On the Stanley Depth of Squarefree Veronese Ideals

Let $K$ be a field and $S=K[x_1,...,x_n]$. In 1982, Stanley defined what is now called the Stanley depth of an $S$-module $M$, denoted \sdepth(M), and conjectured that \depth(M) \le \sdepth(M) for all finitely generated $S$-modules $M$. This conjecture remains open for most cases. However, Herzog, Vladoiu and Zheng recently proposed a method of attack in the case when $M = I / J$ with $J \subset I$ being monomial $S$-ideals. Specifically, their method associates $M$ with a partially ordered set. In this paper we take advantage of this association by using combinatorial tools to analyze squarefree Veronese ideals in $S$. In particular, if $I_{n,d}$ is the squarefree Veronese ideal generated by all squarefree monomials of degree $d$, we show that if $1\le d\le n < 5d+4$, then \sdepth(I_{n,d})= \floor{\binom{n}{d+1}\Big/\binom{n}{d}}+d, and if $d\geq 1$ and $n\ge 5d+4$, then d+3\le \sdepth(I_{n,d}) \le \floor{\binom{n}{d+1}\Big/\binom{n}{d}}+d.Comment: 10 page

Impact of imperfect test sensitivity on determining risk factors : the case of bovine tuberculosis

Background Imperfect diagnostic testing reduces the power to detect significant predictors in classical cross-sectional studies. Assuming that the misclassification in diagnosis is random this can be dealt with by increasing the sample size of a study. However, the effects of imperfect tests in longitudinal data analyses are not as straightforward to anticipate, especially if the outcome of the test influences behaviour. The aim of this paper is to investigate the impact of imperfect test sensitivity on the determination of predictor variables in a longitudinal study. Methodology/Principal Findings To deal with imperfect test sensitivity affecting the response variable, we transformed the observed response variable into a set of possible temporal patterns of true disease status, whose prior probability was a function of the test sensitivity. We fitted a Bayesian discrete time survival model using an MCMC algorithm that treats the true response patterns as unknown parameters in the model. We applied our approach to epidemiological data of bovine tuberculosis outbreaks in England and investigated the effect of reduced test sensitivity in the determination of risk factors for the disease. We found that reduced test sensitivity led to changes to the collection of risk factors associated with the probability of an outbreak that were chosen in the ‘best’ model and to an increase in the uncertainty surrounding the parameter estimates for a model with a fixed set of risk factors that were associated with the response variable. Conclusions/Significance We propose a novel algorithm to fit discrete survival models for longitudinal data where values of the response variable are uncertain. When analysing longitudinal data, uncertainty surrounding the response variable will affect the significance of the predictors and should therefore be accounted for either at the design stage by increasing the sample size or at the post analysis stage by conducting appropriate sensitivity analyses

A Heterosynaptic Learning Rule for Neural Networks

In this article we intoduce a novel stochastic Hebb-like learning rule for neural networks that is neurobiologically motivated. This learning rule combines features of unsupervised (Hebbian) and supervised (reinforcement) learning and is stochastic with respect to the selection of the time points when a synapse is modified. Moreover, the learning rule does not only affect the synapse between pre- and postsynaptic neuron, which is called homosynaptic plasticity, but effects also further remote synapses of the pre- and postsynaptic neuron. This more complex form of synaptic plasticity has recently come under investigations in neurobiology and is called heterosynaptic plasticity. We demonstrate that this learning rule is useful in training neural networks by learning parity functions including the exclusive-or (XOR) mapping in a multilayer feed-forward network. We find, that our stochastic learning rule works well, even in the presence of noise. Importantly, the mean learning time increases with the number of patterns to be learned polynomially, indicating efficient learning.Comment: 19 page

Religious Styles Predict Interreligious Prejudice: A Study of German Adolescents with the Religious Schema Scale

Streib H, Klein C. Religious Styles Predict Interreligious Prejudice: A Study of German Adolescents with the Religious Schema Scale. International Journal for the Psychology of Religion. 2014;24(2):151-163.Based on a sample of 340 German adolescents age 12 to 25, this article presents an analysis of the effects of religion on two instances of interreligious prejudice: anti-Islamic and anti-Semitic prejudice. Reflecting the emergent interest in implementing a perspective of religious maturity and religious development into research on religion and prejudice, the present study has included the Religious Schema Scale (RSS) which, with its three subscales, Truth of Texts & Teachings (ttt), Fairness, Tolerance & Rational Choice (ftr), and Xenosophia/Interreligious Dialog (xenos), differentiates religious styles. Regression analyses indicate the superior explanatory power of the RSS in comparison to other measures of religiosity. The RSS subscale ttt relates to and predicts anti-Islamic and anti-Semitic prejudice, whereas ftr and xenos relate to and predict disagreement with interreligious prejudice. Results of an analysis of variance using high agreement on ttt, ftr, and xenos for group construction indicate a decrease in interreligious prejudice in relation to religious development

New approaches to model and study social networks

We describe and develop three recent novelties in network research which are particularly useful for studying social systems. The first one concerns the discovery of some basic dynamical laws that enable the emergence of the fundamental features observed in social networks, namely the nontrivial clustering properties, the existence of positive degree correlations and the subdivision into communities. To reproduce all these features we describe a simple model of mobile colliding agents, whose collisions define the connections between the agents which are the nodes in the underlying network, and develop some analytical considerations. The second point addresses the particular feature of clustering and its relationship with global network measures, namely with the distribution of the size of cycles in the network. Since in social bipartite networks it is not possible to measure the clustering from standard procedures, we propose an alternative clustering coefficient that can be used to extract an improved normalized cycle distribution in any network. Finally, the third point addresses dynamical processes occurring on networks, namely when studying the propagation of information in them. In particular, we focus on the particular features of gossip propagation which impose some restrictions in the propagation rules. To this end we introduce a quantity, the spread factor, which measures the average maximal fraction of nearest neighbors which get in contact with the gossip, and find the striking result that there is an optimal non-trivial number of friends for which the spread factor is minimized, decreasing the danger of being gossiped.Comment: 16 Pages, 9 figure

The transmutation of fluorine by protons

The excitation functions for the production of long range alpha-particles, gamma-rays, and electron pairs by the bombardment of F19 by protons have been observed simultaneously up to a bombarding energy of 1.5 Mev. The long range alpha and pair curves exhibit resonance peaks superimposed on a background of increasing intensity with increasing bombarding energy. Approximate coincidence in two instances of pair and alpha-resonances suggests that full range alphas and the short range alphas preceding pair emission can be products of competing modes of decay of the same intermediate states of Ne20. This in turn suggests that the state of O16 which decays by pair emission has the same parity (even) as the ground states of O16 and thus that the pair emission can be due to ordinary electromagnetic forces. The absolute yields of the various processes have been measured and a discussion of the measurement of high energy gamma-ray and pair yields by means of electroscopes is given. The large ratio of gamma-ray yields to long range alpha and pair yields previously observed has been confirmed

Connections between Classical and Parametric Network Entropies

This paper explores relationships between classical and parametric measures of graph (or network) complexity. Classical measures are based on vertex decompositions induced by equivalence relations. Parametric measures, on the other hand, are constructed by using information functions to assign probabilities to the vertices. The inequalities established in this paper relating classical and parametric measures lay a foundation for systematic classification of entropy-based measures of graph complexity

Hierarchical coordination of periodic genes in the cell cycle of Saccharomyces cerevisiae

<p>Abstract</p> <p>Background</p> <p>Gene networks are a representation of molecular interactions among genes or products thereof and, hence, are forming causal networks. Despite intense studies during the last years most investigations focus so far on inferential methods to reconstruct gene networks from experimental data or on their structural properties, e.g., degree distributions. Their structural analysis to gain functional insights into organizational principles of, e.g., pathways remains so far under appreciated.</p> <p>Results</p> <p>In the present paper we analyze cell cycle regulated genes in <it>S. cerevisiae</it>. Our analysis is based on the transcriptional regulatory network, representing causal interactions and not just associations or correlations between genes, and a list of known periodic genes. No further data are used. Partitioning the transcriptional regulatory network according to a graph theoretical property leads to a hierarchy in the network and, hence, in the information flow allowing to identify two groups of periodic genes. This reveals a novel conceptual interpretation of the working mechanism of the cell cycle and the genes regulated by this pathway.</p> <p>Conclusion</p> <p>Aside from the obtained results for the cell cycle of yeast our approach could be exemplary for the analysis of general pathways by exploiting the rich causal structure of inferred and/or curated gene networks including protein or signaling networks.</p

Predicting Cell Cycle Regulated Genes by Causal Interactions

The fundamental difference between classic and modern biology is that technological innovations allow to generate high-throughput data to get insights into molecular interactions on a genomic scale. These high-throughput data can be used to infer gene networks, e.g., the transcriptional regulatory or signaling network, representing a blue print of the current dynamical state of the cellular system. However, gene networks do not provide direct answers to biological questions, instead, they need to be analyzed to reveal functional information of molecular working mechanisms. In this paper we propose a new approach to analyze the transcriptional regulatory network of yeast to predict cell cycle regulated genes. The novelty of our approach is that, in contrast to all other approaches aiming to predict cell cycle regulated genes, we do not use time series data but base our analysis on the prior information of causal interactions among genes. The major purpose of the present paper is to predict cell cycle regulated genes in S. cerevisiae. Our analysis is based on the transcriptional regulatory network, representing causal interactions between genes, and a list of known periodic genes. No further data are used. Our approach utilizes the causal membership of genes and the hierarchical organization of the transcriptional regulatory network leading to two groups of periodic genes with a well defined direction of information flow. We predict genes as periodic if they appear on unique shortest paths connecting two periodic genes from different hierarchy levels. Our results demonstrate that a classical problem as the prediction of cell cycle regulated genes can be seen in a new light if the concept of a causal membership of a gene is applied consequently. This also shows that there is a wealth of information buried in the transcriptional regulatory network whose unraveling may require more elaborate concepts than it might seem at first