Semisimple algebras of almost minimal rank over the reals

A famous lower bound for the bilinear complexity of the multiplication in associative algebras is the Alder–Strassen bound. Algebras for which this bound is tight are called algebras of minimal rank. After 25 years of research, these algebras are now well understood. Here we start the investigation of the algebras for which the Alder–Strassen bound is off by one. As a first result, we completely characterize the semisimple algebras over R$\mathbb{R}$ whose bilinear complexity is by one larger than the Alder–Strassen bound. Furthermore, we characterize all algebras A$A$ (with radical) of minimal rank plus one over R$\mathbb{R}$ for which A/radA$A/radA$ has minimal rank plus one. The other possibility is that A/radA$A/radA$ has minimal rank. For this case, we only present a partial result.     

Constructing algebraic groups from their Lie algebras

A connected algebraic group in characteristic 0$0$ is uniquely determined by its Lie algebra. In this paper algorithms are given for constructing an algebraic group in characteristic 0$0$, given its Lie algebra. In particular, this leads to an algorithm for finding a maximal reductive subgroup and the unipotent radical of an algebraic group.     

The effect of code-mixing on accent identification accuracy

We investigate whether accent identification is more effective for English utterances embedded in a different language as part of a mixed code than for English utterances that are part of a monolingual dialogue. Our focus is on Xhosa and Zulu, two South African languages for which code-mixing with English is very common. In order to carry out our investigation, we extract English utterances from mixed-code Xhosa and Zulu speech corpora, as well as comparable utterances from an English-only corpus by Xhosa and Zulu mother-tongue speakers. Experiments using automatic accent identification systems show that identification is substantially more accurate for the utterances originating from the mixed-code speech. These findings are supported by a corresponding set of perceptual experiments in which human subjects were asked to identify the accents of recorded utterances. We conclude that accent identification is more successful for these utterances because accents are more pronounced for English embedded in mother-tongue speech than for English spoken as part of a monolingual dialogue by non-native speakers. Furthermore we find that this is true for human listeners as well as for automatic identification systems.     

Coinductive big-step operational semantics

Using a call-by-value functional language as an example, this article illustrates the use of coinductive definitions and proofs in big-step operational semantics, enabling it to describe diverging evaluations in addition to terminating evaluations. We formalize the connections between the coinductive big-step semantics and the standard small-step semantics, proving that both semantics are equivalent. We then study the use of coinductive big-step semantics in proofs of type soundness and proofs of semantic preservation for compilers. A methodological originality of this paper is that all results have been proved using the Coq proof assistant. We explain the proof-theoretic presentation of coinductive definitions and proofs offered by Coq, and show that it facilitates the discovery and the presentation of the results.     

On graph reasoning

In this paper, we study the (positive) graph relational calculus. The basis for this calculus was introduced by Curtis and Lowe in 1996 and some variants, motivated by their applications to semantics of programs and foundations of mathematics, appear scattered in the literature. No proper treatment of these ideas as a logical system seems to have been presented. Here, we give a formal presentation of the system, with precise formulation of syntax, semantics, and derivation rules. We show that the set of rules is sound and complete for the valid inclusions, and prove a finite model result as well as decidability. We also prove that the graph relational language has the same expressive power as a first-order positive fragment (both languages define the same binary relations), so our calculus may be regarded as a notational variant of the positive existential first-order logic of binary relations. The graph calculus, however, has a playful aspect, with rules easy to grasp and use. This opens a wide range of applications which we illustrate by applying our calculus to the positive relational calculus (whose set of valid inclusions is not finitely axiomatizable), obtaining an algorithm for deciding the valid inclusions and equalities of the latter.     

A formal analysis of database replication protocols with SI replicas and crash failures

This paper provides a formal specification and proof of correctness of a basic Generalized Snapshot Isolation certification-based data replication protocol for database middleware architectures. It has been modeled using a state transition system, as well as the main system components, allowing a perfect match with the usual deployment in a middleware system. The proof encompasses both safety and liveness properties, as it is commonly done for a distributed algorithm. Furthermore, a crash failure model has been assumed for the correctness proof, although recovery analysis is not the aim of this paper. This allows an easy extension toward a crash-recovery model support in future works. The liveness proof focuses in the uniform commit: if a site has committed a transaction, the rest of sites will either commit it or it would have crashed.     

Toward a human-like biped robot with compliant legs

Conventional models of bipedal walking generally assume rigid body structures, while elastic material properties seem to play an essential role in nature. On the basis of a novel theoretical model of bipedal walking, this paper investigates a model of biped robot which makes use of minimum control and elastic passive joints inspired from the structures of biological systems. The model is evaluated in simulation and a physical robotic platform by analyzing the kinematics and ground reaction force. The experimental results show that, with a proper leg design of passive dynamics and elasticity, an attractor state of human-like walking gait patterns can be achieved through extremely simple control without sensory feedback. The detailed analysis also explains how the dynamic human-like gait can contribute to adaptive biped walking.     

Anodic stripping voltammetric determination of copper(II) using a functionalized carbon nanotubes paste electrode modified with crosslinked chitosan

The development and application of a functionalized carbon nanotubes paste electrode (CNPE) modified with crosslinked chitosan for determination of Cu(II) in industrial wastewater, natural water and human urine samples by linear scan anodic stripping voltammetry (LSASV) are described. Different electrodes were constructed using chitosan and chitosan crosslinked with glutaraldehyde (CTS-GA) and epichlorohydrin (CTS-ECH). The best voltammetric response for Cu(II) was obtained with a paste composition of 65% (m/m) of functionalized carbon nanotubes, 15% (m/m) of CTS-ECH, and 20% (m/m) of mineral oil using a solution of 0.05 mol L⁻¹ KNO₃ with pH adjusted to 2.25 with HNO₃, an accumulation potential of −0.3 V vs. Ag/AgCl (3.0 mol L⁻¹ KCl) for 300 s and a scan rate of 100 mV s⁻¹. Under these optimal experimental conditions, the voltammetric response was linearly dependent on the Cu(II) concentration in the range from 7.90 × 10⁻⁸ to 1.60 × 10⁻⁵ mol L⁻¹ with a detection limit of 1.00 × 10⁻⁸ mol L⁻¹. The samples analyses were evaluated using the proposed sensor and a good recovery of Cu(II) was obtained with results in the range from 98.0% to 104%. The analysis of industrial wastewater, natural water and human urine samples obtained using the proposed CNPE modified with CTS-ECH electrode and those obtained using a comparative method are in agreement at the 95% confidence level.     

Pattern classification with mixtures of weighted least-squares support vector machine experts

Support Vector Machine (SVM) classifiers are high-performance classification models devised to comply with the structural risk minimization principle and to properly exploit the kernel artifice of nonlinearly mapping input data into high-dimensional feature spaces toward the automatic construction of better discriminating linear decision boundaries. Among several SVM variants, Least-Squares SVMs (LS-SVMs) have gained increased attention recently due mainly to their computationally attractive properties coming as the direct result of applying a modified formulation that makes use of a sum-squared-error cost function jointly with equality, instead of inequality, constraints. In this work, we present a flexible hybrid approach aimed at augmenting the proficiency of LS-SVM classifiers with regard to accuracy/generalization as well as to hyperparameter calibration issues. Such approach, named as Mixtures of Weighted Least-Squares Support Vector Machine Experts, centers around the fusion of the weighted variant of LS-SVMs with Mixtures of Experts models. After the formal characterization of the novel learning framework, simulation results obtained with respect to both binary and multiclass pattern classification problems are reported, ratifying the suitability of the novel hybrid approach in improving the performance issues considered.     

Performance analysis of allocation policies for interGrid resource provisioning

Several Grids have been established and used for varying science applications during the last years. Most of these Grids, however, work in isolation and with different utilisation levels. Previous work has introduced an architecture and a mechanism to enable resource sharing amongst Grids. It has demonstrated that there can be benefits for a Grid to offload requests or provide spare resources to another Grid. In this work, we address the problem of resource provisioning to Grid applications in multiple-Grid environments. The provisioning is carried out based on availability information obtained from queueing-based resource management systems deployed at the provider sites which are the participants of the Grids. We evaluate the performance of different allocation policies. In contrast to existing work on load sharing across Grids, the policies described here take into account the local load of resource providers, imprecise availability information and the compensation of providers for the resources offered to the Grid. In addition, we evaluate these policies along with a mechanism that allows resource sharing amongst Grids. Experimental results obtained through simulation show that the mechanism and policies are effective in redirecting requests thus improving the applications’ average weighted response time.