Class Notes for Math 901/902: Abstract Algebra, Instructor Tom Marley

Topics include: Free groups and presentations; Automorphism groups; Semidirect products; Classification of groups of small order; Normal series: composition, derived, and solvable series; Algebraic field extensions, splitting fields, algebraic closures; Separable algebraic extensions, the Primitive Element Theorem; Inseparability, purely inseparable extensions; Finite fields; Cyclotomic field extensions; Galois theory; Norm and trace maps of an algebraic field extension; Solvability by radicals, Galois' theorem; Transcendence degree; Rings and modules: Examples and basic properties; Exact sequences, split short exact sequences; Free modules, projective modules; Localization of (commutative) rings and modules; The prime spectrum of a ring; Nakayama's lemma; Basic category theory; The Hom functors; Tensor products, adjointness; Left/right Noetherian and Artinian modules; Composition series, the Jordan-Holder Theorem; Semisimple rings; The Artin-Wedderburn Theorem; The Density Theorem; The Jacobson radical; Artinian rings; von Neumann regular rings; Wedderburn's theorem on finite division rings; Group representations, character theory; Integral ring extensions; Burnside's paqb Theorem; Injective modules.

Obstacles to Inter-Racial Understanding: Some Clinical Implications for Mental Health Practitioners in Predominantly White Institutions

in the context of predominantly white institutions. In this paper concepts such as projection, projective identification, splitting, scapegoating, superiority and denial will be employed to illustrate why racial prejudice is a deeply-rooted collective psychological disorder that affects even educated mental health practitioners. Clinicians have an ethical responsibility to demonstrate cultural sensitivity and empathy when working with minority clients, colleagues, staff and students, to examine and root out their own prejudices, and to encourage others to do the same.

Montagem e avaliação de um sistema de varredura a LASER embarcado em VANT

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Consumo de energia em escalonadores de transações em sistemas de memória transacional em software

Pós-graduação em Ciência da Computação - IBILCE

Localizador de faltas por ondas viajantes em linhas de transmissão

It is important to ensure smoothly operation of a transmission line, sending energy to the consumption centers with minimal interruptions and safer. With this necessity, the fault location techniques have grown, in order to mitigate the impact of the fault and its correction can be more quickly and accurately. This paper presents a comparison between two different techniques of fault location, the fault location by impedance method, which uses the line parameters, the impedance per distance, voltage and current signals, and the other is the traveling wave method, which uses only a very fast analysis of time, synchronization and length between the line ends, do not using voltage and current values, but the temporal perception of the fault. Using travelling waves fault detection makes the previous knowledge of line parameters obsolete, which helps a lot network technicians and engineers with a quick and easy analysis. The methods are simulated in ATP Draw software, so both algorithms can be evaluated for their effectively and accuracy

Effects of two estradiol esters (benzoate and cypionate) on the induction of synchronized ovulations in Bos indicus cows submitted to a timed artificial insemination protocol

The effects of estradiol benzoate (EB) and estradiol cypionate (EC) on induction of ovulation after a synchronized LH surge and on fertility of Bos indicus females submitted to timed AI (TAI) were evaluated. In Experiment 1, ovariectomized Nelore heifers were used to evaluate the effect of EB (n = 5) and EC (n = 5) on the circulating LH profile. The LH surge timing (19.6 and 50.5 h; P = 0.001), magnitude (20.5 and 9.4 ng/mL; P = 0.005), duration (8.6 and 16.5 h; P = 0.001), and area under the LH curve (158.6 and 339.4 ng/mL; P = 0.01) differed between the EB and EC treatments, respectively. In Experiment 2 (follicular responses; n = 60) and 3 (pregnancy per AI; P/AI; n = 953) suckled Bos indicus beef cows submitted to an estradiol/progesterone-based synchronization protocol were assigned to receive one of two treatments to induce synchronized ovulation: 1 mg of EB im 24 h after progesterone (P4) device removal or 1 mg of EC im at P4 device removal. There was no difference (P > 0.05) between EB and EC treatments on follicular responses (maximum diameter of the ovulatory follicle, 13.1 vs. 13.9 mm; interval from progesterone device removal to ovulation, 70.2 vs. 68.5 h; and ovulation rate, 77.8 vs. 82.8%, respectively). In addition, P/AI was similar (P < 0.22) between the cows treated with EB (57.5%; 277/482) and EC (61.8%; 291/471). In conclusion, despite pharmacologic differences, both esters of estradiol administered either at P4 device removal (EC) or 24 h later (EB) were effective in inducing an LH surge which resulted in synchronized ovulations and similar P/AI in suckled Bos indicus beef cows submitted to TAI. (C) 2012 Elsevier Inc. All rights reserved.

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.

Collective Almost Synchronisation in Complex Networks

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

Chaos-based communication systems in non-ideal channels

Recently, many chaos-based communication systems have been proposed. They can present the many interesting properties of spread spectrum modulations. Besides, they can represent a low-cost increase in security. However, their major drawback is to have a Bit Error Rate (BER) general performance worse than their conventional counterparts. In this paper, we review some innovative techniques that can be used to make chaos-based communication systems attain lower levels of BER in non-ideal environments. In particular, we succinctly describe techniques to counter the effects of finite bandwidth, additive noise and delay in the communication channel. Although much research is necessary for chaos-based communication competing with conventional techniques, the presented results are auspicious. (C) 2011 Elsevier B. V. All rights reserved.

External temporal organization in biological rhythms

This paper is intended as a proposition of a new concept in the field of chronobiology, External Temporal Organization, a notion complementary to that of the Internal Temporal Organization. We will try to explain the possibility that a set of external elements, that occur in a particular order, can act together as a single synchronizing element of the circadian system. We will see that this is not a zeitgeber, in the classic sense, but a much more complex factor, consisting of several elements that appear in the real environment at different times ( phases), constituting as a whole a powerful temporal frame, closer to the way the stimuli occur in the natural environment, in which the entrainment does not take place just in a specific time of the day.

A scheme for synchronizing clocks connected by a packet communication network

Consider a communication system in which a transmitter equipment sends fixed-size packets of data at a uniform rate to a receiver equipment. Consider also that these equipments are connected by a packet-switched network, which introduces a random delay to each packet. Here we propose an adaptive clock recovery scheme able of synchronizing the frequencies and the phases of these devices, within specified limits of precision. This scheme for achieving frequency and phase synchronization is based on measurements of the packet arrival times at the receiver, which are used to control the dynamics of a digital phase-locked loop. The scheme performance is evaluated via numerical simulations performed by using realistic parameter values. (C) 2011 Elsevier By. All rights reserved.

Modeling the Emergence of Circadian Rhythms in a Clock Neuron Network

Circadian rhythms in pacemaker cells persist for weeks in constant darkness, while in other types of cells the molecular oscillations that underlie circadian rhythms damp rapidly under the same conditions. Although much progress has been made in understanding the biochemical and cellular basis of circadian rhythms, the mechanisms leading to damped or self-sustained oscillations remain largely unknown. There exist many mathematical models that reproduce the circadian rhythms in the case of a single cell of the Drosophila fly. However, not much is known about the mechanisms leading to coherent circadian oscillation in clock neuron networks. In this work we have implemented a model for a network of interacting clock neurons to describe the emergence (or damping) of circadian rhythms in Drosophila fly, in the absence of zeitgebers. Our model consists of an array of pacemakers that interact through the modulation of some parameters by a network feedback. The individual pacemakers are described by a well-known biochemical model for circadian oscillation, to which we have added degradation of PER protein by light and multiplicative noise. The network feedback is the PER protein level averaged over the whole network. In particular, we have investigated the effect of modulation of the parameters associated with (i) the control of net entrance of PER into the nucleus and (ii) the non-photic degradation of PER. Our results indicate that the modulation of PER entrance into the nucleus allows the synchronization of clock neurons, leading to coherent circadian oscillations under constant dark condition. On the other hand, the modulation of non-photic degradation cannot reset the phases of individual clocks subjected to intrinsic biochemical noise.

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

Alpha-band power in the left frontal cortex discriminates the execution of fixed stimulus during saccadic eye movement

Introduction: The saccadic paradigm has been used to investigate specific cortical networks involving attention. The behavioral and electrophysiological investigations of the SEM contribute significantly to the understanding of attentive patterns presented of neurological and psychiatric disorders and sports performance. Objective: The current study aimed to investigate absolute alpha power changes in sensorimotor brain regions and the frontal eye fields during the execution of a saccadic task. Methods: Twelve healthy volunteers (mean age: 26.25; SD: +/- 4.13) performed a saccadic task while the electroencephalographic signal was simultaneously recorded for the cerebral cortex electrodes. The participants were instructed to follow the LEDs with their eyes, being submitted to two different task conditions: a fixed pattern versus a random pattern. Results: We found a moment main effect for the C3, C4, F3 and F4 electrodes and a condition main effect for the F3 electrode. We also found interaction between factor conditions and frontal electrodes. Conclusions: We conclude that absolute alpha power in the left frontal cortex discriminates the execution of the two stimulus presentation patterns during SEM. (C) 2012 Elsevier Ireland Ltd. All rights reserved.

Experimental study on vortex-induced motions of a semi-submersible platform with four square columns, Part I: Effects of current incidence angle and hull appendages

An experimental study on Vortex-Induced Motion (VIM) of the semi-submersible platform concept with four square columns is presented. Model tests were carried out to check the influence of different headings and hull appendages (riser supports located at the pontoons; fairleads and the mooring stretches located vertically at the external column faces; and hard pipes located vertically at the internal column faces). The results comprise in-line, transverse and yaw motions, as well as combined motions in the XY plane, drag and lift forces and spectral analysis. The main results showed that VIM in the transverse direction occurred in a range of reduced velocity 4.0 up to 14.0 with amplitude peaks around reduced velocities around 7.0 and 8.0. The largest transverse amplitudes obtained were around 40% of the column width for 30 degrees and 45 degrees incidences. Another important result observed was a considerable yaw motion oscillation, in which a synchronization region could be identified as a resonance phenomenon. The largest yaw motions were verified for the 0 degrees incidence and the maxima amplitudes around 4.5 degrees. The hull appendages located at columns had the greatest influence on the VIM response of the semi-submersible. (C) 2012 Elsevier Ltd. All rights reserved.