage under 100% N-2 (A). Based on the obtained results, a systematic spoilage characterization protocol was established and used for identifying potential volatile spoilage indicators under all tested storage conditions. In conclusion, LDA could be used for extracting sets of underlying VOC profiles and identifying those signifying salmon spoilage, giving rise to an extensive discussion regarding the key points associated with model tuning and/or spoilage analysis. The identified compounds were well in accordance with a previously established approach based on partial least squares regression analysis (PLS). Overall, the outcomes of the study not only reflect the promising potential of LDA in spoilage characterization, but also provide several new insights into the development of data-driven methods for food quality analysis

The effect of loss of foot sole sensitivity on H-reflex of triceps surae muscles and functional gait

Objective: To investigate the effects of foot sole insensitivity on the outcomes of the triceps surae muscle H-reflex and functional gait.Material and Methods: People with peripheral neuropathy were recruited and divided into two groups: people with more (n = 13, 73.3 ± 4.3 years old) or less (n = 10, 73.5 ± 5.3) sensitive tactile sensation. Their monofilament testing scores were 9.0 ± 1.5 (range: 7–10) and 2.3 ± 2.4 (range: 0–6) out of 10, respectively. H-reflex of the triceps surae muscles during quiet standing and their relationship with functional gait, 6 min walking distance (6MWD), and timed-up-and-go duration (TUG), were compared between groups.Results: No significant difference was detected for H-reflex parameters between the groups. The less sensitive group showed reduced (p < .05) functional gait capacity compared to the other group, 38.4 ± 52.7 vs. 463.5 ± 47.6 m for 6MWD, and 9.0 ± 1.5 vs. 7.2 ± 1.1s for TUG, respectively. A significant correlation (p < .05), worse functional gait related to greater H/M ratio, was observed in the less sensitive group, not the other group.Conclusion: Although there was no significant H-reflex difference between the groups, more pronounced tactile sensation degeneration affected functional gaits and their relationship with H-reflex

Mapping cultural tightness and its links to innovation, urbanization, and happiness across 31 provinces in China

10.1073/pnas.1815723116Proceedings of the National Academy of Sciences1-