On coalescence time in graphs: When is coalescing as fast as meeting?

Coalescing random walks is a fundamental stochastic process, where a set of particles perform independent discrete-time random walks on an undirected graph. Whenever two or more particles meet at a given node, they merge and continue as a single random walk. The coalescence time is defined as the expected time until only one particle remains, starting from one particle at every node. Despite recent progress the coalescence time for graphs such as binary trees, d-dimensional tori, hypercubes and more generally, vertex-transitive graphs, remains unresolved. We provide a powerful toolkit that results in tight bounds for various topologies including the aforementioned ones. The meeting time is defined as the worst-case expected time required for two random walks to arrive at the same node at the same time. As a general result, we establish that for graphs whose meeting time is only marginally larger than the mixing time (a factor of log^2 n), the coalescence time of n random walks equals the meeting time up to constant factors. This upper bound is complemented by the construction of a graph family demonstrating that this result is the best possible up to constant factors. For almost-regular graphs, we bound the coalescence time by the hitting time, resolving the discrete-time variant of a conjecture by Aldous for this class of graphs. Finally, we prove that for any graph the coalescence time is bounded by O(n^3) (which is tight for the Barbell graph); surprisingly even such a basic question about the coalescing time was not answered before this work. By duality, our results give bounds on the voter model and therefore give bounds on the consensus time in arbitrary undirected graphs. We also establish a new bound on the hitting time and cover time of regular graphs, improving and tightening previous results by Broder and Karlin, as well as those by Aldous and Fill

Community-Acquired MRSA Pyomyositis: Case Report and Review of the Literature

Community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA) is responsible for a broad range of infections. We report the case of a 46-year-old gentleman with a history of untreated, uncomplicated Hepatitis C who presented with a 2-month history of back pain and was found to have abscesses in his psoas and right paraspinal muscles with subsequent lumbar spine osteomyelitis. Despite drainage and appropriate antibiotic management the patient's clinical condition deteriorated and he developed new upper extremity weakness and sensory deficits on physical exam. Repeat imaging showed new, severe compression of the spinal cord and cauda equina from C1 to the sacrum by a spinal epidural abscess. After surgical intervention and continued medical therapy, the patient recovered completely. This case illustrates a case of CA-MRSA pyomyositis that progressed to lumbar osteomyelitis and a spinal epidural abscess extending the entire length of the spinal canal

Genetic transformation in bacteria

Certain species of bacteria can become competent to take up high molecular weight DNA from the surrounding medium. DNA homologous to resident chromosomal DNA is transported, processed and recombined with the resident DNA. There are some variations in steps leading to transformation between Gram-positive bacteria likebiplococcus pneumoniae and Gram-negative bacteria represented byHaemophilus influenzae but the integration is by single-strand displacement in both cases. Plasmid (RSF0885) transformation is low inHaemophilus influenzae but this is increased significantly if (homologous) chromosomal DNA is spliced to plasmid DNA. In Haemophilus influenzae, rec1 function is required for peak transformation with chimeric plasmids. Chimeric plasmid fixed presumably extrachromosomally undergoes frequent recombination between homologous segments contained in resident chromosome and the plasmid

Functional outcome in people with diabetic neuropathy at four stages of foot complications.

This study was designed to investigate the nature of the course of functional outcome across the four patient groups with diabetic neuropathy at consequent stages of foot complications namely: diabetic neuropathy without history of plantar ulceration (DMPN), active plantar ulceration (DFU), healed unilateral partial foot amputations (PFA) and healed unilateral trans-tibial amputations (TTA). The secondary objective was to compare the functional outcome between patients with DFU and PFA and patients with PFA and TTA. Methods: In this cross-sectional case control study, 4 matched groups of patients with DMPN were studied: DMPN (n=23); DFU (n=23); PFA (n=16) and TTA (n=22). Appropriate outcome measures were used to evaluate function in 3 domains, namely Mobility and its impact on weight-bearing (sit-to-stand, standing balance, gait and plantar pressures during walking), Level of Activity (capacity and performance of walking) and H-RQOL. One-way ANOVA was used to compare 4 groups and linear polynomial contrast detected the trend across groups. In cases of significant difference between the 4 groups, an Independent sample t-test was used for specific group comparison. Results: There was a significant difference in functional outcome between the four groups demonstrating an overall decline in the level of function with the progression of impairment (standing balance: p=0.002, gait velocity: p<0.001, daily strides: p<0.001, SF-36 Physical function: p<0.001). The risk of plantar injury to the entire affected foot during walking increased from DMPN to DFU to PFA (p=0.013). There was no significant difference between the overall function of DFU and PFA. The PFA and TTA groups also varied significantly only in the domain of activity performance wherein the TTA group demonstrated a low daily walking performance compared to the PFA group (p=0.006). Conclusion: The overall decline demonstrated in this study in the three domains of function with progression of physical impairment from the DMPN to TTA group, calls for an urgent need to define a tailormade rehabilitation programme to maximise function of these patient groups. The increasing risk of plantar injury from DMPN to DFU to PFA during walking warrants a greater and precise focus on footcare of the affected as well as the contra-lateral foot

Local Algorithms for Block Models with Side Information

There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding large independent sets in sparse random regular graphs. Montanari (2015) showed that local algorithms are suboptimal for finding a community with high connectivity in the sparse Erd\H{o}s-R\'enyi random graphs. For the symmetric planted partition problem (also named community detection for the block models) on sparse graphs, a simple observation is that local algorithms cannot have non-trivial performance. In this work we consider the effect of side information on local algorithms for community detection under the binary symmetric stochastic block model. In the block model with side information each of the $n$ vertices is labeled $+$ or $-$ independently and uniformly at random; each pair of vertices is connected independently with probability $a/n$ if both of them have the same label or $b/n$ otherwise. The goal is to estimate the underlying vertex labeling given 1) the graph structure and 2) side information in the form of a vertex labeling positively correlated with the true one. Assuming that the ratio between in and out degree $a/b$ is $\Theta(1)$ and the average degree $(a+b) / 2 = n^{o(1)}$, we characterize three different regimes under which a local algorithm, namely, belief propagation run on the local neighborhoods, maximizes the expected fraction of vertices labeled correctly. Thus, in contrast to the case of symmetric block models without side information, we show that local algorithms can achieve optimal performance for the block model with side information.Comment: Due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract here is shorter than that in the PDF fil

Influence of winding parameters on yarn content and package geometry of wound packages

492-496This study is aimed at evaluating the step-precision assembly winding in terms of its potential to accommodate maximum yarn content on a given size of tube. The influence of various parameters related to step-precision winding on yarn content and package geometry of a close step-precision wound package has been studied. The outcome of this study is presumed to be very useful to manufacturers of winding as well as buyers of assembly winding systems. Step-precision winding parameters, like coil angle at start, angle up to which it is allowed to change and the number of diamonds along the circumference (Y value), influence yarn content on package; lower values of start angle and Y but higher value of change angle give increased yarn content. At the same time, it is also observed that the package with lower start angle and higher change angle give greater projection of package side flanks

Influence of winding parameters on yarn content and package geometry of wound packages

This study is aimed at evaluating the step-precision assemblywinding in terms of its potential to accommodate maximum yarncontent on a given size of tube. The influence of various parametersrelated to step-precision winding on yarn content and packagegeometry of a close step-precision wound package has been studied.The outcome of this study is presumed to be very useful tomanufacturers of winding as well as buyers of assembly windingsystems. Step-precision winding parameters, like coil angle at start,angle up to which it is allowed to change and the number ofdiamonds along the circumference (Y value), influence yarn contenton package; lower values of start angle and Y but higher value ofchange angle give increased yarn content. At the same time, it isalso observed that the package with lower start angle and higherchange angle give greater projection of package side flanks

Simultaneous estimation of atazanavir and ritonavir in combined Tablet dosage form: A Review

In present study describe the development of new method and parameter which will be considered during method development and validation. Article give brief idea for a simple, sensitive, precise and accurate High-performance thin-layer chromatographic method for simultaneous determination of Ritonavir and Atazanavir in their combined tablet dosage form has been developed, validated and used for determination of the compounds in commercial pharmaceutical products. Chromatographic separation will be achieved on different column like C8, C18, etc. used as the stationary phase and different mobile phase. Keywords: High-performance thin-layer chromatography, Ritonavir, Atazanavi