Brownian Web and Oriented Percolation: Density Bounds

In a recent work, we proved that under diffusive scaling, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice Z^2 converges in distribution to the Brownian web. In that proof, the FKG inequality played an important role in establishing a density bound, which is a part of the convergence criterion for the Brownian web formulated by Fontes et al (2004). In this note, we illustrate how an alternative convergence criterion formulated by Newman et al (2005) can be verified in this case, which involves a dual density bound that can be established without using the FKG inequality. This alternative approach is in some sense more robust. We will also show that the spatial density of the collection of rightmost infinite open paths starting at time 0 decays asymptotically in time as c/\sqrt{t} for some c>0.Comment: 12 pages. This is a proceeding article for the RIMS workshop "Applications of Renormalization Group Methods in Mathematical Sciences", held at Kyoto University from September 12th to 14th, 2011. Submitted to the RIMS Kokyuroku serie

Rigorous results on the threshold network model

We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the vertex degree, degree correlation, and the number of prescribed subgraphs. We also generalize some results in the spatially extended cases.Comment: 21 pages, Journal of Physics A, in pres

The 2d-directed spanning forest converges to the Brownian web

The two-dimensional directed spanning forest (DSF) introduced by Baccelli and Bordenave is a planar directed forest whose vertex set is given by a homogeneous Poisson point process $\mathcal{N}$ on $\mathbb{R}^2$. If the DSF has direction $-e_y$, the ancestor $h(u)$ of a vertex $u \in \mathcal{N}$ is the nearest Poisson point (in the $L_2$ distance) having strictly larger $y$-coordinate. This construction induces complex geometrical dependencies. In this paper we show that the collection of DSF paths, properly scaled, converges in distribution to the Brownian web (BW). This verifies a conjecture made by Baccelli and Bordenave in 2007

Brownian Web in the Scaling Limit of Supercritical Oriented Percolation in Dimension 1+1

We prove that, after centering and diffusively rescaling space and time, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice Z^2_{even}:={(x,i) in Z^2: x+i is even} converges in distribution to the Brownian web. This proves a conjecture of Wu and Zhang. Our key observation is that each rightmost infinite open path can be approximated by a percolation exploration cluster, and different exploration clusters evolve independently before they intersect.Comment: 25 pages, 4 figures. To appear in Electronic Journal of Probabilit

Inflammation Of The Taste Sensory System: Cyclophosphamide And Amifostine

Chemotherapeutics are used extensively to treat cancer patients and often induce adverse effects, including taste dysfunctions. Disturbances in taste are detrimental to the overall well-being of cancer patients, causing malnutrition and weight loss that aggravate their condition even further. Inflammation due to an infection of the taste sensory system as previously shown, has detrimental effects on the taste sensation. Our study focused on if chemotherapy induced an inflammatory response in the taste buds using cyclophosphamide (CYP), a pro-drug. Once metabolized by the P450 enzyme complex, its primary metabolite functions as an alkylating agent, involved in inhibiting cell replication cycle and cell death. We used immunohistochemistry and fluorescent microscopy to analyze and observe the expression of the pro-inflammatory cytokine TNF-α in different types of taste sensory cells. Previously we found that a sulfhydryl cytoprotective drug, amifostine, can prevent taste bud damage and therefore we asked if it could prevent an inflammatory response. Our research observed an inflammatory response in both Type II and Type III cells in taste buds of fungiform and circumvallate papilla. Type II cells showed a peak response at 8- and 24-hour post-CYP injection whereas Type III cells had a peak expression at 24-hour post-CYP injection in the circumvallate papillae. Pre-treatment with amifostine appeared to prevent an inflammatory response within taste buds from CYP induced cytokine response. Identifying inflammation as a potential factor in taste related disorders could help clinicians develop better treatment modalities such as cytoprotective drugs preventing chemotherapy induced long term adverse effects such as malnutrition. In the future, we would like to expand our research to investigate expression of other pro-inflammatory cytokines and possible signaling mechanisms that could be responsible for CYP-induced inflammatory response in Type III cells

Convergence of tail sum for records

Suppose {Rn(L) (F): n≥1} is the sequence of lower records from a distribution F, where F is continuous with inf {x ∈ supp(F)}=0. We derive conditions under which logarithm of the tail sum of records, ∑ j=n ∞=Rn (L) (F), properly centered and scaled, converge weakly. We also prove two results on ?-varying and regularly varying functions, which are of independent interest

Effect of alloy treatment and coiling temperature on microstructure and bending performance of ultra-high strength strip steel

Two different high strength B-containing microalloyed steel strips produced in industrial processing conditions, one treated with Ti and the other treated with Al, processed by controlled rolling, accelerated cooling and coiling in two different temperatures ranges [723 K to 733 K (450 °C to 460 °C)] and [633 K to 653 K (360 °C to 380 °C)] were subjected to bend testing. The Ti treated steel coiled at the higher temperature 733 K (460 °C) showed the best bending performance. The relatively softer (tensile strength of and even {112} in the sub-surface region as well as uniformity of through thickness texture of the rolled sheet improve the bendability. In the presence of crack initiators, like coarse and brittle TiN particles found in the Ti treated steel, a harder microstructure and the presence of Cube and Goss texture in the sub-surface layer, seen for the lower coiling temperature can cause local transgranular cleavage cracking. Finally the post-uniform elongation obtained from tensile testing and bendability follow a good correlation