In this paper,we study a class of online continuous optimization *** each round,the utility function is the sum of a weakly diminishing-returns(DR)submodular function and a concave function,certain cost associated wit...
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In this paper,we study a class of online continuous optimization *** each round,the utility function is the sum of a weakly diminishing-returns(DR)submodular function and a concave function,certain cost associated with the action will occur,and the problem has total limited *** the two methods,the penalty function and Frank-Wolfe strategies,we present an online method to solve the considered *** appropriate stepsize and penalty parameters,the performance of the online algorithm is guaranteed,that is,it achieves sub-linear regret bound and certain mild constraint violation bound in expectation.
Heider's balance theory emphasizes cognitive consistency in assessing others, as expressed by the phrase “The enemy of my enemy is my friend.” At the same time, the theory of indirect reciprocity provides us wit...
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Heider's balance theory emphasizes cognitive consistency in assessing others, as expressed by the phrase “The enemy of my enemy is my friend.” At the same time, the theory of indirect reciprocity provides us with a dynamical framework to study how to assess others based on their actions as well as how to act toward them based on the assessments. Well known are the “leading eight” from L1 to L8, the eight norms for assessment and action to foster cooperation in social dilemmas while resisting the invasion of mutant norms prescribing alternative actions. In this work, we begin by showing that balance is equivalent to stationarity of dynamics only for L4 and L6 (stern judging) among the leading eight. Stern judging reflects an intuitive idea that good merits reward, whereas evil warrants punishment. By analyzing the dynamics of stern judging in complete graphs, we prove that this norm almost always segregates the graph into two mutually hostile groups as the graph size grows. We then compare L4 with stern judging: The only difference of L4 is that a good player's cooperative action toward a bad one is regarded as good. This subtle difference transforms large populations governed by L4 to a “paradise” where cooperation prevails and positive assessments abound. Our study thus helps us understand the relationship between individual norms and their emergent consequences at a population level, shedding light on the nuanced interplay between cognitive consistency and segregation dynamics.
Recent progress in maximizing submodular functions with a cardinality constraint through centralized and streaming modes has demonstrated a wide range of applications and also developed comprehensive theoretical *** s...
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Recent progress in maximizing submodular functions with a cardinality constraint through centralized and streaming modes has demonstrated a wide range of applications and also developed comprehensive theoretical *** submodularity was investigated to capture the diversity and representativeness of the utilities,and the monotonicity has the advantage of improving the *** submodular optimization models were developed in the latest studies(such as a house on fire),which aimed to sieve subsets with constraints to optimize regularized *** study is motivated by the setting in which the input stream is partitioned into several disjoint parts,and each part has a limited size constraint.A first threshold-based bicriteria(1/3,2/3/)-approximation for the problem is provided.
作者：
GUO YixiaoMING PingbingLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences
University of Chinese Academy of SciencesBeijing 100049China
The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architectu...
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The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the *** improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded *** authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger *** an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.
Gradient method is an important method for solving large scale problems. In this paper, a new gradient method framework for unconstrained optimization problem is proposed, where the stepsize is updated in a cyclic way...
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The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,whic...
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The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration *** analyze the optimization dynamics and convergence of the algorithm *** of the trial step and structure step are *** results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD *** algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.
The Hiperwalk package is designed to facilitate the simulation of quantum walks using heterogeneous high-performance computing, taking advantage of the parallel processing power of diverse processors such as CPUs, GPU...
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This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem...
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This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem(CLT)of the temporal average of the BEM method,which characterizes its asymptotics in *** the deviation order is smaller than the optimal strong order,we directly derive the CLT of the temporal average through that of original equations and the uniform strong order of the BEM *** the case that the deviation order equals to the optimal strong order,the CLT is established via the Poisson equation associated with the generator of original *** experiments are performed to illustrate the theoretical *** main contribution of this work is to generalize the existing CLT of the temporal average of numerical methods to that for SODEs with super-linearly growing drift coefficients.
Expressing data parallel programs using C++ standard parallelism is attractive not only due to the simplicity of the model, but also due to its highly idiomatic nature. This programming model, commonly referred to as ...
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In this paper the author investigates the following predator-prey model with prey-taxis and rotational?ux terms■in a bounded domain with smooth *** presents the global existence of generalized solutions to the model...
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In this paper the author investigates the following predator-prey model with prey-taxis and rotational?ux terms■in a bounded domain with smooth *** presents the global existence of generalized solutions to the model■in any dimension.
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