Feasibility in reverse convex mixed-integer programming

In this paper we address the problem of the infeasibility of systems defined by reverse convex inequality constraints, where some or all of the variables are integer. In particular, we provide a polynomial algorithm that identifies a set of all constraints critical to feasibility (CF), that is constraints that may affect a feasibility status of the system after some perturbation of the right-hand sides. Furthermore, we will investigate properties of the irreducible infeasible sets and infeasibility sets, showing in particular that every irreducible infeasible set as well as infeasibility sets in the considered system, are subsets of the set CF of constraints critical to feasibility.     

Remarks on the Analytic Centers of Convex Sets

In this paper we analyze properties of the analytic centers for perturbed convex problems. In particular we study the continuity of convex regions with respect to such characteristics as boundedness, full dimensionality and the existence of an analytic centre. Furthermore, we state the necessary and sufficient conditions for the existence of the analytic centre for possibly unbounded regions and we show that the analytic centre is identical for any minimal representation of the convex set. We are also concerned with the limiting behaviour of the central path as it approaches the set of optimal solutions of the problem.     

Minimal infeasible constraint sets in convex integer programs

In this paper we investigate certain aspects of infeasibility in convex integer programs, where the constraint functions are defined either as a composition of a convex increasing function with a convex integer valued function of n variables or the sum of similar functions. In particular we are concerned with the problem of an upper bound for the minimal cardinality of the irreducible infeasible subset of constraints defining the model. We prove that for the considered class of functions, every infeasible system of inequality constraints in the convex integer program contains an inconsistent subsystem of cardinality not greater than 2 ⁿ , this way generalizing the well known theorem of Scarf and Bell for linear systems. The latter result allows us to demonstrate that if the considered convex integer problem is bounded below, then there exists a subset of at most 2 ⁿ −1 constraints in the system, such that the minimum of the objective function subject to the inequalities in the reduced subsystem, equals to the minimum of the objective function over the entire system of constraints.     

Quantitation of bacteria through adsorption of intracellular biomolecules on carbon paste and screen-printed carbon electrodes and voltammetry of redox-active probes

A new electrochemical method for the quantitation of bacteria that is rapid, inexpensive, and amenable to miniaturization is reported. Cyclic voltammetry was used to quantitate M. luteus, C. sporogenes, and E. coli JM105 in exponential and stationary phases, following exposure of screen-printed carbon working electrodes (SPCEs) to lysed culture samples. Ferricyanide was used as a probe. The detection limits (3s) were calculated and the dynamic ranges for E. coli (exponential and stationary phases), M. luteus (exponential and stationary phases), and C. sporogenes (exponential phase) lysed by lysozyme were 3 × 10⁴ to 5 × 10⁶ colony-forming units (CFU) mL⁻¹, 5 × 10⁶ to 2 × 10⁸ CFU mL⁻¹ and 3 × 10³ to 3 × 10⁵ CFU mL⁻¹, respectively. Good overlap was obtained between the calibration curves when the electrochemical signal was plotted against the dry bacterial weight, or between the protein concentration in the bacterial lysate. In contrast, unlysed bacteria did not change the electrochemical signal of ferricyanide. The results indicate that the reduction of the electrochemical signal in the presence of the lysate is mainly due to the fouling of the electrode by proteins. Similar results were obtained with carbon-paste electrodes although detection limits were better with SPCEs. The method described herein was applied to quantitation of bacteria in a cooling tower water sample. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Unboundedness in reverse convex and concave integer programming

In this paper we are concerned with the problem of unboundedness and existence of an optimal solution in reverse convex and concave integer optimization problems. In particular, we present necessary and sufficient conditions for existence of an upper bound for a convex objective function defined over the feasible region contained in ${\mathbb{Z}^n}$ . The conditions for boundedness are provided in a form of an implementable algorithm, showing that for the considered class of functions, the integer programming problem is unbounded if and only if the associated continuous problem is unbounded. We also address the problem of boundedness in the global optimization problem of maximizing a convex function over a set of integers contained in a convex and unbounded region. It is shown in the paper that in both types of integer programming problems, the objective function is either unbounded from above, or it attains its maximum at a feasible integer point.     

教师教学水平的时齐马尔可夫链评估方法

采用时齐马尔可夫链方法给出了一种评估教师教学水平的方法,对文［１］所给方法做了适当的改进,拓宽了该方法的应用范围,在多民族院校,使用本法可以克服由于学生基础不同等多方面的原因造成难以比较教师教学水平的难题．