MEDUSA - New Model of Internet Topology Using k-shell Decomposition

The k-shell decomposition of a random graph provides a different and more insightful separation of the roles of the different nodes in such a graph than does the usual analysis in terms of node degrees. We develop this approach in order to analyze the Internet's structure at a coarse level, that of the "Autonomous Systems" or ASes, the subnetworks out of which the Internet is assembled. We employ new data from DIMES (see http://www.netdimes.org), a distributed agent-based mapping effort which at present has attracted over 3800 volunteers running more than 7300 DIMES clients in over 85 countries. We combine this data with the AS graph information available from the RouteViews project at Univ. Oregon, and have obtained an Internet map with far more detail than any previous effort. The data suggests a new picture of the AS-graph structure, which distinguishes a relatively large, redundantly connected core of nearly 100 ASes and two components that flow data in and out from this core. One component is fractally interconnected through peer links; the second makes direct connections to the core only. The model which results has superficial similarities with and important differences from the "Jellyfish" structure proposed by Tauro et al., so we call it a "Medusa." We plan to use this picture as a framework for measuring and extrapolating changes in the Internet's physical structure. Our k-shell analysis may also be relevant for estimating the function of nodes in the "scale-free" graphs extracted from other naturally-occurring processes.Comment: 24 pages, 17 figure

A bulk manifestation of Krylov complexity

There are various definitions of the concept of complexity in Quantum Field Theory as well as for finite quantum systems. For several of them there are conjectured holographic bulk duals. In this work we establish an entry in the AdS/CFT dictionary for one such class of complexity, namely Krylov or K-complexity. For this purpose we work in the double-scaled SYK model which is dual in a certain limit to JT gravity, a theory of gravity in AdS$_2$. In particular, states on the boundary have a clear geometrical definition in the bulk. We use this result to show that Krylov complexity of the infinite-temperature thermofield double state on the boundary of AdS$_2$ has a precise bulk description in JT gravity, namely the length of the two-sided wormhole. We do this by showing that the Krylov basis elements, which are eigenstates of the Krylov complexity operator, are mapped to length eigenstates in the bulk theory by subjecting K-complexity to the bulk-boundary map identifying the bulk/boundary Hilbert spaces. Our result makes extensive use of chord diagram techniques and identifies the Krylov basis of the boundary quantum system with fixed chord number states building the bulk gravitational Hilbert space.Comment: v1: 37 pages + appendices, 12 figures. v2: published versio

Bayesian log-Gaussian Cox process regression: applications to meta-analysis of neuroimaging working memory studies

Working memory (WM) was one of the first cognitive processes studied with functional magnetic resonance imaging. With now over 20 years of studies on WM, each study with tiny sample sizes, there is a need for meta-analysis to identify the brain regions that are consistently activated by WM tasks, and to understand the interstudy variation in those activations. However, current methods in the field cannot fully account for the spatial nature of neuroimaging meta-analysis data or the heterogeneity observed among WM studies. In this work, we propose a fully Bayesian random-effects metaregression model based on log-Gaussian Cox processes, which can be used for meta-analysis of neuroimaging studies. An efficient Markov chain Monte Carlo scheme for posterior simulations is presented which makes use of some recent advances in parallel computing using graphics processing units. Application of the proposed model to a real data set provides valuable insights regarding the function of the WM

Displacement experiments provide evidence for path integration in Drosophila

Like many other animals, insects are capable of returning to previously visited locations using path integration, which is a memory of travelled direction and distance. Recent studies suggest that Drosophila can also use path integration to return to a food reward. However, the existing experimental evidence for path integration in Drosophila has a potential confound: pheromones deposited at the site of reward might enable flies to find previously rewarding locations even without memory. Here, we show that pheromones can indeed cause naïve flies to accumulate where previous flies had been rewarded in a navigation task. Therefore, we designed an experiment to determine if flies can use path integration memory despite potential pheromonal cues by displacing the flies shortly after an optogenetic reward. We found that rewarded flies returned to the location predicted by a memory-based model. Several analyses are consistent with path integration as the mechanism by which flies returned to the reward. We conclude that although pheromones are often important in fly navigation and must be carefully controlled for in future experiments, Drosophila may indeed be capable of performing path integration

Hypermatrix factors for string and membrane junctions

The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric products of two vector spaces, and hence are matrix representations. We consider the analogous products of three vector spaces and study when they appear as summands in Lie algebra decompositions. The Z3-grading of the exceptional Lie algebras provide such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of three-junctions of strings and membranes. Generalizations are also considered.Comment: 25 pages, 4 figures, presentation improved, minor correction

Fractal Boundaries of Complex Networks

We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We find that for both Erd\"{o}s-R\'{e}nyi and scale-free model networks, as well as for several real networks, the boundaries have fractal properties. In particular, the number of boundaries nodes {\it B} follows a power-law probability density function which scales as $B^{-2}$. The clusters formed by the boundary nodes are fractals with a fractal dimension $d_{f} \approx 2$. We present analytical and numerical evidence supporting these results for a broad class of networks. Our findings imply potential applications for epidemic spreading

Epidermal Growth Factor–PEG Functionalized PAMAM-Pentaethylenehexamine Dendron for Targeted Gene Delivery Produced by Click Chemistry

Aim of this study was the site-specific conjugation of an epidermal growth factor (EGF)-polyethylene glycol (PEG) chain by click chemistry onto a poly(amido amine) (PAMAM) dendron, as a key step toward defined multifunctional carriers for targeted gene delivery. For this purpose, at first propargyl amine cored PAMAM dendrons with ester ends were synthesized. The chain terminal ester groups were then modified by oligoamines with different secondary amino densities. The oligoamine-modified PAMAM dendrons were well biocompatible, as demonstrated in cytotoxicity assays. Among the different oligoamine-modified dendrons, PAMAM-pentaethylenehexamine (PEHA) dendron polyplexes displayed the best gene transfer ability. Conjugation of PAMAM-PEHA dendron with PEG spacer was conducted via click reaction, which was performed before amidation with PEHA. The resultant PEG-PAMAM-PEHA copolymer was then coupled with EGF ligand. pDNA transfections in HuH-7 hepatocellular carcinoma cells showed a 10-fold higher efficiency with the polyplexes containing conjugated EGF as compared to the ligand-free ones, demonstrating the concept of ligand targeting. Overall gene transfer efficiencies, however, were moderate, suggesting that additional measures for overcoming subsequent intracellular bottlenecks in delivery have to be taken

Frequency Locking of an Optical Cavity using LQG Integral Control

This paper considers the application of integral Linear Quadratic Gaussian (LQG) optimal control theory to a problem of cavity locking in quantum optics. The cavity locking problem involves controlling the error between the laser frequency and the resonant frequency of the cavity. A model for the cavity system, which comprises a piezo-electric actuator and an optical cavity is experimentally determined using a subspace identification method. An LQG controller which includes integral action is synthesized to stabilize the frequency of the cavity to the laser frequency and to reject low frequency noise. The controller is successfully implemented in the laboratory using a dSpace DSP board.Comment: 18 pages, 9 figure