Limited-Memory BFGS with Displacement Aggregation

A displacement aggregation strategy is proposed for the curvature pairs stored in a limited-memory BFGS method such that the resulting (inverse) Hessian approximations are equal to those that would be derived from a full-memory BFGS method. This means that, if a sufficiently large number of pairs are stored, then an optimization algorithm employing the limited-memory method can achieve the same theoretical convergence properties as when full-memory (inverse) Hessian approximations are stored and employed, such as a local superlinear rate of convergence under assumptions that are common for attaining such guarantees. To the best of our knowledge, this is the first work in which a local superlinear convergence rate guarantee is offered by a quasi-Newton scheme that does not either store all curvature pairs throughout the entire run of the optimization algorithm or store an explicit (inverse) Hessian approximation.Comment: 24 pages, 3 figure

Role of Epigenetic Modification and Immunomodulation in a Murine Prostate Cancer Model

INTRODUCTION. Decreased expression of highly immunogenic cancer-testis antigens (CTA) might help tumor to achieve low immunogenicity, escape immune surveillance and grow unimpeded. Our aim was to evaluate CTA expression in tumor and normal tissues and to investigate possible means of improving the immune response in a murine prostate cancer (CaP) model by using the combination of epigenetic modifier 5-azacitidine (5-AzaC) and immunomodulator lenalidomide. No study to date has examined the effect of this combination on the prostate cancer or its impact on antigen-presenting cells (APC). MATERIALS AND METHODS. Gene microarrays were performed to compare expression of several CTA in murine prostate cancer (RM-1 cells) and normal prostate. RM-1 cells were treated with 5-AzaC and real-time PCR was performed to investigate the expression of several CTA. Western blotting was used to determine whether expression of CTA-specific mRNA induced by 5-AzaC resulted in increase in the corresponding protein. Effect of the epigenetic agents and immunomodulators was assessed on dendritic cells (DC) using flow cytometry, ELISA and T-cell proliferation assay. RESULTS. Gene arrays demonstrated decreased expression of 35 CTA in CaP tissue compared to normal prostate. 5-AzaC treatment of RM-1 prostate cancer cells upregulated the expression of all 13 CTA tested in a dose-dependent fashion. DC were treated with 5-AzaC and lenalidomide and the expression of surface markers MHC Class I, MHC Class II, CD80, CD86, CD 205, and CD40 was increased. Combination of 5-AzaC and lenalidomide enhances the ability of DC to stimulate T-cell proliferation in mixed leukocyte reaction. Secretion of IL-12 and IL-15 by DC increased significantly with addition of 5-AzaC or 5-AzaC and lenalidomide. CONCLUSIONS. Decreased expression of CTA by prostate cancer may be a means of escaping immune monitoring. Combination of epigenetic modifications and immunomodulation by 5-AzaC and lenalidomide increased tumor immunogenicity and enhanced DC function and may be used in the treatment of advanced prostate cancer

Constrained spin dynamics description of random walks on hierarchical scale-free networks

We study a random walk problem on the hierarchical network which is a scale-free network grown deterministically. The random walk problem is mapped onto a dynamical Ising spin chain system in one dimension with a nonlocal spin update rule, which allows an analytic approach. We show analytically that the characteristic relaxation time scale grows algebraically with the total number of nodes $N$ as $T \sim N^z$. From a scaling argument, we also show the power-law decay of the autocorrelation function C_{\bfsigma}(t)\sim t^{-\alpha}, which is the probability to find the Ising spins in the initial state {\bfsigma} after $t$ time steps, with the state-dependent non-universal exponent $\alpha$. It turns out that the power-law scaling behavior has its origin in an quasi-ultrametric structure of the configuration space.Comment: 9 pages, 6 figure

Hierarchical characterization of complex networks

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work discusses on how the concepts of hierarchical node degree and hierarchical clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, can be used in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.Comment: 19 pages, 23 figure

Resistance distance, information centrality, node vulnerability and vibrations in complex networks

We discuss three seemingly unrelated quantities that have been introduced in different fields of science for complex networks. The three quantities are the resistance distance, the information centrality and the node displacement. We first prove various relations among them. Then we focus on the node displacement, showing its usefulness as an index of node vulnerability.We argue that the node displacement has a better resolution as a measure of node vulnerability than the degree and the information centrality

Random Sierpinski network with scale-free small-world and modular structure

In this paper, we define a stochastic Sierpinski gasket, on the basis of which we construct a network called random Sierpinski network (RSN). We investigate analytically or numerically the statistical characteristics of RSN. The obtained results reveal that the properties of RSN is particularly rich, it is simultaneously scale-free, small-world, uncorrelated, modular, and maximal planar. All obtained analytical predictions are successfully contrasted with extensive numerical simulations. Our network representation method could be applied to study the complexity of some real systems in biological and information fields.Comment: 7 pages, 9 figures; final version accepted for publication in EPJ

Network Landscape from a Brownian Particle's Perspective

Given a complex biological or social network, how many clusters should it be decomposed into? We define the distance $d_{i,j}$ from node $i$ to node $j$ as the average number of steps a Brownian particle takes to reach $j$ from $i$. Node $j$ is a global attractor of $i$ if $d_{i,j}\leq d_{i,k}$ for any $k$ of the graph; it is a local attractor of $i$, if $j\in E_i$ (the set of nearest-neighbors of $i$) and $d_{i,j}\leq d_{i,l}$ for any $l\in E_i$. Based on the intuition that each node should have a high probability to be in the same community as its global (local) attractor on the global (local) scale, we present a simple method to uncover a network's community structure. This method is applied to several real networks and some discussion on its possible extensions is made.Comment: 5 pages, 4 color-figures. REVTeX 4 format. To appear in PR

Decision making under uncertainty in environmental projects using mathematical simulation modeling

The final publication is available at Springer via http://dx.doi.org/10.1007/s12665-016-6135-yIn decision-making processes, reliability and risk aversion play a decisive role. The aim of this study is to perform an uncertainty assessment of the effects of future scenarios of sustainable groundwater pumping strategies on the quantitative and chemical status of an aquifer. The good status of the aquifer is defined according to the terms established by the EU Water Framework Directive (WFD). A decision support systems (DSS) is presented, which makes use of a stochastic inverse model (GC method) and geostatistical approaches to calibrate equally likely realizations of hydraulic conductivity (K) fields for a particular case study. These K fields are conditional to available field data, including hard and soft information. Then, different future scenarios of groundwater pumping strategies are generated, based on historical information and WFD standards, and simulated for each one of the equally likely K fields. The future scenarios lead to different environmental impacts and levels of socioeconomic development of the region and, hence, to a different degree of acceptance among stakeholders. We have identified the different stakeholders implied in the decision-making process, the objectives pursued and the alternative actions that should be considered by stakeholders in a public participation project (PPP). The MonteCarlo simulation provides a highly effective way for uncertainty assessment and allows presenting the results in a simple and understandable way even for non-experts stakeholders. The methodology has been successfully applied to a real case study and lays the foundations to performa PPP and stakeholders' involvement in a decisionmaking process as required by the WFD. 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