On Some Schützenberger Conjectures

In this paper we consider factorizing codes C over A, i.e., codes verifying the factorization conjecture by Schützenberger. Let n be the positive integer such that aⁿC, we show how we can construct C starting with factorizing codes C′ with a^n′C′ and n′ < n, under the hypothesis that all words aⁱza^j in C, with z(A\a)A*(A\a) (A\a), satisfy i, j, > n. The operation involved, already introduced by Anselmo, is also used to show that all maximal codes C=P(A−1)S+1 with P, SZA and P or S in Za can be constructed by means of this operation starting with prefix and suffix codes. Old conjectures by Schützenberger have been revised.     

The mean-shift outlier model in general weighted regression and its applications

Consider the general weighted linear regression model y=Xβ+, where E()=0, Cov()=Vσ², σ² is an unknown positive scalar, and V is a symmetric positive-definite matrix not necessary diagonal. Two models, the mean-shift outlier model and the case-deletion model, can be employed to develop multiple case-deletion diagnostics for the linear model. The multiple case-deletion diagnostics are obtained via the mean-shift outlier model in this article and are shown to be equivalent to the deletion diagnostics via the case deletion model obtained by Preisser and Qaqish (1996, Biometrika, 83, 551–562). In addition, computing the multiple case-deletion diagnostics obtained via the mean-shift outlier model is faster than computing the one based on the more commonly used case-deletion model in some situations. Applications of the multiple deletion diagnostics developed from the mean-shift outlier model are also given for regression analysis with the likelihood function available and regression analysis based on generalized estimating equations. These applications include survival models and the generalized estimating equations of Liang and Zeger (1986, Biometrika, 73, 13–22). Several numerical experiments as well as a real example are given as illustrations.     

Sentences over Integral Domains and Their Computational Complexities

LetRbe a Hilbertian domain and letKbe its fraction field. Letψ(x₁, …, x_n, y) be a quantifier free arithmetical formula overR. We may also takeψ(x₁, …, x_n, y) to be an arithmetical formula overK[x₁, …, x_n] and write it asψ(y). In this paper we show that ifRhas enough non-units and x₁…x_n y ψ(x₁, …, x_n, y), called an ⁿ  sentence, is true inR, then y ψ(y) is true inK[x₁, …, x_n]. Also, ifR=K[T], whereKis an infinite integral domain andx₁…x_n y ψ(x₁, …, x_n, y)is true inR, then y ψ(y) is true inR[x₁, …, x_n]. These results are applied to find the upper and lower bounds of the time complexities of various decision problems on diophantine equations with parameters and arithmetical sentences. Some of the results are: 1. The decision problem of sentences and diophantine equations with parameters over the ring of integers of a global field are co-NP-complete. 2. The decision problem of sentences over the ring of integers of a global field is NP-complete. 3. LetKbe an infinite domain, the time complexities of the decision problems of equations with parameters and sentences over the polynomial ringK[t] are polynomial time reducible to factoring polynomials overK. 4. The decision problem of sentences over all algebraic integer rings is in P. 5. The decision problem of sentences over all integral domains with characteristic 0 is in P. 6. The time complexity of the decision problem of sentences over all integral domains is polynomial time reducible to factoring integers overZand factoring polynomials over finite fields.     

Drag and lift coefficients of inclined finite circular cylinders at moderate Reynolds numbers

The flow around two-dimensional cylinders at moderate Reynolds numbers has been much studied, both for cylinders perpendicular to the flow and for cylinders yawed to the flow. In contrast, yawed finite aspect ratio cylinders have received little attention. In this article we describe computer simulations of cylinders with aspect ratios 2  L/D  20 yawed at angles 0°  α  90° relative to a free stream. The simulations were carried out for Reynolds numbers in the range 1  Re  40. The simulations show that the Independence Principle [Zdravkovich MM. Flow around circular cylinders, vol. 2: applications. New York: Oxford University Press; 2003[1]] is not accurate for α  45°. We have also found that for all aspect ratios, the ratio of the lift to drag force reaches a maximum for 40° < α < 50°. Finally, we present C_L and C_D relationships as best curve fits to computational data.     

Convergence performance comparison of quantum-inspired multi-objective evolutionary algorithms

In recent research, we proposed a general framework of quantum-inspired multi-objective evolutionary algorithms (QMOEA) and gave one of its sufficient convergence conditions to the Pareto optimal set. In this paper, two Q-gate operators, H gate and R&N gate, are experimentally validated as two Q-gate paradigms meeting the convergence condition. The former is a modified rotation gate, and the latter is a combination of rotation gate and NOT gate with the specified probability. To investigate their effectiveness and applicability, several experiments on the multi-objective 0/1 knapsack problems are carried out. Compared to two typical evolutionary algorithms and the QMOEA only with rotation gate, the QMOEA with H gate and R&N gate have more powerful convergence ability in high complex instances. Moreover, the QMOEA with R&N gate has the best convergence in almost all of the experimental problems. Furthermore, the appropriate ε value regions for two Q-gates are verified.     

Fully Scalable Fault-Tolerant Simulations for BSP and CGM

In this paper we consider general simulations of algorithms designed for fully operational BSP and CGM machines on machines with faulty processors. The BSP (or CGM) machine is a parallel multicomputer consisting of p processors for which a memory of n words is evenly distributed and each processor can send and receive at most h messages in a superstep. The faults are deterministic (i.e., worst-case distributions of faults are considered) and static (i.e., they do not change in the course of computation). We assume that a constant fraction of processors are faulty.  We present two fault-tolerant simulation techniques for BSP and CGM:  1. A deterministic simulation that achieves O(1) slowdown for local computations and O((log_h p)²) slowdown for communications per superstep, provided that a preprocessing is done that requires O((log_h p)²) supersteps and linear (in h) computation per processor in each superstep.  2. A randomized simulation that achieves O(1) slowdown for local computations and O(log_h p) slowdown for communications per superstep with high probability, after the same (deterministic) preprocessing as above.  Our results are fully scalable over all values of p from Θ(1) to Θ(n). Furthermore, our results imply that if pn for 0<<1 and h=Θ((n/p)^δ) for 0<δ1 (which hold in almost all practical BSP and CGM computations), algorithms can be made resilient to a constant fraction of processor faults without any asymptotic slowdown.     

Communication Protocols for Secure Distributed Computation of Binary Functions

A common task in parallel processing is the distributed computation of a function by a number of processors, each of which possesses partial information relevant to the value of that function. In this paper we develop communication protocols which allow for such computation to take place while maintaining the value of the function secret to an eavesdropper. Of interest is the communication complexity of such protocols. We begin by considering two processors and two channels, one secret and one public, and present a protocol which minimizes the number of bits exchanged over the secret channel, while maintaining -uncertainty about the value of the function for the eavesdropper. We show that all binary functions can be kept -secret using a constant number of bits independent of the size of their domain. We then generalize our results to N processors communicating over a network of arbitrary topology.     

A Logic for Reasoning about Generic Judgments

This paper presents an extension of a proof system for encoding generic judgments, the logic FOλ^Δ of Miller and Tiu, with an induction principle. The logic FOλ^Δ is itself an extension of intuitionistic logic with fixed points and a “generic quantifier”, , which is used to reason about the dynamics of bindings in object systems encoded in the logic. A previous attempt to extend FOλ^Δ with an induction principle has been unsuccessful in modeling some behaviours of bindings in inductive specifications. It turns out that this problem can be solved by relaxing some restrictions on , in particular by adding the axiom B≡x.B, where x is not free in B. We show that by adopting the equivariance principle, the presentation of the extended logic can be much simplified. Cut-elimination for the extended logic is stated, and some applications in reasoning about an object logic and a simply typed λ-calculus are illustrated.     

Generating fuzzy rules from training instances for fuzzy classification systems

In recent years, many methods have been proposed to generate fuzzy rules from training instances for handling the Iris data classification problem. In this paper, we present a new method to generate fuzzy rules from training instances for dealing with the Iris data classification problem based on the attribute threshold value α, the classification threshold value β and the level threshold value γ, where α  [0, 1], β  [0, 1] and γ  [0, 1]. The proposed method gets a higher average classification accuracy rate than the existing methods.     

A generalization of ACP using Belnap’s logic

ACP is combined with Belnap’s four-valued logic via conditional composition (if–then–else). We show that the operators of ACP can be seen as instances of more general, conditional operators. For example, both the choice operator + and δ (deadlock) can be seen as instances of conditional composition, and the axiom x + δ = x follows from this perspective. Parallel composition is generalized to the binary conditional merge _ψ where covers the choice between interleaving and synchronization, and ψ determines the order of execution. The instance _BB is ACP’s parallel composition, where B (both) is the truth value that models both true and false in Belnap’s logic. Other instances of this conditional merge are sequential composition, pure interleaving and synchronous merge. We investigate the expression of scheduling strategies in the conditions of the conditional merge.     

Modelling Generic Judgements

We propose a semantics for the -quantifier of Miller and Tiu. First we consider the case for classical first-order logic. In this case, the interpretation is close to standard Tarski-semantics and completeness can be shown using a standard argument. Then we put our semantics into a broader context by giving a general interpretation of in categories with binding structure. Since categories with binding structure also encompass nominal logic, we thus show that both -logic and nominal logic can be modelled using the same definition of binding. As a special case of the general semantics in categories with binding structure, we recover Gabbay & Cheney's translation of FOλ into nominal logic.     

The Undecidability of the First-Order Theories of One Step Rewriting in Linear Canonical Systems

By reduction from the halting problem for Minsky's two-register machines we prove that there is no algorithm capable of deciding the -theory of one step rewriting of an arbitrary finite linear confluent finitely terminating term rewriting system (weak undecidability). We also present a fixed such system with undecidable *-theory of one step rewriting (strong undecidability). This improves over all previously known results of the same kind.     

Response time of nanostructured relative humidity sensors

Capacitive relative humidity (RH) sensors were fabricated by coating countersunk interdigitated electrode substrates with nanostructured TiO₂ films produced using glancing angle deposition. Areal capacitance increased from 1 nF cm⁻² to 800 nF cm⁻² as relative humidity was increased from 2% RH and 95% RH. For films deposited at 81° and with a thickness below 4 m, response time was (162±4) ms m⁻¹. Response times increased from 64 ms to 1440 ms as film thickness increased from 280 nm to 8.5 m. The linear dependence of response time with film thickness indicates that device response time is dominated by surface adsorption. Response time decreased with increasing deposition angle, with a slope of (−15.2±1.6) ms degree⁻¹ for the adsorption data, and (−17.3±2.5) ms degree⁻¹ for the desorption data. The optimum operating range of the sensors depends on deposition angle, and can be tuned to different ranges to match application needs.     

Predicate Abstraction for Dense Real-Time Systems

We propose predicate abstraction as a means for verifying a rich class of safety and liveness properties for dense real-time systems. First, we define a restricted semantics of timed systems which is observationally equivalent to the standard semantics in that it validates the same set of μ-calculus formulas without a next-step operator. Then, we recast the model checking problem S for a timed automaton S and a μ-calculus formula in terms of predicate abstraction. Whenever a set of abstraction predicates forms a so-called basis, the resulting abstraction is strongly preserving in the sense that S validates iff the corresponding finite abstraction validates this formula . Now, the abstracted system can be checked using familiar μ-calculus model checking. Like the region graph construction for timed automata, the predicate abstraction algorithm for timed automata usually is prohibitively expensive. In many cases it suffices to compute an approximation of a finite bisimulation by using only a subset of the basis of abstraction predicates. Starting with some coarse abstraction, we define a finite sequence of refined abstractions that converges to a strongly preserving abstraction. In each step, new abstraction predicates are selected nondeterministically from a finite basis. Counterexamples from failed μ-calculus model checking attempts can be used to heuristically choose a small set of new abstraction predicates for refining the abstraction.     

Interactions Between PVS and Maple in Symbolic Analysis of Control Systems

This paper presents a decision procedure for problems relating polynomial and transcendental functions. The procedure applies to functions that are continuously differentiable with a finite number of points of inflection in a closed convex set. It decides questions of the form ‘is f0?’, where {=,>,<}. An implementation of the procedure in Maple and PVS exploits the existing Maple, PVS and QEPCAD connections. It is at present limited to those twice differentiable functions whose derivatives are rational functions (rationally differentiable). This procedure is particularly applicable to the analysis of control systems in determining important properties such as stability.     

Modeling of the angle of shearing resistance of soils using soft computing systems

Precise determination of the effective angle of shearing resistance (′) value is a major concern and an essential criterion in the design process of the geotechnical structures, such as foundations, embankments, roads, slopes, excavation and liner systems for the solid waste. The experimental determination of ′ is often very difficult, expensive and requires extreme cautions and labor. Therefore many statistical and numerical modeling techniques have been suggested for the ′ value. However they can only consider no more than one parameter, in a simplified manner and do not provide consistent accurate prediction of the ′ value. This study explores the potential of Genetic Expression Programming, Artificial Neural Network (ANN) and Adaptive Neuro Fuzzy (ANFIS) computing paradigm in the prediction of ′ value of soils. The data from consolidated-drained triaxial tests (CID) conducted in this study and the different project in Turkey and literature were used for training and testing of the models. Four basic physical properties of soils that cover the percentage of fine grained (FG), the percentage of coarse grained (CG), liquid limit (LL) and bulk density (BD) were presented to the models as input parameters. The performance of models was comprehensively evaluated some statistical criteria. The results revealed that GEP model is fairly promising approach for the prediction of angle of shearing resistance of soils. The statistical performance evaluations showed that the GEP model significantly outperforms the ANN and ANFIS models in the sense of training performances and prediction accuracies.     

Wireless network design via 3-decompositions

We consider some network design problems with applications for wireless networks. The input for these problems is a metric space (X,d) and a finite subset UX of terminals. In the Steiner Tree with Minimum Number of Steiner Points (STMSP) problem, the goal is to find a minimum size set SX−U of points so that the unit-disc graph of S+U is connected. Let Δ be the smallest integer so that for any finite VX for which the unit-disc graph is connected, this graph contains a spanning tree with maximum degree Δ. The best known approximation ratio for STMSP was Δ−1 [I.I. Măndoiu, A.Z. Zelikovsky, A note on the MST heuristic for bounded edge-length Steiner trees with minimum number of Steiner points, Information Processing Letters 75 (4) (2000) 165–167]. We improve this ratio to (Δ+1)/2+1+ε.In the Minimum Power Spanning Tree (MPST) problem, V=X is finite, and the goal is to find a “range assignment” on the nodes so that the edge set contains a spanning tree, and ∑_vVp(v) is minimized. We consider a particular case {0,1}-MPST of MPST when the distances are in {0,1}; here the goal is to find a minimum size set SV of “active” nodes so that the graph (V,E₀+E₁(S)) is connected, where , and E₁(S) is the set the edges in with both endpoints in S. We will show that the (5/3+ε)-approximation scheme for MPST of [E. Althaus, G. Calinescu, I. Măndoiu, S. Prasad, N. Tchervenski, A. Zelikovsky, Power efficient range assignment for symmetric connectivity in static ad hoc wireless networks, Wireless Networks 12 (3) (2006) 287–299] achieves a ratio 3/2 for {0,1}-distances. This answers an open question posed in [E. Lloyd, R. Liu, S. Ravi, Approximating the minimum number of maximum power users in ad hoc networks, Mobile Networks and Applications 11 (2006) 129–142].     

Approximating the Minimum Chain Completion problem

A bipartite graph G=(U,V,E) is a chain graph [M. Yannakakis, Computing the minimum fill-in is NP-complete, SIAM J. Algebraic Discrete Methods 2 (1) (1981) 77–79] if there is a bijection such that Γ(π(1))Γ(π(2))Γ(π(|U|)), where Γ is a function that maps a node to its neighbors.We give approximation algorithms for two variants of the Minimum Chain Completion problem, where we are given a bipartite graph G(U,V,E), and the goal is find the minimum set of edges F that need to be added to G such that the bipartite graph G^′=(U,V,E^′) (E^′=EF) is a chain graph.     

Ordering the order of a distributive lattice by itself

We order the ordering relation of an arbitrary poset P component-wise by itself, obtaining a poset Φ(P) extending P. In particular, the effects of Φ on L  DLAT01, the category of all bounded distributive lattices, are studied, mainly with the aid of Priestley duality. We characterize those L  DLAT01 which occur as Φ(K) for some K  DLAT01, decide this situation in polynomial time for finite L, characterize fixpoints of Φ within DLAT01 and relate them to free objects in DLAT01.     

Liquid–solid equilibria in quinary system Na,Mg/Cl,SO4,NO3–H2O at 298.15 K

In order to develop the nitrate deposits found close to Lop Nur in the Xinjiang region in China, the solubilities of the system Na⁺,Mg²⁺/Cl⁻,SO₄²⁻, NO₃⁻–H₂O and its subsystems, the quaternary systems Na⁺,Mg²⁺/SO₄²⁻,NO₃⁻–H₂O and Mg²⁺/Cl⁻,SO₄²⁻,NO₃⁻–H₂O, were studied at 298.15 K. The phase diagrams were plotted according to the solubilities achieved. In the equilibrium phase diagram of Mg²⁺/Cl⁻,SO₄²⁻,NO₃⁻–H₂O, there are two invariant points, five univariant curves and four regions of crystallization: Mg(NO₃)₂6H₂O,MgCl₂6H₂O,MgSO₄7H₂O and MgSO₄(1–6)H₂O. In the equilibrium phase diagram of Na⁺,Mg²⁺/SO₄²⁻, NO₃⁻–H₂O, there are five invariant points, eleven univariant curves and seven regions of crystallization: Na₂SO₄,Na₂SO₄10H₂O,NaNO₃,MgSO₄Na₂SO₄4H₂O,NaNO₃Na₂SO₄2H₂O,Mg(NO₃)₂6H₂O and MgSO₄7H₂O. In the equilibrium phase diagram of the Na⁺, Mg²⁺/Cl⁻,SO₄²⁻,NO₃⁻–H₂O system, there are six invariant points, and ten regions of crystallization: NaCl, NaNO₃,Na₂SO₄,Na₂SO₄10H₂O,MgSO₄Na₂SO₄4H₂O, NaNO₃Na₂SO₄2H₂O,MgCl₂6H₂O,Mg(NO₃)₂6H₂O, MgSO₄(1–6)H₂O and MgSO₄7H₂O.