Fluid limits for networks with bandwidth sharing and general document size distributions

We consider a stochastic model of Internet congestion control, introduced by Massouli\'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows in a network where bandwidth is shared among document transfers. In contrast to an earlier work by Kelly and Williams [Ann. Appl. Probab. 14 (2004) 1055--1083], the present paper allows interarrival times and document sizes to be generally distributed, rather than exponentially distributed. Furthermore, we allow a fairly general class of bandwidth sharing policies that includes the weighted $\alpha$-fair policies of Mo and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556--567], as well as certain other utility based scheduling policies. To describe the evolution of the system, measure valued processes are used to keep track of the residual document sizes of all flows through the network. We propose a fluid model (or formal functional law of large numbers approximation) associated with the stochastic flow level model. Under mild conditions, we show that the appropriately rescaled measure valued processes corresponding to a sequence of such models (with fixed network structure) are tight, and that any weak limit point of the sequence is almost surely a fluid model solution. For the special case of weighted $\alpha$-fair policies, we also characterize the invariant states of the fluid model.Comment: Published in at http://dx.doi.org/10.1214/08-AAP541 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Guided Neuronal Growth on Arrays of Biofunctionalized GaAs/InGaAs Semiconductor Microtubes

We demonstrate embedded growth of cortical mouse neurons in dense arrays of semiconductor microtubes. The microtubes, fabricated from a strained GaAs/InGaAs heterostructure, guide axon growth through them and enable electrical and optical probing of propagating action potentials. The coaxial nature of the microtubes -- similar to myelin -- is expected to enhance the signal transduction along the axon. We present a technique of suppressing arsenic toxicity and prove the success of this technique by overgrowing neuronal mouse cells.Comment: 3 pages, 4 figure

Multifactor Dimensionality Reduction Reveals a Three-Locus Epistatic Interaction Associated with Susceptibility to Pulmonary Tuberculosis

Background: Identifying high-order genetics associations with non-additive (i.e. epistatic) effects in population-based studies of common human diseases is a computational challenge. Multifactor dimensionality reduction (MDR) is a machine learning method that was designed specifically for this problem. The goal of the present study was to apply MDR to mining high-order epistatic interactions in a population-based genetic study of tuberculosis (TB). Results: The study used a previously published data set consisting of 19 candidate single-nucleotide polymorphisms (SNPs) in 321 pulmonary TB cases and 347 healthy controls from Guniea-Bissau in Africa. The ReliefF algorithm was applied first to generate a smaller set of the five most informative SNPs. MDR with 10-fold cross-validation was then applied to look at all possible combinations of two, three, four and five SNPs. The MDR model with the best testing accuracy (TA) consisted of SNPs rs2305619, rs187084, and rs11465421 (TA = 0.588) in PTX3, TLR9 and DC-Sign, respectively. A general 1000-fold permutation test of the null hypothesis of no association confirmed the statistical significance of the model (p = 0.008). An additional 1000-fold permutation test designed specifically to test the linear null hypothesis that the association effects are only additive confirmed the presence of non-additive (i.e. nonlinear) or epistatic effects (p = 0.013). An independent information-gain measure corroborated these results with a third-order epistatic interaction that was stronger than any lower-order associations. Conclusions: We have identified statistically significant evidence for a three-way epistatic interaction that is associated with susceptibility to TB. This interaction is stronger than any previously described one-way or two-way associations. This study highlights the importance of using machine learning methods that are designed to embrace, rather than ignore, the complexity of common diseases such as TB. We recommend future studies of the genetics of TB take into account the possibility that high-order epistatic interactions might play an important role in disease susceptibility

Atom gravimeters and gravitational redshift

In a recent paper, H. Mueller, A. Peters and S. Chu [A precision measurement of the gravitational redshift by the interference of matter waves, Nature 463, 926-929 (2010)] argued that atom interferometry experiments published a decade ago did in fact measure the gravitational redshift on the quantum clock operating at the very high Compton frequency associated with the rest mass of the Caesium atom. In the present Communication we show that this interpretation is incorrect.Comment: 2 pages, Brief Communication appeared in Nature (2 September 2010

Deep Learning with Photonic Neural Cellular Automata

Rapid advancements in deep learning over the past decade have fueled an insatiable demand for efficient and scalable hardware. Photonics offers a promising solution by leveraging the unique properties of light. However, conventional neural network architectures, which typically require dense programmable connections, pose several practical challenges for photonic realizations. To overcome these limitations, we propose and experimentally demonstrate Photonic Neural Cellular Automata (PNCA) for photonic deep learning with sparse connectivity. PNCA harnesses the speed and interconnectivity of photonics, as well as the self-organizing nature of cellular automata through local interactions to achieve robust, reliable, and efficient processing. We utilize linear light interference and parametric nonlinear optics for all-optical computations in a time-multiplexed photonic network to experimentally perform self-organized image classification. We demonstrate binary classification of images in the fashion-MNIST dataset using as few as 3 programmable photonic parameters, achieving an experimental accuracy of 98.0% with the ability to also recognize out-of-distribution data. The proposed PNCA approach can be adapted to a wide range of existing photonic hardware and provides a compelling alternative to conventional photonic neural networks by maximizing the advantages of light-based computing whilst mitigating their practical challenges. Our results showcase the potential of PNCA in advancing photonic deep learning and highlights a path for next-generation photonic computers

Wittgenstein's Thought Experiments and Relativity Theory

In this paper, I discuss the similarity between Wittgenstein’s use of thought experiments and Relativity Theory. I begin with introducing Wittgenstein’s idea of “thought experiments” and a tentative classification of different kinds of thought experiments in Wittgenstein’s work. Then, after presenting a short recap of some remarks on the analogy between Wittgenstein’s point of view and Einstein’s, I suggest three analogies between the status of Wittgenstein’s mental experiments and Relativity theory: the topics of time dilation, the search for invariants, and the role of measuring tools in Special Relativity. This last point will help to better define Wittgenstein’s idea of description as the core of his philosophical enterprise

The Multiscale Backbone of the Human Phenotype Network Based on Biological Pathways

Background: Networks are commonly used to represent and analyze large and complex systems of interacting elements. In systems biology, human disease networks show interactions between disorders sharing common genetic background. We built pathway-based human phenotype network (PHPN) of over 800 physical attributes, diseases, and behavioral traits; based on about 2,300 genes and 1,200 biological pathways. Using GWAS phenotype-to-genes associations, and pathway data from Reactome, we connect human traits based on the common patterns of human biological pathways, detecting more pleiotropic effects, and expanding previous studies from a gene-centric approach to that of shared cell-processes. Results: The resulting network has a heavily right-skewed degree distribution, placing it in the scale-free region of the network topologies spectrum. We extract the multi-scale information backbone of the PHPN based on the local densities of the network and discarding weak connection. Using a standard community detection algorithm, we construct phenotype modules of similar traits without applying expert biological knowledge. These modules can be assimilated to the disease classes. However, we are able to classify phenotypes according to shared biology, and not arbitrary disease classes. We present examples of expected clinical connections identified by PHPN as proof of principle. Conclusions: We unveil a previously uncharacterized connection between phenotype modules and discuss potential mechanistic connections that are obvious only in retrospect. The PHPN shows tremendous potential to become a useful tool both in the unveiling of the diseases’ common biology, and in the elaboration of diagnosis and treatments

Loss of Conformational Stability in Calmodulin upon Methionine Oxidation

We have used electrospray ionization mass spectrometry (ESI-MS), circular dichroism (CD), and fluorescence spectroscopy to investigate the secondary and tertiary structural consequences that result from oxidative modification of methionine residues in wheat germ calmodulin (CaM), and prevent activation of the plasma membrane Ca-ATPase. Using ESI-MS, we have measured rates of modification and molecular mass distributions of oxidatively modified CaM species (CaMox) resulting from exposure to H2O2. From these rates, we find that oxidative modification of methionine to the corresponding methionine sulfoxide does not predispose CaM to further oxidative modification. These results indicate that methionine oxidation results in no large-scale alterations in the tertiary structure of CaMox, because the rates of oxidative modification of individual methionines are directly related to their solvent exposure. Likewise, CD measurements indicate that methionine oxidation results in little change in the apparent α-helical content at 28°C, and only a small (0.3 ± 0.1 kcal mol−1) decrease in thermal stability, suggesting the disruption of a limited number of specific noncovalent interactions. Fluorescence lifetime, anisotropy, and quenching measurements of N-(1-pyrenyl)-maleimide (PMal) covalently bound to Cys26 indicate local structural changes around PMal in the amino-terminal domain in response to oxidative modification of methionine residues in the carboxyl-terminal domain. Because the opposing globular domains remain spatially distant in both native and oxidatively modified CaM, the oxidative modification of methionines in the carboxyl-terminal domain are suggested to modify the conformation of the amino-terminal domain through alterations in the structural features involving the interdomain central helix. The structural basis for the linkage between oxidative modification and these global conformational changes is discussed in terms of possible alterations in specific noncovalent interactions that have previously been suggested to stabilize the central helix in CaM

Geometric characterization of nodal domains: the area-to-perimeter ratio

In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength $1/\sqrt{E}$. We show that the distribution function $P(\rho)$ can distinguish between domains in which the classical dynamics is regular or chaotic. For separable surfaces, we compute the limiting distribution, and show that it is supported by an interval, which is independent of the properties of the surface. In systems which are chaotic, or in random-waves, the area-to-perimeter distribution has substantially different features which we study numerically. We compare the features of the distribution for chaotic wave functions with the predictions of the percolation model to find agreement, but only for nodal domains which are big with respect to the wavelength scale. This work is also closely related to, and provides a new point of view on isoperimetric inequalities.Comment: 22 pages, 11 figure