Deterministic construction of compressed sensing matrices based on semilattices

A central problem in compressed sensing is the construction of sensing matrices. In this paper, we show how to construct sensing matrices by using semilattices, and give many examples of sensing matrices constructed from specific semilattices. Moreover, we show that the new construction for some examples with small parameters gives better sensing matrices compared with previously known constructions.     

Code for polyomino and computer search of isospectral polyominoes

A new code, binary 2-dimentional code (B2DC), is proposed for polyominoes. An algorithm based on the B2DC and the reverse search method are proposed for enumerating nonisomorphic planar simply connected polyominoes. An enumeration tree and a new father-son relationship are defined for enumerating polyominoes. Then we propose an algorithm to build adjacent matrices and laplacian matrices by B2DCs of polyominoes and search isospectral polyomino graphs by computing characteristic polynomials of those matrices.     

A modified power spectral density test applied to?weighing matrices with small weight

The power spectral density test has been used for at least a decade in the search for many kinds of combinatorial matrices, such as weighing matrices for instance. In this paper we establish a modified power spectral density test that we apply to the search for weighing matrices of small weights constructed from two circulants. The main novelty of our approach is to define the Discrete Fourier Transform on the support of the first rows of the two circulants, thus exploiting the inherent sparsity of the problem. This new formalism turns out to be very efficient for small weights 9,18,36 and we find 10 new weighing matrices W(2⋅p,18) for prime p∈{37,47,53,59,61,67,73,79,83,97}. These matrices are given here for the first time. We also discuss briefly a connection with Combinatorial Optimization.     

How to Design Rating Schemes of Risk Matrices: A Sequential Updating Approach

Risk matrices have been widely used as a risk evaluation tool in many fields due to their simplicity and intuitive nature. Designing a rating scheme, i.e., determining the number of ratings used in a risk matrix and assigning different ratings to different cells, is an essential part of risk matrix construction. However, most of the related literature has focused on applying a risk matrix to various fields, instead of researching how to design risk matrices. Based on the analysis of several current rules, we propose a new approach, namely, the sequential updating approach (SUA), to design the rating scheme of a risk matrix in a reliable way. In this article, we propose three principles and a rating algorithm based on these principles. The three principles, namely, adjusted weak consistency, consistent internality, and continuous screening, characterize a good rating scheme. The resulting rating scheme has been proven to be unique. A global rating algorithm is then proposed to create the design that satisfies the three principles. We then explore the performance of the SUA. An illustrative application is first given to explain the feasibility of our approach. The sensitivity analysis shows that our method captures a resolution‐reliability tradeoff for decisionmakers in choosing an appropriate rating scheme for a risk matrix. Finally, we compare the designs based on the SUA and Cox's axioms, highlighting the advantages of the SUA.     

A generalization of Macula’s disjunct matrices

As a generalization of the novel construction of disjunct matrices by Macula (Discrete Math. 162:311–312, 1996), we construct a new family of disjunct matrices and discuss its error-tolerant property.     

Do colored cells in risk matrices affect decision-making and risk perception? Insights from randomized controlled studies

Risk matrices communicate the likelihood and potential impact of risks and are often used to inform decision-making around risk mitigations. The merits and demerits of risk matrices in general have been discussed extensively, yet little attention has been paid to the potential influence of color in risk matrices on their users. We draw from fuzzy-trace theory and hypothesize that when color is present, individuals are likely to place greater value on reducing risks that cross color boundaries (i.e., the boundary-crossing effect), leading to sub-optimal decision making. In two randomized controlled studies, employing forced-choice and willingness-to-pay measures to investigate the boundary-crossing effect in two different color formats for risk matrices, we find preliminary evidence to support our hypotheses that color can influence decision making. The evidence also suggests that the boundary-crossing effect is only present in, or is stronger for, higher numeracy individuals. We therefore recommend that designers should consider avoiding color in risk matrices, particularly in situations where these are likely to be used by highly numerate individuals, if the communication goal is to inform in an unbiased way.     

基于可控提前期的随机寄售库存模型

本文通过假定需求提前期为随机且可控的,将寄售库存（Consignment Stock,CS）模型拓展到随机情形。本文首先将库存成本分为与财务相关的成本和与储存相关的成本两部分,得出CS方式下买卖双方的联合期望总成本公式,然后将订货量、订货点、提前期、运送次数作为决策变量,求得系统的最优参数设置及最小总成本。文章最后提出一个算法,并通过仿真的形式表明无论在确定还是随机环境中,CS方式的总成本都可能优于集成化库存方式。     

Two-stage stochastic mixed-integer linear programming: The conditional scenario approach

In this paper we consider the two-stage stochastic mixed-integer linear programming problem with recourse, which we call the RP problem. A common way to approximate the RP problem, which is usually formulated in terms of scenarios, is to formulate the so-called Expected Value (EV) problem, which only considers the expectation of the random parameters of the RP problem. In this paper we introduce the Conditional Scenario (CS) problem which represents a midpoint between the RP and the EV problems regarding computational tractability and ability to deal with uncertainty. In the theoretical section we have analyzed some useful bounds related to the RP, EV and CS problems. In the numerical example here presented, the CS problem has outperformed both the EV problem in terms of solution quality, and the RP problem with the same number of scenarios as in the CS problem, in terms of solution time.     

The arrangement of subspaces in the orthogonal spaces and tighter analysis of an error-tolerant pooling design

In this paper, we construct a d ^z -disjunct matrix with the orthogonal spaces over finite fields of odd characteristic. We consider the arrangement problem of d (m−1,2(s−1),s−1)-subspaces and the tighter bounds for an error-tolerant pooling design. Moreover, we give the tighter analysis of our construction by the results of the arrangement problem. Additionally, by comparing our construction with the previous construction out of vector spaces, we find that our construction is better under some conditions.     

股票市场融资管制与公司最优资本结构

资本市场不完美对企业融资和资本结构带来的"供给方效应"日益受到公司金融学术界关注。转轨时期的中国资本市场存在严格证券发行管制与金融创新管制,给企业融资和资本结构带来了供给方约束。本文选取了1993~2007年期间A股市场发生过股权再融资的上市公司为研究对象,研究股票再融资管制政策变更对上市公司资本结构的影响。结果表明,股票再融资管制政策的变更,是影响上市公司资本结构的重要因素;股票市场估值的"市场时机"并不是影响上市公司资本结构的显著因素。     

Opportunistic data structures for range queries

In this paper, we study the problem of supporting range sum queries on a compressed sequence of values. For a sequence of n k-bit integers, k ≤ O(log n), our data structures require asymptotically the same amount of storage as the compressed sequence if compressed using the Lempel-Ziv algorithm. The basic structure supports range sum queries in O(log n) time. With an increase by a constant factor in the storage complexity, the query time can be improved to O(log log n + k). The work described in this paper is fully supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region, China (CityU 1071/02E). A preliminary version has appeared in 11th International Conference in Computing and Combinatorics (COCOON'05).     

Competent genetic algorithms for weighing matrices

In this paper, we demonstrate that the search for weighing matrices constructed from two circulants can be viewed as a minimization problem together with two competent genetic algorithms to locate optima of an objective function. The motivation to deal with the messy genetic algorithm (mGA) is given from the pioneering results of Goldberg, regarding the ability of the mGA to put tight genes together in a solution which points directly to structural patterns in weighing matrices. In order to take into advantage certain properties of two ternary sequences with zero autocorrelation we use an adaptation of the fast messy GA (fmGA) where we combine mGA with advanced techniques, such as thresholding and tie-breaking. This transformation of the weighing matrices problem to an instance of a combinatorial optimization problem seems to be promising, since we resolved two open cases for weighing matrices as these are listed in the second edition of the Handbook of Combinatorial Designs.     

Robotic-Cell Scheduling: Special Polynomially Solvable Cases of the Traveling Salesman Problem on Permuted Monge Matrices

In this paper, we introduce the 1 − K robotic-cell scheduling problem, whose solution can be reduced to solving a TSP on specially structured permuted Monge matrices, we call b-decomposable matrices. We also review a number of other scheduling problems which all reduce to solving TSP-s on permuted Monge matrices. We present the important insight that the TSP on b-decomposable matrices can be solved in polynomial time by a special adaptation of the well-known subtour-patching technique. We discuss efficient implementations of this algorithm on newly defined subclasses of permuted Monge matrices.     

A robust branch-and-cut approach for the minimum-energy symmetric network connectivity problem

This paper considers the minimum-energy symmetric network connectivity problem (MESNC) in wireless sensor networks. The aim of the MESNC is to assign transmission power to each sensor node such that the resulting network, using only bidirectional links, is connected and the total energy consumption is minimized. We first present two new models of this problem and then propose new branch-and-cut algorithms. Based on an existing formulation, we present the first model by introducing additional constraints. These additional constraints allow us to relax certain binary variables to continuous ones and thus to reduce significantly the number of binary variables. Our second model strengthens the first one by adding an exponential number of lifted directed-connectivity constraints. We present two branch-and-cut procedures based on these proposed improvements. The computational results are reported and show that our approaches, using the proposed formulations, can efficiently solve instances with up to 120 nodes, which significantly improve our ability to solve much larger instances in comparison with other exact algorithms in the literature.     

Distributed algorithms for barrier coverage via sensor rotation in wireless sensor networks

When deploying sensors to monitor boundaries of battlefields or country borders, sensors are usually dispersed from an aircraft following a predetermined path. In such scenarios sensing gaps are usually unavoidable. We consider a wireless sensor network consisting of directional sensors deployed using the line-based sensor deployment model. In this paper we propose distributed algorithms for weak and strong barrier coverage that allow sensors to determine their orientation such that the total number of gaps is minimized. We use simulations to analyze the performance of our algorithms and to compare them with related works.     

Safety and Aircraft Maintenance: A Moral Evaluation

In this article I will discuss the construction of safety in high reliability organizations. This construction is then evaluated from a moral point of view. I will argue that accidents happening to high reliability organizations make clear that we have to reconceptualize our notion of moral responsibility. This revised version was published online in July 2006 with corrections to the Cover Date.     

THE EFFECTS OF LEAD TIME ON PLANT TIMING AND SIZE

An important issue in planning capacity expansion under uncertain demand is the effect of lead time on the timing of plant construction. Our model helps decide whether (1) plant construction is initiated after a certain deficit is accumulated, or (2) plant construction is initiated ahead of demand when a certain capacity surplus is reached. In addition to our analytical results, we present computational results to show that it is economically attractive to delay plant construction beyond the time when existing excess capacity becomes fully absorbed, with relatively short construction lead time.     

A Simulation Study of Quantitative Risk Assessment for Bivariate Continuous Outcomes

The neurotoxic effects of chemical agents are often investigated in controlled studies on rodents, with binary and continuous multiple endpoints routinely collected. One goal is to conduct quantitative risk assessment to determine safe dose levels. Yu and Catalano (2005) describe a method for quantitative risk assessment for bivariate continuous outcomes by extending a univariate method of percentile regression. The model is likelihood based and allows for separate dose‐response models for each outcome while accounting for the bivariate correlation. The approach to benchmark dose (BMD) estimation is analogous to that for quantal data without having to specify arbitrary cutoff values. In this article, we evaluate the behavior of the BMD relative to background rates, sample size, level of bivariate correlation, dose‐response trend, and distributional assumptions. Using simulations, we explore the effects of these factors on the resulting BMD and BMDL distributions. In addition, we illustrate our method with data from a neurotoxicity study of parathion exposure in rats.     

Modeling Fetal Death and Malformation in Developmental Toxicity Studies

We review approaches to dose-response modeling and risk assessment for binary data from developmental toxicity studies. In particular, we focus on jointly modeling fetal death and malformation and use a continuation ratio formulation of the multinomial distribution to provide a model for risk. Generalized estimating equations are used to account for clustering of animals within litters. The fitted model is then used to calculate doses corresponding to a specified level of excess risk. Two methods of arriving at a lower confidence limit or Benchmark dose are illustrated and compared. We also discuss models based on single binary end points and compare our approach to a binary analysis of whether or not the animal was 'affected' (either dead or malformed). The models are illustrated using data from four developmental toxicity studies in EG, DEHP, TGDM, and DYME conducted through the National Toxicology Program.     

A feasibility approach for constructing combinatorial designs of circulant type

In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelation. The problem is formulated as a so-called feasibility problem having three sets, to which the Douglas–Rachford projection algorithm is applied. The approach is illustrated on three different classes of circulant combinatorial designs: circulant weighing matrices, D-optimal matrices of circulant type, and Hadamard matrices with two circulant cores. Furthermore, we explicitly construct two new circulant weighing matrices, a CW(126, 64) and a CW(198, 100), whose existence was previously marked as unresolved in the most recent version of Strassler’s table.