COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p(3)

A loop is said to be automorphic if its inner mappings are automorphisms. For a prime p, denote by A(p) the class of all 2-generated commutative automorphic loops Q possessing a central subloop Z congruent to Z(p) such that Q/Z congruent to Z(p) x Z(p). Upon describing the free 2-generated nilpotent class two commutative automorphic loop and the free 2-generated nilpotent class two commutative automorphic p-loop F-p in the variety of loops whose elements have order dividing p(2) and whose associators have order dividing p, we show that every loop of A(p) is a quotient of F-p by a central subloop of order p(3). The automorphism group of F-p induces an action of GL(2)(p) on the three-dimensional subspaces of Z(F-p) congruent to (Z(p))(4). The orbits of this action are in one-to-one correspondence with the isomorphism classes of loops from A(p). We describe the orbits, and hence we classify the loops of A(p) up to isomorphism. It is known that every commutative automorphic p-loop is nilpotent when p is odd, and that there is a unique commutative automorphic loop of order 8 with trivial center. Knowing A(p) up to isomorphism, we easily obtain a classification of commutative automorphic loops of order p(3). There are precisely seven commutative automorphic loops of order p(3) for every prime p, including the three abelian groups of order p(3).

Influence of the magnetization damping on dynamic hysteresis loops in single domain particles

This article reports on the influence of the magnetization damping on dynamic hysteresis loops in single-domain particles with uniaxial anisotropy. The approach is based on the Neel-Brown theory and the hierarchy of differential recurrence relations, which follow from averaging over the realizations of the stochastic Landau-Lifshitz equation. A new method of solution is proposed, where the resulting system of differential equations is solved directly using optimized algorithms to explore its sparsity. All parameters involved in uniaxial systems are treated in detail, with particular attention given to the frequency dependence. It is shown that in the ferromagnetic resonance region, novel phenomena are observed for even moderately low values of the damping. The hysteresis loops assume remarkably unusual shapes, which are also followed by a pronounced reduction of their heights. Also demonstrated is that these features remain for randomly oriented ensembles and, moreover, are approximately independent of temperature and particle size. (C) 2012 American Institute of Physics. [doi:10.1063/1.3684629]

THE STRUCTURE OF FREE AUTOMORPHIC MOUFANG LOOPS

We describe the structure of a free loop of rank n in the variety of automorphic Moufang loops as a subdirect product of a free group and a free commutative Moufang loop, both of rank n. In particular, the variety of automorphic Moufang loops is the join of the variety of groups and the variety of commutative Moufang loops.

Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system

Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the micro-cantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Q) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. (C) 2011 Elsevier B.V. All rights reserved.

Dynamic symmetry loss of high-frequency hysteresis loops in single-domain particles with uniaxial anisotropy

Understanding how magnetic materials respond to rapidly varying magnetic fields, as in dynamic hysteresis loops, constitutes a complex and physically interesting problem. But in order to accomplish a thorough investigation, one must necessarily consider the effects of thermal fluctuations. Albeit being present in all real systems, these are seldom included in numerical studies. The notable exceptions are the Ising systems, which have been extensively studied in the past, but describe only one of the many mechanisms of magnetization reversal known to occur. In this paper we employ the Stochastic Landau-Lifshitz formalism to study high-frequency hysteresis loops of single-domain particles with uniaxial anisotropy at an arbitrary temperature. We show that in certain conditions the magnetic response may become predominantly out-of-phase and the loops may undergo a dynamic symmetry loss. This is found to be a direct consequence of the competing responses due to the thermal fluctuations and the gyroscopic motion of the magnetization. We have also found the magnetic behavior to be exceedingly sensitive to temperature variations, not only within the superparamagnetic-ferromagnetic transition range usually considered, but specially at even lower temperatures, where the bulk of interesting phenomena is seen to take place. (C) 2011 Elsevier B.V. All rights reserved.

Hard Thermal Loops in the n-Dimensional phi(3) Theory

We derive a closed-form result for the leading thermal contributions which appear in the n-dimensional I center dot (3) theory at high temperature. These contributions become local only in the long wavelength and in the static limits, being given by different expressions in these two limits.

Two extensions for the ALWABP: Parallel stations and collaborative approach

In this article, we introduce two new variants of the Assembly Line Worker Assignment and Balancing Problem (ALWABP) that allow parallelization of and collaboration between heterogeneous workers. These new approaches suppose an additional level of complexity in the Line Design and Assignment process, but also higher flexibility; which may be particularly useful in practical situations where the aim is to progressively integrate slow or limited workers in conventional assembly lines. We present linear models and heuristic procedures for these two new problems. Computational results show the efficiency of the proposed approaches and the efficacy of the studied layouts in different situations. (C) 2012 Elsevier B.V. All rights reserved.

Low-energy electron collisions with glycine

We report cross sections for elastic electron scattering by gas phase glycine (neutral form), obtained with the Schwinger multichannel method. The present results are the first obtained with a new implementation that combines parallelization with OpenMP directives and pseudopotentials. The position of the well known pi* shape resonance ranged from 2.3 eV to 2.8 eV depending on the polarization model and conformer. For the most stable isomer, the present result (2.4 eV) is in fair agreement with electron transmission spectroscopy assignments (1.93 +/- 0.05 eV) and available calculations. Our results also point out a shape resonance around 9.5 eV in the A' symmetry that would be weakly coupled to vibrations of the hydroxyl group. Since electron attachment to a broad and lower lying sigma* orbital located on the OH bond has been suggested the underlying mechanism leading to dissociative electron attachment at low energies, we sought for a shape resonance around similar to 4 eV. Though we obtained cross sections with the target molecule at the equilibrium geometry and with stretched OH bond lengths, least-squares fits to the calculated eigenphase sums did not point out signatures of this anion state (though, in principle, it could be hidden in the large background). The low energy (similar to 1 eV) integral cross section strongly scales as the bond length is stretched, and this could indicate a virtual state pole, since dipole supported bound states are not expected at the geometries addressed here. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3687345]

Generalizations of Lie Algebras

The generalizations of Lie algebras appeared in the modern mathematics and mathematical physics. In this paper we consider recent developments and remaining open problems on the subject. Some of that developments have been influenced by lectures given by Professor Jaime Keller in his research seminar. The survey includes Lie superalgebras, color Lie algebras, Lie algebras in symmetric categories, free Lie tau-algebras, and some generalizations with non-associative enveloping algebras: tangent algebras to analytic loops, bialgebras and primitive elements, non-associative Hopf algebras.

Architectures, stability and optimization for clock distribution networks

Synchronous telecommunication networks, distributed control systems and integrated circuits have its accuracy of operation dependent on the existence of a reliable time basis signal extracted from the line data stream and acquirable to each node. In this sense, the existence of a sub-network (inside the main network) dedicated to the distribution of the clock signals is crucially important. There are different solutions for the architecture of the time distribution sub-network and choosing one of them depends on cost, precision, reliability and operational security. In this work we expose: (i) the possible time distribution networks and their usual topologies and arrangements. (ii) How parameters of the network nodes can affect the reachability and stability of the synchronous state of a network. (iii) Optimizations methods for synchronous networks which can provide low cost architectures with operational precision, reliability and security. (C) 2011 Elsevier B. V. All rights reserved.

Special identities for Bol algebras

Bol algebras appear as the tangent algebra of Bol loops. A (left) Bol algebra is a vector space equipped with a binary operation [a, b] and a ternary operation {a, b, c} that satisfy five defining identities. If A is a left or right alternative algebra then A(b) is a Bol algebra, where [a, b] := ab - ba is the commutator and {a, b, c} := < b, c, a > is the Jordan associator. A special identity is an identity satisfied by Ab for all right alternative algebras A, but not satisfied by the free Bol algebra. We show that there are no special identities of degree <= 7, but there are special identities of degree 8. We obtain all the special identities of degree 8 in partition six-two. (C) 2011 Elsevier Inc. All rights reserved.

On the Evolution of Hexose Transporters in Kinetoplastid Potozoans

Glucose, an almost universally used energy and carbon source, is processed through several well-known metabolic pathways, primarily glycolysis. Glucose uptake is considered to be the first step in glycolysis. In kinetoplastids, a protozoan group that includes relevant human pathogens, the importance of glucose uptake in different phases of the life cycles is well established, and hexose transporters have been proposed as targets for therapeutic drugs. However, little is known about the evolutionary history of these hexose transporters. Hexose transporters contain an intracellular N- and C-termini, and 12 transmembrane spans connected by alternate intracellular and extracellular loops. In the present work we tested the hypothesis that the evolutionary rate of the transmembrane span is different from that of the whole sequence and that it is possible to define evolutionary units inside the sequence. The phylogeny of whole molecules was compared to that of their transmembrane spans and the loops connecting the transmembrane spans. We show that the evolutionary units in these proteins primarily consist of clustered rather than individual transmembrane spans. These analyses demonstrate that there are evolutionary constraints on the organization of these proteins; more specifically, the order of the transmembrane spans along the protein is highly conserved. Finally, we defined a signature sequence for the identification of kinetoplastid hexose transporters.

Gray Matter Volumes in Obsessive-Compulsive Disorder Before and After Fluoxetine or Cognitive-Behavior Therapy: A Randomized Clinical Trial

Serotonin reuptake inhibitors and cognitive-behavior therapy (CBT) are considered first-line treatments for obsessive-compulsive disorder (OCD). However, little is known about their modulatory effects on regional brain morphology in OCD patients. We sought to document structural brain abnormalities in treatment-naive OCD patients and to determine the effects of pharmacological and cognitive-behavioral treatments on regional brain volumes. Treatment-naive patients with OCD (n = 38) underwent structural magnetic resonance imaging scan before and after a 12-week randomized clinical trial with either fluoxetine or group CBT. Matched-healthy controls (n = 36) were also scanned at baseline. Voxel-based morphometry was used to compare regional gray matter (GM) volumes of regions of interest (ROIs) placed in the orbitofrontal, anterior cingulate and temporolimbic cortices, striatum, and thalamus. Treatment-naive OCD patients presented smaller GM volume in the left putamen, bilateral medial orbitofrontal, and left anterior cingulate cortices than did controls (p<0.05, corrected for multiple comparisons). After treatment with either fluoxetine or CBT (n = 26), GM volume abnormalities in the left putamen were no longer detectable relative to controls. ROI-based within-group comparisons revealed that GM volume in the left putamen significantly increased (p<0.012) in fluoxetine-treated patients (n = 13), whereas no significant GM volume changes were observed in CBT-treated patients (n = 13). This study supports the involvement of orbitofronto/cingulo-striatal loops in the pathophysiology of OCD and suggests that fluoxetine and CBT may have distinct neurobiological mechanisms of action. Neuropsychopharmacology (2012) 37, 734-745; doi: 10.1038/npp.2011.250; published online 26 October 2011

ON SOME GENERALIZATIONS OF GROUPS WITH TRIALITY

In the present paper we generalize the concept of groups with triality and apply it to the theory of the Moufang, Bol and Bruck loops. Such generalizations allow us to reduce certain problems from the loop theory to problems in the theory of groups.

BF Integrase Genes of HIV-1 Circulating in Sao Paulo, Brazil, with a Recurrent Recombination Region

Although some studies have shown diversity in HIV integrase (IN) genes, none has focused particularly on the gene evolving in epidemics in the context of recombination. The IN gene in 157 HIV-1 integrase inhibitor-naive patients from the Sao Paulo State, Brazil, were sequenced tallying 128 of subtype B (23 of which were found in non-B genomes), 17 of subtype F (8 of which were found in recombinant genomes), 11 integrases were BF recombinants, and 1 from subtype C. Crucially, we found that 4 BF recombinant viruses shared a recurrent recombination breakpoint region between positions 4900 and 4924 (relative to the HXB2) that includes 2 gRNA loops, where the RT may stutter. Since these recombinants had independent phylogenetic origin, we argue that these results suggest a possible recombination hotspot not observed so far in BF CRF in particular, or in any other HIV-1 CRF in general. Additionally, 40% of the drug-naive and 45% of the drug-treated patients had at least 1 raltegravir (RAL) or elvitegravir (EVG) resistance-associated amino acid change, but no major resistance mutations were found, in line with other studies. Importantly, V151I was the most common minor resistance mutation among B, F and BF IN genes. Most codon sites of the IN genes had higher rates of synonymous substitutions (dS) indicative of a strong negative selection. Nevertheless, several codon sites mainly in the subtype B were found under positive selection. Consequently, we observed a higher genetic diversity in the B portions of the mosaics, possibly due to the more recent introduction of subtype F on top of an ongoing subtype B epidemics and a fast spread of subtype F alleles among the B population.