Degree Distribution of Competition-Induced Preferential Attachment Graphs

We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment random graph models with upper cutoffs. This is the first explanation of how preferential attachment can arise from a more basic underlying mechanism of local competition. We rigorously determine the degree distribution for the family of random graph models, showing that it obeys a power law up to a finite threshold and decays exponentially above this threshold. We also rigorously analyze a generalized version of our graph process, with two natural parameters, one corresponding to the cutoff and the other a ``fertility'' parameter. We prove that the general model has a power-law degree distribution up to a cutoff, and establish monotonicity of the power as a function of the two parameters. Limiting cases of the general model include the standard preferential attachment model without cutoff and the uniform attachment model.Comment: 24 pages, one figure. To appear in the journal: Combinatorics, Probability and Computing. Note, this is a long version, with complete proofs, of the paper "Competition-Induced Preferential Attachment" (cond-mat/0402268

Fermionized photons in the ground state of one-dimensional coupled cavities

The Density Matrix Renormalization Group algorithm is used to characterize the ground states of one-dimensional coupled cavities in the regime of low photon densities. Numerical results for photon and spin excitation densities, one- and two-body correlation functions, superfluid and condensate fractions, as well as the entanglement entropy and localizable entanglement are obtained for the Jaynes-Cummings-Hubbard (JCH) model, and are compared with those for the Bose-Hubbard (BH) model where applicable. The results indicate that a Tonks-Girardeau phase, in which the photons are strongly fermionized, appears between the Mott-insulating and superfluid phases as a function of the inter-cavity coupling. In fact, the superfluid density is found to be zero in a wide region outside the Mott-insulator phase boundary. The presence of two different species of excitation (spin and photon) in the JCH model gives rise to properties with no analog in the BH model, such as the (quasi)condensation of spin excitations and the spontaneous generation of entanglement between the atoms confined to each cavity.Comment: 17 pages, 11 figure

Rho GTPases and signaling networks

The Rho GTPases form a subgroup of the Ras superfamily of 20- to 30-kD GTP-binding proteins that have been shown to regulate a wide spectrum of cellular functions. These proteins are ubiquitously expressed across the species, from yeast to man. The mammalian Rho-like GTPases comprise at least 10 distinct proteins: RhoA, B, C, D, and E; Rac1 and 2; RacE; Cdc42Hs, and TC10. A comparison of the amino acid sequences of the Rho proteins from various species has revealed that they are conserved in primary structure and are 50%–55% homologous to each other. Like all members of the Ras superfamily, the Rho GTPases function as molecular switches, cycling between an inactive GDP-bound state and an active GTP-bound state. Until recently, members of the Rho subfamily were believed to be involved primarily in the regulation of cytoskeletal organization in response to extracellular growth factors. However, research from a number of laboratories over the past few years has revealed that the Rho GTPases play crucial roles in diverse cellular events such as membrane trafficking, transcriptional regulation, cell growth control, and development. Consequently, a major challenge has been to unravel the underlying molecular mechanisms by which the Rho GTPases mediate these various activities. Many targets of the Rho GTPases have now been identified and further characterization of some of them has provided major insights toward our understanding of Rho GTPase function at the molecular level. This review aims to summarize the general established principles about the Rho GTPases and some of the more recent exciting findings, hinting at novel, unanticipated functions of the Rho GTPases

Holistic generational offsets: Fostering a primitive online abstraction for human vs. machine cognition

We propose a unified architecture for next generation cognitive, low cost, mobile internet. The end user platform is able to scale as per the application and network requirements. It takes computing out of the data center and into end user platform. Internet enables open standards, accessible computing and applications programmability on a commodity platform. The architecture is a super-set to present day infrastructure web computing. The Java virtual machine (JVM) derives from the stack architecture. Applications can be developed and deployed on a multitude of host platforms. O(1) O(N). Computing and the internet today are more accessible and available to the larger community. Machine learning has made extensive advances with the availability of modern computing. It is used widely in NLP, Computer Vision, Deep learning and AI. A prototype device for mobile could contain N compute and N MB of memory.Comment: 11 pages, extended architecture details, added references. arXiv admin note: text overlap with arXiv:1809.0779

Incremental online learning in high dimensions

this article, however, is problematic, as it requires a careful selection of initial ridge regression parameters to stabilize the highly rank-deficient full covariance matrix of the input data, and it is easy to create too much bias or too little numerical stabilization initially, which can trap the local distance metric adaptation in local minima.While the LWPR algorithm just computes about a factor 10 times longer for the 20D experiment in comparison to the 2D experiment, RFWR requires a 1000-fold increase of computation time, thus rendering this algorithm unsuitable for high-dimensional regression. In order to compare LWPR's results to other popular regression methods, we evaluated the 2D, 10D, and 20D cross data sets with gaussian process regression (GP) and support vector (SVM) regression in addition to our LWPR method. It should be noted that neither SVM nor GP methods is an incremental method, although they can be considered state-of-the-art for batch regression under relatively small numbers of training data and reasonable input dimensionality. The computational complexity of these methods is prohibitively high for real-time applications. The GP algorithm (Gibbs & MacKay, 1997) used a generic covariance function and optimized over the hyperparameters. The SVM regression was performed using a standard available package (Saunders et al., 1998) and optimized for kernel choices. Figure 6 compares the performance of LWPR and gaussian processes for the above-mentioned data sets using 100, 300, and 500 training data point

Robust Bain distortion in the premartensite phase of platinum substituted Ni2MnGa magnetic shape memory alloy

The premartensite phase of shape memory and magnetic shape memory alloys (MSMAs) is believed to be a precursor state of the martensite phase with preserved austenite phase symmetry. The thermodynamic stability of the premartensite phase and its relation to the martensitic phase is still an unresolved issue, even though it is critical to the understanding of the functional properties of MSMAs. We present here unambiguous evidence for macroscopic symmetry breaking leading to robust Bain distortion in the premartensite phase of 10% Pt substituted Ni2MnGa. We show that the robust Bain distorted premartensite (T2) phase results from another premartensite (T1) phase with preserved cubic-like symmetry through an isostructural phase transition. The T2 phase finally transforms to the martensite phase with additional Bain distortion on further cooling. Our results demonstrate that the premartensite phase should not be considered as a precursor state with the preserved symmetry of the cubic austenite phase

Pterodactyl: Thermal Protection System for Integrated Control Design of a Mechanically Deployed Entry Vehicle

The need for precision landing of high mass payloads on Mars and the return of sensitive samples from other planetary bodies to specific locations on Earth is driving the development of an innovative NASA technology referred to as the Deployable Entry Vehicle (DEV). A DEV has the potential to deliver an equivalent science payload with a stowed diameter 3 to 4 times smaller than a traditional rigid capsule configuration. However, the DEV design does not easily lend itself to traditional methods of directional control. The NASA Space Technology Mission Directorate (STMD)s Pterodactyl project is currently investigating the effectiveness of three different Guidance and Control (G&C) systems actuated flaps, Center of Gravity (CG) or mass movement, and Reaction Control System (RCS) for use with a DEV using the Adaptable, Deployable, Entry, and Placement Technology (ADEPT) design. This paper details the Thermal Protection System (TPS) design and associated mass estimation efforts for each of the G&C systems. TPS is needed for the nose cap of the DEV and the flaps of the actuated flap control system. The development of a TPS selection, sizing, and mass estimation method designed to deal with the varying requirements for the G&C options throughout the trajectory is presented. The paper discusses the methods used to i) obtain heating environments throughout the trajectory with respect to the chosen control system and resulting geometry; ii) determine a suitable TPS material; iii) produce TPS thickness estimations; and, iv) determine the final TPS mass estimation based on TPS thickness, vehicle control system, vehicle structure, and vehicle payload