Polyomino coloring and complex numbers

Usually polyominoes are represented as subsets of the lattice . In this paper we study a representation of polyominoes by Gaussian integers. Polyomino is represented by the set

Then we consider functions of type from the set of all polyominoes to an abelian group G, given by , where v is prime in (N(v) is the norm of v). Using the arithmetic of the ring we find necessary and sufficient conditions for such a function to be a coloring map.     

Structural properties of oracle classes

Denote by the class of oracles relative to which (collapsing oracles), and by the class of oracles relative to which (separating oracles). We present structural results on and . Using a diagonalization argument, we show that neither nor is closed under disjoint union, also known as join. We show that this implies that neither nor is closed under union, intersection, or symmetric difference. Consequently , the first level of the extended low hierarchy, is not closed under join.     

An iterative algorithm for solving a pair of matrix equations over generalized centro-symmetric matrices

A matrix is said to be a symmetric orthogonal matrix if . A matrix is said to be generalized centro-symmetric (generalized central anti-symmetric) with respect to P, if A=PAP (A=−PAP). The generalized centro-symmetric matrices have wide applications in information theory, linear estimate theory and numerical analysis. In this paper, we propose a new iterative algorithm to compute a generalized centro-symmetric solution of the linear matrix equations . We show, when the matrix equations are consistent over generalized centro-symmetric matrix Y, for any initial generalized centro-symmetric matrix Y₁, the sequence {Y_k} generated by the introduced algorithm converges to a generalized centro-symmetric solution of matrix equations . The least Frobenius norm generalized centro-symmetric solution can be derived when a special initial generalized centro-symmetric matrix is chosen. Furthermore, the optimal approximation generalized centro-symmetric solution to a given generalized centro-symmetric matrix can be derived. Several numerical examples are given to show the efficiency of the presented method.     

Reconstruction of a word from a multiset of its factors

Let be the multiset containing all factors of w of length k including repetitions. One of the main results is that if for all , then w=v. The bound is optimal; however we will also show that if for all , then w and v are structurally similar.     

Combining OWL ontologies using -Connections

The standardization of the Web Ontology Language (OWL) leaves (at least) two crucial issues for Web-based ontologies unsatisfactorily resolved, namely how to represent and reason with multiple distinct, but linked ontologies, and how to enable effective knowledge reuse and sharing on the Semantic Web.In this paper, we present a solution for these fundamental problems based on -Connections. We aim to use -Connections to provide modelers with suitable means for developing Web ontologies in a modular way and to provide an alternative to the owl:imports construct.With such motivation, we present in this paper a syntactic and semantic extension of the Web Ontology language that covers -Connections of OWL-DL ontologies. We show how to use such an extension as an alternative to the owl:imports construct in many modeling situations. We investigate different combinations of the logics , and for which it is possible to design and implement reasoning algorithms, well-suited for optimization.Finally, we provide support for -Connections in both an ontology editor, SWOOP, and an OWL reasoner, Pellet.     

Comparison between a measurement error model and a linear model without measurement error

The regression of a response variable on an explanatory variable from observations on , where is a measurement of , is a special case of errors-in-variables model or measurement error model (MEM). In this work we attempt to answer the following question: given the data under a MEM, is it possible to not consider the measurement error on the covariable in order to use a simpler model? To the best of our knowledge, this problem has not been treated in the Bayesian literature. To answer that question, we compute Bayes factors, the deviance information criterion and the posterior mean of the logarithmic discrepancy. We apply these Bayesian model comparison criteria to two real data sets obtaining interesting results. We conclude that, in order to simplify the MEM, model comparison criteria can be useful to compare structural MEM and a random effect model, but we would also need other statistic tools and take into account the final goal of the model.     

Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem

We propose an index calculus algorithm for the discrete logarithm problem on general abelian varieties of small dimension. The main difference with the previous approaches is that we do not make use of any embedding into the Jacobian of a well-suited curve. We apply this algorithm to the Weil restriction of elliptic curves and hyperelliptic curves over small degree extension fields. In particular, our attack can solve an elliptic curve discrete logarithm problem defined over in heuristic asymptotic running time ; and an elliptic problem over or a genus 2 problem over in heuristic asymptotic running time .     

Matrices of 3-iet preserving morphisms

We study matrices of morphisms preserving the family of words coding 3-interval exchange transformations. It is well known that matrices of morphisms preserving Sturmian words (i.e. words coding 2-interval exchange transformations with the maximal possible factor complexity) form the monoid , where .We prove that in the case of exchange of three intervals, the matrices preserving words coding these transformations and having the maximal possible subword complexity belong to the monoid , where .     

Rewrite-Based Decision Procedures

The rewrite-based approach to satisfiability modulo theories consists of using generic theorem-proving strategies for first-order logic with equality. If one can prove that an inference system generates finitely many clauses from the presentation of a theory and a finite set of ground unit clauses, then any fair strategy based on that system can be used as a -satisfiability procedure. In this paper, we introduce a set of sufficient conditions to generalize the entire framework of rewrite-based -satisfiability procedures to rewrite-based -decision procedures. These conditions, collectively termed subterm-inactivity, will allow us to obtain rewrite-based -decision procedures for several theories, namely those of equality with uninterpreted functions, arrays with or without extensionality and two of its extensions, finite sets with extensionality and recursive data structures.     

Robustness of exponential stability of a class of stochastic functional differential equations with infinite delay

We regard the stochastic functional differential equation with infinite delay as the result of the effects of stochastic perturbation to the deterministic functional differential equation , where is defined by x_t(θ)=x(t+θ),θ(−∞,0]. We assume that the deterministic system with infinite delay is exponentially stable. In this paper, we shall characterize how much the stochastic perturbation can bear such that the corresponding stochastic functional differential system still remains exponentially stable.     

Two methods for computing bounds for the distribution of cumulative reward for large Markov models

Degradable fault-tolerant systems can be evaluated using rewarded continuous-time Markov chain (CTMC) models. In that context, a useful measure to consider is the distribution of the cumulative reward over a time interval [0,t]. All currently available numerical methods for computing that measure tend to be very expensive when the product of the maximum output rate of the CTMC model and t is large and, in that case, their application is limited to CTMC models of moderate size. In this paper, we develop two methods for computing bounds for the cumulative reward distribution of CTMC models with reward rates associated with states: BT/RT (Bounding Transformation/Regenerative Transformation) and BT/BRT (Bounding Transformation/Bounding Regenerative Transformation). The methods require the selection of a regenerative state, are numerically stable and compute the bounds with well-controlled error. For a class of rewarded CTMC models, class , and a particular, natural selection for the regenerative state the BT/BRT method allows us to trade off bound tightness with computational cost and will provide bounds at a moderate computational cost in many cases of interest. For a class of models, class , slightly wider than class , and a particular, natural selection for the regenerative state, the BT/RT method will yield tighter bounds at a higher computational cost. Under additional conditions, the bounds obtained using the less expensive version of BT/BRT and BT/RT seem to be tight for any value of t or not small values of t, depending on the initial probability distribution of the model. Class and class models with these additional conditions include both exact and bounding typical failure/repair performability models of fault-tolerant systems with exponential failure and repair time distributions and repair in every state with failed components and a reward rate structure which is a non-increasing function of the collection of failed components. We illustrate both the applicability and the performance of the methods using a large CTMC performability example of a fault-tolerant multiprocessor system.     

On global continuity of Coons mappings in patching CAD surfaces

We tessellate a closed surface bounding a solid into four-sided patches . Each patch is the image of the unit square by which is the composition of a 2D Coons mapping and a bivariate function coming from a trimmed surface. Here, we concentrate on the analysis of the global continuity of the mappings over the whole surface. While using Coons functions to generate the mappings , arc length parametrization ensures that the images of the functions match pointwise at surface joints independently of the blending functions. We will describe a reparametrization technique based on cubic Bézier whose goal is to keep the shape of the initial curves while achieving arc length parametrization. The required accuracy of length computation is shown in L^∞-norm in order not to deteriorate the accuracy of the cubic spline approximation. Practical results from simulated and real CAD data which come from IGES files are reported.     

First-principles study of ground-state properties and phase stability of vanadium nitrides

Using a series of density functional electronic structure total energy calculations, we have systematically studied the ground-state properties and phase stability of vanadium nitrides. Comparison of enthalpy of formation shows that V ₂N is equally stable (polymorphic) in , and Fe₂C phases within a few meV. Formation enthalpy of the various phases considered for perfect stoichiometric V N_1.0 shows that it has enhanced stability in hexagonal WC and NiAs structures in relation to NaCl-type δ-phase. The TiAs phase of VN has nearly same energy as NaCl structure. Comparison of energetics of -type , for x=0 and 0.3333 and of , for x=0, 0.0625, 0.125 and 0.25 shows that vacancies on the nitrogen sublattice lowers the formation enthalpy in relation to respective stoichiometric phases which is in agreement with experiments, as bulk vanadium nitrides are known to be generally non-stoichiometric. The calculated dilute heat of solution for the interstitial nitrogen is found to be in good agreement with experimental values and shows that nitrogen prefers to occupy the octahedral sites in bcc vanadium. The α^′-FeN and martensite structures, considered for the metastable phases of vanadium nitrides, have higher formation enthalpy in relation to equilibrium phases. Analysis of electronic density of states of V ₂N shows that the low energy , and Fe₂C phases are characterized by broad V 3d-N 2p and V 3d bonding bands. Density of states of VN shows that in the low energy WC and NiAs phases some of the antibonding states are made empty, leading to a minimum near the Fermi level. For and , density of states shows that vacancies on the nitrogen sublattice introduce additional filled states in the 3d band below Fermi level enabling enhanced bonding. Comparison between bulk moduli and atomic volumes for the various phases of vanadium nitrides shows that higher bulk moduli are dominated by increased V–N bonds combined with low atomic volumes.     

The global existence of nonlinear observers with linear error dynamics: A topological point of view

In this paper we show that under suitable assumptions, there exists a global homeomorphism Ψ(=Φ^-1) of which maps a nonlinear system onto a linear system with output injection . Thus, an observer for state x can be directly constructed as , which is a generalized version of Luenberger observer. An important feature of the obtained result is that there is no need to find the corresponding change of coordinates Ψ explicitly, which is different from current various existing approaches.     

Matrix representations for toric parametrizations

In this paper we show that a surface in parametrized over a 2-dimensional toric variety can be represented by a matrix of linear syzygies if the base points are finite in number and form locally a complete intersection. This constitutes a direct generalization of the corresponding result over established in [Busé, L., Jouanolou, J.-P., 2003. J. Algebra 265 (1), 312–357] and [Busé, L., Chardin, M.J., 2005. Symbolic Comput. 40 (4–5), 1150–1168]. Exploiting the sparse structure of the parametrization, we obtain significantly smaller matrices than in the homogeneous case and the method becomes applicable to parametrizations for which it previously failed. We also treat the important case in detail and give numerous examples.     

Martingale families and dimension in P

We introduce a new measure notion on small complexity classes (called F-measure), based on martingale families, that gets rid of some drawbacks of previous measure notions: it can be used to define dimension because martingale families can make money on all strings, and it yields random sequences with an equal frequency of 0’s and 1’s. On larger complexity classes ( and above), F-measure is equivalent to Lutz resource-bounded measure. As applications to F-measure, we answer a question raised in [E. Allender, M. Strauss, Measure on small complexity classes, with application for BPP, in: Proc. of the 35th Ann. IEEE Symp. on Found. of Comp. Sci., 1994, pp. 807–818] by improving their result to: for almost every language A decidable in subexponential time, . We show that almost all languages in  do not have small non-uniform complexity. We compare F-measure to previous notions and prove that martingale families are strictly stronger than Γ-measure [E. Allender, M. Strauss, Measure on small complexity classes, with application for BPP, in: Proc. of the 35th Ann. IEEE Symp. on Found. of Comp. Sci., 1994, pp. 807–818], we also discuss the limitations of martingale families concerning finite unions. We observe that all classes closed under polynomial many-one reductions have measure zero in  iff they have measure zero in . We use martingale families to introduce a natural generalization of Lutz resource-bounded dimension [J.H. Lutz, Dimension in complexity classes, in: Proceedings of the 15th Annual IEEE Conference on Computational Complexity, 2000, pp. 158–169] on , which meets the intuition behind Lutz’s notion. We show that -dimension lies between finite-state dimension and dimension on . We prove an analogue of a Theorem of Eggleston in , i.e. the class of languages whose characteristic sequence contains 1’s with frequency α, has dimension the Shannon entropy of α in .     

Minimality considerations for graph energy over a class of graphs

Let G be a graph on n vertices, and let CHP(G;λ) be the characteristic polynomial of its adjacency matrix A(G). All n roots of CHP(G;λ), denoted by , are called to be its eigenvalues. The energy E(G) of a graph G, is the sum of absolute values of all eigenvalues, namely, . Let be the set of n-vertex unicyclic graphs, the graphs with n vertices and n edges. A fully loaded unicyclic graph is a unicyclic graph taken from with the property that there exists no vertex with degree less than 3 in its unique cycle. Let be the set of fully loaded unicyclic graphs. In this article, the graphs in with minimal and second-minimal energies are uniquely determined, respectively.     

Design and analysis of a polymeric photo-thermal microactuator

This paper presents the modeling, simulation and characterization of a photo-thermally actuated bent-beam microactuator. The microactuator consists of a single polymeric layer (SU-8) fabricated with conventional photolithography techniques. The principle of operation is based on the thermal expansion of the bent-beams that absorb the required heat by laser illumination. This provides an effective non-contact actuation mechanism by laser beam focusing. A theoretical model of the microactuator is derived and verified by finite element simulations and experiments. The experiments show that a bent-beam actuator with 800 m long, 40 m wide, 100 m thick and 6° bent arms achieves a tip displacement of 16 m with an incident laser beam of 50 mW power while keeping the maximum temperature less than 125 °C. This study merges the advantages of photo-thermal actuation with practicality of polymeric materials. To verify the effectiveness of the proposed microactuator mechanism, a microgripper with bent-beam actuator was fabricated and characterized. It has been demonstrated that the opening of the gripping fingers can be increased from 20 to 50 m for a microgripper with 1000 m long fingers with an incident laser power of 50 mW. This polymeric microgripper with photo-thermal actuation provides a way of gentle grasping with electrical isolation, high repeatability and low temperature operation that is particularly crucial for biomanipulation applications. The polymeric photo-thermal actuator described in this study expands the practical applications of microactuators/microgrippers which are critical tools in bioMEMS devices.     

The Stable Revivals Model in CSP-Prover

The stable revivals model provides a new semantic framework for the process algebra Csp. The model has recently been added to the realm of established Csp models. Within the Csp context, it enhances the analysis of systems with regards to properties such as responsiveness and stuckness. These properties are essential in component based system design. In this paper we report on the implementation of different variants of the model within Csp-Prover. Based on Isabelle/HOL, Csp-Prover is an interactive proof tool for Csp refinement, which is generic in the underlying Csp model. On the practical side, our encoding of the model provides semi-automatic proof support for reasoning on responsiveness and stuckness. On the theoretical side, our implementation also yields a machine verification of the model 's soundness as well as of its expected properties.