The Computational Power of Beeps

In this paper, we study the quantity of computational resources (state machine states and/or probabilistic transition precision) needed to solve specific problems in a single hop network where nodes communicate using only beeps. We begin by focusing on randomized leader election. We prove a lower bound on the states required to solve this problem with a given error bound, probability precision, and (when relevant) network size lower bound. We then show the bound tight with a matching upper bound. Noting that our optimal upper bound is slow, we describe two faster algorithms that trade some state optimality to gain efficiency. We then turn our attention to more general classes of problems by proving that once you have enough states to solve leader election with a given error bound, you have (within constant factors) enough states to simulate correctly, with this same error bound, a logspace TM with a constant number of unary input tapes: allowing you to solve a large and expressive set of problems. These results identify a key simplicity threshold beyond which useful distributed computation is possible in the beeping model.Comment: Extended abstract to appear in the Proceedings of the International Symposium on Distributed Computing (DISC 2015

Sequence correlations shape protein promiscuity

We predict analytically that diagonal correlations of amino acid positions within protein sequences statistically enhance protein propensity for nonspecific binding. We use the term 'promiscuity' to describe such nonspecific binding. Diagonal correlations represent statistically significant repeats of sequence patterns where amino acids of the same type are clustered together. The predicted effect is qualitatively robust with respect to the form of the microscopic interaction potentials and the average amino acid composition. Our analytical results provide an explanation for the enhanced diagonal correlations observed in hubs of eukaryotic organismal proteomes [J. Mol. Biol. 409, 439 (2011)]. We suggest experiments that will allow direct testing of the predicted effect

Correlated Multiphoton Holes

We generate bipartite states of light which exhibit an absence of multiphoton coincidence events between two modes amid a constant background flux. These `correlated photon holes' are produced by mixing a coherent state and relatively weak spontaneous parametric down-conversion using a balanced beamsplitter. Correlated holes with arbitrarily high photon numbers may be obtained by adjusting the relative phase and amplitude of the inputs. We measure states of up to five photons and verify their nonclassicality. The scheme provides a route for observation of high-photon-number nonclassical correlations without requiring intense quantum resources.Comment: 4 pages, 3 figures, comments are welcom

Quantum state measurements using multi-pixel photon detectors

The characterization and conditional preparation of multi-photon quantum states requires the use of photon number resolving detectors. We study the use of detectors based on multiple avalanche photodiode pixels in this context. We develop a general model that provides the positive operator value measures for these detectors. The model incorporates the effect of cross-talk between pixels which is unique to these devices. We validate the model by measuring coherent state photon number distributions and reconstructing them with high precision. Finally, we evaluate the suitability of such detectors for quantum state tomography and entanglement-based quantum state preparation, highlighting the effects of dark counts and cross-talk between pixels.Comment: 7 pages, 6 figure

Void Formation and Roughening in Slow Fracture

Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Post mortem analysis of the resulting fracture surfaces of ductile and brittle materials on the $\mu$m-mm and the nm scales respectively, reveals self-affine cracks with anomalous scaling exponent $\zeta\approx 0.8$ in 3-dimensions and $\zeta\approx 0.65$ in 2-dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation and the fracture growth, culminating in estimates of the roughening exponents in 2-dimensions. In the simplest realization of the model we allow one void ahead of the crack, and address the robustness of the roughening exponent. Next we develop the theory further, to include two voids ahead of the crack. This development necessitates generalizing the method of iterated conformal maps to include doubly connected regions (maps from the annulus rather than the unit circle). While mathematically and numerically feasible, we find that the employment of the stress field as computed from elasticity theory becomes questionable when more than one void is explicitly inserted into the material. Thus further progress in this line of research calls for improved treatment of the plastic dynamics.Comment: 15 pages, 20 figure

Collective behaviour of partons could be a source of energetic hadrons

We discuss the idea that collective behaviour of the quarks/partons, which has been intensely discussed for the last 40 years in relativistic hadron-nuclear and nuclear-nuclear interactions and confirmed by new data coming from the ultrarelativistic heavy ion collisions, can lead to energetic particle production. Created from hadronization of the quark/parton (or quarks/partons), energetic particles could get the energy of grouped partons from coherent interactions. Therefore, we think that in the centre of some massive stars, a medium with high density, close to Quantum Chromodynamic one could be a source of the super high-energy cosmic rays.Comment: 8 pages, 8 figure

Entanglement-enhanced probing of a delicate material system

Quantum metrology uses entanglement and other quantum effects to improve the sensitivity of demanding measurements. Probing of delicate systems demands high sensitivity from limited probe energy and has motivated the field's key benchmark-the standard quantum limit. Here we report the first entanglement-enhanced measurement of a delicate material system. We non-destructively probe an atomic spin ensemble by means of near-resonant Faraday rotation, a measurement that is limited by probe-induced scattering in quantum-memory and spin-squeezing applications. We use narrowband, atom-resonant NOON states to beat the standard quantum limit of sensitivity by more than five standard deviations, both on a per-photon and per-damage basis. This demonstrates quantum enhancement with fully realistic loss and noise, including variable-loss effects. The experiment opens the way to ultra-gentle probing of single atoms, single molecules, quantum gases and living cells.Comment: 7 pages, 8 figures; Nature Photonics, advance online publication, 16 December 201

How Many Cooks Spoil the Soup?

In this work, we study the following basic question: "How much parallelism does a distributed task permit?" Our definition of parallelism (or symmetry) here is not in terms of speed, but in terms of identical roles that processes have at the same time in the execution. We initiate this study in population protocols, a very simple model that not only allows for a straightforward definition of what a role is, but also encloses the challenge of isolating the properties that are due to the protocol from those that are due to the adversary scheduler, who controls the interactions between the processes. We (i) give a partial characterization of the set of predicates on input assignments that can be stably computed with maximum symmetry, i.e., $\Theta(N_{min})$, where $N_{min}$ is the minimum multiplicity of a state in the initial configuration, and (ii) we turn our attention to the remaining predicates and prove a strong impossibility result for the parity predicate: the inherent symmetry of any protocol that stably computes it is upper bounded by a constant that depends on the size of the protocol.Comment: 19 page

Quantum-Dense Metrology

Quantum metrology utilizes entanglement for improving the sensitivity of measurements. Up to now the focus has been on the measurement of just one out of two non-commuting observables. Here we demonstrate a laser interferometer that provides information about two non-commuting observables, with uncertainties below that of the meter's quantum ground state. Our experiment is a proof-of-principle of quantum dense metrology, and uses the additional information to distinguish between the actual phase signal and a parasitic signal due to scattered and frequency shifted photons. Our approach can be readily applied to improve squeezed-light enhanced gravitational-wave detectors at non-quantum noise limited detection frequencies in terms of a sub shot-noise veto-channel.Comment: 5 pages, 3 figures; includes supplementary material

Statistical Physics of Fracture Surfaces Morphology

Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich phenomenology of anomalous scaling. We argue that traditional models of fracture fail to reproduce this rich phenomenology and new ideas and concepts are called for. We present some recent models that introduce the effects of deviations from homogeneous linear elasticity theory on the morphology of fracture surfaces, succeeding to reproduce the multiscaling phenomenology at least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel methods of analysis based on projecting the data on the irreducible representations of the SO(2) symmetry group. It appears that this approach organizes effectively the rich scaling properties. We end up with the proposition of new experiments in which the rotational symmetry is not broken, such that the scaling properties should be particularly simple.Comment: A review paper submitted to J. Stat. Phy