Analysis of Basis Pursuit Via Capacity Sets

Finding the sparsest solution $\alpha$ for an under-determined linear system of equations $D\alpha=s$ is of interest in many applications. This problem is known to be NP-hard. Recent work studied conditions on the support size of $\alpha$ that allow its recovery using L1-minimization, via the Basis Pursuit algorithm. These conditions are often relying on a scalar property of $D$ called the mutual-coherence. In this work we introduce an alternative set of features of an arbitrarily given $D$, called the "capacity sets". We show how those could be used to analyze the performance of the basis pursuit, leading to improved bounds and predictions of performance. Both theoretical and numerical methods are presented, all using the capacity values, and shown to lead to improved assessments of the basis pursuit success in finding the sparest solution of $D\alpha=s$

Ergogenic and psychological effects of synchronous music during circuit-type exercise

This is the post print version of the article. The official published version can be obtained from the link below.Objectives: Motivational music when synchronized with movement has been found to improve performance in anaerobic and aerobic endurance tasks, although gender differences pertaining to the potential benefits of such music have seldom been investigated. The present study addresses the psychological and ergogenic effects of synchronous music during circuit-type exercise. Design: A mixed-model design was employed in which there was a within-subjects factor (two experimental conditions and a control) and a between-subjects factor (gender). Methods: Participants (N ¼ 26) performed six circuit-type exercises under each of three synchronous conditions: motivational music, motivationally-neutral (oudeterous) music, and a metronome control. Dependent measures comprised anaerobic endurance, which was assessed using the number of repetitions performed prior to the failure to maintain synchronicity, and post-task affect, which was assessed using Hardy and Rejeski’s (1989) Feeling Scale. Mixed-model 3 (Condition) X 2 (Gender) ANOVAs, ANCOVAs, and MANOVA were used to analyze the data. Results: Synchronous music did not elicit significant (p < .05) ergogenic or psychological effects in isolation; rather, significant (p < .05) Condition X Gender interaction effects emerged for both total repetitions and mean affect scores. Women and men showed differential affective responses to synchronous music and men responded more positively than women to metronomic regulation of their movements. Women derived the greatest overall benefit from both music conditions. Conclusions: Men may place greater emphasis on the metronomic regulation of movement than the remaining, extra-rhythmical, musical qualities. Men and women appear to exhibit differential responses in terms of affective responses to synchronous music

Fermi liquid interactions and the superfluid density in d-wave superconductors

We construct a phenomenological superfluid Fermi liquid theory for a two-dimensional d-wave superconductor on a square lattice, and study the effect of quasiparticle interactions on the superfluid density. Using simple models for the dispersion and the Landau interaction function, we illustrate the deviation of these results from those for the isotropic superfluid. This allows us to reconcile the value and doping dependence of the superfluid density slope at low temperature obtained from penetration depth measurements, with photoemission data on nodal quasiparticles.Comment: 5 latex pages, 1 eps-figure. submitted to PR

Pairing symmetry and long range pair potential in a weak coupling theory of superconductivity

We study the superconducting phase with two component order parameter scenario, such as, $d_{x^2-y^2} + e^{i\theta}s_{\alpha}$, where $\alpha = xy, x^2+y^2$. We show, that in absence of orthorhombocity, the usual $d_{x^2-y^2}$ does not mix with usual $s_{x^2+y^2}$ symmetry gap in an anisotropic band structure. But the $s_{xy}$ symmetry does mix with the usual d-wave for $\theta =0$. The d-wave symmetry with higher harmonics present in it also mixes with higher order extended $s$ wave symmetry. The required pair potential to obtain higher anisotropic $d_{x^2-y^2}$ and extended s-wave symmetries, is derived by considering longer ranged two-body attractive potential in the spirit of tight binding lattice. We demonstrate that the dominant pairing symmetry changes drastically from $d$ to $s$ like as the attractive pair potential is obtained from longer ranged interaction. More specifically, a typical length scale of interaction $\xi$, which could be even/odd multiples of lattice spacing leads to predominant $s/d$ wave symmetry. The role of long range interaction on pairing symmetry has further been emphasized by studying the typical interplay in the temperature dependencies of these higher order $d$ and $s$ wave pairing symmetries.Comment: Revtex 8 pages, 7 figures embeded in the text, To appear in PR

Quantum mechanics: Myths and facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.Comment: 51 pages, pedagogic review, revised, new references, to appear in Found. Phy

Quantum mechanical effect of path-polarization contextuality for a single photon

Using measurements pertaining to a suitable Mach-Zehnder(MZ) type setup, a curious quantum mechanical effect of contextuality between the path and the polarization degrees of freedom of a polarized photon is demonstrated, without using any notion of realism or hidden variables - an effect that holds good for the product as well as the entangled states. This form of experimental context-dependence is manifested in a way such that at \emph{either} of the two exit channels of the MZ setup used, the empirically verifiable \emph{subensemble} statistical properties obtained by an arbitrary polarization measurement depend upon the choice of a commuting(comeasurable) path observable, while this effect disappears for the \emph{whole ensemble} of photons emerging from the two exit channels of the MZ setup.Comment: To be published in IJT

Patient-specific Alzheimer-like pathology in trisomy 21 cerebral organoids reveals BACE2 as a gene dose-sensitive AD suppressor in human brain

A population of >6 million people worldwide at high risk of Alzheimer’s disease (AD) are those with Down Syndrome (DS, caused by trisomy 21 (T21)), 70% of whom develop dementia during lifetime, caused by an extra copy of β-amyloid-(Aβ)-precursor-protein gene. We report AD-like pathology in cerebral organoids grown in vitro from non-invasively sampled strands of hair from 71% of DS donors. The pathology consisted of extracellular diffuse and fibrillar Aβ deposits, hyperphosphorylated/pathologically conformed Tau, and premature neuronal loss. Presence/absence of AD-like pathology was donor-specific (reproducible between individual organoids/iPSC lines/experiments). Pathology could be triggered in pathology-negative T21 organoids by CRISPR/Cas9-mediated elimination of the third copy of chromosome-21-gene BACE2, but prevented by combined chemical β and γ-secretase inhibition. We found that T21-organoids secrete increased proportions of Aβ-preventing (Aβ1-19) and Aβ-degradation products (Aβ1-20 and Aβ1-34). We show these profiles mirror in cerebrospinal fluid of people with DS. We demonstrate that this protective mechanism is mediated by BACE2-trisomy and cross-inhibited by clinically trialled BACE1-inhibitors. Combined, our data prove the physiological role of BACE2 as a dose-sensitive AD-suppressor gene, potentially explaining the dementia delay in ~30% of people with DS. We also show that DS cerebral organoids could be explored as pre-morbid AD-risk population detector and a system for hypothesis-free drug screens as well as identification of natural suppressor genes for neurodegenerative diseases

Microwave determination of the quasiparticle scattering time in YBa2Cu3O6.95

We report microwave surface resistance (Rs) measurements on two very-high-quality YBa2Cu3O6.95 crystals which exhibit extremely low residual loss at 1.2 K (2-6 μΩ at 2 GHz), a broad, reproducible peak at around 38 K, and a rapid increase in loss, by 4 orders of magnitude, between 80 and 93 K. These data provide one ingredient in the determination of the temperature dependence of the real part of the microwave conductivity, σ1(T), and of the quasiparticle scattering time. The other necessary ingredient is an accurate knowledge of the magnitude and temperature dependence of the London penetration depth, λ(T). This is derived from published data, from microwave data of Anlage, Langley, and co-workers and from, high-quality μSR data. We infer, from a careful analysis of all available data, that λ2(0)/λ2(T) is well approximated by the simple function 1-t2, where t=T/Tc, and that the low-temperature data are incompatible with the existence of an s-wave, BCS-like gap. Combining the Rs and λ(T) data, we find that σ1(T), has a broad peak around 32 K with a value about 20 times that at Tc. Using a generalized two-fluid model, we extract the temperature dependence of the quasiparticle scattering rate which follows an exponential law, exp(T/T0), where T0≊12 K, for T between 15 and 84 K. Such a temperature dependence has previously been observed in measurements of the nuclear spin-lattice relaxation rate. Both the uncertainties in our analysis and the implications for the mechanism of high-temperature superconductivity are discussed

The ecogenetic link between demography and evolution : can we bridge the gap between theory and data?

Calls to understand the links between ecology and evolution have been common for decades. Population dynamics, i.e. the demographic changes in populations, arise from life history decisions of individuals and thus are a product of selection, and selection, on the contrary, can be modified by such dynamical properties of the population as density and stability. It follows that generating predictions and testing them correctly requires considering this ecogenetic feedback loop whenever traits have demographic consequences, mediated via density dependence (or frequency dependence). This is not an easy challenge, and arguably theory has advanced at a greater pace than empirical research. However, theory would benefit from more interaction between related fields, as is evident in the many near-synonymous names that the ecogenetic loop has attracted. We also list encouraging examples where empiricists have shown feasible ways of addressing the question, ranging from advanced data analysis to experiments and comparative analyses of phylogenetic data