Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.Two heuristic algorithms (M65 and M52) for finding respectively unitals and maximal arcs in projective planes of order 16 are described. The exact algorithms based on exhaustive search are impractical because of the combinatorial explosion (huge number of combinations to be checked). Algorithms M65 and M52 use unions of orbits of di erent subgroups of the automorphism group of the 273x273 bipartite graph of the projective plane. Two very efficient algorithms (developed by the author and not described here) are used in M65 and M52: (i) algorithm VSEPARN for computing the generators, orbits and order of the graph automorphism group; (ii) graph isomorphism algorithm derived from VSEPARN. Four properties are proved and used to speed up the algorithms M65 and M52. The results of these algorithms are published. After changing only the parameters of these algorithms they can be used for determining unitals in projective planes of different orders

Unitals in projective planes of order 16

In this study, we perform computer searches for unitals in planes of order 16. The number of known nonisomorphic unitals in these planes is improved to be 261. Some data related to 2- (65, 5, 1) designs associated with unitals are given. New lower bounds on the number of unital designs in projective planes of order 16 and 2- (65, 5, 1) designs are established. The computations show that thirty-nine unitals can be embedded in two or more nonisomorphic projective planes of order 16. Fifteen new connections between planes of order 16 (based on unitals) are found. All unitals found by the algorithms used in this study are explicitly listed. We assume familiarity with the basic facts from combinatorial design theory and finite geometries [5, 9, 16]. A t-(v, k, ?) design (t-design) is a pair D = {X, B} of a set X of cardinality v, called points, and a collection B of k-subsets of X, called blocks, such that every t points appear together in exactly ? blocks. A 2-design with ? = 1 is called a Steiner design. The incidence matrix of a 2-(v, k, ?) design D is a matrix M = (mij) with rows labeled by the blocks of D, columns labeled by the points of D, where mi,j = 1 if the ith block contains the j th point and mi,j = 0 otherwise. For a prime p, the rank of the incidence matrix of design D over a finite field of characteristic p is called the p-rank of D. Two designs D and D? are called isomorphic if there is a bijection between their point sets that map

Bulgarian sport policy 1945-1989: A strategic relation perspective

The 2008 Beijing Olympic Games have stimulated discussions about the success of different sport systems and the Chinese model in particular. Revisiting explanations of sport in the former communist countries of Eastern Europe during the Cold War seems timely, as the current Chinese model of sport was largely designed after the Soviet example established in this period. This paper examines Bulgarian sport policy between 1945 and 1989. It employs a Strategic Relation approach (Jessop, 1990) to analyse sport policy making as a strategic relation closely linked to the dominant state project of building a new stateness. It goes beyond ideological interpretations and argues that the state represents a strategic terrain where these relations have to be established in struggles, the outcomes of which are always uncertain. Furthermore, past and present struggles and their outcomes create various socio-political environments that presuppose the forms of state selectivity and intervention in sport. The process of constructing sport policy was influenced by two main categories of strategic relations: intra-state, including political, organisational and personal relations between the Party, state apparatus and various sport and non-sport organisations and their managers, and transnational, concerning ideological, political, economic and organisational relations with both communist and western countries and international sport organisations

The Effect of <i>Dreissena polymorpha</i> on Bacterioplankton, Nematode Fauna and their Relations to Environmental Factors in Ogosta Reservoir (Danube Basin)

Abstract Spatial, seasonal, and annual bacterioplankton dynamics in recently infested by the species Dreissena polymorpha Ogosta Reservoir were studied for the first time during three year period. Bacterioplankton total number was higher in spring in ecotone zones, than in summer at thermocline. NH4-N, PO4-P, turbidity, dissolved oxygen, COD and chlorophyll-a correlate positively, while transparency and Ca2+ negatively with bacteria. Nematode species composition, included 22 species studied (13 rarely found and Rhabditis brevispina new for Bulgaria) belonging to nine families. The D. polymorpha impact is positive on nematodes and phytoplankton, negative on zooplankton and bacterioplankton, but weak positive on larger bacteria, rods and attached bacteria.</jats:p

Changes in biophysical properties and behavior of aging human erythrocytes treated with natural polyelectrolytes

Performing their functions as transporters of oxygen and carbon dioxide in the body, human erythrocytes constantly circulate and are exposed to the constant influence of various substances, including nutrients, drugs, medical devices covered with coatings, etc. Therefore, we aim to investigate the biophysical behavior of erythrocytes obtained from healthy volunteers to observe their morphological type changes, alterations in the zeta potential, the electrical conductivity of the erythrocytes in suspensions, and hemolysis in percentages during cells senescence, both in presence and in absence of natural polyelectrolytes pectin (PE) and chitosan (Chi) in form of multilayer films (PEM-films). Being constructed using the layer–by–layer technique, films are an object of interest of many researchers because of their high potential to be incorporated in biomedicine. By applying optical profilometry, electrophoretic light scattering, and spectrophotometry, we tested the polyelectrolytes for any potential harm on the erythrocytes. Based on our results and the one-way analysis of variance (ANOVA) statistical analysis, we reached the conclusion that the above-mentioned polyelectrolytes were harmlessness; therefore, PE and Chi are suitable substances to implement in the clinical practice in the form of drug delivery carriers and medical devices coatings, thereby directly contacting with the human blood

Predictors of successful weaning in patients requiring extremely prolonged mechanical ventilation

Introduction: For patients on prolonged mechanical ventilation (PMV; &gt; 21 days), successful weaning has been attributed to various factors. The aim of this study is to determine the usefulness of the rapid shallow breathing index (RSBI) and other potential predictors of successful weaning in patients unable to wean and requiring extreme PMV at a hospital-based long-term ventilator facility in Israel. Material and ethods: Retrospective analysis of prospectively collected data over 5 years. Results: A total of 150 subjects on PMV, ready to undergo a weaning process, were included in the study. Of them, 60 (40.0%) were males. The mean age of the whole study population was 76.5 years (SD = 13.6; range 22.0–96.0 years). The subjects were on MV for a mean period of 170.1 days (SD = 237.6; range 25.0–1624.0 days). Sixty patients (40%) were successfully weaned. The mean RSBI in the successfully weaned population was 41.9 breaths/min/L (SD = 12.3; range 13.0–80.4 breaths/min/L), in the population where weaning failed, it was 114.8 breaths/min/L (SD = 69.2; range 47.5–450.0 breaths/min/L). By univariate logistic regression analysis, younger age (p &lt; 0.007), female gender (p &lt; 0.001), decreased duration of MV (p &lt; 0.023), re-spiratory rate (p &lt; 0.001) and RSBI (p &lt; 0.001), increased tidal volume/ideal body weight (p &lt; 0.001) and minute ventilation (p &lt; 0.01) were found to be factors that significantly predict successful weaning. By multivariate analysis, increased tidal volume/ /ideal body weight (p &lt; 0.007) and decreased RSBI (p &lt; 0.046) were found to be independent predictors of successful weaning (p &lt; 0.001; R2 Nagelkerke = 0.90). Conclusions: Factors independently predicting successful weaning in patients requiring extreme PMV included increased tidal volume/ideal body weight and decreased RSBI