Blow-up behavior of collocation solutions to Hammerstein-type volterra integral equations

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the exact solution. Based on the local convergence of the collocation methods for VIEs, we present the convergence analysis for the numerical blow-up time. Numerical experiments illustrate the analysis

Menger's Theorem in bidirected graphs

Bidirected graphs are a generalisation of directed graphs that arises in the study of undirected graphs with perfect matchings. Menger's famous theorem - the minimum size of a set separating two vertex sets $X$ and $Y$ is the same as the maximum number of disjoint paths connecting them - is generally not true in bidirected graphs. We introduce a sufficient condition for $X$ and $Y$ which yields a version of Menger's Theorem in bidirected graphs that in particular implies its directed counterpart.Comment: 23 pages, 6 figure

A Bose-Einstein Approach to the Random Partitioning of an Integer

Consider N equally-spaced points on a circle of circumference N. Choose at random n points out of $N$ on this circle and append clockwise an arc of integral length k to each such point. The resulting random set is made of a random number of connected components. Questions such as the evaluation of the probability of random covering and parking configurations, number and length of the gaps are addressed. They are the discrete versions of similar problems raised in the continuum. For each value of k, asymptotic results are presented when n,N both go to infinity according to two different regimes. This model may equivalently be viewed as a random partitioning problem of N items into n recipients. A grand-canonical balls in boxes approach is also supplied, giving some insight into the multiplicities of the box filling amounts or spacings. The latter model is a k-nearest neighbor random graph with N vertices and kn edges. We shall also briefly consider the covering problem in the context of a random graph model with N vertices and n (out-degree 1) edges whose endpoints are no more bound to be neighbors

Non-newtonian flow and pressure drop of pineapple juice in a plate heat exchanger

The study of non-Newtonian flow in plate heat exchangers (PHEs) is of great importance for the food industry. The objective of this work was to study the pressure drop of pineapple juice in a PHE with 50º chevron plates. Density and flow properties of pineapple juice were determined and correlated with temperature (17.4 < T < 85.8ºC) and soluble solids content (11.0 < Xs < 52.4 ºBrix). The Ostwald-de Waele (power law) model described well the rheological behavior. The friction factor for non-isothermal flow of pineapple juice in the PHE was obtained for diagonal and parallel/side flow. Experimental results were well correlated with the generalized Reynolds number (20 < Re g < 1230) and were compared with predictions from equations from the literature. The mean absolute error for pressure drop prediction was 4% for the diagonal plate and 10% for the parallel plate.(FAPESP) São Paulo Research Foundatio

A preferential attachment model with random initial degrees

In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$ edges attached to it, is added to the graph. The new edges added at time t are then preferentially connected to older vertices, i.e., conditionally on $G(t-1)$, the probability that a given edge is connected to vertex i is proportional to $d_i(t-1)+\delta$, where $d_i(t-1)$ is the degree of vertex $i$ at time $t-1$, independently of the other edges. The main result is that the asymptotical degree sequence for this process is a power law with exponent $\tau=\min\{\tau_{W}, \tau_{P}\}$, where $\tau_{W}$ is the power-law exponent of the initial degrees $(W_t)_{t\geq 1}$ and $\tau_{P}$ the exponent predicted by pure preferential attachment. This result extends previous work by Cooper and Frieze, which is surveyed.Comment: In the published form of the paper, the proof of Proposition 2.1 is incomplete. This version contains the complete proo

DNA sequencing by MALDI-TOF MS using alkali cleavage of RNA/DNA chimeras

Approaches developed for sequencing DNA with detection by mass spectrometry use strategies that deviate from the Sanger-type methods. Procedures demonstrated so far used the sequence specificity of RNA endonucleases, as unfortunately equivalent enzymes for DNA do not exist and therefore require transcription of DNA into RNA prior to fragmentation

Targeting mitochondrial 18 kDa translocator protein (TSPO) regulates macrophage cholesterol efflux and lipid phenotype

Abstract The aim of the present study was to establish mitochondrial cholesterol trafficking 18 kDa translocator protein (TSPO) as a potential therapeutic target, capable of increasing macrophage cholesterol efflux to (apo)lipoprotein acceptors. Expression and activity of TSPO in human (THP-1) macrophages were manipulated genetically and by the use of selective TSPO ligands

Evaluation of Microwave Applicator Design on Electromagnetic Field Distribution and Heating Pattern of Cooked Peeled Shrimp

Non-uniform temperature distribution within solid food is a major problem associated with microwave heating, which limits industrial applications. Therefore, an experimentally validated 3D model was proposed to study the effect of microwave applicator geometry on the electromagnetic field distribution and heating pattern of shrimp under different processing conditions. Simulation results were compared with physical experiments, in which a cooked peeled shrimp sample was heated using two different laboratory-scale microwave applicators (rectangular and cylindrical cavities). For the rectangular applicator, the temperature distribution within the shrimp, when examined in cross-section, was more homogeneous compared to that of the cylindrical applicator. The results showed the influence of the complex shape of the food on the temperature distribution during microwave heating, as well as of process parameters (input power and geometry cavity). Moreover, this modelling method could provide a better understanding of the microwave heating process and assist manufacturing companies to evaluate a suitable microwave applicator according to their specific purpose

dbDNV: a resource of duplicated gene nucleotide variants in human genome

Gene duplications are scattered widely throughout the human genome. A single-base difference located in nearly identical duplicated segments may be misjudged as a single nucleotide polymorphism (SNP) from individuals. This imperfection is undistinguishable in current genotyping methods. As the next-generation sequencing technologies become more popular for sequence-based association studies, numerous ambiguous SNPs are rapidly accumulated. Thus, analyzing duplication variations in the reference genome to assist in preventing false positive SNPs is imperative. We have identified >10% of human genes associated with duplicated gene loci (DGL). Through meticulous sequence alignments of DGL, we systematically designated 1 236 956 variations as duplicated gene nucleotide variants (DNVs). The DNV database (dbDNV) (http://goods.ibms.sinica.edu.tw/DNVs/) has been established to promote more accurate variation annotation. Aside from the flat file download, users can explore the gene-related duplications and the associated DNVs by DGL and DNV searches, respectively. In addition, the dbDNV contains 304 110 DNV-coupled SNPs. From DNV-coupled SNP search, users observe which SNP records are also variants among duplicates. This is useful while ∼58% of exonic SNPs in DGL are DNV-coupled. Because of high accumulation of ambiguous SNPs, we suggest that annotating SNPs with DNVs possibilities should improve association studies of these variants with human diseases