Osculating and neighbour-avoiding polygons on the square lattice

We study two simple modifications of self-avoiding polygons. Osculating polygons are a super-set in which we allow the perimeter of the polygon to touch at a vertex. Neighbour-avoiding polygons are only allowed to have nearest neighbour vertices provided these are joined by the associated edge and thus form a sub-set of self-avoiding polygons. We use the finite lattice method to count the number of osculating polygons and neighbour-avoiding polygons on the square lattice. We also calculate their radius of gyration and the first area-weighted moment. Analysis of the series confirms exact predictions for the critical exponents and the universality of various amplitude combinations. For both cases we have found exact solutions for the number of convex and almost-convex polygons.Comment: 14 pages, 5 figure

Configuration-Space Location of the Entanglement between Two Subsystems

In this paper we address the question: where in configuration space is the entanglement between two particles located? We present a thought-experiment, equally applicable to discrete or continuous-variable systems, in which one or both parties makes a preliminary measurement of the state with only enough resolution to determine whether or not the particle resides in a chosen region, before attempting to make use of the entanglement. We argue that this provides an operational answer to the question of how much entanglement was originally located within the chosen region. We illustrate the approach in a spin system, and also in a pair of coupled harmonic oscillators. Our approach is particularly simple to implement for pure states, since in this case the sub-ensemble in which the system is definitely located in the restricted region after the measurement is also pure, and hence its entanglement can be simply characterised by the entropy of the reduced density operators. For our spin example we present results showing how the entanglement varies as a function of the parameters of the initial state; for the continuous case, we find also how it depends on the location and size of the chosen regions. Hence we show that the distribution of entanglement is very different from the distribution of the classical correlations.Comment: RevTex, 12 pages, 9 figures (28 files). Modifications in response to journal referee

Temporal Feedback for Tweet Search with Non-Parametric Density Estimation

This paper investigates the temporal cluster hypothesis: in search tasks where time plays an important role, do relevant documents tend to cluster together in time? We explore this question in the context of tweet search and temporal feedback: starting with an initial set of results from a baseline retrieval model, we estimate the temporal density of relevant documents, which is then used for result reranking. Our contributions lie in a method to characterize this temporal density function using kernel density estimation, with and without human relevance judgments, and an approach to integrating this information into a standard retrieval model. Experiments on TREC datasets confirm that our temporal feedback formulation improves search effectiveness, thus providing support for our hypothesis. Our approach outperforms both a standard baseline and previous temporal retrieval models. Temporal feedback improves over standard lexical feedback (with and without human judgments), illustrating that temporal relevance signals exist independently of document content

Exact Scaling Functions for Self-Avoiding Loops and Branched Polymers

It is shown that a recently conjectured form for the critical scaling function for planar self-avoiding polygons weighted by their perimeter and area also follows from an exact renormalization group flow into the branched polymer problem, combined with the dimensional reduction arguments of Parisi and Sourlas. The result is generalized to higher-order multicritical points, yielding exact values for all their critical exponents and exact forms for the associated scaling functions.Comment: 5 pages; v2: factors of 2 corrected; v.3: relation with existing theta-point results clarified, some references added/update

On the critical condition in gravitational shock wave collision and heavy ion collisions

In this paper, we derived a critical condition for matter equilibration in heavy ion collisions using a holographic approach. A gravitational shock waves with infinite transverse extension is used to model infinite nucleus. We constructed the trapped surface in the collision of two asymmetric planar shock waves with sources at different depth in the bulk AdS and formulated a critical condition for matter equilibration in collision of "nucleus" in the dual gauge theory. We found the critical condition is insensitive to the depth of the source closer to the AdS boundary. To understand the origin of the critical condition, we computed the Next to Leading Order stress tensor in the boundary field theory due to the interaction of the nucleus and found the critical condition corresponds to the breaking down of the perturbative expansion. We indeed expect non-perturbative effects be needed to describe black hole formation.Comment: 26 pages, 3 figure

The z < 1.2 optical luminosity function from a sample of ∼410,000 galaxies in Boötes

Using a sample of ~410,000 galaxies to a depth of IAB=24 over 8.26 deg2 in the Boötes field (~10 times larger than the z~1 luminosity function (LF) studies in the prior literature), we have accurately measured the evolving B-band LF of red galaxies at z&lt;1.2 and blue galaxies at z&lt;1.0 In addition to the large sample size, we utilize photometry that accounts for the varying angular sizes of galaxies, photometric redshifts verified with spectroscopy, and absolute magnitudes that should have very small random and systematic errors. Our results are consistent with the migration of galaxies from the blue cloud to the red sequence as they cease to form stars and with downsizing in which more massive and luminous blue galaxies cease star formation earlier than fainter less massive ones. Comparing the observed fading of red galaxies with that expected from passive evolution alone, we find that the stellar mass contained within the red galaxy population has increased by a factor of ~3.6 from z~1.1 to z~0.1 The bright end of the red galaxy LF fades with decreasing redshift, with the rate of fading increasing from ~0.2 mag per unit redshift at z = 1.0 to ~0.8 at z = 0.2. The overall decrease in luminosity implies that the stellar mass in individual highly luminous red galaxies increased by a factor of ~2.2 from z = 1.1 to z = 0.1