On the spectrum of hypergraphs

Here we study the spectral properties of an underlying weighted graph of a non-uniform hypergraph by introducing different connectivity matrices, such as adjacency, Laplacian and normalized Laplacian matrices. We show that different structural properties of a hypergrpah, can be well studied using spectral properties of these matrices. Connectivity of a hypergraph is also investigated by the eigenvalues of these operators. Spectral radii of the same are bounded by the degrees of a hypergraph. The diameter of a hypergraph is also bounded by the eigenvalues of its connectivity matrices. We characterize different properties of a regular hypergraph characterized by the spectrum. Strong (vertex) chromatic number of a hypergraph is bounded by the eigenvalues. Cheeger constant on a hypergraph is defined and we show that it can be bounded by the smallest nontrivial eigenvalues of Laplacian matrix and normalized Laplacian matrix, respectively, of a connected hypergraph. We also show an approach to study random walk on a (non-uniform) hypergraph that can be performed by analyzing the spectrum of transition probability operator which is defined on that hypergraph. Ricci curvature on hypergraphs is introduced in two different ways. We show that if the Laplace operator, $\Delta$, on a hypergraph satisfies a curvature-dimension type inequality $CD (\mathbf{m}, \mathbf{K})$ with $\mathbf{m}>1$ and $\mathbf{K}>0$ then any non-zero eigenvalue of $- \Delta$ can be bounded below by $\frac{ \mathbf{m} \mathbf{K}}{ \mathbf{m} -1 }$. Eigenvalues of a normalized Laplacian operator defined on a connected hypergraph can be bounded by the Ollivier's Ricci curvature of the hypergraph

Experimentally increased group diversity improves disease resistance in an ant species.

A leading hypothesis linking parasites to social evolution is that more genetically diverse social groups better resist parasites. Moreover, group diversity can encompass factors other than genetic variation that may also influence disease resistance. Here, we tested whether group diversity improved disease resistance in an ant species with natural variation in colony queen number. We formed experimental groups of workers and challenged them with the fungal parasite Metarhizium anisopliae. Workers originating from monogynous colonies (headed by a single queen and with low genetic diversity) had higher survival than workers originating from polygynous ones, both in uninfected groups and in groups challenged with M. anisopliae. However, an experimental increase of group diversity by mixing workers originating from monogynous colonies strongly increased the survival of workers challenged with M. anisopliae, whereas it tended to decrease their survival in absence of infection. This experiment suggests that group diversity, be it genetic or environmental, improves the mean resistance of group members to the fungal infection, probably through the sharing of physiological or behavioural defences

Using Regular Languages to Explore the Representational Capacity of Recurrent Neural Architectures

The presence of Long Distance Dependencies (LDDs) in sequential data poses significant challenges for computational models. Various recurrent neural architectures have been designed to mitigate this issue. In order to test these state-of-the-art architectures, there is growing need for rich benchmarking datasets. However, one of the drawbacks of existing datasets is the lack of experimental control with regards to the presence and/or degree of LDDs. This lack of control limits the analysis of model performance in relation to the specific challenge posed by LDDs. One way to address this is to use synthetic data having the properties of subregular languages. The degree of LDDs within the generated data can be controlled through the k parameter, length of the generated strings, and by choosing appropriate forbidden strings. In this paper, we explore the capacity of different RNN extensions to model LDDs, by evaluating these models on a sequence of SPk synthesized datasets, where each subsequent dataset exhibits a longer degree of LDD. Even though SPk are simple languages, the presence of LDDs does have significant impact on the performance of recurrent neural architectures, thus making them prime candidate in benchmarking tasks.Comment: International Conference of Artificial Neural Networks (ICANN) 201

Acute influence of cigarette smoke in platelets, catecholamines and neurophysins in the normal conditions of daily life

Cigarette smoking is firmly linked to the occurrence of acute coronary events. In twenty-two healthy volunteers in normal conditions of daily life we studied the acute influence of smoking on the following parameters: beta-thromboglobulin, thromboxane B2, epinephrine, norepinephrine, estrogen-stimulated neurophysin, and nicotine-stimulated-neurophysin. Our results show that in our population and following our protocol, smoking did not induce platelet activation, thromboxane formation, catecholamine release or estrogen-stimulated-neurophysin secretion. However, smoking did provoke a significant increase of nicotine-stimulated-neurophysin (p<0.05) which reflects vasopressin increase and which might explain the high incidence of ischaemic accidents in cigarette smoking via the vasoactive properties of vasopressi

Quantum Lattice Fluctuations and Luminescence in C_60

We consider luminescence in photo-excited neutral C_60 using the Su-Schrieffer-Heeger model applied to a single C_60 molecule. To calculate the luminescence we use a collective coordinate method where our collective coordinate resembles the displacement of the carbon atoms of the Hg(8) phonon mode and extrapolates between the ground state "dimerisation" and the exciton polaron. There is good agreement for the existing luminescence peak spacing and fair agreement for the relative intensity. We predict the existence of further peaks not yet resolved in experiment. PACS Numbers : 78.65.Hc, 74.70.Kn, 36.90+