Neighborhood Homogeneous Labelings of Graphs

Given a labeling of the vertices and edges of a graph, we define a type of homogeneity that requires that the neighborhood of every vertex contains the same number of each of the labels. This homogeneity constraint is a generalization of regularity – all such graphs are regular. We consider a specific condition in which both the edge and vertex label sets have two elements and every neighborhood contains two of each label. We show that vertex homogeneity implies edge homogeneity (so long as the number of edges in any neighborhood is four), and give two theorems describing how to build new homogeneous graphs (or multigraphs) from others. Keywords: vertex labeling; edge labeling; homogenous graph; regular graph 1

Role of TNFR-related 2 mediated immune responses in dextran sulfate sodium-induced inflammatory bowel disease

Previous work has suggested that the LIGHT-TR2 costimulatory pathway plays a role in the acute and chronic stages of dextran sulfate sodium (DSS)-induced colitis [Steinberg et al. (2008); Wang et al. (2005)]. To clarify the role of TNFR-related 2 (TR2) signaling in the maintenance of intestinal homeostasis, we generated a TR2 knock-out (KO) mouse. Using DSS to induce colitis, we compared the colitic symptoms and pathological changes in wild type (WT) and TR2 KO mice, and the production of cytokines by the diseased colons. We also studied the role of TR2 in suppressing innate and adaptive immunity in the DSS model. TR2 deficient mice were characterized by reduced symptoms of intestinal inflammation compared with wildtype mice, and reduced production of cytokines. We therefore generated a monoclonal antibody against mouse TR2 which was specific to TR2 and capable of blocking TR2 signals. With this antibody, we demonstrated that antagonizing TR2 during the development of DSS-induced colitis reduced the symptoms of inflammation. Our findings suggest that TR2 is an important mediator in colitis, and may serve as a therapeutic target in inflammatory bowel disease

Analysis of temporal firing patterns of primary afferent C-fibers for different sensations in mice

Some people with amputated limbs can benefit from neural prosthetics to restore tactile sensation through electrical stimulation of the afferent nerve. The temporal spike train pattern generated in healthy subject's nerve by various types of somatosensation could provide key information to closely mimic natural sensations using electrical stimulation. However, the temporal firing patterns of peripheral sensory fibers have not been well understood yet. To interpret somatosensory spike trains, we performed ex vivo singlefiber recordings from the saphenous nerve in isolated skin-nerve preparations from mice. Some mechanically sensitive primary afferent C-fibers could also be activated by hot, cold, and itching stimuli, and we observed stimulus-specific firing patterns. These temporal patterns of the C-fibers for chemical stimuli were analyzed using a computational model based on quadruplets of spikes, which we classified into three groups of responses, i.e., capsaicin (hot), allyl-isothiocyanate (cold), and alpha-methyl-serotonin (itching). Each group of responses to the chemical stimuli was different from that evoked by mechanical stimuli. Therefore, these findings indicate that nontactile somatosensation can be decoded and used as input to a computerized system. Our quadruplet approach to the temporal patterns of spike trains contributes valuable insight to the identification of temporal profiles of other biological conditions