The Brownian Web: Characterization and Convergence

The Brownian Web (BW) is the random network formally consisting of the paths of coalescing one-dimensional Brownian motions starting from every space-time point in ${\mathbb R}\times{\mathbb R}$. We extend the earlier work of Arratia and of T\'oth and Werner by providing characterization and convergence results for the BW distribution, including convergence of the system of all coalescing random walkssktop/brownian web/finale/arXiv submits/bweb.tex to the BW under diffusive space-time scaling. We also provide characterization and convergence results for the Double Brownian Web, which combines the BW with its dual process of coalescing Brownian motions moving backwards in time, with forward and backward paths ``reflecting'' off each other. For the BW, deterministic space-time points are almost surely of ``type'' $(0,1)$ -- {\em zero} paths into the point from the past and exactly {\em one} path out of the point to the future; we determine the Hausdorff dimension for all types that actually occur: dimension 2 for type $(0,1)$, 3/2 for $(1,1)$ and $(0,2)$, 1 for $(1,2)$, and 0 for $(2,1)$ and $(0,3)$.Comment: 52 pages with 4 figure

A computationally efficacious free-energy functional for studies of inhomogeneous liquid water

We present an accurate equation of state for water based on a simple microscopic Hamiltonian, with only four parameters that are well-constrained by bulk experimental data. With one additional parameter for the range of interaction, this model yields a computationally efficient free-energy functional for inhomogeneous water which captures short-ranged correlations, cavitation energies and, with suitable long-range corrections, the non-linear dielectric response of water, making it an excellent candidate for studies of mesoscale water and for use in ab initio solvation methods.Comment: 6 pages, 5 figure

Single-Trial {MEG} Data Can Be Denoised Through Cross-Subject Predictive Modeling

A pervasive challenge in brain imaging is the presence of noise that hinders investigation of underlying neural processes, with Magnetoencephalography (MEG) in particular having very low Signal-to-Noise Ratio (SNR). The established strategy to increase MEG's SNR involves averaging multiple repetitions of data corresponding to the same stimulus. However, repetition of stimulus can be undesirable, because underlying neural activity has been shown to change across trials, and repeating stimuli limits the breadth of the stimulus space experienced by subjects. In particular, the rising popularity of naturalistic studies with a single viewing of a movie or story necessitates the discovery of new approaches to increase SNR. We introduce a simple framework to reduce noise in single-trial MEG data by leveraging correlations in neural responses across subjects as they experience the same stimulus. We demonstrate its use in a naturalistic reading comprehension task with 8 subjects, with MEG data collected while they read the same story a single time. We find that our procedure results in data with reduced noise and allows for better discovery of neural phenomena. As proof-of-concept, we show that the N400m's correlation with word surprisal, an established finding in literature, is far more clearly observed in the denoised data than the original data. The denoised data also shows higher decoding and encoding accuracy than the original data, indicating that the neural signals associated with reading are either preserved or enhanced after the denoising procedure

Randomness amplification against no-signaling adversaries using two devices

Recently, a physically realistic protocol amplifying the randomness of Santha-Vazirani sources producing cryptographically secure random bits was proposed; however for reasons of practical relevance, the crucial question remained open whether this can be accomplished under the minimal conditions necessary for the task. Namely, is it possible to achieve randomness amplification using only two no-signaling components and in a situation where the violation of a Bell inequality only guarantees that some outcomes of the device for specific inputs exhibit randomness? Here, we solve this question and present a device-independent protocol for randomness amplification of Santha-Vazirani sources using a device consisting of two non-signaling components. We show that the protocol can amplify any such source that is not fully deterministic into a fully random source while tolerating a constant noise rate and prove the composable security of the protocol against general no-signaling adversaries. Our main innovation is the proof that even the partial randomness certified by the two-party Bell test (a single input-output pair ($\textbf{u}^*, \textbf{x}^*$) for which the conditional probability $P(\textbf{x}^* | \textbf{u}^*)$ is bounded away from $1$ for all no-signaling strategies that optimally violate the Bell inequality) can be used for amplification. We introduce the methodology of a partial tomographic procedure on the empirical statistics obtained in the Bell test that ensures that the outputs constitute a linear min-entropy source of randomness. As a technical novelty that may be of independent interest, we prove that the Santha-Vazirani source satisfies an exponential concentration property given by a recently discovered generalized Chernoff bound.Comment: 15 pages, 3 figure

Dynamics of a spin-exchange model

AbstractWe study a model on the non-negative half line Z+0, {0, 1, 2, …} in which particles created at the origin at rate 1 jump to the right at rate 1. If a particle jumps onto an already occupied site the two particles annihilate each other. In addition, whenever a particle jumps its closest neighbor to the right jumps along with it. We find that the spatial decay rate of the particle density in the stationary state is of order 1√x at distance x from the origin. This model provides an approximation to the dynamics of an anchored Toom interface which can be represented as a spin-exchange model

Spin Decoherence from Hamiltonian dynamics in Quantum Dots

The dynamics of a spin-1/2 particle coupled to a nuclear spin bath through an isotropic Heisenberg interaction is studied, as a model for the spin decoherence in quantum dots. The time-dependent polarization of the central spin is calculated as a function of the bath-spin distribution and the polarizations of the initial bath state. For short times, the polarization of the central spin shows a gaussian decay, and at later times it revives displaying nonmonotonic time dependence. The decoherence time scale dep ends on moments of the bath-spin distribuition, and also on the polarization strengths in various bath-spin channels. The bath polarizations have a tendency to increase the decoherence time scale. The effective dynamics of the central spin polarization is shown to be describ ed by a master equation with non-markovian features.Comment: 11 pages, 6 figures Accepted for publication in Phys.Rev