Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Implementing a Two-Photon Three-Degrees-of-Freedom Hyper-Parallel Controlled Phase Flip Gate Through Cavity-Assisted Interactions

Hyper-parallel quantum information processing is a promising and beneficial research field. Herein, a method to implement a hyper-parallel controlled-phase-flip (hyper-CPF) gate for frequency-, spatial-, and time-bin-encoded qubits by coupling flying photons to trapped nitrogen vacancy (NV) defect centers is presented. The scheme, which differs from their conventional parallel counterparts, is specifically advantageous in decreasing against the dissipate noise, increasing the quantum channel capacity, and reducing the quantum resource overhead. The gate qubits with frequency, spatial, and time-bin degrees of freedom (DOF) are immune to quantum decoherence in optical fibers, whereas the polarization photons are easily disturbed by the ambient noise.     

Aggregate error locator and error value computation in AG codes

The aggregate error locator is defined and a computation method is given. The aggregate error locator is then used in a type of Forney algorithm to compute the error values in the received words of a Ca,b algebraic geometry code.     

Bit-parallel approximate string matching algorithms with transposition

Using bit-parallelism has resulted in fast and practical algorithms for approximate string matching under Levenshtein edit distance, which permits a single edit operation to insert, delete or substitute a character. Depending on the parameters of the search, currently the fastest non-filtering algorithms in practice are the O(km/wn) algorithm of Wu and Manber, the O((k+2)(m−k)/wn) algorithm of Baeza-Yates and Navarro, and the O(m/wn) algorithm of Myers, where m is the pattern length, n is the text length, k is the error threshold and w is the computer word size. In this paper we discuss a uniform way of modifying each of these algorithms to permit also a fourth type of edit operation: transposing two adjacent characters in the pattern. This type of edit distance is also known as Damerau edit distance. In the end we also present an experimental comparison of the resulting algorithms.     

量子计算与超冷离子

通过介绍量子计算的基本概念和特点，并对比目前人们使用的计算机的计算方式，对于如何利用囚禁在离子阱中的超冷离子进行量子计算作了简要的叙述．     

On Binary Computation Structures

Based on a modification of Moss' and Parikh's topological modal language [8], we study a generalization of a weakly expressive fragment of a certain propositional modal logic of time. We define a bimodal logic comprising operators for knowledge and nexttime. These operators are interpreted in binary computation structures. We present an axiomatization of the set T of theorems valid for this class of semantical domains and prove – as the main result of this paper – its completeness. Moreover, the question of decidability of T is treated.     

A numerical experimental study of inverse preconditioning for the parallel iterative solution to 3D finite element flow equations

Integration of the subsurface flow equation by finite elements (FE) in space and finite differences (FD) in time requires the repeated solution to sparse symmetric positive definite systems of linear equations. Iterative techniques based on preconditioned conjugate gradients (PCG) are one of the most attractive tool to solve the problem on sequential computers. A present challenge is to make PCG attractive in a parallel computing environment as well. To this aim a key factor is the development of an efficient parallel preconditioner. FSAI (factorized sparse approximate inverse) and enlarged FSAI relying on the approximate inverse of the coefficient matrix appears to be a most promising parallel preconditioner. In the present paper PCG using FSAI, diagonal and pARMS (parallel algebraic recursive multilevel solvers) preconditioners is implemented on the IBM SP4/512 and CLX/768 supercomputers with up to 32 processors to solve underground flow problems of a large size. The results show that FSAI may allow for a parallel relative efficiency larger than 50% on the largest problems with p=32 processors. Moreover, FSAI turns out to be significantly less expensive and more robust than pARMS. Finally, it is shown that for p in the upper range may be much improved if PCG–FSAI is implemented on CLX.     

A parametric representation of linguistic hedges in Zadeh’s fuzzy logic

This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth-value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth-values is introduced.     

Speedup estimates for some variants of the parallel implementations of the branch-and-bound method

The efficiency of parallel implementations of the branch-and-bound method in discrete optimization problems is considered. A theoretical analysis and comparison of two parallel implementations of this method is performed. A mathematical model of the computation process is constructed and used to obtain estimates of the maximum possible speedup. Examples of problems in which none of these two parallel implementations can speed up the computations are considered.     

Approximate symmetries and conservation laws for Itô and Stratonovich dynamical systems

A new definition for the approximate symmetries of Itô dynamical system is given. Determining systems of approximate symmetries for Itô and Stratonovich dynamical systems have been obtained. It has been shown that approximate conservation laws can be found from the approximate symmetries of stochastic dynamical systems which do not arise from a Hamiltonian. The results have been applied to an example.