Steady-State Analysis of Load Balancing with Coxian-22 Distributed Service Times

This paper studies load balancing for many-server ($N$ servers) systems. Each server has a buffer of size $b-1,$ and can have at most one job in service and $b-1$ jobs in the buffer. The service time of a job follows the Coxian-2 distribution. We focus on steady-state performance of load balancing policies in the heavy traffic regime such that the normalized load of system is $\lambda = 1 - N^{-\alpha}$ for $0<\alpha<0.5.$ We identify a set of policies that achieve asymptotic zero waiting. The set of policies include several classical policies such as join-the-shortest-queue (JSQ), join-the-idle-queue (JIQ), idle-one-first (I1F) and power-of-$d$-choices (Po$d$) with $d=O(N^\alpha\log N)$. The proof of the main result is based on Stein's method and state space collapse. A key technical contribution of this paper is the iterative state space collapse approach that leads to a simple generator approximation when applying Stein's method

Sampling and counting genome rearrangement scenarios

Even for moderate size inputs, there are a tremendous number of optimal rearrangement scenarios, regardless what the model is and which specific question is to be answered. Therefore giving one optimal solution might be misleading and cannot be used for statistical inferring. Statistically well funded methods are necessary to sample uniformly from the solution space and then a small number of samples are sufficient for statistical inferring

Validity of Ligand Efficiency Metrics

A recent viewpoint article (Improving the plausibility of success with inefficient metrics. ACS Med. Chem. Lett. 2014, 5, 2-5) argued that the standard definition of ligand efficiency (LE) is mathematically invalid. In this viewpoint, we address this criticism and show categorically that the definition of LE is mathematically valid. LE and other metrics such as lipophilic ligand efficiency (LLE) can be useful during the multiparameter optimization challenge faced by medicinal chemists

Fluorescence spectroscopic evaluation of the interactions of quercetin, isorhamnetin, and quercetin-3'-sulfate with different albumins

Quercetin is one of the most commonly occurring flavonoids in nature. Although, quercetin and its metabolites express negligible fluorescence, the albumin-bound form of quercetin has a strong fluorescence property. Considering the structural variance of different albumins, we hypothesized that the fluorescence of albumin complexes of quercetin and its metabolites may vary significantly. Therefore, in this study the fluorescence enhancement of quercetin and some of its major metabolites in the presence of bovine (BSA), human (HSA), porcine (PSA), and rat serum albumins (RSA) were investigated by steady-state fluorescence spectroscopy in PBS buffer (pH 7.4). Among the tested quercetin metabolites, significant fluorescence signal was shown by albumin complexes of quercetin, isorhamnetin, and quercetin-3’-sulfate, while other metabolites (tamarixetin, quercetin-3-glucuronide, and isorhamnetin-3-glucuronide) expressed negligible fluorescence. BSA was the most potent enhancer of quercetin-3’-sulfate but it showed poor effects regarding other flavonoids. The strongest enhancement of isorhamnetin was caused by HSA, while it was less effective enhancer of quercetin and quercetin-3’-sulfate. PSA showed a strong fluorescence enhancement of quercetin and quercetin-3’-sulfate but it was poorly effective regarding isorhamnetin. RSA was the most potent enhancer of quercetin but it caused only a weak enhancement of isorhamnetin and quercetin-3’-sulfate. Large changes of the pH (such as pH 5.0 and pH 10.0) almost completely abolished the fluorescence signals of the complexes. Nevertheless, slight decrease (pH 7.0) reduced and slight increase (pH 7.8) generally enhanced the fluorescence of flavonoid-albumin complexes (only exceptions were quercetin-PSA and quercetin-RSA). Complex formations were also investigated by fluorescence quenching studies. Based on our results, the formations of quercetin-BSA, quercetin-HSA, isorhamnetin-BSA, isorhamnetin-HSA, isorhamnetin-PSA, and quercetin-3’-sulfate – HSA complexes followed 1:1 stoichiometry, while the presence of a secondary binding site of flavonoids was assumed regarding other tested albumin complexes. Our study highlights that albumins can induce significantly different fluorescence enhancement of flavonoids, and even the stoichiometry of flavonoid-albumin complexes may differ

Regression games

The solution of a TU cooperative game can be a distribution of the value of the grand coalition, i.e. it can be a distribution of the payo (utility) all the players together achieve. In a regression model, the evaluation of the explanatory variables can be a distribution of the overall t, i.e. the t of the model every regressor variable is involved. Furthermore, we can take regression models as TU cooperative games where the explanatory (regressor) variables are the players. In this paper we introduce the class of regression games, characterize it and apply the Shapley value to evaluating the explanatory variables in regression models. In order to support our approach we consider Young (1985)'s axiomatization of the Shapley value, and conclude that the Shapley value is a reasonable tool to evaluate the explanatory variables of regression models

Implementing EM and Viterbi algorithms for Hidden Markov Model in linear memory

<p>Abstract</p> <p>Background</p> <p>The Baum-Welch learning procedure for Hidden Markov Models (HMMs) provides a powerful tool for tailoring HMM topologies to data for use in knowledge discovery and clustering. A linear memory procedure recently proposed by <it>Miklós, I. and Meyer, I.M. </it>describes a memory sparse version of the Baum-Welch algorithm with modifications to the original probabilistic table topologies to make memory use independent of sequence length (and linearly dependent on state number). The original description of the technique has some errors that we amend. We then compare the corrected implementation on a variety of data sets with conventional and checkpointing implementations.</p> <p>Results</p> <p>We provide a correct recurrence relation for the emission parameter estimate and extend it to parameter estimates of the Normal distribution. To accelerate estimation of the prior state probabilities, and decrease memory use, we reverse the originally proposed forward sweep. We describe different scaling strategies necessary in all real implementations of the algorithm to prevent underflow. In this paper we also describe our approach to a linear memory implementation of the Viterbi decoding algorithm (with linearity in the sequence length, while memory use is approximately independent of state number). We demonstrate the use of the linear memory implementation on an extended Duration Hidden Markov Model (DHMM) and on an HMM with a spike detection topology. Comparing the various implementations of the Baum-Welch procedure we find that the checkpointing algorithm produces the best overall tradeoff between memory use and speed. In cases where sequence length is very large (for Baum-Welch), or state number is very large (for Viterbi), the linear memory methods outlined may offer some utility.</p> <p>Conclusion</p> <p>Our performance-optimized Java implementations of Baum-Welch algorithm are available at <url>http://logos.cs.uno.edu/~achurban</url>. The described method and implementations will aid sequence alignment, gene structure prediction, HMM profile training, nanopore ionic flow blockades analysis and many other domains that require efficient HMM training with EM.</p

How reliably can we predict the reliability of protein structure predictions?

Background: Comparative methods have been the standard techniques for in silico protein structure prediction. The prediction is based on a multiple alignment that contains both reference sequences with known structures and the sequence whose unknown structure is predicted. Intensive research has been made to improve the quality of multiple alignments, since misaligned parts of the multiple alignment yield misleading predictions. However, sometimes all methods fail to predict the correct alignment, because the evolutionary signal is too weak to find the homologous parts due to the large number of mutations that separate the sequences. Results: Stochastic sequence alignment methods define a posterior distribution of possible multiple alignments. They can highlight the most likely alignment, and above that, they can give posterior probabilities for each alignment column. We made a comprehensive study on the HOMSTRAD database of structural alignments, predicting secondary structures in four different ways. We showed that alignment posterior probabilities correlate with the reliability of secondary structure predictions, though the strength of the correlation is different for different protocols. The correspondence between the reliability of secondary structure predictions and alignment posterior probabilities is the closest to the identity function when the secondary structure posterior probabilities are calculated from the posterior distribution of multiple alignments. The largest deviation from the identity function has been obtained in the case of predicting secondary structures from a single optimal pairwise alignment. We also showed that alignment posterior probabilities correlate with the 3D distances between C α amino acids in superimposed tertiary structures. Conclusion: Alignment posterior probabilities can be used to a priori detect errors in comparative models on the sequence alignment level. </p