The Number of Tree Stars Is <Emphasis Type="Italic">O</Emphasis><Superscript>*</Superscript>(1.357<Superscript><Emphasis Type="Italic">k</Emphasis></Superscript>)

Every rectilinear Steiner tree problem admits an optimal tree T ^* which is composed of tree stars. Moreover, the currently fastest algorithms for the rectilinear Steiner tree problem proceed by composing an optimum tree T ^* from tree star components in the cheapest way. The efficiency of such algorithms depends heavily on the number of tree stars (candidate components). Fößmeier and Kaufmann (Algorithmica 26, 68–99, 2000) showed that any problem instance with k terminals has a number of tree stars in between 1.32 ^k and 1.38 ^k (modulo polynomial factors) in the worst case. We determine the exact bound O ^*(ρ ^k ) where ρ≈1.357 and mention some consequences of this result.     

A new extended LMI-based robust gain scheduled state feedback <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript> controller design

This paper proposes an improved robust H ₂ state feedback control synthesis for the Linear Parameter Varying (LPV) systems by attaining the affine quadratic stability. In place of standard H ₂ computation in the literature, a new H ₂ computation based on extended Linear Matrix Inequality (LMI) is improved by means of the slack variable, where it is obtained by separation Lyapunov matrix from system matrix. State feedback H ₂ synthesis is improved for the systems, and is more effective and less conservative than the common ones in the literature. Therefore, the less conservative results are obtained for gain scheduling controller design for LPV systems. The numerical examples are presented to show the superiority of the proposed controller design.     

<Emphasis Type="Italic">I</Emphasis><Subscript>DDT</Subscript>: Fundamentals and test generation

It is the time to explore the fundamentals ofI _DDT testing when extensive work has been done forI _DDT testing since it was proposed. This paper precisely defines the concept of average transient current (I _DDT) of CMOS digital ICs, and experimentally analyzes the feasibility ofI _DDT test generation at gate level. Based on the SPICE simulation results, the paper suggests a formula to calculateI _DDT by means of counting only logical up-transitions, which enablesI _DDT test generation at logic level. The Bayesian optimization algorithm is utilized forI _DDT test generation. Experimental results show that about 25% stuck-open faults are withI _DDT test generation. 2.5, and likely to beI _DDT testable. It is also found that mostI _DDT testable faults are located near the primary inputs of a circuit under test.I _DDT test generation does not require fault sensitization procedure compared with stuck-at fault test generation. Furthermore, some redundant stuck-at faults can be detected by usingI _DDT testing.     

The <Emphasis Type="Italic">B</Emphasis><Superscript><Emphasis Type="Italic">dual</Emphasis></Superscript>-Tree: indexing moving objects by space filling curves in the dual space

Existing spatiotemporal indexes suffer from either large update cost or poor query performance, except for the B ^x -tree (the state-of-the-art), which consists of multiple B ⁺-trees indexing the 1D values transformed from the (multi-dimensional) moving objects based on a space filling curve (Hilbert, in particular). This curve, however, does not consider object velocities, and as a result, query processing with a B ^x -tree retrieves a large number of false hits, which seriously compromises its efficiency. It is natural to wonder “can we obtain better performance by capturing also the velocity information, using a Hilbert curve of a higher dimensionality?”. This paper provides a positive answer by developing the B ^dual -tree, a novel spatiotemporal access method leveraging pure relational methodology. We show, with theoretical evidence, that the B ^dual -tree indeed outperforms the B ^x -tree in most circum- stances. Furthermore, our technique can effectively answer progressive spatiotemporal queries, which are poorly supported by B ^x -trees.     

Sparse Support Vector Machine with <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> Penalty for Feature Selection

We study the strategies in feature selection with sparse support vector machine (SVM). Recently, the socalled L _p -SVM (0 < p < 1) has attracted much attention because it can encourage better sparsity than the widely used L ₁-SVM. However, L _p -SVM is a non-convex and non-Lipschitz optimization problem. Solving this problem numerically is challenging. In this paper, we reformulate the L _p -SVM into an optimization model with linear objective function and smooth constraints (LOSC-SVM) so that it can be solved by numerical methods for smooth constrained optimization. Our numerical experiments on artificial datasets show that LOSC-SVM (0 < p < 1) can improve the classification performance in both feature selection and classification by choosing a suitable parameter p. We also apply it to some real-life datasets and experimental results show that it is superior to L ₁-SVM.     

Emergence of anti-<Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity in type-IV bouncing cosmology as due to <Emphasis Type="Italic">M</Emphasis><Subscript>0</Subscript>-brane

Recently, some authors considered the origin of a type-IV singular bounce in modified gravity and obtained the explicit form of F(R) which can produce this type of cosmology. In this paper, we show that during the contracting branch of type-IV bouncing cosmology, the sign of gravity changes, and antigravity emerges. In our model, M0 branes get together and shape a universe, an anti-universe, and a wormhole which connects them. As time passes, this wormhole is dissolved in the universes, F(R) gravity emerges, and the universe expands. When the brane universes become close to each other, the squared energy of their system becomes negative, and some tachyonic states are produced. To remove these states, universes are assumed to be compact, the sign of compacted gravity changes, and anti-F(R) gravity arises, which causes getting away of the universes from each other. In this theory, a Type-IV singularity occurs at t = t _s , which is the time of producing tachyons between expansion and contraction branches.     

Positive <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>-gain filter design for positive continuous-time Markovian jump systems with partly known transition rates

The paper is concerned with the problem of positive L ₁-gain filter design for positive continuous-time Markovian jump systems with partly known transition rates. Our aim is to design a positive full-order filter such that the corresponding filtering error system is positive and stochastically stable with L ₁-gain performance. By applying a linear co-positive Lyapunov function and free-connection weighting vectors, the desired positive L ₁-gain filter is provided. The obtained theoretical results are demonstrated by numerical examples.     

Efficient <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript> norm based sparse subspace clustering via smooth IRLS and ADMM

Recently, sparse subspace clustering, as a subspace learning technique, has been successfully applied to several computer vision applications, e.g. face clustering and motion segmentation. The main idea of sparse subspace clustering is to learn an effective sparse representation that are used to construct an affinity matrix for spectral clustering. While most of existing sparse subspace clustering algorithms and its extensions seek the forms of convex relaxation, the use of non-convex and non-smooth l _q (0 < q < 1) norm has demonstrated better recovery performance. In this paper we propose an l _q norm based Sparse Subspace Clustering method (lqSSC), which is motivated by the recent work that l _q norm can enhance the sparsity and make better approximation to l ₀ than l ₁. However, the optimization of l _q norm with multiple constraints is much difficult. To solve this non-convex problem, we make use of the Alternating Direction Method of Multipliers (ADMM) for solving the l _q norm optimization, updating the variables in an alternating minimization way. ADMM splits the unconstrained optimization into multiple terms, such that the l _q norm term can be solved via Smooth Iterative Reweighted Least Square (SIRLS), which converges with guarantee. Different from traditional IRLS algorithms, the proposed algorithm is based on gradient descent with adaptive weight, making it well suit for general sparse subspace clustering problem. Experiments on computer vision tasks (synthetic data, face clustering and motion segmentation) demonstrate that the proposed approach achieves considerable improvement of clustering accuracy than the convex based subspace clustering methods.     

On (<Emphasis Type="Italic">a</Emphasis>, <Emphasis Type="Italic">d</Emphasis> )-Distance Anti-Magic and 1-Vertex Bimagic Vertex Labelings of Certain Types of Graphs

The results for the corona P _n ?°?P₁ are generalized, which make it possible to state that P _n ?°?P₁ is not an ( a, d)-distance antimagic graph for arbitrary values of a and d. A condition for the existence of an ( a, d)-distance antimagic labeling of a hypercube Q _n is obtained. Functional dependencies are found that generate this type of labeling for Q _n . It is proved by the method of mathematical induction that Q _n is a (2 ⁿ ?+?n???1,?n???2) -distance antimagic graph. Three types of graphs are defined that do not allow a 1-vertex bimagic vertex labeling. A relation between a distance magic labeling of a regular graph G and a 1-vertex bimagic vertex labeling of G?∪?G is established.     

(<Emphasis Type="Italic">a</Emphasis>, <Emphasis Type="Italic">d</Emphasis>)-Distance Antimagic Labeling of Some Types of Graphs

We analyze the necessary existence conditions for (a, d)-distance antimagic labeling of a graph G = (V, E) of order n. We obtain theorems that expand the family of not (a, d) -distance antimagic graphs. In particular, we prove that the crown P _n ○ P ₁ does not admit an (a, 1)-distance antimagic labeling for n ≥ 2 if a ≥ 2. We determine the values of a at which path P _n can be an (a, 1)-distance antimagic graph. Among regular graphs, we investigate the case of a circulant graph.     

Some properties of the disjunctive languages contained in <Emphasis Type="Italic">Q</Emphasis>

The set of all primitive words Q over an alphabet X was first defined and studied by Shyr and Thierrin (Proceedings of the 1977 Inter. FCT-Conference, Poznan, Poland, Lecture Notes in Computer Science 56. pp. 171–176 (1977)). It showed that for the case |X| ≥ 2, the set along with \({Q^{(i)} = \{f^i\,|\,f \in Q\}, i\geq 2}\) are all disjunctive. Since then these disjunctive sets are often be quoted. Following Shyr and Thierrin showed that the half sets \({Q_{ev} = \{f \in Q\,|\,|f| = {\rm even}\}}\) and Q _od = Q \ Q _ev of Q are disjunctive, Chien proved that each of the set \({Q_{p,r}= \{u\in Q\,|\,|u|\equiv r\,(mod\,p) \},\,0\leq r < p}\) is disjunctive, where p is a prime number. In this paper, we generalize this property to that all the languages \({Q_{n,r}= \{u\in Q\,|\,|u|\equiv r\,(mod\,n) \},\, 0\leq r < n}\) are disjunctive languages, where n is any positive integer. We proved that for any n ≥ 1, k ≥ 2, (Q _n,0) ^k are all regular languages. Some algebraic properties related to the family of languages {Q _n,r | n ≥ 2, 0 ≤ r < n } are investigated.     

On the <Emphasis Type="Italic">k</Emphasis>-accessibility of cores of <Emphasis Type="Italic">TU</Emphasis>-cooperative games

This paper proposes a strengthening of the author’s core-accessibility theorem for balanced TU-cooperative games. The obtained strengthening relaxes the influence of the nontransitivity of classical domination αv on the quality of the sequential improvement of dominated imputations in a game v. More specifically, we establish the k-accessibility of the core C(α _v ) of any balanced TU-cooperative game v for all natural numbers k: for each dominated imputation x, there exists a converging sequence of imputations x₀, x₁,..., such that x₀ = x, lim x _r ∈ C(α _v ) and x_r?m is dominated by any successive imputation x _r with m ∈ [1, k] and r ≥ m. For showing that the TU-property is essential to provide the k-accessibility of the core, we give an example of an NTU-cooperative game G with a ”black hole” representing a nonempty closed subset B ? G(N) of dominated imputations that contains all the α _G -monotonic sequential improvement trajectories originating at any point x ∈ B.     

Pareto optimal generalized <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>-control and vibroprotection problems

We consider a novel multi-objective control problem where the criteria are generalized H ₂-norms of transfer matrices of individual channels from the disturbance input to various objective outputs. We obtain necessary conditions for Pareto optimality. We show that synthesis of Pareto optimal controls can be done in terms of linear matrix inequalities based on optimizing Germeier’s convolution, which also turns out to be the generalized H ₂-norm of the closed-loop system with output composed of the objective outputs multiplied by scalars. As applications we consider multi-objective problems of vibration isolation and oscillation suppression with new types of criteria.     

<Emphasis Type="Italic">D</Emphasis>-decomposition technique state-of-the-art

It is a survey of recent extensions and new applications for the classical D-decomposition technique. We investigate the structure of the parameter space decomposition into root invariant regions for single-input single-output systems linear depending on the parameters. The D-decomposition for uncertain polynomials is considered as well as the problem of describing all stabilizing controllers of the certain structure (for instance, PID-controllers) that satisfy given H _∞-criterion. It is shown that the D-decomposition technique can be naturally linked with M-Δ framework (a general scheme for analysis of uncertain systems) and it is applicable for describing feasible sets for linear matrix inequalities. The problem of robust synthesis for linear systems can be also treated via D-decomposition technique.     

On transitive partitions of an <Emphasis Type="Italic">n</Emphasis>-cube into codes

We present methods to construct transitive partitions of the set E ⁿ of all binary vectors of length n into codes. In particular, we show that for all n = 2 ^k ? 1, k ≥ 3, there exist transitive partitions of E ⁿ into perfect transitive codes of length n.     

Determining Steady-State Characteristics of Some Queuing Systems with Erlangian Distributions

This article proposes a method to study M / E _s / 1 / m, E _r E _s /1 / m, and E _r / M / n / m queuing systems including the case when m = ∞. Recurrence relations are obtained to compute the stationary distribution of the number of customers in a system and its steady-state characteristics. The developed algorithms are tested on examples using simulation models constructed with the help of the GPSS World tools.     

Some high-rate linear codes over <Emphasis Type="Italic">GF</Emphasis>(5) and <Emphasis Type="Italic">GF</Emphasis>(7)

Let an [n, k, d] _q code be a linear code of length n, dimension k, and with minimum Hamming distance d over GF(q). The ratio R = k/n is called the rate of a code. In this paper, [62, 53, 6]₅, [62, 48, 8]₅, [71, 56, 8]₅, [124, 113, 6]₅, [43, 36, 6]₇, [33, 23, 7]₇, and [27, 18, 7]₇ high-rate codes and new codes with parameters [42, 14, 19]₅, [42, 15, 18]₅, [48, 13, 24]₅, [52, 12, 28]₅, [71, 15, 38]₅, [71, 16, 36]₅, [72, 12, 41]₅, [78, 10, 50]₅, [88, 11, 54]₅, [88, 13, 51]₅, [124, 14, 77]₅, [32, 12, 15]₇, [32, 10, 17]₇, [36, 10, 20]₇, and [48, 10, 29]₇ are constructed. The codes with parameters [62, 53, 6]₅ and [43, 36, 6]₇ are optimal.     

Transit cosmological models with domain walls in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R,T</Emphasis>) gravity

We study the physical behavior of the transition of a 5D perfect fluid universe from an early decelerating phase to the current accelerating phase in the framework of f(R, T) theory of gravity in the presence of domain walls. The fifth dimension is not observed because it is compact. To determine the solution of the field equations, we use the concept of a time-dependent deceleration parameter which yields the scale factor a(t) = sinh^1/n(αt), where n and α are positive constants. For 0 < n ≤ 1, this generates a class of accelerating models, while for n > 1 the universe attains a phase transition from an early decelerating phase to the present accelerating phase, consistent with the recent observations. Some physical and geometric properties of the models are also discussed.