Local-Aggregate Modeling for Big-Data via Distributed Optimization: Applications to Neuroimaging

Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging scans. This is an ultra-high-dimensional problem that consists of a matrix of covariates (brain locations by time points) for each subject; few methods currently exist to fit supervised models directly to this tensor data. We propose a novel modeling and algorithmic strategy to apply generalized linear models (GLMs) to this massive tensor data in which one set of variables is associated with locations. Our method begins by fitting GLMs to each location separately, and then builds an ensemble by blending information across locations through regularization with what we term an aggregating penalty. Our so called, Local-Aggregate Model, can be fit in a completely distributed manner over the locations using an Alternating Direction Method of Multipliers (ADMM) strategy, and thus greatly reduces the computational burden. Furthermore, we propose to select the appropriate model through a novel sequence of faster algorithmic solutions that is similar to regularization paths. We will demonstrate both the computational and predictive modeling advantages of our methods via simulations and an EEG classification problem.Comment: 41 pages, 5 figures and 3 table

Theory of DNA translocation through narrow ion channels and nanopores with charged walls

Translocation of a single stranded DNA through genetically engineered $\alpha$-hemolysin channels with positively charged walls is studied. It is predicted that transport properties of such channels are dramatically different from neutral wild type $\alpha$-hemolysin channel. We assume that the wall charges compensate the fraction $x$ of the bare charge $q_{b}$ of the DNA piece residing in the channel. Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with $x$. (ii) The effective charge $q$ of DNA piece, which is very small at $x = 0$ (neutral channel) grows with $x$ and at $x=1$ reaches $q_{b}$. (iii) The rate of DNA capture by the channel exponentially grows with $x$. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls.Comment: 3 pages, 1 figur

Hopping conductivity of a suspension of nanowires in an insulator

We study the hopping conduction in a composite made of straight metallic nanowires randomly and isotropically suspended in an insulator. Uncontrolled donors and acceptors in the insulator lead to random charging of wires and hence finite bare density of states at the Fermi level. Then the Coulomb interactions between electrons of distant wires result in the soft Coulomb gap. At low temperatures the conductivity is due to variable range hopping of electrons between wires and obeys the Efros-Shklovskii (ES) law $\ln\sigma \propto -(T_{ES}/T)^{1/2}$. We show that $T_{ES} \propto 1/(nL^3)^2$, where $n$ is the concentration of wires and $L$ is the wire length. Due to enhanced screening of Coulomb potentials, at large enough $nL^3$, the ES law is replaced by the Mott law.Comment: 5 pages, 5 figure

How a protein searches for its specific site on DNA: the role of intersegment transfer

Proteins are known to locate their specific targets on DNA up to two orders of magnitude faster than predicted by the Smoluchowski three-dimensional diffusion rate. One of the mechanisms proposed to resolve this discrepancy is termed "intersegment transfer". Many proteins have two DNA binding sites and can transfer from one DNA segment to another without dissociation to water. We calculate the target search rate for such proteins in a dense globular DNA, taking into account intersegment transfer working in conjunction with DNA motion and protein sliding along DNA. We show that intersegment transfer plays a very important role in cases where the protein spends most of its time adsorbed on DNA.Comment: 9 pages, 7 figure

A behavioural model of the adoption and use of new telecommunications media: the effects of communication scenarios and media product/service attributes

Recent years have seen the dramatic growth of new modes of communication. Above and beyond using land line and mobile phone for voice real-time communication, people spend increasing amounts of time receiving and sending messages through social networks (e.g. Myspace or Facebook) and also through real-time communication software (e.g. Skype or MSN). As indicated by the significant decline on the amount of call volumes of land line and mobile phone during the period from 2000 to 2006 in UK and in Taiwan, we conjecture that consumers are transferring to these new forms of communication in order to satisfy their communication needs, diminishing the demand for established channels. The purpose of this research is to develop a behavioural model to analyse the perceived value and weight of the specific media attributes that drive people to adopt or use these new communication channels. Seven telecommunications media available in 2010 have been categorised in this research included land-line, mobile phone, short message service (SMS), E-mail, Internet telephony, instant messaging and social networking. Various media product/service attributes such as synchronicity, multi-tasking, price, quality, mobility, privacy and video which might affect the media choice of consumers were first identified. Importantly, this research has designed six types of communication scenarios in the online survey with 894 valid responses to clarify the effects of different communication aims, distinguish consumers' intended behaviours toward these telecommunications media. --Multi-attribute choice model,Telecommunications media,Communication scenario,New product adoption,Substitution effect,ICT forecasting

Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations

Quantum virial expansion provides an ideal tool to investigate the high-temperature properties of a strongly correlated Fermi gas. Here, we construct the virial expansion in the presence of spin population imbalance. Up to the third order, we calculate the high-temperature free energy of a unitary Fermi gas as a function of spin imbalance, with infinitely large, attractive or repulsive interactions. In the latter repulsive case, we show that there is no itinerant ferromagnetism when quantum virial expansion is applicable. We therefore estimate an upper bound for the ferromagnetic transition temperature $T_{c}$. For a harmonically trapped Fermi gas at unitarity, we find that $(T_{c})_{uppper}<T_{F}$, where $T_{F}$ is the Fermi temperature at the center of the trap. Our result for the high-temperature equations of state may confront future high-precision thermodynamic measurements.Comment: 7 pages, 5 figures, accepted in Phys. Rev.