Search of wormholes in different dimensional non-commutative inspired space-time with lorentzian distribution

In this paper we are searching whether the wormhole solutions exists in different dimensional non- commutative inspired spacetimes. It is well known that the noncommutativity of the space is an outcome of string theory and it replaced the usual point like object by a smeared object. Here we have chosen Lorentzian distribution as the density function in the noncommutative inspired space- time. We have observed that the wormhole solutions exist only in four and five dimension, however, higher than fine dimension no wormhole exists. For five dimensional spacetime, we get a wormhole for a restricted region. In usual four dimensional spacetime, we get a stable wormhole which is asymptotically flat.Comment: 13 pages,23 figures, Accepted in European Physical Journal

Spatial Structures in a Generalized Ginzburg-Landau Free Energy

Searching for characteristic signatures of a higher order phase transition (specifically of order three or four), we have calculated the spatial profiles and the energies of a spatially varying order parameter in one dimension. In the case of a $p^{th}$ order phase transition to a superconducting ground state, the free energy density depends on temperature as $a^p$, where $a = a_o(1-T/T_c)$ is the reduced temperature. The energy of a domain wall between two degenerate ground states is $\epsilon_p \simeq a^{p-1/2}$. We have also investigated the effects of a supercurrent in a narrow wire. These effects are limited by a critical current which has a temperature dependence $J_c(T) \simeq a^{(2p-1)/2}$. The phase slip center profiles and their energies are also calculated. Given the suggestion that the superconducting transtion in \bkbox, for $x = 0.4$, may be of order four, these predictions have relevance for future experiments.Comment: 7 pages, 5 figure

Incremental dimension reduction of tensors with random index

We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low and predictable. Component encoding and decoding are performed on-line without computationally expensive re-analysis of the data set. The range of tensor indices can be extended dynamically without modifying the component representation. This idea originates from a mathematical model of semantic memory and a method known as random indexing in natural language processing. We generalize the random-indexing algorithm to tensors and present signal-to-noise-ratio simulations for representations of vectors and matrices. We present also a mathematical analysis of the approximate orthogonality of high-dimensional ternary vectors, which is a property that underpins this and other similar random-coding approaches to dimension reduction. To further demonstrate the properties of random indexing we present results of a synonym identification task. The method presented here has some similarities with random projection and Tucker decomposition, but it performs well at high dimensionality only (n>10^3). Random indexing is useful for a range of complex practical problems, e.g., in natural language processing, data mining, pattern recognition, event detection, graph searching and search engines. Prototype software is provided. It supports encoding and decoding of tensors of order >= 1 in a unified framework, i.e., vectors, matrices and higher order tensors.Comment: 36 pages, 9 figure

Gossip-Based Indexing Ring Topology for 2-Dimension Spatial Data in Overlay Networks

AbstractOverlay networks are used widely in the Internet, such as retrieval and share of files, multimedia games and so on. However, in distributed system, the retrieval and share of 2-dimension spatial data still have some difficult problems and can not solve the complex retrieval of 2-dimension spatial data efficiently. This article presents a new indexing overlay networks, named 2D-Ring, which is the ring topology based on gossip for 2-dimension spatial data. The peers in our overlay networks exchange the information periodically and update each local view by constructing algorithm. 2-dimension spatial data is divided by quad-tree and mapped into control points, which are hashed into 2D-Ring by SHA-1 hash function. In such way, the problem of 2-dimension spatial data indexing is converted to the problem of searching peers in the 2D-Ring. A large of extensive experiments show that the time complexity of constructing algorithm of 2D-Ring can reach convergence logarithmically as a function of the network size and hold higher hit rate and lower query delay

Finding Maximal 2-Dimensional Palindromes

This paper extends the problem of palindrome searching into a higher dimension, addressing two definitions of 2D palindromes. The first definition implies a square, while the second definition (also known as a centrosymmetric factor), can be any rectangular shape. We describe two algorithms for searching a 2D text for maximal palindromes, one for each type of 2D palindrome. The first algorithm is optimal; it runs in linear time, on par with Manacher\u27s linear time 1D palindrome algorithm. The second algorithm searches a text of size n_1 x n_2 (n_1 >= n_2) in O(n_2) time for each of its n_1 x n_2 positions. Since each position may have up to O(n_2) maximal palindromes centered at that location, the second result is also optimal in terms of the worst-case output size

Potential Odor Intensity Grid Based UAV Path Planning Algorithm with Particle Swarm Optimization Approach

International audienceThis paper proposes a potential odor intensity grid based optimization approach for unmanned aerial vehicle (UAV) path planning with particle swarm optimization (PSO) technique. Odor intensity is created to color the area in the searching space with highest probability where candidate particles may locate. A potential grid construction operator is designed for standard PSO based on different levels of odor intensity. The potential grid construction operator generates two potential location grids with highest odor intensity. Then the middle point will be seen as the final position in current particle dimension. The global optimum solution will be solved as the average. In addition, solution boundaries of searching space in each particle dimension are restricted based on properties of threats in the flying field to avoid prematurity. Objective function is redesigned by taking minimum direction angle to destination into account and a sampling method is introduced. A paired samples -test is made and an index called straight line rate (SLR) is used to evaluate the length of planned path. Experiments are made with other three heuristic evolutionary algorithms. The results demonstrate that the proposed method is capable of generating higher quality paths efficiently for UAV than any other tested optimization techniques

Higgs Mechanism for Gravitons

Just like the vector gauge bosons in the gauge theories, it is now known that gravitons acquire mass in the process of spontaneous symmetry breaking of diffeomorphisms through the condensation of scalar fields. The point is that we should find the gravitational Higgs mechanism such that it results in massive gravity in a flat Minkowski space-time without non-unitary propagating modes. This is usually achieved by including higher-derivative terms in scalars and tuning the cosmological constant to be a negative value in a proper way. Recently, a similar but different gravitational Higgs mechanism has been advocated by Chamseddine and Mukhanov where one can relax the negative cosmological constant to zero or positive one. In this work, we investigate why the non-unitary ghost mode decouples from physical Hilbert space in a general space-time dimension. Moreover, we generalize the model to possess an arbitrary potential and clarify under what conditions the general model exhibits the gravitational Higgs mechanism. By searching for solutions to the conditions, we arrive at two classes of potentials exhibiting gravitational Higgs mechanism. One class includes the model by Chamseddine and Mukhanov in a specific case while the other is completely a new model.Comment: 11 page