Edge-weighting of gene expression graphs

In recent years, considerable research efforts have been directed to micro-array technologies and their role in providing simultaneous information on expression profiles for thousands of genes. These data, when subjected to clustering and classification procedures, can assist in identifying patterns and providing insight on biological processes. To understand the properties of complex gene expression datasets, graphical representations can be used. Intuitively, the data can be represented in terms of a bipartite graph, with weighted edges corresponding to gene-sample node couples in the dataset. Biologically meaningful subgraphs can be sought, but performance can be influenced both by the search algorithm, and, by the graph-weighting scheme and both merit rigorous investigation. In this paper, we focus on edge-weighting schemes for bipartite graphical representation of gene expression. Two novel methods are presented: the first is based on empirical evidence; the second on a geometric distribution. The schemes are compared for several real datasets, assessing efficiency of performance based on four essential properties: robustness to noise and missing values, discrimination, parameter influence on scheme efficiency and reusability. Recommendations and limitations are briefly discussed

Fourier-based Function Secret Sharing with General Access Structure

Function secret sharing (FSS) scheme is a mechanism that calculates a function f(x) for x in {0,1}^n which is shared among p parties, by using distributed functions f_i:{0,1}^n -> G, where G is an Abelian group, while the function f:{0,1}^n -> G is kept secret to the parties. Ohsawa et al. in 2017 observed that any function f can be described as a linear combination of the basis functions by regarding the function space as a vector space of dimension 2^n and gave new FSS schemes based on the Fourier basis. All existing FSS schemes are of (p,p)-threshold type. That is, to compute f(x), we have to collect f_i(x) for all the distributed functions. In this paper, as in the secret sharing schemes, we consider FSS schemes with any general access structure. To do this, we observe that Fourier-based FSS schemes by Ohsawa et al. are compatible with linear secret sharing scheme. By incorporating the techniques of linear secret sharing with any general access structure into the Fourier-based FSS schemes, we show Fourier-based FSS schemes with any general access structure.Comment: 12 page

OT 060420: A Seemingly Optical Transient Recorded by All-Sky Cameras

We report on a ~5th magnitude flash detected for approximately 10 minutes by two CONCAM all-sky cameras located in Cerro Pachon - Chile and La Palma - Spain. A third all-sky camera, located in Cerro Paranal - Chile did not detect the flash, and therefore the authors of this paper suggest that the flash was a series of cosmic-ray hits, meteors, or satellite glints. Another proposed hypothesis is that the flash was an astronomical transient with variable luminosity. In this paper we discuss bright optical transient detection using fish-eye all-sky monitors, analyze the apparently false-positive optical transient, and propose possible causes to false optical transient detection in all-sky cameras.Comment: 7 figures, 3 tables, accepted PAS

Before sailing on a domain-wall sea

We discuss the very different roles of the valence-quark and the sea-quark residual masses ($m_{res}^v$ and $m_{res}^s$) in dynamical domain-wall fermions simulations. Focusing on matrix elements of the effective weak hamiltonian containing a power divergence, we find that $m_{res}^v$ can be a source of a much bigger systematic error. To keep all systematic errors due to residual masses at the 1% level, we estimate that one needs $a m_{res}^s \le 10^{-3}$ and $a m_{res}^v \le 10^{-5}$, at a lattice spacing $a\sim 0.1$ fm. The practical implications are that (1) optimal use of computer resources calls for a mixed scheme with different domain-wall fermion actions for the valence and sea quarks; (2) better domain-wall fermion actions are needed for both the sea and the valence sectors.Comment: latex, 25 pages. Improved discussion in appendix, including correction of some technical mistakes; ref. adde

Localization properties of lattice fermions with plaquette and improved gauge actions

We determine the location $\lambda_c$ of the mobility edge in the spectrum of the hermitian Wilson operator in pure-gauge ensembles with plaquette, Iwasaki, and DBW2 gauge actions. The results allow mapping a portion of the (quenched) Aoki phase diagram. We use Green function techniques to study the localized and extended modes. Where $\lambda_c>0$ we characterize the localized modes in terms of an average support length and an average localization length, the latter determined from the asymptotic decay rate of the mode density. We argue that, since the overlap operator is commonly constructed from the Wilson operator, its range is set by the value of $\lambda_c^{-1}$ for the Wilson operator. It follows from our numerical results that overlap simulations carried out with a cutoff of 1 GeV, even with improved gauge actions, could be afflicted by unphysical degrees of freedom as light as 250 MeV.Comment: RevTeX, 37 pages, 10 figures. Some textual changes. Final for

Mobility edge in lattice QCD

We determine the location $\lambda_c$ of the mobility edge in the spectrum of the hermitian Wilson operator on quenched ensembles. We confirm a theoretical picture of localization proposed for the Aoki phase diagram. When $\lambda_c>0$ we also determine some key properties of the localized eigenmodes with eigenvalues $|\lambda|<\lambda_c$. Our results lead to simple tests for the validity of simulations with overlap and domain-wall fermions.Comment: revtex, 4 pages, 1 figure, minor change

Residual Chiral Symmetry Breaking in Domain-Wall Fermions

We study the effective quark mass induced by the finite separation of the domain walls in the domain-wall formulation of chiral fermion as the function of the size of the fifth dimension ($L_s$), the gauge coupling $\beta$ and the physical volume $V$. We measure the mass by calculating the small eigenvalues of the hermitian domain-wall Dirac operator ($H_{\rm DWF}(m_0))$ in the topologically-nontrivial quenched SU(3) gauge configurations. We find that the induced quark mass is nearly independent of the physical volume, decays exponentially as a function of $L_s$, and has a strong dependence on the size of quantum fluctuations controlled by $\beta$. The effect of the choice of the lattice gluon action is also studied.Comment: 12 pages, 7 figure

The overlap lattice Dirac operator and dynamical fermions

I show how to avoid a two level nested conjugate gradient procedure in the context of Hybrid Monte Carlo with the overlap fermionic action. The resulting procedure is quite similar to Hybrid Monte Carlo with domain wall fermions, but is more flexible and therefore has some potential worth exploring.Comment: Further expanded version. 12 pages, plain Te

Domain-Wall Induced Quark Masses in Topologically-Nontrivial Background

In the domain-wall formulation of chiral fermion, the finite separation between domain-walls ($L_s$) induces an effective quark mass ($m_{\rm eff}$) which complicates the chiral limit. In this work, we study the size of the effective mass as the function of $L_s$ and the domain-wall height $m_0$ by calculating the smallest eigenvalue of the hermitian domain-wall Dirac operator in the topologically-nontrivial background fields. We find that, just like in the free case, $m_{\rm eff}$ decreases exponentially in $L_s$ with a rate depending on $m_0$. However, quantum fluctuations amplify the wall effects significantly. Our numerical result is consistent with a previous study of the effective mass from the Gell-Mann-Oakes-Renner relation.Comment: 10 pages, an appendix and minor changes adde