A linear programming approach for estimating the structure of a sparse linear genetic network from transcript profiling data

Background: A genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN) from transcript profiling data. Results: The structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (l1-constrained fitting) problem and solved finally by formulating a Linear Program (LP). A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the INSILICO1, INSILICO2 and INSILICO3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published Saccharomyces cerevisae cell cycle transcript profiling data sets capture known regulatory associations. In each S. cerevisiae LP-SLGN, the number of nodes with a particular degree follows an approximate power law suggesting that its degree distributions is similar to that observed in real-world networks. Inspection of these LP-SLGNs suggests biological hypotheses amenable to experimental verification. Conclusion: A statistically robust and computationally efficient LP-based method for estimating the topology of a large sparse undirected graph from high-dimensional data yields representations of genetic networks that are biologically plausible and useful abstractions of the structures of real genetic networks. Analysis of the statistical and topological properties of learned LP-SLGNs may have practical value; for example, genes with high random walk betweenness, a measure of the centrality of a node in a graph, are good candidates for intervention studies and hence integrated computational – experimental investigations designed to infer more realistic and sophisticated probabilistic directed graphical model representations of genetic networks. The LP-based solutions of the sparse linear regression problem described here may provide a method for learning the structure of transcription factor networks from transcript profiling and transcription factor binding motif data.

Effect of curve crossing on absorption and resonance Raman spectra: analytical treatment for delta-function coupling in parabolic potentials

We propose an exactly solvable model for the two-state curve-crossing problem. Our model assumes the coupling to be a delta function. It is used to calculate the effect of curve crossing on the electronic absorption spectrum and the resonance Raman excitation profile.

Dependence of low-lying energy eigenvalues on the short- and long-range parts of confining potentials

The potential description of a quark-antiquark system seems to work very well in describing a number of hadronic properties. However, the precise form of the potential is unknown. The changes in the low-lying eigenvalues as a result of changes in the long-range part of the potential are investigated in a non-perturbative manner. It is shown by considering a variety of examples that the low-lying eigenvalues are insensitive to the long-range part of the potential.

Exact evaluation of Gaussian path integrals involving non-local potentials

An exact expression for the calculation of gaussian path integrals involving non-local potentials is given. Its utility is demonstrated by using it to evaluate a path integral arising in the study of an electron gas in a random potential.

Validation-Based Sparse Gaussian Process Classifier Design

Gaussian processes (GPs) are promising Bayesian methods for classification and regression problems. Design of a GP classifier and making predictions using it is, however, computationally demanding, especially when the training set size is large. Sparse GP classifiers are known to overcome this limitation. In this letter, we propose and study a validation-based method for sparse GP classifier design. The proposed method uses a negative log predictive (NLP) loss measure, which is easy to compute for GP models. We use this measure for both basis vector selection and hyperparameter adaptation. The experimental results on several real-world benchmark data sets show better orcomparable generalization performance over existing methods.

Calculation of Sparking Potentials of SF6 and SF6-GAS Mixtures in Uniform and Non-Uniform Electric Fields

A simple formula is developed to predict the sparking potentials of SF6 and SF6-gas mixture in uniform and non-uniform fields. The formula has been shown to be valid over a very wide range from 1 to 1800 kPa·cm of pressure and electrode gap separation for mixtures containing 5 to 100% SF6. The calculated values are found to be in good agreement with the previously reported measurements in the literature. The formula should aid design engineers in estimating electrode-spacings and clearances in power apparatus and systems.

Sparking potentials and swarm coefficients in Freon and mixtures of Freon and air

The sparking potentials and swarm coefficients ( ionization and attachment coefficients) were measured in Freon and Freon-air mixtures over the range of 24·3 times 10-16≤ E/ N ≤ 303 times 10-16 V cm2. Addition of Freon increased the sparking potential, and the rate of increase of the attachment coefficient with increasing percentage of Froon in the mixture was much larger than the rate of change of the first ionization coefficient.

Townsend's First Ionization Coefficients and Sparking Potentials in Crossed Electric and Magnetic Fields

Townsend's first ionization coefficients have been measured in corssed electric and magnetic fields for values of B/p ranging from 0.013 TESLA. TORR-1 to 0.064 TESLA.TORR-1 and for 103 x 102¿ E/p 331 x 102 V.M-1. TORR-1 in oxygen and for 122 x 102¿ E/pÂ488 x 102 V.M-1.TORR-1 for dry air. The values of effective collision frequencies determined from the equivalent pressure (pe) concept generally increase with E/p at constant B/p and decrease with increasing B/p at constant E/p. Effective collision frequencies determined from measured sparking potentials at high values of E/p increase with decreasing E/pe. The drift velocity and mean energy of electrons in oxygen in crossed electric and magnetic fields have been derived.

Intermolecular potentials in the dimer, the excimers, and the dimer ions of ethylene

Calculations are reported on the interaction energies in the dimer, the excimers, and the dimer ions of ethylene. The various a- and u-electron terms for different conformations of the dimeric species are determined by using the exchange perturbation method. The results predict that the singlet excimer and the dimer cation are stable primarily because of the large magnitude of the exciton-resonance and charge-resonance terms, respectively, while the neutral dimer, the triplet excimer, and the dimer anion are weakly stable. The variations of the various energy terms with conformations suggest that these dimeric species cannot have identifical structure.

Quinone Studies—II : Reduction potentials of some 3-substituted phenanthrene quinones

Polarographic reduction potentials of seven 3-substituted phenanthrenequinones have been determined in aqueous dioxan and aqueous ethanol under different pH conditions. The substituent effects on the reduction potentials could be correlated with the Hammett σ- constants (correlation coefficients> 0·995). The possibility of using reduction potentials as an accurate measure of resonance energy has been pointed out.

Chemical potentials of oxygen for fayalite-quartz-lron and fayalite-quartz-magnetite equilibria

The oxygen potentials corresponding to fayalite-quartz-iron (FQI) and fayalite-quartz-magnetite (FQM) equilibria have been determined using solid-state galvanic cells: Pt,Fe + Fe2SiO4 + SiO2/(Y2O3)ZrO2/Fe + \r"FeO,\l"Pt and Pt, Fe3O4 + Fe2SiO4 + SiO2/(Y2O3)ZrO2/Ni + NiO, Pt in the temperature ranges 900 to 1400 K and 1080 to 1340 K, respectively. The cells are written such that the right-hand electrodes are positive. Silica used in this study had the quartz structure. The emf of both cells was found to be reversible and to vary linearly with temperature. From the emf, Gibbs energy changes were deduced for the reactions: 0.106Fe (s) + 2Fe0.947O (r.s.) + SiO2 (qz) → Fe2SiO4 (ol) δG‡= -39,140+ 15.59T(± 150) J mol-1 and 3Fe2SiO4 (ol) + O2 (g) → 2Fe3O4 (sp) + 3SiO2 (qz) δG‡ = -471,750 + 160.06 T±} 1100) J mol-1 The “third-law≓ analysis of fayalite-quartz-wustite and fayalite-quartz-magnetite equilibria gives value for δH‡298 as -35.22 (±0.1) and -528.10 (±0.1) kJ mol-1, respectively, independent of temperature. The Gibbs energy of formation of the spinel form of Fe2SiO4 is derived by com-bining the present results on FQI equilibrium with the high-pressure data on olivine to spinel transformation of Fe2SiO4.

Lessons from the Sparse Sensor Network Deployment in Rural India

We discuss the key issues in the deployment of sparse sensor networks. The network monitors several environment parameters and is deployed in a semi-arid region for the benefit of small and marginal farmers. We begin by discussing the problems of an existing unreliable 1 sq km sparse network deployed in a village. The proposed solutions are implemented in a new cluster. The new cluster is a reliable 5 sq km network. Our contributions are two fold. Firstly, we describe a. novel methodology to deploy a sparse reliable data gathering sensor network and evaluate the ``safe distance'' or ``reliable'' distance between nodes using propagation models. Secondly, we address the problem of transporting data from rural aggregation servers to urban data centres. This paper tracks our steps in deploying a sensor network in a village,in India, trying to provide better diagnosis for better crop management. Keywords - Rural, Agriculture, CTRS, Sparse.

Bond length distortions associated with torsion potentials; ab-initio studies on methanedio

The 4-31G basis set is used to study the bond length variations as functions of dihedral angels in methanediol. This study is compared with O---C---O bond angle optimization studies by Gorenstein and Kar and the possible reason for bond length shorteing in the trans---trans configuration is analysed.

Nonadiabatic charge pumping by oscillating potentials in one dimension: Results for infinite system and finite ring

We study charge pumping when a combination of static potentials and potentials oscillating with a time period T is applied in a one-dimensional system of noninteracting electrons. We consider both an infinite system using the Dirac equation in the continuum approximation and a periodic ring with a finite number of sites using the tight-binding model. The infinite system is taken to be coupled to reservoirs on the two sides which are at the same chemical potential and temperature. We consider a model in which oscillating potentials help the electrons to access a transmission resonance produced by the static potentials and show that nonadiabatic pumping violates the simple sin phi rule which is obeyed by adiabatic two-site pumping. For the ring, we do not introduce any reservoirs, and we present a method for calculating the current averaged over an infinite time using the time evolution operator U(T) assuming a purely Hamiltonian evolution. We analytically show that the averaged current is zero if the Hamiltonian is real and time-reversal invariant. Numerical studies indicate another interesting result, namely, that the integrated current is zero for any time dependence of the potential if it is applied to only one site. Finally we study the effects of pumping at two sites on a ring at resonant and nonresonant frequencies, and show that the pumped current has different dependences on the pumping amplitude in the two cases.