Most vital segment barriers

We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of "most vital arcs" for flows/paths to geometric environments. We give hardness results and efficient algorithms for various versions of the problem, (almost) completely separating hard and polynomially-solvable cases

A Numerical Study of Coulomb Interaction Effects on 2D Hopping Transport

We have extended our supercomputer-enabled Monte Carlo simulations of hopping transport in completely disordered 2D conductors to the case of substantial electron-electron Coulomb interaction. Such interaction may not only suppress the average value of hopping current, but also affect its fluctuations rather substantially. In particular, the spectral density $S_I (f)$ of current fluctuations exhibits, at sufficiently low frequencies, a $1/f$-like increase which approximately follows the Hooge scaling, even at vanishing temperature. At higher $f$, there is a crossover to a broad range of frequencies in which $S_I (f)$ is nearly constant, hence allowing characterization of the current noise by the effective Fano factor F\equiv S_I(f)/2e \left. For sufficiently large conductor samples and low temperatures, the Fano factor is suppressed below the Schottky value (F=1), scaling with the length $L$ of the conductor as $F = (L_c / L)^{\alpha}$. The exponent $\alpha$ is significantly affected by the Coulomb interaction effects, changing from $\alpha = 0.76 \pm 0.08$ when such effects are negligible to virtually unity when they are substantial. The scaling parameter $L_c$, interpreted as the average percolation cluster length along the electric field direction, scales as $L_c \propto E^{-(0.98 \pm 0.08)}$ when Coulomb interaction effects are negligible and $L_c \propto E^{-(1.26 \pm 0.15)}$ when such effects are substantial, in good agreement with estimates based on the theory of directed percolation.Comment: 19 pages, 7 figures. Fixed minor typos and updated reference

Sub-electron Charge Relaxation via 2D Hopping Conductors

We have extended Monte Carlo simulations of hopping transport in completely disordered 2D conductors to the process of external charge relaxation. In this situation, a conductor of area $L \times W$ shunts an external capacitor $C$ with initial charge $Q_i$. At low temperatures, the charge relaxation process stops at some "residual" charge value corresponding to the effective threshold of the Coulomb blockade of hopping. We have calculated the r.m.s$.$ value $Q_R$ of the residual charge for a statistical ensemble of capacitor-shunting conductors with random distribution of localized sites in space and energy and random $Q_i$, as a function of macroscopic parameters of the system. Rather unexpectedly, $Q_{R}$ has turned out to depend only on some parameter combination: $X_0 \equiv L W \nu_0 e^2/C$ for negligible Coulomb interaction and $X_{\chi} \equiv LW \kappa^2/C^{2}$ for substantial interaction. (Here $\nu_0$ is the seed density of localized states, while $\kappa$ is the dielectric constant.) For sufficiently large conductors, both functions $Q_{R}/e =F(X)$ follow the power law $F(X)=DX^{-\beta}$, but with different exponents: $\beta = 0.41 \pm 0.01$ for negligible and $\beta = 0.28 \pm 0.01$ for significant Coulomb interaction. We have been able to derive this law analytically for the former (most practical) case, and also explain the scaling (but not the exact value of the exponent) for the latter case. In conclusion, we discuss possible applications of the sub-electron charge transfer for "grounding" random background charge in single-electron devices.Comment: 12 pages, 5 figures. In addition to fixing minor typos and updating references, the discussion has been changed and expande

A Numerical Study of Transport and Shot Noise at 2D Hopping

We have used modern supercomputer facilities to carry out extensive Monte Carlo simulations of 2D hopping (at negligible Coulomb interaction) in conductors with the completely random distribution of localized sites in both space and energy, within a broad range of the applied electric field $E$ and temperature $T$, both within and beyond the variable-range hopping region. The calculated properties include not only dc current and statistics of localized site occupation and hop lengths, but also the current fluctuation spectrum. Within the calculation accuracy, the model does not exhibit $1/f$ noise, so that the low-frequency noise at low temperatures may be characterized by the Fano factor $F$. For sufficiently large samples, $F$ scales with conductor length $L$ as $(L_c/L)^{\alpha}$, where $\alpha=0.76\pm 0.08 < 1$, and parameter $L_c$ is interpreted as the average percolation cluster length. At relatively low $E$, the electric field dependence of parameter $L_c$ is compatible with the law $L_c\propto E^{-0.911}$ which follows from directed percolation theory arguments.Comment: 17 pages, 8 figures; Fixed minor typos and updated reference

Allele-specific disparity in breast cancer

Background In a cancer cell the number of copies of a locus may vary due to amplification and deletion and these variations are denoted as copy number alterations (CNAs). We focus on the disparity of CNAs in tumour samples, which were compared to those in blood in order to identify the directional loss of heterozygosity. Methods We propose a numerical algorithm and apply it to data from the Illumina 109K-SNP array on 112 samples from breast cancer patients. B-allele frequency (BAF) and log R ratio (LRR) of Illumina were used to estimate Euclidian distances. For each locus, we compared genotypes in blood and tumour for subset of samples being heterozygous in blood. We identified loci showing preferential disparity from heterozygous toward either the A/B-allele homozygous (allelic disparity). The chi-squared and Cochran-Armitage trend tests were used to examine whether there is an association between high levels of disparity in single nucleotide polymorphisms (SNPs) and molecular, clinical and tumour-related parameters. To identify pathways and network functions over-represented within the resulting gene sets, we used Ingenuity Pathway Analysis (IPA). Results To identify loci with a high level of disparity, we selected SNPs 1) with a substantial degree of disparity and 2) with substantial frequency (at least 50% of the samples heterozygous for the respective locus). We report the overall difference in disparity in high-grade tumours compared to low-grade tumours (p-value < 0.001) and significant associations between disparity in multiple single loci and clinical parameters. The most significantly associated network functions within the genes represented in the loci of disparity were identified, including lipid metabolism, small-molecule biochemistry, and nervous system development and function. No evidence for over-representation of directional disparity in a list of stem cell genes was obtained, however genes appeared to be more often altered by deletion than by amplification. Conclusions Our data suggest that directional loss and amplification exist in breast cancer. These are highly associated with grade, which may indicate that they are enforced with increasing number of cell divisions. Whether there is selective pressure for some loci to be preferentially amplified or deleted remains to be confirmed

Clinical decision-making: physicians' preferences and experiences

BACKGROUND: Shared decision-making has been advocated; however there are relatively few studies on physician preferences for, and experiences of, different styles of clinical decision-making as most research has focused on patient preferences and experiences. The objectives of this study were to determine 1) physician preferences for different styles of clinical decision-making; 2) styles of clinical decision-making physicians perceive themselves as practicing; and 3) the congruence between preferred and perceived style. In addition we sought to determine physician perceptions of the availability of time in visits, and their role in encouraging patients to look for health information. METHODS: Cross-sectional survey of a nationally representative sample of U.S. physicians. RESULTS: 1,050 (53% response rate) physicians responded to the survey. Of these, 780 (75%) preferred to share decision-making with their patients, 142 (14%) preferred paternalism, and 118 (11%) preferred consumerism. 87% of physicians perceived themselves as practicing their preferred style. Physicians who preferred their patients to play an active role in decision-making were more likely to report encouraging patients to look for information, and to report having enough time in visits. CONCLUSION: Physicians tend to perceive themselves as practicing their preferred role in clinical decision-making. The direction of the association cannot be inferred from these data; however, we suggest that interventions aimed at promoting shared decision-making need to target physicians as well as patients

Bioinformatics approaches for cross-species liver cancer analysis based on microarray gene expression profiling

BACKGROUND: The completion of the sequencing of human, mouse and rat genomes and knowledge of cross-species gene homologies enables studies of differential gene expression in animal models. These types of studies have the potential to greatly enhance our understanding of diseases such as liver cancer in humans. Genes co-expressed across multiple species are most likely to have conserved functions. We have used various bioinformatics approaches to examine microarray expression profiles from liver neoplasms that arise in albumin-SV40 transgenic rats to elucidate genes, chromosome aberrations and pathways that might be associated with human liver cancer. RESULTS: In this study, we first identified 2223 differentially expressed genes by comparing gene expression profiles for two control, two adenoma and two carcinoma samples using an F-test. These genes were subsequently mapped to the rat chromosomes using a novel visualization tool, the Chromosome Plot. Using the same plot, we further mapped the significant genes to orthologous chromosomal locations in human and mouse. Many genes expressed in rat 1q that are amplified in rat liver cancer map to the human chromosomes 10, 11 and 19 and to the mouse chromosomes 7, 17 and 19, which have been implicated in studies of human and mouse liver cancer. Using Comparative Genomics Microarray Analysis (CGMA), we identified regions of potential aberrations in human. Lastly, a pathway analysis was conducted to predict altered human pathways based on statistical analysis and extrapolation from the rat data. All of the identified pathways have been known to be important in the etiology of human liver cancer, including cell cycle control, cell growth and differentiation, apoptosis, transcriptional regulation, and protein metabolism. CONCLUSION: The study demonstrates that the hepatic gene expression profiles from the albumin-SV40 transgenic rat model revealed genes, pathways and chromosome alterations consistent with experimental and clinical research in human liver cancer. The bioinformatics tools presented in this paper are essential for cross species extrapolation and mapping of microarray data, its analysis and interpretation

Polar vortex formation in giant-planet atmospheres due to moist convection

A strong cyclonic vortex has been observed on each of Saturn’s poles, coincident with a local maximum in observed tropospheric temperature. Neptune also exhibits a relatively warm, although much more transient, region on its south pole. Whether similar features exist on Jupiter will be resolved by the 2016 Juno mission. Energetic, small-scale storm-like features that originate from the water-cloud level or lower have been observed on each of the giant planets and attributed to moist convection, suggesting that these storms play a significant role in global heat transfer from the hot interior to space. Nevertheless, the creation and maintenance of Saturn’s polar vortices, and their presence or absence on the other giant planets, are not understood. Here we use simulations with a shallow-water model to show that storm generation, driven by moist convection, can create a strong polar cyclone throughout the depth of a planet’s troposphere. We find that the type of shallow polar flow that occurs on a giant planet can be described by the size ratio of small eddies to the planetary radius and the energy density of its atmosphere due to latent heating from moist convection. We suggest that the observed difference in these parameters between Saturn and Jupiter may preclude a Jovian polar cyclone.National Science Foundation (U.S.). Graduate Research FellowshipNational Science Foundation (U.S.) (ATM-0850639)National Science Foundation (U.S.) (AGS-1032244)National Science Foundation (U.S.) (AGS-1136480)United States. Office of Naval Research (N00014-14-1-0062