We consider a family of problems that combine network Design and facility location. Such problems arise in many practical applications in di, erent , elds such as telecommunications, transportation networks, logistic, and energy supply networks. In facility location problems, we want to decide which facilities to open and how to assign clients to the open facilities so as to minimize the sum of the facility opening costs and client connection costs. These problems typically do not involve decisions concerning the routing of the clients' demands to the open facilities,once we decided on the set of open facilities, each client is served by the closest open facility. In network Design problems, on the other hand, we generally want to Design and dimension a minimum-cost routing network providing su, cient capacities to route all clients' demands to their destinations. These problems involve deciding on the routing of each client's demand. But, in contrast to facility location problems, demands' destinations are predetermined. In many modern day applications, however, all these decisions are interdependent and a, ect each other. Hence, they should be taken simultaneously. The aim of this work is to survey models, Algorithmic approaches and methodologies concerning such combined network Design facility location problems.

The ileum has been candidate more frequently for endoscopic biopsy compared to the past. Most of those biopsies show either completely normal tissue or non-specific changes. Nevertheless, in some diseases, ileal biopsy would be diagnostic, and in some cases, it may be the only anatomical involved location by the disease. Endoscopically, normal mucosal biopsy is unlikely to provide useful diagnostic information and is not routinely recommended. However, in the presence of ileitis, ulcers, or erosions, biopsies can be very helpful. Ileitis might be induced by various conditions including infectious diseases, vasculitis, medication-induced, ischemia, eosinophilic enteritis, tumors etc. The conclusive cause of the condition is proposed by a comprehensive clinical background and physical examination, laboratory investigations, ileocolonoscopy, and imaging findings. Ileoscopy and biopsy are mainly useful in correctly selected cases such as patients who present with inflammatory diarrhea and endoscopic lesions. The purpose of this review article is to provide a simple Algorithmic approach to the ileal biopsy samples through several boxes that give diagnostic clues and an idea behind the categories of ileal disorders. This review is written based on those that were previously reported in the literature as well as the authors' experiences. We have summarized different histological patterns in the ileal biopsy specimens that can be used in the diagnosis of inflammatory disorders of the ileum. This review provides an Algorithmic approach to the clinicopathological features of inflammatory disorders of the ileum with a brief discussion of some important related issues.

Febrile seizures (FS) are the most common form of convulsive phenomena in human being and affect 2% to 14% of children. It is the most common type of seizures that every pediatrician is dealing with. It is the most benign type of all seizures occurring in childhood. There are many debates on how to approach to febrile seizures in pediatric neurology and there are many possible malpractices in this field. Some of the most common frequent queries are - How could we differentiate FS from seizures and fever associated with serious infections involving the central nervous system?- When should we refer the affected child for further investigations such as lumbar puncture, EEG, neuroimaging, and routine biochemical studies?- How should we treat FS in its acute phase?- How could we assess the risk for further recurrences as well as other risks threatening the child's health in future?- How could we select the patients for treatment or prophylaxis?- Which medication(s) should be selected for treatment or prophylaxis?Trying to answer the above-mentioned questions, this review article will present a four steps Algorithmic clinical approach model to a child with febrile seizures based on the current medical literature.

Let G = (V, E) be a graph. A double Roman dominating function (DRDF) of G is a function f: V →, { 0,1,2,3} such that, for each v ,V with f(v) = 0, there is a vertex u adjacent to v with f(u) = 3 or there are vertices x and y adjacent to v such that f(x) = f(y) = 2 and for each v ,V with f(v) = 1, there is a vertex u adjacent to v with f(u) > 1. The weight of a DRDF f is f(V ) =∑, v, V f(v). Let n and k be integers such that 3 ≥,2k + 1 ≥,n. The generalized Petersen graph GP(n,k) = (V, E) is the graph with V = {u1,u2,…, , un},{v1,v2,…, , vn} and E = {uiui+1,uivi,vivi+k: 1 ≥,i ≥,n}, where addition is taken modulo n. In this paper, we _rstly prove that the decision problem associated with double Roman domination is NP-complete even restricted to planar bipartite graphs with maximum degree at most 4. Next, we give a dynamic programming algorithm for computing a minimum DRDF (i. e., a DRDF with minimum weight along all DRDFs) of GP(n,k) in O(n81k) time and space and so a minimum DRDF of GP(n, O(1)) can be computed in O(n) time and space.

A dominating set D of a graph G = (V, E) is called a certified dominating set of G if |N(v)∩, (V \D)| is either 0 or at least 2 for all v ,D. The certified domination number ɤ, cer(G) is the minimum cardinality of a certified dominating set of G. In this paper, we prove that the decision problem corresponding to ɤ, cer(G) is NP-complete for split graphs, star convex bipartite graphs, comb convex bipartite graphs and planar graphs. We also prove that it is linear time solvable for chain graphs, threshold graphs and bounded tree-width graphs.