On the subset sum problem over finite fields

The subset sum problem over finite fields is a well-known {\bf NP}-complete problem. It arises naturally from decoding generalized Reed-Solomon codes. In this paper, we study the number of solutions of the subset sum problem from a mathematical point of view. In several interesting cases, we obtain explicit or asymptotic formulas for the solution number. As a consequence, we obtain some results on the decoding problem of Reed-Solomon codes.Comment: 16 page

Finding Support Documents with a Logistic Regression Approach

Entity retrieval finds the relevant results for a user’s information needs at a finer unit called “entity”. To retrieve such entity, people usually first locate a small set of support documents which contain answer entities, and then further detect the answer entities in this set. In the literature, people view the support documents as relevant documents, and their findings as a conventional document retrieval problem. In this paper, we will state that finding support documents and that of relevant documents, although sounds similar, have important differences. Further, we propose a logistic regression approach to find support documents. Our experiment results show that the logistic regression method performs significantly better than a baseline system that treat the support document finding as a conventional document retrieval problem

On the minimum distance of elliptic curve codes

Computing the minimum distance of a linear code is one of the fundamental problems in algorithmic coding theory. Vardy [14] showed that it is an \np-hard problem for general linear codes. In practice, one often uses codes with additional mathematical structure, such as AG codes. For AG codes of genus $0$ (generalized Reed-Solomon codes), the minimum distance has a simple explicit formula. An interesting result of Cheng [3] says that the minimum distance problem is already \np-hard (under \rp-reduction) for general elliptic curve codes (ECAG codes, or AG codes of genus $1$). In this paper, we show that the minimum distance of ECAG codes also has a simple explicit formula if the evaluation set is suitably large (at least $2/3$ of the group order). Our method is purely combinatorial and based on a new sieving technique from the first two authors [8]. This method also proves a significantly stronger version of the MDS (maximum distance separable) conjecture for ECAG codes.Comment: 13 page

Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching

In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or extinctive, and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions. In the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the population model. Finally, we illustrate our conclusions through two examples

Algebraic Cayley Graphs over Finite Fields

A new algebraic Cayley graph is constructed using finite fields. Its connectedness and diameter bound are studied via Weil's estimate for character sums. These graphs provide a new source of expander graphs, extending classical results of Chung

Development of a High Temperature Water Heat Pump in Vent-less Dishwasher Application

In typical commercial dishwasher application, high temperature water (\u3e82.2°C) is needed for rinse process and electrical booster heater is used to provide such hot water. In the same time, exhausted high humidity hot vapor must be vented out with specially installed hood. This paper presents the development of a high temperature water heat pump to reclaim the heat in the exhaust vapor and deliver high temperature hot water to save electrical energy used in booster heater. While in the same time, the dehumidified exhaust air can be vented directly indoor without a specially installed hood. Both R-134a and R-513A refrigerant are tested successfully in a prototype system on a typical conveyor commercial dishwasher. More than 80% dehumidification target achieved and more than 20 kW energy saving potential demonstrated with the prototype system