Properties and performance of folded hypercubes

A new hypercube-type structure, the folded hypercube (FHC), which is basically a standard hypercube with some extra links established between its nodes, is proposed and analyzed. The hardware overhead is almost 1/n, n being the dimensionality of the hypercube, which is negligible for large n. For this new design, optimal routing algorithms are developed and proven to be remarkably more efficient than those of the conventional n-cube. For one-to-one communication, each node can reach any other node in the network in at most [n/2] hops (each hop corresponds to the traversal of a single link), as opposed to n hops in the standard hypercube. One-to-all communication (broadcasting) can also be performed in only [n/2] steps, yielding a 50% improvement in broadcasting time over that of the standard hypercube. All routing algorithms are simple and easy to implement. Correctness proofs for the algorithms are given. For the proposed architecture, communication parameters such as average distance, message traffic density, and communication time delay are derived. In addition, some fault tolerance capabilities of this architecture are quantified and compared to those of the standard cube. It is shown that this structure offers substantial improvement over existing hypercube-type networks in terms of the above-mentioned network parameters     

Forward and backward finite differences for isotropic gradients on a square lattice derived from a rectangular lattice formulation

In this research, forward and backward isotropic finite differences for the gradient operator are developed up to fourth order. Isotropic gradients are characterized by error terms which have small directional preference. Currently, only centred finite differences are available for isotropic discretization in the scientific literature; however, these finite differences are not suited for evaluation on domain boundaries or at multilevel lattice interfaces. We show that the order of accuracy with respect to the gradient direction with isotropic discretizations can be higher in some situations, and, at the same time, use neighbours that are closer to the evaluation point than with standard discretizations. The isotropic discretizations presented here were developed for a special rectangular lattice formulation, and general stencil weights are provided. When the rectangular lattice has a certain aspect ratio, forward and backward isotropic gradients can be obtained on a square lattice.     

On a family of copulas constructed from the diagonal section

We characterize the class of copulas that can be constructed from the diagonal section by means of the functional equation C(x,y)+|x−y|=C(x∨y,x∨y), for all (x,y) in the unit square such that C(x,y)>0. Some statistical properties of this class are given.     

Optimal layout and reconfiguration of a fixturing system constructed from passive Stewart platforms

The distinguishing property of Reconfigurable Manufacturing Systems (RMS) is that they can rapidly and efficiently adapt to new production requirements, both in terms of their capacity and functionalities. For this type of systems to achieve the desired efficiency, it should be possible to easily and quickly setup and reconfigure all of their components. This includes fixturing jigs that are used to hold workpieces firmly in place to enable a robot to carry out the desired production processes.In this paper, we formulate a constrained nonlinear optimization problem that must be solved to determine an optimal layout of reconfigurable fixtures for a given set of workpieces. The optimization problem takes into account the kinematic limitations of the fixtures, which are built in shape of Sterwart platforms, and the characteristics of the workpieces that need to be fastened into the fixturing system. Experimental results are presented that demonstrate that the automatically computed fixturing system layouts satisfy different constraints typically imposed in production environments.     

Generating near-spherical range panoramas by fusing optical flow and stereo from a single-camera folded catadioptric rig

We design a novel “folded” spherical catadioptric rig (formed by two coaxially-aligned spherical mirrors of distinct radii and a single perspective camera) to recover near-spherical range panoramas (about 360° × 153°) from the fusion of depth given by optical flow and stereoscopy. We observe that for rigid motion that is parallel to a plane, optical flow and stereo generate nearly complementary distributions of depth resolution. While optical flow provides strong depth cues in the periphery and near the poles of the view-sphere, stereo generates reliable depth in a narrow band about the equator instead. We exploit this dual-modality principle by modeling (separately) the depth resolution of optical flow and stereo in order to fuse them later on a probabilistic spherical panorama. We achieve a desired vertical field-of-view and optical resolution by deriving a linearized model of the rig in terms of three parameters (radii of the two mirrors plus axial distance between the mirrors’ centers). We analyze the error due to the violation of the single viewpoint constraint and formulate additional constraints on the design to minimize this error. We evaluate our proposed method via a synthetic model and with real-world prototypes by computing dense spherical panoramas of depth from cluttered indoor environments after fusing the two modalities (stereo and optical flow).     

Heavy-baryon spectroscopy from lattice QCD

We use a four-dimensional lattice calculation of the full-QCD (quantum chromodynamics, the non-abelian gauge theory of the strong interactions of quarks and gluons) path integrals needed to determine the masses of the charmed and bottom baryons. In the charm sector, our results are in good agreement with experiment within our systematics, except for the spin-1/2 Ξcc, for which we found the isospin-averaged mass to be Ξcc to be . We predict the mass of the (isospin-averaged) spin-1/2 Ωcc to be . In the bottom sector, our results are also in agreement with experimental observations and other lattice calculations within our statistical and systematic errors. In particular, we find the mass of the Ωb to be consistent with the recent CDF measurement. We also predict the mass for the as yet unobserved to be 5955(27) MeV.     

Optimization of folded plate roofs

Increased usage of prefabricated structural components and the advantages offered by folded plate roofs necessitates the optimization of their configurations. In order to reduce the material expenditure, transportation and erection costs the dead-weight of the roof systems need to be minimized.The reported study defines a technique for the optimization of the structural weight of the folded plate roof without intermediate stiffeners and subjected to one loading system. The developed method enabled the generation of the different, and consequently the optimum, geometries by starting with an arbitrary initial geometry. The azimuthal angles, the width and the thickness of the individual panels were permitted to vary. The optimization employed a variational approach and flexibility formulation. The total weight of the roof was taken as the target function, subject to minimization. The equilibrium equations for the panels were taken as the constraint equations for the optimization process. The pseudo-weight function was established through the use of the Lagrangian multipliers. The standard Lagrangian formulation was then applied to the pseudo-weight function, and a set of optimization equations were generated. These equations, along with the original equilibrium equations, formed a system of simultaneous nonlinear transcendental equations. This set was solved using an iterative approach.The overall formulation was kept general enough to permit the inclusion of any given loading condition to permit the application of the given methodology to any folded plate roof system.     

前向安全的格上基于身份签密方案

针对目前基于格的签密方案尚不能满足前向安全性,提出一个具有前向安全的基于身份的签密方案。首先,该方案利用格基授权算法对用户和发送者的公私钥对进行更新;其次,结合基于格上错误学习问题的原像采样算法进行用户签名,并利用包含签名信息的哈希值对消息进行加密。在随机预言机模型下,证明该方案是适应性选择身份和选择密文攻击安全（IND-sID-CCA2）和强不可伪造选择消息攻击安全（sUF-CMA）的,同时证明了该方案具有前向安全性。相对于基于配对的签密方案,所提方案在计算速度和密文扩展率的优势都较为明显。     

Fault tolerance of hypercubes and folded hypercubes

Let \(G = (V,E)\) be a connected graph. The conditional edge connectivity \(\lambda _\delta ^k(G)\) is the cardinality of the minimum edge cuts, if any, whose deletion disconnects \(G\) and each component of \(G - F\) has \(\delta \ge k\) . We assume that \(F \subseteq E\) is an edge set, \(F\) is called edge extra-cut, if \(G - F\) is not connected and each component of \(G - F\) has more than \(k\) vertices. The edge extraconnectivity \(\lambda _\mathrm{e}^k(G)\) is the cardinality of the minimum edge extra-cuts. In this paper, we study the conditional edge connectivity and edge extraconnectivity of hypercubes and folded hypercubes.     

Conceptual feature generation for textual information using a conceptual network constructed from Wikipedia

A proper semantic representation of textual information underlies many natural language processing tasks. In this paper, a novel semantic annotator is presented to generate conceptual features for text documents. A comprehensive conceptual network is automatically constructed with the aid of Wikipedia that has been represented as a Markov chain. Furthermore, semantic annotator gets a fragment of natural language text and initiates a random walk to generate conceptual features that represent topical semantic of the input text. The generated conceptual features are applicable to many natural language processing tasks where the input is textual information and the output is a decision based on its context. Consequently, the effectiveness of the generated features is evaluated in the task of document clustering and classification. Empirical results demonstrate that representing text using conceptual features and considering the relations between concepts can significantly improve not only the bag of words representation but also other state‐of‐the‐art approaches.     

New quantum codes constructed from quaternary BCH codes

In this paper, we firstly study construction of new quantum error-correcting codes (QECCs) from three classes of quaternary imprimitive BCH codes. As a result, the improved maximal designed distance of these narrow-sense imprimitive Hermitian dual-containing quaternary BCH codes are determined to be much larger than the result given according to Aly et al. (IEEE Trans Inf Theory 53:1183–1188, 2007) for each different code length. Thus, families of new QECCs are newly obtained, and the constructed QECCs have larger distance than those in the previous literature. Secondly, we apply a combinatorial construction to the imprimitive BCH codes with their corresponding primitive counterpart and construct many new linear quantum codes with good parameters, some of which have parameters exceeding the finite Gilbert–Varshamov bound for linear quantum codes.     

Entanglement-assisted quantum MDS codes constructed from negacyclic codes

Recently, entanglement-assisted quantum codes have been constructed from cyclic codes by some scholars. However, how to determine the number of shared pairs required to construct entanglement-assisted quantum codes is not an easy work. In this paper, we propose a decomposition of the defining set of negacyclic codes. Based on this method, four families of entanglement-assisted quantum codes constructed in this paper satisfy the entanglement-assisted quantum Singleton bound, where the minimum distance satisfies \(q+1 \le d\le \frac{n+2}{2}\). Furthermore, we construct two families of entanglement-assisted quantum codes with maximal entanglement.     

Entanglement-assisted quantum MDS codes constructed from constacyclic codes

Recently, entanglement-assisted quantum error-correcting codes (EAQECCs) have been constructed by cyclic codes and negacyclic codes. In this paper, by decomposing the defining set of constacyclic codes, we construct four classes of new EAQECCs, which satisfy the entanglement-assisted quantum Singleton bound.     

Modelling of spatial point processes derived from a sequence of auto-Poisson lattice schemes

Spatial point processes form a set of statistical tools capable of modelling many environmental processes. They can deal with spatial interactions and dependencies between individuals which is an essential framework in environmental modelling. In this context, we focus on inhibitory pairwise interaction point processes that can be obtained as the limit of a suitable sequence of auto-Poisson lattice schemes. We review the limit theorems concerned, present a computer software (SPPA) and analyze the results of a Monte Carlo simulation study based on a particular pairwise interaction model.     

Fuzzy logic models in a category of fuzzy relations

We investigate interpretations of formulas ψ in a first order fuzzy logic in models which are based on objects of a category SetR(Ω) which consists of Ω-sets, i.e. sets with similarity relations with values in a complete MV-algebra Ω and with morphisms defined as special fuzzy relations between Ω-sets. The interpretations are then morphisms in a category SetR(Ω) from some Ω-set to the object . We define homomorphisms between models in a category SetR(Ω) and we prove that if is a (special) homomorphism of models in a category SetR(Ω) then there is a relation between interpretations of a formula ψ in models . Supported by MSM6198898701, grant 201/07/0191 of GAČR and grant 1M0572.