A Conic Algorithm for the Group Minimization Problem

A new algorithm for the group minimization problem (GP) is proposed. The algorithm can be broadly described as follows. A suitable relaxation of(GP) is defined, in which any feasible point satisfies the group equation but may have negative components. The feasible points of the relaxation are then generated in order of ascending costs by a variant of a well-known algorithm of Glover, and checked for non-negativity. The first non-negative point is an optimal solution of (GP). Advantages and disadvantages of the algorithm are discussed; in particular, the implementation of the algorithm (which can be easily extended so as to solve integer linear programming problems) does not require group arithmetics.

Weighted Voronoi Region Algorithms for Political Districting

Automated political districting shares with electronic voting the aim of preventing electoral manipulation and pursuing an impartial electoral mechanism. Political districting can be modelled as multiobjective partitioning of a graph into connected components, where population equality and compactness must hold if a majority voting rule is adopted. This leads to the formulation of combinatorial optimization problems that are extremely hard to solve exactly. We propose a class of heuristics, based on discrete weighted Voronoi regions, for obtaining compact and balanced districts, and discuss some formal properties of these algorithms. Their performance has been tested on randomly generated rectangular grids, as well as on real-life benchmarks; for the latter instances the resulting district maps are compared with the institutional ones adopted in the Italian political elections from 1994 to 2001

Weighted Voronoi Region Algorithms for Political Districting

Automated political districting shares with electronic voting the aim of preventing electoral manipulation and pursuing an impartial electoral mechanism. Political districting can be modelled as multiobjective partitioning of a graph into connected components, where population equality and compactness must hold if a majority voting rule is adopted. This leads to the formulation of combinatorial optimization problems that are extremely hard to solve exactly. We propose a class of heuristics, based on discrete weighted Voronoi regions, for obtaining compact and balanced districts, and discuss some formal properties of these algorithms. Their performance has been tested on randomly generated rectangular grids, as well as on real-life benchmarks; for the latter instances the resulting district maps are compared with the institutional ones adopted in the Italian political elections from 1994 to 2001

Block linear majorants in quadratic 0–1 optimization

AbstractA usual technique to generate upper bounds on the optimum of a quadratic 0–1 maximization problem is to consider a linear majorant (LM) of the quadratic objective function f and then solve the corresponding linear relaxation. Several papers have considered LMs obtained by termwise bounding, but the possibility of bounding groups of terms simultaneously does not appear to have been given much attention so far. In the present paper a broad and flexible computational framework is developed for implementing such a strategy. Here is a brief overview of our approach: in the first place, a suitable collection of “elementary” quadratic functions of few variables (typically, 3 or 4) is generated. All the coefficients of any such function (block) are either 1 or −1, and agree in sign with the corresponding coefficients of the given quadratic function. Next, for each block, a tightest LM (i.e., one having the same value as the block in as many points as possible), or a closest LM (i.e., one minimizing the sum of slacks) is computed. This can be accomplished through the solution of a small mixed-integer program, or a small linear program, respectively. Finally, the objective function is written as a weighted sum of blocks, with non-negative weights. Replacing in this expression each block by the corresponding LM yields an LM of f. We shall choose the weights in this process so that the maximum value of the resulting linear function is as small as possible. This amounts to a large-scale (but still polynomial-size) linear program, which may be solved exactly or, for larger instances, approximately by truncated column generation. The results of a set of 480 numerical tests with up to 200 variables are presented: the upper bounds on the quadratic optimum obtained by the above procedure are (provably) never worse, and often turn out to be substantially sharper, than those resulting from termwise bounding. Moreover, our bounds turn out to be close to the optimum in many (although not all) instances of some well-known benchmarks

Product form parametric representation of the solutions to a quadratic boolean equation

A parametric représentation of the solutions to a consistent quadratic boolean equation in n variables is obtained. Each variable (or its complement) is expressed as a product of free boolean parameters or their complements. These expressions provide a complete description of the solution set of the equation. An O (n^3) algorithm is proposed to produce such a representation. An application to the maximization of some classes of pseudoboolean functions is discussed

Serial Analysis of Gene Expression (SAGE) in the Skeletal Muscle of Pig

Skeletal muscle growth represents one of the main economic traits in pig production. To gain a better understanding of expressions profile in pig muscle, serial analysis of gene expression (SAGE) was performed in Longissimus dorsi of two pigs at 3 and 9 months of age. A total of 53,120 long tags were obtained and sequenced from the four muscle SAGE libraries, representing 17,902 different tags, or putative transcripts, 0.64% (+0.09) of which had a relative expression level higher than 1‰. Overall, a total of 218 tags were highly expressed and 31 had a frequency higher than 3‰. Functional characterisation of the expression profiles was performed using Kyoto Encyclopedia of Genes and Genomes metabolic maps and 139 pathways were identified for swine skeletal muscle. Focal adhesion, Mitogen-Activated Protein Kinase signalling, oxidative phosphorylation, ribosomal proteins, regulation of actin cytoskeleton and insulin signalling pathways showed an abundance of genes greater than 1.5% of all the expressed transcripts. A comparison with human SAGE library indicated no statistical differences for the frequency of genes involved in these metabolic pathways

Raw meat based diet influences faecal microbiome and end products of fermentation in healthy dogs

Background: Dietary intervention studies are required to deeper understand the variability of gut microbial ecosystem in healthy dogs under different feeding conditions and to improve diet formulations. The aim of the study was to investigate in dogs the influence of a raw based diet supplemented with vegetable foods on faecal microbiome in comparison with extruded food. Methods: Eight healthy adult Boxer dogs were recruited and randomly divided in two experimental blocks of 4 individuals. Dogs were regularly fed a commercial extruded diet (RD) and starting from the beginning of the trial, one group received the raw based diet (MD) and the other group continued to be fed with the RD diet (CD) for a fortnight. After 14 days, the two groups were inverted, the CD group shifted to the MD and the MD shifted to the CD, for the next 14 days. Faeces were collected at the beginning of the study (T0), after 14 days (T14) before the change of diet and at the end of experimental period (T28) for DNA extraction and analysis of metagenome by sequencing 16SrRNA V3 and V4 regions, short chain fatty acids (SCFA), lactate and faecal score. Results: A decreased proportion of Lactobacillus, Paralactobacillus (P < 0.01) and Prevotella (P < 0.05) genera was observed in the MD group while Shannon biodiversity Index significantly increased (3.31 +/- 0.15) in comparison to the RD group (2.92 +/- 0.31; P < 0.05). The MD diet significantly (P < 0.05) decreased the Faecal Score and increased the lactic acid concentration in the feces in comparison to the RD treatment (P < 0.01). Faecal acetate was negatively correlated with Escherichia/Shigella and Megamonas (P < 0.01), whilst butyrate was positively correlated with Blautia and Peptococcus (P < 0.05). Positive correlations were found between lactate and Megamonas (P < 0.05), Escherichia/Shigella (P < 0.01) and Lactococcus (P < 0.01). Conclusion: These results suggest that the diet composition modifies faecal microbial composition and end products of fermentation. The administration of MD diet promoted a more balanced growth of bacterial communities and a positive change in the readouts of healthy gut functions in comparison to RD diet