Good Random Matrices over Finite Fields

The random matrix uniformly distributed over the set of all m-by-n matrices over a finite field plays an important role in many branches of information theory. In this paper a generalization of this random matrix, called k-good random matrices, is studied. It is shown that a k-good random m-by-n matrix with a distribution of minimum support size is uniformly distributed over a maximum-rank-distance (MRD) code of minimum rank distance min{m,n}-k+1, and vice versa. Further examples of k-good random matrices are derived from homogeneous weights on matrix modules. Several applications of k-good random matrices are given, establishing links with some well-known combinatorial problems. Finally, the related combinatorial concept of a k-dense set of m-by-n matrices is studied, identifying such sets as blocking sets with respect to (m-k)-dimensional flats in a certain m-by-n matrix geometry and determining their minimum size in special cases.Comment: 25 pages, publishe

Грунти як об’єкт науки

Висвітлюються деякі аспекти розвитку наших уявлень про ґрунтознавство як науковий напрямок природознавства та про ґрунти як об’єкт науки.Освещаются некоторые аспекты развития наших представлений о почвоведении как научном направлении природоведения и о почвах как объекте науки.The author highlights several aspects of human knowledge about soil research as a field of natural science, and about soils as a research object

Single Molecule Statistics and the Polynucleotide Unzipping Transition

We present an extensive theoretical investigation of the mechanical unzipping of double-stranded DNA under the influence of an applied force. In the limit of long polymers, there is a thermodynamic unzipping transition at a critical force value of order 10 pN, with different critical behavior for homopolymers and for random heteropolymers. We extend results on the disorder-averaged behavior of DNA's with random sequences to the more experimentally accessible problem of unzipping a single DNA molecule. As the applied force approaches the critical value, the double-stranded DNA unravels in a series of discrete, sequence-dependent steps that allow it to reach successively deeper energy minima. Plots of extension versus force thus take the striking form of a series of plateaus separated by sharp jumps. Similar qualitative features should reappear in micromanipulation experiments on proteins and on folded RNA molecules. Despite their unusual form, the extension versus force curves for single molecules still reveal remnants of the disorder-averaged critical behavior. Above the transition, the dynamics of the unzipping fork is related to that of a particle diffusing in a random force field; anomalous, disorder-dominated behavior is expected until the applied force exceeds the critical value for unzipping by roughly 5 pN.Comment: 40 pages, 18 figure

Long range correlations generated by phase separation. Exact results from field theory

We consider near-critical planar systems with boundary conditions inducing phase separation. While order parameter correlations decay exponentially in pure phases, we show by direct field theoretical derivation how phase separation generates long range correlations in the direction parallel to the interface, and determine their exact analytic form. The latter leads to specific contributions to the structure factor of the interface

Development of pig welfare assessment protocol integrating animal-, environment-, and management-based measures

Abstract Background Due to increased interest in animal welfare, there is now a need for a comprehensive assessment protocol to be used in intensive pig farming systems. There are two current welfare assessment protocols for pigs: Welfare Quality® Assessment Protocols (applicable in the Europe Union), that mostly focuses on animal-based measures, and the Swine Welfare Assurance Program (applicable in the United States), that mostly focuses on management- and environment-based measures. In certain cases, however, animal-based measures might not be adequate for properly assessing pig welfare status. Similarly, welfare assessment that relies only on environment- and management-based measures might not represent the actual welfare status of pigs. Therefore, the objective of this paper was to develop a new welfare protocol by integrating animal-, environment-, and management-based measures. The background for selection of certain welfare criteria and modification of the scoring systems from existing welfare assessment protocols are described. Methods The developed pig welfare assessment protocol consists of 17 criteria that are related to four main principles of welfare (good feeding, good housing, good health, and appropriate behavior). Good feeding, good housing, and good health were assessed using a 3-point scale: 0 (good welfare), 1 (moderate welfare), and 2 (poor welfare). In certain cases, only a 2-point scale was used: 0 (certain condition is present) or 2 (certain condition is absent). Appropriate behavior was assessed by scan sampling of positive and negative social behaviors based on qualitative behavior assessment and human-animal relationship tests. Results Modification of the body condition score into a 3-point scale revealed pigs with a moderate body condition (score 1). Moreover, additional criteria such as feed quality confirmed that farms had moderate (score 1) or poor feed quality (score 2), especially those farms located in a high relative humidity region. Conclusions The developed protocol can be utilized to assess welfare status in an intensive pig farming system. Although further improvements are still needed, this study is a first step in developing a pig welfare assessment protocol that combines animal-, environment-, and management-based measures

The development of a novel model of direct fracture healing in the rat

OBJECTIVES: Small animal models of fracture repair primarily investigate indirect fracture healing via external callus formation. We present the first described rat model of direct fracture healing. METHODS: A rat tibial osteotomy was created and fixed with compression plating similar to that used in patients. The procedure was evaluated in 15 cadaver rats and then in vivo in ten Sprague-Dawley rats. Controls had osteotomies stabilised with a uniaxial external fixator that used the same surgical approach and relied on the same number and diameter of screw holes in bone. RESULTS: Fracture healing occurred without evidence of external callus on plain radiographs. At six weeks after fracture fixation, the mean stress at failure in a four-point bending test was 24.65 N/mm(2) (sd 6.15). Histology revealed ‘cutting-cones’ traversing the fracture site. In controls where a uniaxial external fixator was used, bone healing occurred via external callus formation. CONCLUSIONS: A simple, reproducible model of direct fracture healing in rat tibia that mimics clinical practice has been developed for use in future studies of direct fracture healing