Exploring Non-Determinism in Graph Algorithms

Abstract. Graph algorithms that are based on the computation of one or more paths are often written in an implicitly non-deterministic way, which suggests that the result of the algorithm does not depend on a particular path, but any path that satisfies a given property. Such algorithms provide an additional challenge in typical implementations, because one needs to replace the non-determinism with an actual implementation. In this paper we explore the effects of using non-determinism explicitly in the functional logic programming language Curry. To that end we consider three algorithms and implement them in a prototypically non-deterministic fashion

Entwurf funktionaler Implementierungen von Graphalgorithmen

Classic graph algorithms are usually presented and analysed in imperative programming languages. Imperative programming languages are well-suited for the description of a program flow, in which the order in which the operations are performed is important. One common example of such a description is the successive, typically destructive modification of objects. This kind of iteration often occurs in the context of graph algorithms that deal with a certain kind of optimisation. In functional programming, the order of execution is abstracted and problem solutions are described as compositions of intermediate solutions. Additionally, functional programming languages are referentially transparent and thus destructive updates of objects are discouraged. The development of purely functional graph algorithms begins with the decomposition of a given problem into simpler problems. In many cases the solutions of these partial problems can be used to solve different problems as well. What is more, this compositionality allows exchanging functions for more efficient or more comprehensible versions with little effort. An algebraic approach with a focus on relation algebra as defined by Tarski is used as an intermediate step in this dissertation. One advantage of this approach is the formality of the resulting specifications. Despite their formality, the resulting expressions are still readable, because the algebraic operations have intuitive interpretations. Another advantage is that the specification is executable, once the necessary operations are implemented. This dissertation presents the basics of the algebraic approach in the functional programming language Haskell. Using this foundation, some exemplary graph-theoretic problems are solved in the presented framework. Finally, optimisations of the presented implementations are discussed and pointers are provided to further problems that can be solved using the above methods.Klassische Graphalgorithmen werden üblicherweise in imperativen Programmiersprachen beschrieben und analysiert. Imperative Programmiersprachen eignen sich gut, um Programmabläufe zu beschreiben, in welchen die Reihenfolge der Operationen wichtig ist. Dies betrifft insbesondere die schrittweise, in der Regel destruktive Veränderung von Objekten, wie sie häufig im Falle von Optimierungsproblemen auf Graphen vorkommt. In der funktionalen Programmierung abstrahiert man von einer festen Berechnungsreihenfolge und beschreibt Problemlösungen als Kompositionen von Teillösungen. Ferner sind funktionale Programmiersprachen referentiell transparent, sodass destruktive Veränderungen nur bedingt möglich sind. Die Entwicklung rein funktionaler Graphalgorithmen setzt bei der Zerlegung der bestehenden Probleme in einfachere Probleme an. Oftmals können Lösungen dieser Teilprobleme auch in anderen Situationen eingesetzt werden. Darüber hinaus erlaubt es diese Kompositionalität, einzelne Funktionen mit wenig Aufwand durch effizientere oder verständlichere Fassungen auszutauschen. Als Zwischenschritt in der Entwicklung wird in dieser Dissertation ein algebraischer Ansatz basierend auf der Relationenalgebra im Sinne von Tarski verwendet. Ein Vorteil dieses Ansatzes ist die Formalität der entstehenden Spezifikationen. Trotz ihrer Formalität bleiben die entstehenden Ausdrücke oft leserlich, weil die algebraischen Operationen anschauliche Interpretationen zulassen. Ein weiterer Vorteil ist, dass Spezifikationen ausführbar werden, sobald bestimmte Basisoperationen implementiert sind. In dieser Dissertation werden Grundlagen einer Implementierung des algebraischen Ansatzes in der funktionalen Programmiersprache Haskell behandelt. Ausgehend hiervon werden exemplarisch einige Probleme der Graphentheorie gelöst. Schließlich werden Optimierungen der vorgestellten Implementierungen und weitere Probleme, welche mit den obigen Methoden lösbar sind, diskutiert

Improvement of Pork Quality at Different Values of Pig Productivity

This article examines how to increase pork meat productivity and quality indicators through the use of crossbreeding. The aim is to increase the meat productivity of animals; reduce losses during production and processing; and improve the criteria for assessing the quality of meat and the organization of its rational use. The purpose of our research is to study the productive quality of the steppe type of pigs, used in the Rostov region in breeding and crossing systems, and the complex of biological and internal indicators in connection with the defects in the quality of pork. Four groups with 16 animals in each were formed: the first group – with the intensive cultivation technology, included pigs of the DM-1 breed, the second – SM-1, the third – the SM-1 × DM-1 crossbreed, the fourth – the DM-1 × SM-1 crossbreed. Analysis of the raw meat showed that the pork had a good ability to emulsify and gel, and had a high nutritional value. The toxicity index in the muscle and fat tissue samples corresponded to the first permissible toxicity group. The study shows the advantages of crossbred individuals over purebred ones, which can be explained by the consequences of heterosis. According to the research results, the use of pig breeding in the industrial production of pork can be recommended in order to improve feedstock and meat productivity, biological and interior indicators, as well as the quality of raw meat. Keywords: pork, crossbreeding, meat productivity, meat quality, steppe type of pigs, interior indicators, fattening qualities, biological and nutritional value of por

Effects of Three Feed Additives on the Culturable Microbiota Composition and Histology of the Anterior and Posterior Intestines of Zebrafish (<i>Danio rerio</i>)

In this study, the effect of three promising feed additives (chelated compounds of trace elements, butyric acid, lycopene) on changes in the culturable microbiota and histological parameters of two sections of the intestines of Danio rerio (zebrafish) was studied. The use of these feed additives can help to eliminate the deficiency of trace elements, modulate the composition of the microbiota due to the postbiotic properties of butyric acid, and reduce oxidative stress when using lycopene. Incorporation of the investigated supplements in the feed resulted in a significant change in the relative abundance of certain groups of microorganisms. The taxonomic diversity of cultured microorganisms did not differ in the anterior and posterior intestines, while there were differences in the relative abundance of these microorganisms. The most sensitive groups of microorganisms were the genera Bacillus and Serratia. A significant effect on the composition of the cultured microbiota was caused by lycopene (in all studied concentrations), leading to a significant increase in the relative abundance of Firmicutes in the anterior gut. Studies of the histological structure of the anterior and posterior guts have shown the relationship between the barrier and secretory functions of the gut and the composition of the microbiota while using butyric acid (1 and 2 g kg−1) and trace element chelated compounds (2 mg kg−1). This culture-dependent method of studying the microbiome makes it possible to assess changes in some representatives of the main groups of microorganisms (Firmicutes and Proteobacteria). Despite the incompleteness of the data obtained by the culture-dependent method, its application makes it possible to assess the bioactive properties of feed and feed additives and their impact on the microbiota involved in digestive processes

Complex Changes in the Apoptotic and Cell Differentiation Programs during Initiation of the Hair Follicle Response to Chemotherapy

NoChemotherapy has severe side effects in normal rapidly proliferating organs, such as hair follicles, and causes massive apoptosis in hair matrix keratinocytes followed by hair loss. To define the molecular signature of hair follicle response to chemotherapy, human scalp hair follicles cultured ex vivo were treated with doxorubicin (DXR), and global microarray analysis was performed 3 hours after treatment. Microarray data revealed changes in expression of 504 genes in DXR-treated hair follicles versus controls. Among these genes, upregulations of several tumor necrosis factor family of apoptotic receptors (FAS, TRAIL (tumor necrosis factor–related apoptosisinducing ligand) receptors 1/2), as well as of a large number of keratin-associated protein genes, were seen after DXR treatment. Hair follicle apoptosis induced by DXR was significantly inhibited by either TRAIL-neutralizing antibody or caspase-8 inhibitor, thus suggesting a previously unreported role for TRAIL receptor signaling in mediating DXR-induced hair loss. These data demonstrate that the early phase of the hair follicle response to DXR includes upregulation of apoptosis-associated markers, as well as substantial reorganization of the terminal differentiation programs in hair follicle keratinocytes. These data provide an important platform for further studies toward the design of effective approaches for the management of chemotherapy-induced hair loss