Extended GCD and Hermite normal form algorithms via lattice basis reduction

Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers x(1), ..., x(m) for the equation s = gcd (s(1), ..., s(m)) = x(1)s(1) + ... + x(m)s(m), where s1, ... , s(m) are given integers. The method generalises to produce small unimodular transformation matrices for computing the Hermite normal form of an integer matrix.

An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

Polynomial identities for the ternary cyclic sum

We simplify the results of Bremner and Hentzel [J. Algebra 231 (2000) 387-405] on polynomial identities of degree 9 in two variables satisfied by the ternary cyclic sum [a, b, c] abc + bca + cab in every totally associative ternary algebra. We also obtain new identities of degree 9 in three variables which do not follow from the identities in two variables. Our results depend on (i) the LLL algorithm for lattice basis reduction, and (ii) linearization operators in the group algebra of the symmetric group which permit efficient computation of the representation matrices for a non-linear identity. Our computational methods can be applied to polynomial identities for other algebraic structures.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

A systolic array for linear MIMO detection based on an all-swap lattice reduction algorithm

A systolic array to implement lattice-reduction-aided lineardetection is proposed for a MIMO receiver. The lattice reductionalgorithm and the ensuing linear detections are operated in the same array, which can be hardware-efficient. All-swap lattice reduction algorithm (ASLR) is considered for the systolic design.ASLR is a variant of the LLL algorithm, which processes all lattice basis vectors within one iteration. Lattice-reduction-aided linear detection based on ASLR and LLL algorithms have very similarbit-error-rate performance, while ASLR is more time efficient inthe systolic array, especially for systems with a large number ofantennas.

Deterministic Genericity and the Computation of homological Invariants

The main goal of this thesis is to discuss the determination of homological invariants of polynomial ideals. Thereby we consider different coordinate systems and analyze their meaning for the computation of certain invariants. In particular, we provide an algorithm that transforms any ideal into strongly stable position if char k = 0. With a slight modification, this algorithm can also be used to achieve a stable or quasi-stable position. If our field has positive characteristic, the Borel-fixed position is the maximum we can obtain with our method. Further, we present some applications of Pommaret bases, where we focus on how to directly read off invariants from this basis. In the second half of this dissertation we take a closer look at another homological invariant, namely the (absolute) reduction number. It is a known fact that one immediately receives the reduction number from the basis of the generic initial ideal. However, we show that it is not possible to formulate an algorithm – based on analyzing only the leading ideal – that transforms an ideal into a position, which allows us to directly receive this invariant from the leading ideal. So in general we can not read off the reduction number of a Pommaret basis. This result motivates a deeper investigation of which properties a coordinate system must possess so that we can determine the reduction number easily, i.e. by analyzing the leading ideal. This approach leads to the introduction of some generalized versions of the mentioned stable positions, such as the weakly D-stable or weakly D-minimal stable position. The latter represents a coordinate system that allows to determine the reduction number without any further computations. Finally, we introduce the notion of β-maximal position, which provides lots of interesting algebraic properties. In particular, this position is in combination with weakly D-stable sufficient for the weakly D-minimal stable position and so possesses a connection to the reduction number.

The neurobiological basis of prefrontal cortex impairment in the phencyclidine model of schizophrenia : convergent reduction of synaptic glutamate release, energy metabolism and cognitive performance

RÉSUMÉ : Le traitement répété à la phencyclidine (PCP), un bloqueur du récepteur NMDA (NMDAR), reproduit chez les rongeurs une partie de la symptomatologie typique de la schizophrénie. Le blocage prolongé du NMDAR par la PCP mime une hypofunction du NMDAR, une des principales altérations supposées exister dans les cerveaux des patients schizophréniques. Le but de notre étude était d'examiner les conséquences neurochimiques, métaboliques et fonctionnelles du traitement répété à la phencyclidine in vivo, au niveau du cortex préfrontal (cpf), une région cérébrale qui joue un rôle dans les déficits cognitifs observés chez les patients schizophréniques. Pour répondre à cette question, les rats ou les souris ont reçu chaque jour une injection soit de PCP (5 mg/kg), soit de solution saline, pendant 7 ou 14 jours. Les animaux ont ensuite été sacrifiés au moins 24 heures après le dernier traitement. Des tranches aiguës du cpf ont été préparées rapidement, puis stimulées avec une concentration élevée de KCI, de manière à induire une libération de glutamate à partir des terminaisons synaptiques excitatrices. Les résultats montrent que les tranches du cpf des animaux traités à la PCP ont libéré une quantité de glutamate significativement inférieure par rapport à celles des animaux contrôle. Ce déficit de libération a persisté 72 heures après la fin du traitement, tandis qu'il n'était pas observé dans le cortex visuel primaire, une autre région corticale. En outre, le traitement avec des antipsychotiques, l'halopéridol ou l'olanzapine, a supprimé le déficit induit par la PCP. Le même déficit de libération a été remarqué sur des synaptosomes obtenus à partir du cpf des animaux traités à la phenryclidine. Cette observation indique que la PCP induit une modification plastique adaptative du mécanisme qui contrôle la libération du glutamate dans les terminaisons synaptiques. Nous avons découvert que cette modification implique la sous-régulation d'un NMDAR présynaptique, qui serait doué d'un rôle d'autorécepteur stimulateur de la libération du glutamate. Grâce à des tests comportementaux conduits en parallèle et réalisés pour évaluer la fonctionnalité du cpf, nous avons observé chez les souris traitées à la PCP une flexibilité comportementale réduite lors d'un test de discrimination de stimuli visuels/tactiles. Le déficit cognitif était encore présent 4 jours après la dernière administration de PCP. La technique de l'autoradiographie quantitative du [14C]2-deoxyglucose a permis d'associer ce déficit à une réduction de l'activité métabolique cérébrale pendant le déroulement du test, particulièrement au niveau du cpf. Dans l'ensemble, nos résultats suggèrent que le blocage prolongé du NMDAR lors de l'administration répétée de PCP produit un déficit de libération du glutamate au niveau des terminaisons synaptiques excitatrices du cpf. Un tel déficit pourrait être provoqué par la sousrégulation d'un NMDAR présynaptique, qui aurait une fonction de stimulateur de libération; la transmission excitatrice du cpf s'en trouverait dans ce cas réduite. Ce résultat est en ligne avec l'activité métabolique et fonctionnelle réduite du cpf et l'observation de déficits cognitifs induits lors de l'administration de la PCP. ABSTRACT : Sub-chronic treatment with phencyclidine (PCP), an NMDA receptor (NMDAR) channel blocker, reproduces in rodents part of the symptomatology associated to schizophrenia in humans. Prolonged pharmacological blockade of NMDAR with PCP mimics NMDAR hypofunction, one of the main alterations thought to take place in the brains of schizophrenics. Our study was aimed at investigating the neurochemical, metabolic and behavioral consequences of repeated PCP administration in vivo, focusing on the functioning of the prefrontal cortex (pfc), a brain region highly relevant for the cognitive deficits observed in schizophrenic patients. Rats or mice received a daily administration of either PCP (5 mg/kg) or saline for 7 or 14 days. At least 24 hours after the last treatment the animals were sacrificed. Acute slices of the pfc were quickly prepared and challenged with high KCl to induce synaptic glutamate release. Pfc slices from PCP-treated animals released significantly less glutamate than slices from salinetreated animals. The deficit persisted 72 hours after the end of the treatment, while it was not observed in another cortical region: the primary visual cortex. Interestingly, treatment with antipsychotic drugs, either haloperidol or olanzapine, reverted the glutamate release defect induced by PCP treatment. The same release defect was observed in synaptosomes prepared from the pfc of PCP-treated animals, indicating that PCP induces a plastic adaptive change in the mechanism controlling glutamate release in the glutamatergic terminals. We discovered that such change most likely involves the down-regulation of a newly identified, pre-synaptic NMDAR with stimulatory auto-receptor function on glutamate release. In parallel sets of behavioral experiments challenging pfc function, mice sub-chronically treated with PCP displayed reduced behavioral flexibility (reversal learning) in a visual/tactile-cued discrimination task. The cognitive deficit was still evident 4 days after the last PCP administration and was associated to reduced brain metabolic activity during the performance of the behavioral task, notably in the pfc, as determined by [14C]2-deoxyglucose quantitative autoradiography. Clverall, our findings suggest that prolonged NMDAR blockade by repeated PCP administration results in a defect of glutamate release from excitatory afferents in the pfc, possibly ascribed to down-regulation of apre-synaptic stimulatory NMDAR. Deficient excitatory neurotransmission in the pfc is consistent with the reduced metabolic and functional activation of this area and the observed PCP-induced cognitive deficits.

Microbial perchlorate reduction: A precise laboratory determination of the chlorine isotope fractionation and its possible biochemical basis

Perchlorate-reducing bacteria fractionate chlorine stable isotopes giving a powerful approach to monitor the extent of microbial consumption of perchlorate in contaminated sites undergoing remediation or natural perchlorate containing sites. This study reports the full experimental data and methodology used to re-evaluate the chlorine isotope fractionation of perchlorate reduction in duplicate culture experiments of Azospira suillum strain PS at 37 degrees C (Delta Cl-37(Cr)--ClO4-) previously reported, without a supporting data set by Coleman et al. [Coleman, M.L., Ader, M., Chaudhuri, S., Coates,J.D., 2003. Microbial Isotopic Fractionation of Perchlorate Chlorine. Appl. Environ. Microbiol. 69, 4997-5000] in a reconnaissance study, with the goal of increasing the accuracy and precision of the isotopic fractionation determination. The method fully described here for the first time, allows the determination of a higher precision Delta Cl-37(Cl)--ClO4- value, either from accumulated chloride content and isotopic composition or from the residual perchlorate content and isotopic composition. The result sets agree perfectly, within error, giving average Delta Cl-37(Cl)--ClO4- = -14.94 +/- 0.15%omicron. Complementary use of chloride and perchlorate data allowed the identification and rejection of poor quality data by applying mass and isotopic balance checks. This precise Delta Cl-37(Cl)--ClO4-, value can serve as a reference point for comparison with future in situ or microcosm studies but we also note its similarity to the theoretical equilibrium isotopic fractionation between a hypothetical chlorine species of redox state +6 and perchlorate at 37 degrees C and suggest that the first electron transfer during perchlorate reduction may occur at isotopic equilibrium between art enzyme-bound chlorine and perchlorate. (C) 2008 Elsevier B.V. All rights reserved.

A Learning Function for Parameter Reduction in Spiking Neural Networks with Radial Basis Function

Spiking neural networks - networks that encode information in the timing of spikes - are arising as a new approach in the artificial neural networks paradigm, emergent from cognitive science. One of these new models is the pulsed neural network with radial basis function, a network able to store information in the axonal propagation delay of neurons. Learning algorithms have been proposed to this model looking for mapping input pulses into output pulses. Recently, a new method was proposed to encode constant data into a temporal sequence of spikes, stimulating deeper studies in order to establish abilities and frontiers of this new approach. However, a well known problem of this kind of network is the high number of free parameters - more that 15 - to be properly configured or tuned in order to allow network convergence. This work presents for the first time a new learning function for this network training that allow the automatic configuration of one of the key network parameters: the synaptic weight decreasing factor.

REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

A Learning Function for Parameter Reduction in Spiking Neural Networks with Radial Basis Function

Spiking neural networks - networks that encode information in the timing of spikes - are arising as a new approach in the artificial neural networks paradigm, emergent from cognitive science. One of these new models is the pulsed neural network with radial basis function, a network able to store information in the axonal propagation delay of neurons. Learning algorithms have been proposed to this model looking for mapping input pulses into output pulses. Recently, a new method was proposed to encode constant data into a temporal sequence of spikes, stimulating deeper studies in order to establish abilities and frontiers of this new approach. However, a well known problem of this kind of network is the high number of free parameters - more that 15 - to be properly configured or tuned in order to allow network convergence. This work presents for the first time a new learning function for this network training that allow the automatic configuration of one of the key network parameters: the synaptic weight decreasing factor.

Evaluation of Several Carbon-Supported Nanostructured Ni-Doped Manganese Oxide Materials for the Electrochemical Reduction of Oxygen

Physical and electrochemical properties of nanostructured Ni-doped manganese oxides (MnO(x)) catalysts supported on different carbon powder substrates were investigated so as to characterize any carbon substrate effect toward the oxygen reduction reaction (ORR) kinetics in alkaline medium. These NiMnO(x)/C materials were characterized using physicochemical analyses. Small insertion of Ni atoms in the MnO(x) lattice was observed, which consists of a true doping of the manganese oxide phase. The corresponding NiMnO(x) phase is present in the form of needles or agglomerates, with crystallite sizes in the order of 1.5-6.7 nm (from x-ray diffraction analyses). Layered manganite (MnOOH) phase has been detected for the Monarch 1000-supported NiMnO(x) material, while different species of MnO(x) phases are present at the E350G and MM225 carbons. Electrochemical studies in thin porous coating active layers in the rotating ring-disk electrode setup revealed that the MnO(x) catalysts present better ORR kinetics and electrochemical stability upon Ni doping. The ORR follows the so-called peroxide mechanism on MnO(x)/C catalysts, with the occurrence of minority HO(2)(-) disproportionation reaction. The HO(2)(-) disproportionation reaction progressively increases with the Ni content in NiMnO(x) materials. The catalysts supported on the MM225 and E350G carbons promote faster disproportionation reaction, thus leading to an overall four-electron ORR pathway. (C) 2011 The Electrochemical Society. [DOI: 10.1149/1.3528439] All rights reserved.

PKC beta II inhibition attenuates myocardial infarction induced heart failure and is associated with a reduction of fibrosis and pro-inflammatory responses

Protein kinase C beta II (PKC beta II) levels increase in the myocardium of patients with end-stage heart failure (HF). Also targeted overexpression of PKC beta II in the myocardium of mice leads to dilated cardiomyopathy associated with inflammation, fibrosis and myocardial dysfunction. These reports suggest a deleterious role of PKC beta II in HF development. Using a post-myocardial infarction (MI) model of HF in rats, we determined the benefit of chronic inhibition of PKC beta II on the progression of HF over a period of 6 weeks after the onset of symptoms and the cellular basis for these effects. Four weeks after MI, rats with HF signs that were treated for 6 weeks with the PKC beta II selective inhibitor (beta IIV5-3 conjugated to TAT(47-57) carrier peptide) (3 mg/kg/day) showed improved fractional shortening (from 21% to 35%) compared to control (TAT(47-57) carrier peptide alone). Formalin-fixed mid-ventricle tissue sections stained with picrosirius red, haematoxylin and eosin and toluidine blue dyes exhibited a 150% decrease in collagen deposition, a two-fold decrease in inflammation and a 30% reduction in mast cell degranulation, respectively, in rat hearts treated with the selective PKC beta II inhibitor. Further, a 90% decrease in active TGF beta 1 and a significant reduction in SMAD2/3 phosphorylation indicated that the selective inhibition of PKC beta II attenuates cardiac remodelling mediated by the TGF-SMAD signalling pathway. Therefore, sustained selective inhibition of PKC beta II in a post-MI HF rat model improves cardiac function and is associated with inhibition of pathological myocardial remodelling.