Trace Formulae and Spectral Statistics for Discrete Laplacians on Regular Graphs (II)

Following the derivation of the trace formulae in the first paper in this series, we establish here a connection between the spectral statistics of random regular graphs and the predictions of Random Matrix Theory (RMT). This follows from the known Poisson distribution of cycle counts in regular graphs, in the limit that the cycle periods are kept constant and the number of vertices increases indefinitely. The result is analogous to the so called "diagonal approximation" in Quantum Chaos. We also show that by assuming that the spectral correlations are given by RMT to all orders, we can compute the leading deviations from the Poisson distribution for cycle counts. We provide numerical evidence which supports this conjecture.Comment: 15 pages, 5 figure

Isospectral graphs with identical nodal counts

According to a recent conjecture, isospectral objects have different nodal count sequences. We study generalized Laplacians on discrete graphs, and use them to construct the first non-trivial counter-examples to this conjecture. In addition, these examples demonstrate a surprising connection between isospectral discrete and quantum graphs

Profiling molecular and behavioral circadian rhythms in the non-symbiotic sea anemone Nematostella vectensis

© The Author(s), 2015. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Scientific Reports 5 (2015): 11418, doi:10.1038/srep11418.Endogenous circadian clocks are poorly understood within early-diverging animal lineages. We have characterized circadian behavioral patterns and identified potential components of the circadian clock in the starlet sea anemone, Nematostella vectensis: a model cnidarian which lacks algal symbionts. Using automatic video tracking we showed that Nematostella exhibits rhythmic circadian locomotor activity, which is persistent in constant dark, shifted or disrupted by external dark/light cues and maintained the same rate at two different temperatures. This activity was inhibited by a casein kinase 1δ/ε inhibitor, suggesting a role for CK1 homologue(s) in Nematostella clock. Using high-throughput sequencing we profiled Nematostella transcriptomes over 48 hours under a light-dark cycle. We identified 180 Nematostella diurnally-oscillated transcripts and compared them with previously established databases of adult and larvae of the symbiotic coral Acropora millepora, revealing both shared homologues and unique rhythmic genes. Taken together, this study further establishes Nematostella as a non-symbiotic model organism to study circadian rhythms and increases our understanding about the fundamental elements of circadian regulation and their evolution within the Metazoa.This work was supported by the Israel-US Binational Science Foundation to OL and AMT (Award 2011187). Additional support was provided by the WHOI Early Career Scientist Award to AMT

Representation Learning via Variational Bayesian Networks

We present Variational Bayesian Network (VBN) - a novel Bayesian entity representation learning model that utilizes hierarchical and relational side information and is particularly useful for modeling entities in the ``long-tail'', where the data is scarce. VBN provides better modeling for long-tail entities via two complementary mechanisms: First, VBN employs informative hierarchical priors that enable information propagation between entities sharing common ancestors. Additionally, VBN models explicit relations between entities that enforce complementary structure and consistency, guiding the learned representations towards a more meaningful arrangement in space. Second, VBN represents entities by densities (rather than vectors), hence modeling uncertainty that plays a complementary role in coping with data scarcity. Finally, we propose a scalable Variational Bayes optimization algorithm that enables fast approximate Bayesian inference. We evaluate the effectiveness of VBN on linguistic, recommendations, and medical inference tasks. Our findings show that VBN outperforms other existing methods across multiple datasets, and especially in the long-tail

Archaeal diversity in the Dead Sea: Microbial survival under increasingly harsh conditions

The Dead Sea is rapidly drying out. The lake is supersaturated with NaCl, and precipitated of halite from the water column has led to a decrease in sodium content, while concentrations of magnesium and calcium greatly increased, making the lake an ever more extreme environment for microbial life. In the past decades, blooms of algae (Dunaliella) and halophilic Archaea were twice observed in the lake (1980-1982 and 1992-1995), triggered by massive inflow of freshwater floods, but no conditions suitable for renewed microbial growth have occurred since. To examine whether the Death Sea in its current state (density 1.24 g ml-1, water activity about 0.67) still supports life of halophilic Archaea, we collected particulate matter from a depth of 5 m at an offshore station by means of tangential filtration. Presence of bacterioruberin carotenoids, albeit at low concentrations, in the particulate material showed the members of the Halobactericacae were still present in the lake\u27s water column. Amplification of 16S rRNA genes from the biomass yielded genes with less than 95% identify with environmental sequences reported from other environments and only 85-95% identity with cultivated Halobacteriaceae. It is thus shown that the Dead Sea, in spite of the ever more adverse conditions to life, supports a unique and varied community of halophilic Archaea. We have also isolated a number of strains of Halobacteriaceae from the samples collected, and their characterization is currently in progress