Secret-Sharing for NP

A computational secret-sharing scheme is a method that enables a dealer, that has a secret, to distribute this secret among a set of parties such that a "qualified" subset of parties can efficiently reconstruct the secret while any "unqualified" subset of parties cannot efficiently learn anything about the secret. The collection of "qualified" subsets is defined by a Boolean function. It has been a major open problem to understand which (monotone) functions can be realized by a computational secret-sharing schemes. Yao suggested a method for secret-sharing for any function that has a polynomial-size monotone circuit (a class which is strictly smaller than the class of monotone functions in P). Around 1990 Rudich raised the possibility of obtaining secret-sharing for all monotone functions in NP: In order to reconstruct the secret a set of parties must be "qualified" and provide a witness attesting to this fact. Recently, Garg et al. (STOC 2013) put forward the concept of witness encryption, where the goal is to encrypt a message relative to a statement "x in L" for a language L in NP such that anyone holding a witness to the statement can decrypt the message, however, if x is not in L, then it is computationally hard to decrypt. Garg et al. showed how to construct several cryptographic primitives from witness encryption and gave a candidate construction. One can show that computational secret-sharing implies witness encryption for the same language. Our main result is the converse: we give a construction of a computational secret-sharing scheme for any monotone function in NP assuming witness encryption for NP and one-way functions. As a consequence we get a completeness theorem for secret-sharing: computational secret-sharing scheme for any single monotone NP-complete function implies a computational secret-sharing scheme for every monotone function in NP

Chiral crystals in strong-coupling lattice QCD at nonzero chemical potential

We study the effective action for strong-coupling lattice QCD with one-component staggered fermions in the case of nonzero chemical potential and zero temperature. The structure of this action suggests that at large chemical potentials its ground state is a crystalline `chiral density wave' that spontaneously breaks chiral symmetry and translation invariance. In mean-field theory, on the other hand, we find that this state is unstable. We show that lattice artifacts are partly responsible for this, and suggest that if this phase exists in QCD, then finding it in Monte-Carlo simulations would require simulating on relatively fine lattices. In particular, the baryon mass in lattice units, m_B, should be considerably smaller than its strong-coupling limit of m_B~3.Comment: 33 pages, 8 figure

Lineage tree analysis of immunoglobulin variable-region gene mutations in autoimmune diseases: chronic activation, normal selection

Autoimmune diseases show high diversity in the affected organs, clinical manifestations and disease dynamics. Yet they all share common features, such as the ectopic germinal centers found in many affected tissues. Lineage trees depict the diversification, via somatic hypermutation (SHM), of immunoglobulin variable-region (IGV) genes. We previously developed an algorithm for quantifying the graphical properties of IGV gene lineage trees, allowing evaluation of the dynamical interplay between SHM and antigen-driven selection in different lymphoid tissues, species, and disease situations. Here, we apply this method to ectopic GC B cell clones from patients with Myasthenia Gravis, Rheumatoid Arthritis, and Sjögren’s Syndrome, using data scaling to minimize the effects of the large variability due to methodological differences between groups. Autoimmune trees were found to be significantly larger relative to normal controls. In contrast, comparison of the measurements for tree branching indicated that similar selection pressure operates on autoimmune and normal control clones

Modeling Substitution Errors in Spanish Morphology Learning

In early stages of language acquisition, children often make inflectional errors on regular verbs, e.g., Spanish-speaking children produce –a (present-tense 3rd person singular) when other inflections are expected. Most previous models of morphology learning have focused on later stages of learning relating to productionof irregular verbs. We propose a computational model of Spanish inflection learning to examine the earlier stages of learning and present a novel data set of gold-standard inflectional annotations for Spanish verbs. Our model replicatesdata from Spanish-learning children, capturing the acquisition order of different inflections and correctly predicting the substitution errors they make. Analyses show that the learning trajectory can be explained as a result of the gradualacquisition of inflection-meaning associations. Ours is the first computational model to provide an explanation for this acquisition trajectory in Spanish, and represents a theoretical advance more generally in explaining substitution errors in early morphology learning

Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics

We show that under variation of moduli fields $\phi$ the first law of black hole thermodynamics becomes $dM = {\kappa dA\over 8\pi} + \Omega dJ + \psi dq + \chi dp - \Sigma d\phi$, where $\Sigma$ are the scalar charges. We also show that the ADM mass is extremized at fixed $A$, $J$, $(p,q)$ when the moduli fields take the fixed value $\phi_{\rm fix}(p,q)$ which depend only on electric and magnetic charges. It follows that the least mass of any black hole with fixed conserved electric and magnetic charges is given by the mass of the double-extreme black hole with these charges. Our work allows us to interpret the previously established result that for all extreme black holes the moduli fields at the horizon take a value $\phi= \phi_{\rm fix}(p,q)$ depending only on the electric and magnetic conserved charges: $\phi_{\rm fix}(p,q)$ is such that the scalar charges $\Sigma ( \phi_{\rm fix}, (p,q))=0$.Comment: 3 pages, no figures, more detailed versio

Efficient routing of single photons by one atom and a microtoroidal cavity

Single photons from a coherent input are efficiently redirected to a separate output by way of a fiber-coupled microtoroidal cavity interacting with individual Cesium atoms. By operating in an overcoupled regime for the input-output to a tapered fiber, our system functions as a quantum router with high efficiency for photon sorting. Single photons are reflected and excess photons transmitted, as confirmed by observations of photon antibunching (bunching) for the reflected (transmitted) light. Our photon router is robust against large variations of atomic position and input power, with the observed photon antibunching persisting for intracavity photon number 0.03 \lesssim n \lesssim 0.7

Fertilization and early embryology: Use of lasers in assisted fertilization and hatching

The erbium-yttrium-aluminium-garnet (Er: YAG) laser has been applied to micromanipulation in humans. It was used in the fertilization process for both subzonal insemination (SUZI) and for partial zona dissection (PZD). Laser-assisted micromanipulation achieved significantly higher fertilization rates (34.8%) when compared to mechanical SUZI (16.1%), but use of the laser did not improve the PZD results (laser 14.8% versus mechanical 14%). The Er: YAG laser was used to assist hatching. In the mouse it significantly improved the hatching rate (80 versus 29.3%) 110 h after administration of human chorionic gonadotrophin. This technique was applied in two different centres to patients with previous in-vitro fertilization (IVF) failures. The implantation rate per embryo (14.4% laser-assisted hatching versus 6% control group) and the pregnancy rate per transfer (40 versus 16.2%) were improve

Structure of the Phase in Pure Two-Mode Gaussian States

The two-mode relative phase associated with Gaussian states plays an important role in quantum information processes in optical, atomic and electronic systems. In this work, the origin and structure of the two-mode relative phase in pure Gaussian states is studied in terms of its dependences on the quadratures of the modes. This is done by constructing local canonical transformations to an associated two-mode squeezed state. The results are illustrated by studying the time dependence of the phase under a nonlocal unitary model evolution containing correlations between the modes. In a more general context, this approach may allow the two-mode phase to be studied in situations sensitive to different physical parameters within experimental configurations relevant to quantum information processing tasks

A Slow Axon Antidromic Blockade Hypothesis for Tremor Reduction via Deep Brain Stimulation

Parkinsonian and essential tremor can often be effectively treated by deep brain stimulation. We propose a novel explanation for the mechanism by which this technique ameliorates tremor: a reduction of the delay in the relevant motor control loops via preferential antidromic blockade of slow axons. The antidromic blockade is preferential because the pulses more rapidly clear fast axons, and the distribution of axonal diameters, and therefore velocities, in the involved tracts, is sufficiently long-tailed to make this effect quite significant. The preferential blockade of slow axons, combined with gain adaptation, results in a reduction of the mean delay in the motor control loop, which serves to stabilize the feedback system, thus ameliorating tremor. This theory, without any tuning, accounts for several previously perplexing phenomena, and makes a variety of novel predictions