101 research outputs found
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 , with
homogeneous Dirichlet boundary condition. We establish the existence and
uniqueness of solutions in a setting, and we prove a comparison result
and an -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 , 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 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
Breaking the chains: The inverted-U-shaped relationship between action-state orientation and creativity under low job autonomy
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
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-
Effect of Salusin-ß on Peroxisome Proliferator-Activated Receptor Gamma Gene Expression in Vascular Smooth Muscle Cells and its Possible Mechanism
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