Online Matrix Completion Through Nuclear Norm Regularisation

It is the main goal of this paper to propose a novel method to perform matrix completion on-line. Motivated by a wide variety of applications, ranging from the design of recommender systems to sensor network localization through seismic data reconstruction, we consider the matrix completion problem when entries of the matrix of interest are observed gradually. Precisely, we place ourselves in the situation where the predictive rule should be refined incrementally, rather than recomputed from scratch each time the sample of observed entries increases. The extension of existing matrix completion methods to the sequential prediction context is indeed a major issue in the Big Data era, and yet little addressed in the literature. The algorithm promoted in this article builds upon the Soft Impute approach introduced in Mazumder et al. (2010). The major novelty essentially arises from the use of a randomised technique for both computing and updating the Singular Value Decomposition (SVD) involved in the algorithm. Though of disarming simplicity, the method proposed turns out to be very efficient, while requiring reduced computations. Several numerical experiments based on real datasets illustrating its performance are displayed, together with preliminary results giving it a theoretical basis.Comment: Corrected a typo in the affiliatio

An associative memory for the on-line recognition and prediction of temporal sequences

This paper presents the design of an associative memory with feedback that is capable of on-line temporal sequence learning. A framework for on-line sequence learning has been proposed, and different sequence learning models have been analysed according to this framework. The network model is an associative memory with a separate store for the sequence context of a symbol. A sparse distributed memory is used to gain scalability. The context store combines the functionality of a neural layer with a shift register. The sensitivity of the machine to the sequence context is controllable, resulting in different characteristic behaviours. The model can store and predict on-line sequences of various types and length. Numerical simulations on the model have been carried out to determine its properties.Comment: Published in IJCNN 2005, Montreal, Canad

Differential Interleukin-2 Transcription Kinetics Render Mouse but Not Human T Cells Vulnerable to Splicing Inhibition Early after Activation

T cells are nodal players in the adaptive immune response against pathogens and malignant cells. Alternative splicing plays a crucial role in T cell activation, which is analyzed mainly at later time points upon stimulation. Here we have discovered a 2-h time window early after stimulation where optimal splicing efficiency or, more generally, gene expression efficiency is crucial for successful T cell activation. Reducing the splicing efficiency at 4 to 6 h poststimulation significantly impaired murine T cell activation, which was dependent on the expression dynamics of the Egr1-Nab2-interleukin-2 (IL-2) pathway. This time window overlaps the time of peak IL-2 de novo transcription, which, we suggest, represents a permissive time window in which decreased splicing (or transcription) efficiency reduces mature IL-2 production, thereby hampering murine T cell activation. Notably, the distinct expression kinetics of the Egr1-Nab2-IL-2 pathway between mouse and human render human T cells refractory to this vulnerability. We propose that the rational temporal modulation of splicing or transcription during peak de novo expression of key effectors can be used to fine-tune stimulation-dependent biological outcomes. Our data also show that critical consideration is required when extrapolating mouse data to the human system in basic and translational research

Neutron-star Radius from a Population of Binary Neutron Star Mergers

We show how gravitational-wave observations with advanced detectors of tens to several tens of neutron-star binaries can measure the neutron-star radius with an accuracy of several to a few percent, for mass and spatial distributions that are realistic, and with none of the sources located within 100 Mpc. We achieve such an accuracy by combining measurements of the total mass from the inspiral phase with those of the compactness from the postmerger oscillation frequencies. For estimating the measurement errors of these frequencies we utilize analytical fits to postmerger numerical-relativity waveforms in the time domain, obtained here for the first time, for four nuclear-physics equations of state and a couple of values for the mass. We further exploit quasi-universal relations to derive errors in compactness from those frequencies. Measuring the average radius to well within 10% is possible for a sample of 100 binaries distributed uniformly in volume between 100 and 300 Mpc, so long as the equation of state is not too soft or the binaries are not too heavy.Comment: 9 pages and 7 figure

Quantum Liang Information Flow as Causation Quantifier

Liang information flow is widely used in classical systems and network theory for causality quantification and has been applied widely, for example, to finance, neuroscience, and climate studies. The key part of the theory is to freeze a node of a network to ascertain its causal influence on other nodes. Such a theory is yet to be applied to quantum network dynamics. Here, we generalize the Liang information flow to the quantum domain with respect to von Neumann entropy and exemplify its usage by applying it to a variety of small quantum networks

Superconductivity in Boron under pressure - why are the measured Tc_c's so low?

Using the full potential linear muffin-tin orbitals (FP-LMTO) method we examine the pressure-dependence of superconductivity in the two metallic phases of Boron: bct and fcc. Linear response calculations are carried out to examine the phonon frequencies and electron-phonon coupling for various lattice parameters, and superconducting transition temperatures are obtained from the Eliashberg equation. In both bct and fcc phases the superconducting transition temperature T$_c$ is found to decrease with increasing pressure, due to stiffening of phonons with an accompanying decrease in electron-phonon coupling. This is in contrast to a recent report, where T$_c$ is found to increase with pressure. Even more drastic is the difference between the measured T$_c$, in the range 4-11 K, and the calculated values for both bct and fcc phases, in the range 60-100 K. The calculation reveals that the transition from the fcc to bct phase, as a result of increasing volume or decreasing pressure, is caused by the softening of the X-point transverse phonons. This phonon softening also causes large electron-phonon coupling for high volumes in the fcc phase, resulting in coupling constants in excess of 2.5 and T$_c$ nearing 100 K. We discuss possible causes as to why the experiment might have revealed T$_c$'s much lower than what is suggested by the present study. The main assertion of this paper is that the possibility of high T$_c$, in excess of 50 K, in high pressure pure metallic phases of boron cannot be ruled out, thus substantiating the need for further experimental investigations of the superconducting properties of high pressure pure phases of boron.Comment: 16 pages, 8 figures, 1 Tabl

Spin systems with dimerized ground states

In view of the numerous examples in the literature it is attempted to outline a theory of Heisenberg spin systems possessing dimerized ground states (``DGS systems") which comprises all known examples. Whereas classical DGS systems can be completely characterized, it was only possible to provide necessary or sufficient conditions for the quantum case. First, for all DGS systems the interaction between the dimers must be balanced in a certain sense. Moreover, one can identify four special classes of DGS systems: (i) Uniform pyramids, (ii) systems close to isolated dimer systems, (iii) classical DGS systems, and (iv), in the case of $s=1/2$, systems of two dimers satisfying four inequalities. Geometrically, the set of all DGS systems may be visualized as a convex cone in the linear space of all exchange constants. Hence one can generate new examples of DGS systems by positive linear combinations of examples from the above four classes.Comment: With corrections of proposition 4 and other minor change

Quantum Communication Through a Spin-Ring with Twisted Boundary Conditions

We investigate quantum communication between the sites of a spin-ring with twisted boundary conditions. Such boundary conditions can be achieved by a flux through the ring. We find that a non-zero twist can improve communication through finite odd numbered rings and enable high fidelity multi-party quantum communication through spin rings (working near perfectly for rings of 5 and 7 spins). We show that in certain cases, the twist results in the complete blockage of quantum information flow to a certain site of the ring. This effect can be exploited to interface and entangle a flux qubit and a spin qubit without embedding the latter in a magnetic field.Comment: four pages two figure