Behavior of entanglement entropy near periodic orbits in a hamiltonian dynamical system

Entanglement entropy growth is studied under a form of dynamics that is based on iteration. This approach allows the investigation of the role of decoherence in producing increases of entropy. This has important consequences as far as the study of decoherence is concerned. It is indicated that results are generally independent of Hilbert space partitioning. It is seen that a deep relationship between classical dynamical entropy and the growth of entanglement entropy exists in this kind of model. The former acts to bound the latter and in the asymptotic region, they tend to a common limit.

Charge-Flow Profiles along Curvilinear Paths: A Flexible Scheme for the Analysis of Charge Displacement upon Intermolecular Interactions

The Charge-Displacement (CD) analysis has proven to be a powerful tool for a quantitative characterization of the electron-density flow occurring upon chemical bonding along a suitably chosen interaction axis. In several classes of interesting intermolecular interactions, however, an interaction axis cannot be straightforwardly defined, and the CD analysis loses consistency and usefulness. In this article, we propose a general, flexible reformulation of the CD analysis capable of providing a quantitative view of the charge displacement along custom curvilinear paths. The new scheme naturally reduces to ordinary CD analysis if the path is chosen to be a straight line. An implementation based on a discrete sampling of the electron densities and a Voronoi space partitioning is described and shown in action on two test cases of a metal-carbonyl and a pyridine-ammonia complex.

Testing Performance (Time Analysis) of Nearest Neighbour (NN) Search Algorithms on K-d Trees

K-d tree (k-dimensional tree) is a space partitioning data structure for organizing points in a k-dimensional space. K-d tree, or Multidimensional Binary Search Tree is a useful data structure for several applications such as searches involving a multidimensional search key (e.g., Range Search and Nearest Neighbour Search). K-d trees are a special case of binary space partitioning trees.KNN Search is a searching algorithm with complexity O(N log N) {N= no. of data points}. This search algorithm is relatively better than brute force search {Complexity= O(n*k); where k=No. of neighbours searched, N=No. of Data Points in Kd tree} for dimensions N>>2D {N=No. of Points, D=Dimensionality of Tree}.Furthermore, Parallel KNN Search is much more efficient and performs better than KNN Search, as it harnesses parallel processing capabilities of computers and thus, results in better search time.This paper tests the time performance of KNN Search and Parallel KNN Search and compares them by plotting it on a 3D graph. A more comprehensive comparison is done by use of 2D graphs for each dimension(from 2 to 20).

Improving the Effectiveness and Efficiency of Stochastic Neighbour Embedding with Isolation Kernel

This paper presents a new insight into improving the performance of Stochastic Neighbour Embedding (t-SNE) by using Isolation kernel instead of Gaussian kernel. Isolation kernel outperforms Gaussian kernel in two aspects. First, the use of Isolation kernel in t-SNE overcomes the drawback of misrepresenting some structures in the data, which often occurs when Gaussian kernel is applied in t-SNE. This is because Gaussian kernel determines each local bandwidth based on one local point only, while Isolation kernel is derived directly from the data based on space partitioning. Second, the use of Isolation kernel yields a more efficient similarity computation because data-dependent Isolation kernel has only one parameter that needs to be tuned. In contrast, the use of data-independent Gaussian kernel increases the computational cost by determining n bandwidths for a dataset of n points. As the root cause of these deficiencies in t-SNE is Gaussian kernel, we show that simply replacing Gaussian kernel with Isolation kernel in t-SNE significantly improves the quality of the final visualisation output (without creating misrepresented structures) and removes one key obstacle that prevents t-SNE from processing large datasets. Moreover, Isolation kernel enables t-SNE to deal with large-scale datasets in less runtime without trading off accuracy, unlike existing methods in speeding up t-SNE.

Noise and acoustics in complicated rooms with the sound particle method

The analysis of noise and acoustics in indoor spaces is often performed with geometrical methods from the ray-tracing family, such as the sound particle method. In general, these offer an acceptable balance between physical accuracy and computational effort, but models with large numbers of objects and high levels of detail can lead to long waits for results. In this paper, we consider methods to assist with the efficient analysis of such situations in the context of the sound particle diffraction model. A modern open-plan office and a large cathedral are used as example projects. We look at space partitioning strategies, adaptive placement of receivers in the form of mesh noise maps, and graphics-card-style hardware acceleration techniques, along with iterative modelling methods. The role of geometrical detail in the context of uncertainties in the input data, such as absorption and scattering coefficients, is also studied. From this, we offer a range of recommendations regarding the level-of-detail in acoustic modelling, including consideration of issues such as seating, tables, and curved surfaces.