Digraphs with Isomorphic Underlying and Domination Graphs: Pairs of Paths

A domination graph of a digraph D, dom (D), is created using thc vertex set of D and edge uv ϵ E (dom (D)) whenever (u, z) ϵ A (D) or (v, z) ϵ A (D) for any other vertex z ϵ A (D). Here, we consider directed graphs whose underlying graphs are isomorphic to their domination graphs. Specifically, digraphs are completely characterized where UGc (D) is the union of two disjoint paths

A Characterization of Connected (1,2)-Domination Graphs of Tournaments

Recently. Hedetniemi et aI. introduced (1,2)-domination in graphs, and the authors extended that concept to (1, 2)-domination graphs of digraphs. Given vertices x and y in a digraph D, x and y form a (1,2)-dominating pair if and only if for every other vertex z in D, z is one step away from x or y and at most two steps away from the other. The (1,2)-dominating graph of D, dom1,2 (D), is defined to be the graph G = (V, E ) , where V (G) = V (D), and xy is an edge of G whenever x and y form a (1,2)-dominating pair in D. In this paper, we characterize all connected graphs that can be (I, 2)-dominating graphs of tournaments

Kings and Heirs: A Characterization of the (2,2)-domination Graphs of Tournaments

In 1980, Maurer coined the phrase king when describing any vertex of a tournament that could reach every other vertex in two or fewer steps. A (2,2)-domination graph of a digraph D, dom2,2(D), has vertex set V(D), the vertices of D, and edge uv whenever u and v each reach all other vertices of D in two or fewer steps. In this special case of the (i,j)-domination graph, we see that Maurer’s theorem plays an important role in establishing which vertices form the kings that create some of the edges in dom2,2(D). But of even more interest is that we are able to use the theorem to determine which other vertices, when paired with a king, form an edge in dom2,2(D). These vertices are referred to as heirs. Using kings and heirs, we are able to completely characterize the (2,2)-domination graphs of tournaments

Local Out-Tournaments with Upset Tournament Strong Components I: Full and Equal {0,1}-Matrix Ranks

A digraph D is a local out-tournament if the outset of every vertex is a tournament. Here, we use local out-tournaments, whose strong components are upset tournaments, to explore the corresponding ranks of the adjacency matrices. Of specific interest is the out-tournament whose adjacency matrix has boolean, nonnegative integer, term, and real rank all equal to the number of vertices, n. Corresponding results for biclique covers and partitions of the digraph are provided

Cognitive networks: brains, internet, and civilizations

In this short essay, we discuss some basic features of cognitive activity at several different space-time scales: from neural networks in the brain to civilizations. One motivation for such comparative study is its heuristic value. Attempts to better understand the functioning of "wetware" involved in cognitive activities of central nervous system by comparing it with a computing device have a long tradition. We suggest that comparison with Internet might be more adequate. We briefly touch upon such subjects as encoding, compression, and Saussurean trichotomy langue/langage/parole in various environments.Comment: 16 page

Towards model-based control of Parkinson's disease

Modern model-based control theory has led to transformative improvements in our ability to track the nonlinear dynamics of systems that we observe, and to engineer control systems of unprecedented efficacy. In parallel with these developments, our ability to build computational models to embody our expanding knowledge of the biophysics of neurons and their networks is maturing at a rapid rate. In the treatment of human dynamical disease, our employment of deep brain stimulators for the treatment of Parkinson’s disease is gaining increasing acceptance. Thus, the confluence of these three developments—control theory, computational neuroscience and deep brain stimulation—offers a unique opportunity to create novel approaches to the treatment of this disease. This paper explores the relevant state of the art of science, medicine and engineering, and proposes a strategy for model-based control of Parkinson’s disease. We present a set of preliminary calculations employing basal ganglia computational models, structured within an unscented Kalman filter for tracking observations and prescribing control. Based upon these findings, we will offer suggestions for future research and development

COMPLEMENT SYSTEM AS A MARKER OF IMMUNE DYSFUNCTION IN CHILDREN AUTISM SPECTRUM DISORDERS

It is known that functional activity of complement system depends not only on balance and concentration of components participating in formation of the system end products, but also on levels of inhibitory activities. Numerous relations with hemostasis also substantially contribute to general level of complement system activity. Changes in complement system functioning are inevitable during chronic diseases accompanied with immune system dysregulation. All mental diseases tend to be chronic and are they aggravated by patients’ immune system changes. Autism spectrum disorders in children is a group of mental disorders. Immune system dysregulation is usually detected in such patients, manifesting as excessive susceptibility to viral and bacterial infections. Therefore, the level of its functional activity is diagnostically and prognostically significant in this pathology, since the complement system is a key element of immune system.We have evaluated functional activity of complement system in patients with autistic spectrum disorders, using the method which was developed earlier. It is based on the reaction of the protozoa (Tetrahymena pyriformis) which are both targets and activators for the complement system. The complement system capacity (cSC) was used as the main parameter of complement evaluation. The half-time of protozoa survival (T50) was defined using the BioLat device for each serum specimen added at four concentrations (1/20, 1/40, 1/80, 1/160 dilution). The complement capacity was calculated as the area enclosed by influence curve of the reciprocals of T50 and the serum dilution. According to Mann–Whitney U test, the difference between patients’ and healthy volunteers’ groups was established as Z = 4.43 (by T50 at 1/160 dilution), p < 0.001 and by cSCas Z = 5.8, p < 0.001. cSC was calculated from the results obtained at each serum concentration measured. The difference between the two groups according to Mann–Whitney U test appeared to be more significant than the difference according to T50. Therefore, cSC was taken as the main characteristic of complement system function.The contribution of hemostasis plasma components to complement system functional activity level was estimated by determination of complement capacity in plasma and serum of each blood sample from 6 patients with autism spectrum disorders and 5 healthy donors. All healthy donors showed small difference between plasma and serum complement capacity, and their complement activity was higher in plasma. In patients’ group, the complement capacity levels in plasma and serum differed significantly. The cSC levels of two patients were higher in serum than in plasma, and the cSC levels of three other patients were significantly higher in plasma than in serum. Differential involvement of coagulation into the complement system activation may be indicative for the immune system dysfunction which is observed in patients with autistic spectrum disorders of different etiology