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.     

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.     

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.     

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.     

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.     

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.     

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.     

Ab initio calculations of NO2 and SO2 chemisorption onto non-polar ZnO surfaces

The authors present an ab initio study of NO₂ and SO₂ chemisorption onto non-polar ZnO and ZnO surfaces with the aim of providing theoretical hints for further developments in gas sensors. From first principles calculations (DFT-GGA approximation), the most relevant surface reduction scenarios are analyzed and, subsequently, considered in the chemisorption study. First, calculations indicate that NO₂ adsorbs avidly onto Zn surface atoms. This is compatible with the oxidizing character of NO₂. Second, results also explain the sensor poisoning by SO₂ adsorption (since this molecule competes with NO₂ for the same adsorption sites) and indicate that poisoning can only be reverted at typical operation temperatures (T ≤ 700 °C) in the case of stoichiometric ZnO surfaces.     

On-line SPC with consideration of learning curve

This work identifies a link between on-line statistical process control (SPC) and the learning effect for the process standard deviation (PSD) caused by the quality improvement (QI) program. The learning curve (LC) is used to describe and forecast, and the exponentially weighted root mean square control chart is used to monitor the progress in reducing PSD. A modification of the quality control chart (QCC) that considers LC of PSD is proposed. The reduction rate of PSD may be large during the initial stage of the QI program, and influences QCC construction. Simulation is used to compare the shift-detecting ability of the Shewhart- control chart and EWMA- control chart, without- and with- consideration of LC. The EWMA- chart with consideration of LC performs best. In comparison, the Shewhart- chart without LC consideration has almost no shift-detecting ability when the shift magnitude of the process mean is small, leading to rendering quality control ineffective.     

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.     

Chaos synchronization for a class of discrete dynamical systems on the N-dimensional torus

In this paper, a class of dynamical systems on (the N-dimensional torus) is investigated. It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that the sequences produced are equidistributed for almost every initial data. The above results are then extended to switched affine transformations of . Next, a chaos-synchronization mechanism is introduced and used for masking information in a communication setup.     

Full-rank representation of generalized inverse AT,S and its application

In this paper, we introduce a full-rank representation of the generalized inverse of a given complex matrix A, which is based on an arbitrary full-rank decomposition of G, where G is a matrix such that R(G)=T and N(G)=S. Using this representation, we introduce the minor of the generalized inverse ; as a special case of the minor, a determinantal representation of the generalized inverse is obtained. As an application, we use an example to demonstrate that this representation is correct.     

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.