Exact and Scaling Form of the Bipartite Fidelity of the Infinite XXZ Chain

We find an exact expression for the bipartite fidelity f=|'|^2, where |vac> is the vacuum eigenstate of an infinite-size antiferromagnetic XXZ chain and |vac>' is the vacuum eigenstate of an infinite-size XXZ chain which is split in two. We consider the quantity -ln(f) which has been put forward as a measure of quantum entanglement, and show that the large correlation length xi behaviour is consistent with a general conjecture -ln(f) ~ c/8 ln(xi), where c is the central charge of the UV conformal field theory (with c=1 for the XXZ chain). This behaviour is a natural extension of the existing conformal field theory prediction of -ln(f) ~ c/8 ln(L) for a length L bipartite system with 0<< L <<xi.Comment: 6 page

A mathematical model of the effect of a predator on species diversity

Mathematical model determines reaction between new predator and microbe competitor when the competitor is the predator's sole nutrient resource. The model utilizes differential equations to describe the interactions with the specific growth rates, and analyzes these growth rates as they are affected by population density and nutrient concentration

In vivo characterization of hippocampal electrophysiological processes in the heterozygous Pten knockout model of autism

While cognitive deficits have been described in the heterozygous Pten (+/-) KO mouse model of autism, little work has been done to demonstrate how corresponding in vitro physiological alterations in this model may underpin these cognitive deficits in vivo. As Pten KO (+/-) is known to alter electrophysiological characteristics of neurons in vitro, this study measures the in vivo electrophysiological characteristics of CA1 interneurons, pyramidal cells, and place cells which may underlie the spatial cognitive deficits seen in the model. Four transgenic conditional heterozygous Pten+/loxPloxP;Gfap-cre mice (HetPten) and four homozygous Pten littermate control mice were used in this study. This transgene drives cre expression and excision of the Pten gene in hippocampal granule cells of the dentate gyrus, and neurons in CA2 and CA1, but not astrocytes. In vivo local field potentials and single cell recordings were made in CA1 of each mouse during an open field foraging task in two distinct arenas. HetPten mice were found to have increased interneuron and pyramidal cell firing rates. In addition, place cells demonstrated abnormal properties including increased out-of-field firing rates, an increased number of fields, and trends towards larger field sizes that were less stable in comparison to controls. HetPten mice had slower CA1 fast gamma oscillations and more variable speed/theta oscillation correlations. Behaviorally, there were weak trends towards decreased motor output compared to controls. These data suggest that the electrophysiological alterations due to Pten KO (+/-) in mouse hippocampal neurons lead to hyperactivation of CA1 interneurons, pyramidal cells, and place cells

More than symbioses : orchid ecology ; with examples from the Sydney Region

The Orchidaceae are one of the largest and most diverse families of flowering plants. Orchids grow as terrestrial, lithophytic, epiphytic or climbing herbs but most orchids native to the Sydney Region can be placed in one of two categories. The first consists of terrestrial, deciduous plants that live in fire-prone environments, die back seasonally to dormant underground root tubers, possess exclusively subterranean roots, which die off as the plants become dormant, and belong to the subfamily Orchidoideae. The second consists of epiphytic or lithophytic, evergreen plants that live in fire-free environments, either lack specialised storage structures or possess succulent stems or leaves that are unprotected from fire, possess aerial roots that grow over the surface of, or free of, the substrate, and which do not die off seasonally, and belong to the subfamily Epidendroideae. Orchid seeds are numerous and tiny, lacking cotyledons and endosperm and containing minimal nutrient reserves. Although the seeds of some species can commence germination on their own, all rely on infection by mycorrhizal fungi, which may be species-specific, to grow beyond the earliest stages of development. Many epidendroid orchids are viable from an early stage without their mycorrhizal fungi but most orchidoid orchids rely, at least to some extent, on their mycorrhizal fungi throughout their lives. Some are completely parasitic on their fungi and have lost the ability to photosynthesize. Some orchids parasitize highly pathogenic mycorrhizal fungi and are thus indirectly parasitic on other plants. Most orchids have specialised relationships with pollinating animals, with many species each pollinated by only one species of insect. Deceptive pollination systems, in which the plants provide no tangible reward to their pollinators, are common in the Orchidaceae. The most common form of deceit is food mimicry, while at least a few taxa mimic insect brood sites. At least six lineages of Australian orchids have independently evolved sexual deception. In this syndrome, a flower mimics the female of the pollinating insect species. Male insects are attracted to the flower and attempt to mate with it, and pollinate it in the process. Little is known of most aspects of the population ecology of orchids native to the Sydney Region, especially their responses to fire. Such knowledge would be very useful in informing decisions in wildlife management

FreezeOut: Accelerate Training by Progressively Freezing Layers

The early layers of a deep neural net have the fewest parameters, but take up the most computation. In this extended abstract, we propose to only train the hidden layers for a set portion of the training run, freezing them out one-by-one and excluding them from the backward pass. Through experiments on CIFAR, we empirically demonstrate that FreezeOut yields savings of up to 20% wall-clock time during training with 3% loss in accuracy for DenseNets, a 20% speedup without loss of accuracy for ResNets, and no improvement for VGG networks. Our code is publicly available at https://github.com/ajbrock/FreezeOutComment: Extended Abstrac

Bayesian anomaly detection methods for social networks

Learning the network structure of a large graph is computationally demanding, and dynamically monitoring the network over time for any changes in structure threatens to be more challenging still. This paper presents a two-stage method for anomaly detection in dynamic graphs: the first stage uses simple, conjugate Bayesian models for discrete time counting processes to track the pairwise links of all nodes in the graph to assess normality of behavior; the second stage applies standard network inference tools on a greatly reduced subset of potentially anomalous nodes. The utility of the method is demonstrated on simulated and real data sets.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS329 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Generative and Discriminative Voxel Modeling with Convolutional Neural Networks

When working with three-dimensional data, choice of representation is key. We explore voxel-based models, and present evidence for the viability of voxellated representations in applications including shape modeling and object classification. Our key contributions are methods for training voxel-based variational autoencoders, a user interface for exploring the latent space learned by the autoencoder, and a deep convolutional neural network architecture for object classification. We address challenges unique to voxel-based representations, and empirically evaluate our models on the ModelNet benchmark, where we demonstrate a 51.5% relative improvement in the state of the art for object classification.Comment: 9 pages, 5 figures, 2 table

SMASH: One-Shot Model Architecture Search through HyperNetworks

Designing architectures for deep neural networks requires expert knowledge and substantial computation time. We propose a technique to accelerate architecture selection by learning an auxiliary HyperNet that generates the weights of a main model conditioned on that model's architecture. By comparing the relative validation performance of networks with HyperNet-generated weights, we can effectively search over a wide range of architectures at the cost of a single training run. To facilitate this search, we develop a flexible mechanism based on memory read-writes that allows us to define a wide range of network connectivity patterns, with ResNet, DenseNet, and FractalNet blocks as special cases. We validate our method (SMASH) on CIFAR-10 and CIFAR-100, STL-10, ModelNet10, and Imagenet32x32, achieving competitive performance with similarly-sized hand-designed networks. Our code is available at https://github.com/ajbrock/SMAS