On the dual post correspondence problem

The Dual Post Correspondence Problem asks whether, for a given word α, there exists a pair of distinct morphisms σ,τ, one of which needs to be non-periodic, such that σ(α) = τ(α) is satisfied. This problem is important for the research on equality sets, which are a vital concept in the theory of computation, as it helps to identify words that are in trivial equality sets only. Little is known about the Dual PCP for words α over larger than binary alphabets, especially for so-called ratio-primitive examples. In the present paper, we address this question in a way that simplifies the usual method, which means that we can reduce the intricacy of the word equations involved in dealing with the Dual PCP. Our approach yields large sets of words for which there exists a solution to the Dual PCP as well as examples of words over arbitrary alphabets for which such a solution does not exist

On the dual post correspondence problem

The Dual Post Correspondence Problem asks whether, for a given word α, there exists a pair of distinct morphisms σ, τ, one of which needs to be non-periodic, such that σ(α) = τ(α) is satisfied. This problem is important for the research on equality sets, which are a vital concept in the theory of computation, as it helps to identify words that are in trivial equality sets only. Little is known about the Dual PCP for words α over larger than binary alphabets. In the present paper, we address this question in a way that simplifies the usual method, which means that we can reduce the intricacy of the word equations involved in dealing with the Dual PCP. Our approach yields large sets of words for which there exists a solution to the Dual PCP as well as examples of words over arbitrary alphabets for which such a solution does not exist

On the Dual Post Correspondence Problem

The Dual Post Correspondence Problem asks whether, for a given word α, there exists a pair of distinct morphisms σ,τ, one of which needs to be non-periodic, such that σ(α) = τ(α) is satisfied. This problem is important for the research on equality sets, which are a vital concept in the theory of computation, as it helps to identify words that are in trivial equality sets only. Little is known about the Dual PCP for words α over larger than binary alphabets, especially for so-called ratio-primitive examples. In the present paper, we address this question in a way that simplifies the usual method, which means that we can reduce the intricacy of the word equations involved in dealing with the Dual PCP. Our approach yields large sets of words for which there exists a solution to the Dual PCP as well as examples of words over arbitrary alphabets for which such a solution does not exist

Following the density perturbations through a bounce with AdS/CFT Correspondence

A bounce universe model, known as the coupled-scalar-tachyon bounce (CSTB) universe, has been shown to solve the Horizon, Flatness and Homogeneity problems as well as the Big Bang Singularity problem. Furthermore a scale invariant spectrum of primordial density perturbations generated from the phase of pre-bounce contraction is shown to be stable against time evolution. In this work we study the detailed dynamics of the bounce and its imprints on the scale invariance of the spectrum. The dynamics of the gravitational interactions near the bounce point may be strongly coupled as the spatial curvature becomes big. There is no a prior reason to expect the spectral index of the primordial perturbations of matter density can be preserved. By encoding the bounce dynamics holographically onto the dynamics of dual Yang-Mills system while the latter is weakly coupled, via the AdS/CFT correspondence, we can safely evolve the spectrum of the cosmic perturbations with full control. In this way we can compare the post-bounce spectrum with the pre-bounce one: in the CSTB model we explicitly show that the spectrum of primordial density perturbations generated in the contraction phase preserves its stability as well as scale invariance throughout the bounce process.Comment: 19 pages, 4 figure

Fast plunges into Kerr black holes

Most extreme-mass-ratio-inspirals of small compact objects into supermassive black holes end with a fast plunge from an eccentric last stable orbit. For rapidly rotating black holes such fast plunges may be studied in the context of the Kerr/CFT correspondence because they occur in the near-horizon region where dynamics are governed by the infinite dimensional conformal symmetry. In this paper we use conformal transformations to analytically solve for the radiation emitted from fast plunges into near-extreme Kerr black holes. We find perfect agreement between the gravity and CFT computations.Comment: 16 pages, 2 figure

Precise motion descriptors extraction from stereoscopic footage using DaVinci DM6446

A novel approach to extract target motion descriptors in multi-camera video surveillance systems is presented. Using two static surveillance cameras with partially overlapped field of view (FOV), control points (unique points from each camera) are identified in regions of interest (ROI) from both cameras footage. The control points within the ROI are matched for correspondence and a meshed Euclidean distance based signature is computed. A depth map is estimated using disparity of each control pair and the ROI is graded into number of regions with the help of relative depth information of the control points. The graded regions of different depths will help calculate accurately the pace of the moving target and also its 3D location. The advantage of estimating a depth map for background static control points over depth map of the target itself is its accuracy and robustness to outliers. The performance of the algorithm is evaluated in the paper using several test sequences. Implementation issues of the algorithm onto the TI DaVinci DM6446 platform are considered in the paper

Gravity Waves from Kerr/CFT

Dynamics at large redshift near the horizon of an extreme Kerr black hole are governed by an infinite-dimensional conformal symmetry. This symmetry may be exploited to analytically, rather than numerically, compute a variety of potentially observable processes. In this paper we compute and study the conformal transformation properties of the gravitational radiation emitted by an orbiting mass in the large-redshift near-horizon region.Comment: 23 pages, v2: reference added, minor changes, matches published version, v3: typos correcte

Holographic Relaxation of Finite Size Isolated Quantum Systems

We study holographically the out of equilibrium dynamics of a finite size closed quantum system in 2+1 dimensions, modelled by the collapse of a shell of a massless scalar field in AdS4. In global coordinates there exists a variety of evolutions towards final black hole formation which we relate with different patterns of relaxation in the dual field theory. For large scalar initial data rapid thermalization is achieved as a priori expected. Interesting phenomena appear for small enough amplitudes. Such shells do not generate a black hole by direct collapse, but quite generically an apparent horizon emerges after enough bounces off the AdS boundary. We relate this bulk evolution with relaxation processes at strong coupling which delay in reaching an ergodic stage. Besides the dynamics of bulk fields, we monitor the entanglement entropy, finding that it oscillates quasi-periodically before final equilibration. The radial position of the traveling shell is brought into correspondence with the evolution of the entanglement pattern in the dual field theory. The entanglement entropy is not only able to portrait the streaming of entangled excitations, but it is also a useful probe of interaction effects.Comment: 37 pages, 27 figure