HH-product and HH-threshold graphs

This paper is the continuation of the research of the author and his colleagues of the {\it canonical} decomposition of graphs. The idea of the canonical decomposition is to define the binary operation on the set of graphs and to represent the graph under study as a product of prime elements with respect to this operation. We consider the graph together with the arbitrary partition of its vertex set into $n$ subsets ($n$-partitioned graph). On the set of $n$-partitioned graphs distinguished up to isomorphism we consider the binary algebraic operation $\circ_H$ ($H$-product of graphs), determined by the digraph $H$. It is proved, that every operation $\circ_H$ defines the unique factorization as a product of prime factors. We define $H$-threshold graphs as graphs, which could be represented as the product $\circ_{H}$ of one-vertex factors, and the threshold-width of the graph $G$ as the minimum size of $H$ such, that $G$ is $H$-threshold. $H$-threshold graphs generalize the classes of threshold graphs and difference graphs and extend their properties. We show, that the threshold-width is defined for all graphs, and give the characterization of graphs with fixed threshold-width. We study in detail the graphs with threshold-widths 1 and 2

Krausz dimension and its generalizations in special graph classes

A {\it krausz $(k,m)$-partition} of a graph $G$ is the partition of $G$ into cliques, such that any vertex belongs to at most $k$ cliques and any two cliques have at most $m$ vertices in common. The {\it $m$-krausz} dimension $kdim_m(G)$ of the graph $G$ is the minimum number $k$ such that $G$ has a krausz $(k,m)$-partition. 1-krausz dimension is known and studied krausz dimension of graph $kdim(G)$. In this paper we prove, that the problem $"kdim(G)\leq 3"$ is polynomially solvable for chordal graphs, thus partially solving the problem of P. Hlineny and J. Kratochvil. We show, that the problem of finding $m$-krausz dimension is NP-hard for every $m\geq 1$, even if restricted to (1,2)-colorable graphs, but the problem $"kdim_m(G)\leq k"$ is polynomially solvable for $(\infty,1)$-polar graphs for every fixed $k,m\geq 1$

Surgical treatment of combined biliary and vascular injury following cholecystectomy

Institutul Naţional de Chirurgie şi Transplantologie “A.Shalimov”, Kiev, Ucraina, Al XII-lea Congres al Asociației Chirurgilor „Nicolae Anestiadi” din Republica Moldova cu participare internațională 23-25 septembrie 2015Introducere: Leziunile combinate ale vaselor şi căilor biliare extrahepatice reprezintă una dintre cele mai serioase complicaţii după colecistectomie. Efectuarea rezecţiei sau transplantului hepatic a fost necesară la 13,2-57,0% dintre pacienţii cu leziuni bilio-vasculare combinate (LBV).Materiale şi metode: Au fost incluşi 31 pacienţi cu LBV după colecistectomie în perioada ianuarie 1984 - ianuarie 2015. La 21 (67,7%) pacienţi leziunile au apărut după colecistectomia deschisă, la 10 (32,3%) – după cea laparoscopică. Intraoperator au fost înregistrate 6 (19,4%) leziuni ale ducturilor biliare. În perioada postoperatorie precoce (pînă la 7 zile) prezenţa unei stenoze de ramură a arterei hepatice este stabilită la 4 (12,9%) pacienţi, în perioada tardivă (8 zile – 3 ani) – la 21 (67,7%). În 5 (16,1%) cazuri a fost înregistrată stenoza arterei hepatice comune, în 24 (77,4%) – a ramurii drepte şi în 2 (6,5%) – a ramurii stîngi. Rezultate: La 2 pacienţi s-au efectuat tentative de restabilire a stenozei arteriale. Datorită dezvoltării colateralelor arterei hepatice comune 19 pacienţi au reluat fluxul hepatic arterial şi au suportat numai hepaticojejunoanastomoză. În 2 cazuri preventiv s-a efectuat embolizarea anevrismului arterei hepatice. Rezecţia de ficat s-a efectuat la 9 (29,0%) pacienţi. La 16 pacienţi cu LBV s-a dezvoltat necroza ficatului cu abcese. Concluzii: Rezultate pozitive în termen de 10 ani sunt înregistrate la 27 (86,2%) bolnavi, rezultate nesatisfăcătoare – la 4 (13,8%), un pacient a decedat. Astfel, pacienţii cu LBV combinate necesită tratament multimodal ţinînd cont de caracteristicile clinice actuale.Introduction: The combined damage of extra hepatic biliary ducts and vessels are the most serious complication of a cholecystectomy. Performance of the resection or liver transplantation was required 13.2-57.0% of patients with the combined biliovascular injury (BVI). Methods: 31 patients with the BVI after cholecystectomy, from January 1984 till January 2015. In 21 (67.7%) patients damage occured during open cholecystectomy, at 10 (32.3%) – laparoscopic. Intraoperatively injury of biliary duct is diagnosed in 6 (19.4%) cases. In the early postoperative period (to 7 days) existence of an occlusion of branches of the hepatic artery is established in 4 (12.9%) patients, in late (8 days-3 years) – in 21 (67.7%). In 5 (16.1%) cases the occlusion of the common hepatic artery, 24 (77.4%) – right brunch and 2 (6.5%) – left brunch was found. Results: Two patients had attempts of restoration of an arterial blood groove. Owing to hepatic artery collaterals development 19 patients resumed hepatic artery flow and underwent hepaticojejunostomy as a result only. In two cases it was preceded by embolization of hepatic artery aneurism. Liver resection is performed in 9 (29.0%) patients. At 16 patients with the BVI developed liver necrosis with abscesses. Conclusion: Positive results in terms to 10 years are received at 27 (86.2%), unsatisfactory – 4 (13.8%), one patient died. Thus, patients with the combined BVI need multimodal tactic of treatment taking into account features of their clinical current

Antigenic cooperation in Viral Populations: Transformation of Functions of Intra-Host Viral Variants

In this paper we study intra-host viral adaptation by antigenic cooperation - a mechanism of immune escape that serves as an alternative to the standard mechanism of escape by continuous genomic diversification and allows to explain a number of experimental observations associated with the establishment of chronic infections by highly mutable viruses. Within this mechanism, the topology of a cross-immunoreactivity network forces intra-host viral variants to specialize for complementary roles and adapt to host's immune response as a quasi-social ecosystem. Here we study dynamical changes in immune adaptation caused by evolutionary and epidemiological events. First, we show that the emergence of a viral variant with altered antigenic features may result in a rapid re-arrangement of the viral ecosystem and a change in the roles played by existing viral variants. In particular, it may push the population under immune escape by genomic diversification towards the stable state of adaptation by antigenic cooperation. Next, we study the effect of a viral transmission between two chronically infected hosts, which results in merging of two intra-host viral populations in the state of stable immune-adapted equilibrium. In this case, we also describe how the newly formed viral population adapts to the host's environment by changing the functions of its members. The results are obtained analytically for minimal cross-immunoreactivity networks and numerically for larger populations.Comment: 39 pages (including Appendix), 21 image

Primary non-Hodgekin’s lymphoma of duodenum

Primary non-Hodgekin’s lymphoma of duodenu

Scale-free spanning trees: complexity, bounds and algorithms

We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a connected graph. It is motivated by a particular problem in epidemiology, and may be useful in studies of various dynamical processes in networks. We employ two possible objective functions for this problem and introduce the corresponding algorithmic problems termed $m$-SF and $s$-SF Spanning Tree problems. We prove that those problems are APX- and NP-hard, respectively, even in the classes of cubic, bipartite and split graphs. We study the relations between scale-free spanning tree problems and the max-leaf spanning tree problem, which is the classical algorithmic problem closest to ours. For split graphs, we explicitly describe the structure of optimal spanning trees and graphs with extremal solutions. Finally, we propose two Integer Linear Programming formulations and two fast heuristics for the $s$-SF Spanning Tree problem, and experimentally assess their performance using simulated and real data

Early peroral feeding after pancreaticoduodenecomy

Objective. To analyze the various ways for enteral feeding after pancreaticoduodenectomy. Materials and methods. There were investigated the results of pancreaticoduodenectomy, performed in 78 patients, suffering tumors of pancreatic head and periampullary zone, in whom various methods of nutritive support, in 2003 - 2017 yrs were applied. For comparative analysis the patients were divided into two groups: the first - 39 patients, perioperative treatment of whom was conducted in accordance to the ERAS program, and the second - 39 patients, who were treated using a standard method. In patients of the first group the effects of a peroral way of nutrition were compared, as well as combined peroral and enteral nutrition via microjejunostomy. There were studied the terms of restoration of peroral feeding, the gastrostasis rate, the nutrition calorage during 7 postoperative days, levels of general protein and albumin on the first, third and seventh postoperative day. Results. In 33 (84.6%) patients of the first group the peroral nutrition restoration have occurred in complete order to the protocol. The gastrostasis rate in patients of the first group was essentially lesser, than in patients of the second group. In the first group this complication have occurred in 6 (15.4%) patients, in the second group - in 14 (35.9%) patients (p = 0.009). Dynamics of level of general protein and albumin of the blood in postoperative period did not depend on method and energetic estimate of the nutrition. Conclusion. Application of peroral feeding, in accordance to the concept of the program for accelerated restoration of the patients, survived after pancreaticododenectomy, constitutes an optimal way for the nutrient support of an organism and permits to reduce the gastrostasis rate trustworthily