a three stage production system is considered in this paper. there are two stages to fabricate and ready the parts and an assembly stage to assembly the parts and complete the products in this system. suppose that a number of products of different kinds are ordered. each product is assembled with a set of several parts. at first the parts are produced in the first stage with parallel machines a...

Population risk—the expectation of the loss over the sampling mechanism—is always of primary interest in machine learning. However, learning algorithms only have access to empirical risk, which is the average loss over training examples. Although the two risks are typically guaranteed to be pointwise close, for applications with nonconvex nonsmooth losses (such as modern deep networks), the eff...

This paper proposes an analytical framework for peer-to-peer (P2P) networks and introduces schemes for building P2P networks to approach the minimum weighted average download time (WADT). In the considered P2P framework, the server, which has the information of all the download bandwidths and upload bandwidths of the peers, minimizes the weighted average download time by determining the optimal...

——We propose a technique to localize computation in Instruction Set Extensions (ISEs) that are clocked at very high speed with respect to the processor. In order to save power, data to and from Custom Instruction Units (CIUs) is synchronized via an optical signal that is detected through a Single-Photon Avalanche Diode (SPAD) capable of timing uncertainties as low as 50 ps. The CIUs comprise a ...

In this paper, a local approach to the concept of Hudetz $g$-entropy is presented. The introduced concept is stated in terms of Hudetz $g$-entropy. This representation is based on the concept of $g$-ergodic decomposition which is a result of the Choquet's representation Theorem for compact convex metrizable subsets of locally convex spaces.

We propose a first-order augmented Lagrangian algorithm (FALC) to solve the composite norm minimizationproblemminX∈Rm×n μ1‖σ(F(X)−G)‖α +μ2‖C(X)− d‖β ,subject to A(X)− b ∈ Q,where σ(X) denotes the vector of singular values of X ∈ Rm×n, the matrix norm‖σ(X)‖α denotes either the Frobenius,the nuclear, or the `2-operator norm of X, the vector norm‖.‖β denotes either ...

Molecular shapes play an important role in molecular interactions, e.g., between a protein and a ligand. The ‘outer’ shape of a molecule can be approximated by its solvent excluded surface (SES). In this article we present a new approach to molecular surface alignment which is capable of identifying partial similarities. The approach utilizes an iterative point matching scheme which is applied ...

We uncover relations between robust MDPs and risk-sensitive MDPs. The objective of a robust MDP is to minimize a function, such as the expectation of cumulative cost, for the worst case when the parameters have uncertainties. The objective of a risk-sensitive MDP is to minimize a risk measure of the cumulative cost when the parameters are known. We show that a risk-sensitive MDP of minimizing t...

The mathematical analysis developed for energy minimizing fracture evolutions has been difficult to extend to locally minimizing evolutions. The reasons for this difficulty are not obvious, and our goal in this paper is to describe in some detail what precisely the issues are and why the previous analysis in fact cannot be extended to the most natural models based on local minimality. We also i...