Related papers: ERRATUM: Stochastic evolution equations for large …
Perturbation experiments are carried out by contact process and its mean-field version. Here, the mortality rate is increased or decreased suddenly. It is known that the fluctuation enhancement (FE) occurs after the perturbation, where FE…
In this paper, we show a series of abstract results on fixed point regularity with respect to a parameter. They are based on a Taylor development taking into account a loss of regularity phenomenon, typically occurring for composition…
In this paper, we consider the chance constrained based uncertain portfolio optimization problem in which the uncertain parameters are stochastic in nature. The primary goal of the work is to formulate the uncertain problem into a…
Dropout is a widely utilized regularization technique in the training of neural networks, nevertheless, its underlying mechanism and its impact on achieving good generalization abilities remain poorly understood. In this work, we derive the…
Early-exiting neural networks enable adaptive inference by allowing inputs to exit at intermediate classifiers, reducing computation for easy samples while maintaining high accuracy. In practice, exits can be trained sequentially by…
In [Ritika Garg et al., Phys. Rev. C 100, 069901(E) (2019)] the experimental results on the polarization asysmetry were revised due to a claimed change of the geometry asymmetry. However, the revised results can not be reproduced as claimed…
Estimate (3.39) which appears in the proof of Proposition 3.4 in [Ann. Probab. 27 (1999) 1414--1467, doi:10.1214/aop/1022677454] is wrong. We present below a corrected proof which introduces an extra factor 2 in equations (3.34) and (3.35).…
This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce…
In this paper we develop a new approach to stochastic evolution equations with an unbounded drift $A$ which is dependent on time and the underlying probability space in an adapted way. It is well-known that the semigroup approach to…
Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications,…
Lemma 4.8 in the article [Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions, Electronic J. Probability 21 (18):1-48 (2016), arXiv:1504.02953] contains a mistake, which implies a weaker regularity…
We prove that the proof of existence of weighted local median order of weighted tournaments is wrong and that the proof of the correct statement which asserts that every digraph obtained from a tournament by deleting a set of arcs incident…
Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…
In recent years, many papers have been devoted to the regularity of doubly nonlinear singular evolution equations. Many of the proofs are unnecessarily complicated, rely on superfluous assumptions or follow an inappropriate approximation…
In this paper, first a theorem on the partial sum of a particular series is given. Then, based on it, the origin of obvious simulation deviation from theory is explained: i) why the numerically estimated \hat\gamma (degree exponent) in…
There is an error in the proof (but not the truth) of Theorem 3.2 in the author's 1985 paper "The Double-Wedge Algebra for Quantum Fields on Schwarzschild and Minkowski Spacetimes" in "Communications in Mathematical Physics". The author…
Curve evolution is often used to solve computer vision problems. If the curve evolution fails to converge, we would not be able to solve the targeted problem in a lifetime. This paper studies the theoretical aspect of the convergence of a…
Weak convergence of the stochastic evolutionary system to the average evolutionary system is proved. The method proposed by R.Liptser in for semimartingales is used. But we apply a solution of singular perturbation problem instead of…
Motivated by learning of correlated equilibria in non-cooperative games, we perform a large deviations analysis of a regret minimizing stochastic approximation algorithm. The regret minimization algorithm we consider comprises multiple…
Neural networks are powerful function approximators with tremendous potential in learning complex distributions. However, they are prone to overfitting on spurious patterns. Bayesian inference provides a principled way to regularize neural…