• Open Access close
• National Science Foundation close

In this article, we prove the finite dimensionality of the global attractor and estimate the numbers of the determining modes for the 2D Boussinesq system in a periodic channel with fractional Laplacian in subcritical case.

We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs. Our first result is a deterministic approximation scheme (an FPTAS) for the partition function in bounded degree graphs that is valid over the entire range of parameters $\beta$ (the interaction) and $\lambda$ (the external field), except for the case $\vert{\lambda}\vert=1$ (the "zero-field" case). A randomized algorithm (FPRAS) for all graphs, and all $\beta,\lambda$, has long been known. Unlike most other deterministic approximation algorithms for problems in statistical physics and counting, our algorithm does not rely on the "decay of correlations" property. Rather, we exploit and extend machinery developed recently by Barvinok, and Patel and Regts, based on the location of the complex zeros of the partition function, which can be seen as an algorithmic realization of the classical Lee-Yang approach to phase transitions. Our approach extends to the more general setting of the Ising model on hypergraphs of bounded degree and edge size, where no previous algorithms (even randomized) were known for a wide range of parameters. In order to achieve this extension, we establish a tight version of the Lee-Yang theorem for the Ising model on hypergraphs, improving a classical result of Suzuki and Fisher. Comment: clarified presentation of combinatorial arguments, added new results on optimality of univariate Lee-Yang theorems

Since its discovery in 2008, the Andromeda galaxy nova M31N 2008-12a has been observed in eruption every single year. This unprecedented frequency indicates an extreme object, with a massive white dwarf and a high accretion rate, which is the most promising candidate for the single-degenerate progenitor of a type-Ia supernova known to date. The previous three eruptions of M31N 2008-12a have displayed remarkably homogeneous multi-wavelength properties: (i) From a faint peak, the optical light curve declined rapidly by two magnitudes in less than two days; (ii) Early spectra showed initial high velocities that slowed down significantly within days and displayed clear He/N lines throughout; (iii) The supersoft X-ray source (SSS) phase of the nova began extremely early, six days after eruption, and only lasted for about two weeks. In contrast, the peculiar 2016 eruption was clearly different. Here we report (i) the considerable delay in the 2016 eruption date, (ii) the significantly shorter SSS phase, and (iii) the brighter optical peak magnitude (with a hitherto unobserved cusp shape). Early theoretical models suggest that these three different effects can be consistently understood as caused by a lower quiescence mass-accretion rate. The corresponding higher ignition mass caused a brighter peak in the free-free emission model. The less-massive accretion disk experienced greater disruption, consequently delaying re-establishment of effective accretion. Without the early refueling, the SSS phase was shortened. Observing the next few eruptions will determine whether the properties of the 2016 outburst make it a genuine outlier in the evolution of M31N 2008-12a. 42 pages (28 pages main paper + appendix), 16 figures, 10 tables; accepted for publication in ApJ

Abstract One of the classical approaches for estimating the frequencies and damping factors in a spectrally sparse signal is the MUltiple SIgnal Classification (MUSIC) algorithm, which exploits the low-rank structure of an autocorrelation matrix. Low-rank matrices have also received considerable attention recently in the context of optimization algorithms with partial observations, and nuclear norm minimization (NNM) has been widely used as a popular heuristic of rank minimization for low-rank matrix recovery problems. On the other hand, it has been shown that NNM can be viewed as a special case of atomic norm minimization (ANM), which has achieved great success in solving line spectrum estimation problems. However, as far as we know, the general ANM (not NNM) considered in many existing works can only handle frequency estimation in undamped sinusoids. In this work, we aim to fill this gap and deal with damped spectrally sparse signal recovery problems. In particular, inspired by the dual analysis used in ANM, we offer a novel optimization-based perspective on the classical MUSIC algorithm and propose an algorithm for spectral estimation that involves searching for the peaks of the dual polynomial corresponding to a certain NNM problem, and we show that this algorithm is in fact equivalent to MUSIC itself. Building on this connection, we also extend the classical MUSIC algorithm to the missing data case. We provide exact recovery guarantees for our proposed algorithms and quantify how the sample complexity depends on the true spectral parameters. In particular, we provide a parameter-specific recovery bound for low-rank matrix recovery of jointly sparse signals rather than use certain incoherence properties as in existing literature. Simulation results also indicate that the proposed algorithms significantly outperform some relevant existing methods (e.g., ANM) in frequency estimation of damped exponentials.

We investigate, for two water models displaying a liquid-liquid critical point, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid-liquid critical point. We find a correlation between the dynamic fragility transition and the locus of specific heat maxima $C_P^{\rm max}$ (``Widom line'') emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid-liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between $C_P^{\rm max}$ and dynamic crossover is not limited to the case of water, a hydrogen bond network forming liquid, but is a more general feature of crossing the Widom line. Specifically, we also study the Jagla potential, a spherically-symmetric two-scale potential known to possess a liquid-liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions. Comment: 6 pages and 5 figures

In this paper, we describe a new method for measuring surviving neutrons in neutron lifetime measurements using bottled ultracold neutrons (UCN), which provides better characterization of systematic uncertainties and enables higher precision than previous measurement techniques. An active detector that can be lowered into the trap has been used to measure the neutron distribution as a function of height and measure the influence of marginally trapped UCN on the neutron lifetime measurement. In addition, measurements have demonstrated phase-space evolution and its effect on the lifetime measurement. (C) 2017 Author(s). Los Alamos LDRD office; Department of Energy; National Science Foundation [1307426, 1553861]; DOE Low Energy Nuclear Physics [DE-FG02-97ER41042]; U.S. Department of Energy [DE-AC05-00OR22725]; United States Government This work was supported by the Los Alamos LDRD office, the Department of Energy, the National Science Foundation (Nos. 1307426 and 1553861), and DOE Low Energy Nuclear Physics (No. DE-FG02-97ER41042). The authors would like to thank the staff of LANSCE for their diligent efforts to develop the diagnostics and new techniques required to provide beam for this experiment.; This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

Average consensus underpins key functionalities of distributed systems ranging from distributed information fusion, decision-making, distributed optimization, to load balancing and decentralized control. Existing distributed average consensus algorithms require each node to exchange and disclose state information to its neighbors, which is undesirable in cases where the state is private or contains sensitive information. In this paper, we propose a novel approach that avoids disclosing individual state information in average consensus by letting each node decompose its state into two sub-states. For each node, one of the two sub-states involves in computation and inter-node interactions as if it were the original state, while the other sub-state interacts only with the first sub-state of the same node, being completely invisible to other nodes. The initial values of the two sub-states are chosen randomly but with their mean fixed to the initial value of the original state, which is key to guarantee convergence to the desired consensus value. In direct contrast to differential-privacy based privacy-preserving average-consensus approaches which enable privacy by compromising accuracy in the consensus value, the proposed approach can guarantee convergence to the \emph{exact} desired value without any error. Not only is the proposed approach able to prevent the disclosure of a node's initial state to honest-but-curious neighbors, it can also provide protection against inference by external eavesdroppers able to wiretap communication links. Numerical simulations demonstrate the effectiveness of the approach and its advantages over state-of-the-art counterparts. Comment: accepted to IEEE Transactions on Automatic Control

Attention-deficit/hyperactivity disorder (ADHD) is associated with neurobehavioral reward system dysfunctions that pose debilitating impairments in adaptive decision-making. A candidate mechanism for such anomalies in ADHD may be a compromise in the control of motivated behaviors. Thus, demonstrating and restoring potential motivational control irregularities may serve significant clinical benefit. The motivational control of action guides goal-directed behaviors that are driven by outcome value, and habits that are inflexibly cue-triggered. We examined whether ADHD symptomology within the general population is linked to habitual control, and whether a motivation-based manipulation can break well-learned habits. We obtained symptom severity scores from 106 participants and administered a Go/NoGo task that capitalizes on familiar, well-learned associations (green-Go and red-NoGo) to demonstrate outcome-insensitivity when compared to newly learned Go/NoGo associations. We tested for outcome-insensitive habits by changing the Go and NoGo contingencies, such that Go signals became NoGo signals and vice versa. We found that generally, participants responded less accurately when green and red stimuli were mapped to color-response contingencies that were incongruent with daily experiences, whereas novel Go/NoGo stimuli evoked similar accuracy regardless of color-response mappings. Thus, our Go/NoGo task successfully elicited outcome-insensitive habits (i.e., persistent responses to familiar stimuli without regard for consequences); however, this effect was independent of ADHD symptomology. Nevertheless, we found an association between hyperactivity and congruent Go response latency, suggesting heightened pre-potency to perform habitual Go actions as hyperactivity increases. To examine habit disruption, participants returned to the lab and underwent the familiar version of the Go/NoGo task, but were given mid-experiment performance tracking information and a monetary incentive prior to contingency change. We found that this motivational boost via dual feedback prevented the incongruency-related accuracy impairment, effectively breaking the habit, albeit independent of ADHD symptomology. Our findings present only a modest link between ADHD symptomology and motivational control, which may be due to compensatory mechanisms in ADHD driving goal-directed control, or our task's potential insensitivity to individual differences in ADHD symptomology. Further investigations may be crucial for determining whether ADHD is related to motivational impairments.

Abstract This paper is concerned with the phase estimation algorithm in quantum computing, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unitary operator is approximated by Trotter or Taylor expansion methods; (3) random approximations are used for the unitary operator. We characterize the probability of computing the phase values in terms of the consistency error, including the residual error, Trotter splitting error, or statistical mean-square error. In the first two cases, we show that in order to obtain the phase value with error less or equal to 2−n and probability at least 1 − ϵ, the required number of qubits is t ⩾ n + log 2 + δ 2 2 ϵ Δ E 2 . The parameter δ quantifies the error associated with the inexact eigenvector and/or the unitary operator, and ΔE characterizes the spectral gap, i.e., the separation from the rest of the phase values. This analysis generalizes the standard result (Cleve et al 1998 Phys. Rev X 11 011020; Nielsen and Chuang 2002 Quantum Computation and Quantum Information) by including these effects. More importantly, it shows that when δ < ΔE, the complexity remains the same. For the third case, we found a similar estimate, but the number of random steps has to be sufficiently large.

A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, with zero temperature boundary conditions at the walls. Starting from a positive initial temperature distribution in the interior, the goal is to flux the heat through the walls as efficiently as possible. Here we consider a distinct but closely related problem, that of the integrated mean exit time of Brownian particles starting inside the domain. Since flows favorable to rapid heat exchange should lower exit times, we minimize a norm of the exit time. This is a time-independent optimization problem that we solve analytically in some limits, and numerically otherwise. We find an (at least locally) optimal velocity field that cools the domain on a mechanical time scale, in the sense that the integrated mean exit time is independent on molecular diffusivity in the limit of large-energy flows. 16 pages, 5 figures. SIAM LaTeX style with custom margins. Fixed a few typos