Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

On some Finite-Dimensional Representations of Artin Braid Group

Валентин В. Илиев - Авторът изучава някои хомоморфни образи G на групата на Артин на плитките върху n нишки в крайни симетрични групи. Получените пермутационни групи G са разширения на симетричната група върху n букви чрез подходяща абелева група. Разширенията G зависят от един целочислен параметър q ≥ 1 и се разцепват тогава и само тогава, когато 4 не дели q. В случая на нечетно q са намерени всички крайномерни неприводими представяния на G, а те от своя страна генерират безкрайна редица от неприводими представяния на групата на плитките.

Braid groups, mapping class groups, and Torelli groups

This thesis discusses subgroups of mapping class groups of particular surfaces. First, we study the Torelli group, that is, the subgroup of the mapping class group that acts trivially on the first homology. We investigate generators of the Torelli group, and we give an algorithm that factorizes elements of the Torelli group into products of particular generators. Furthermore, we investigate normal closures of powers of standard generators of the mapping class group of a punctured sphere. By using the Jones representation, we prove that in most cases these normal closures have infinite index in the mapping class group. We prove a similar result for the hyperelliptic mapping class group, that is, the group that consists of mapping classes that commute with a fixed hyperelliptic involution. As a corollary, we recover an older theorem of Coxeter (with 2 exceptional cases), which states that the normal closure of the m-th power of standard generators of the braid group has infinite index in the braid group. Finally, we study finite index subgroups of braid groups, namely, congruence subgroups of braid groups. We discuss presentations of these groups and we provide a topological interpretation of their generating sets.

A mixer design for the pigtail braid

The stirring of a body of viscous fluid using multiple stirring rods is known to be particularly effective when the rods trace out a path corresponding to a nontrivial mathematical braid. The optimal braid is the so-called "pigtail braid", in which three stirring rods execute the usual "over-under" motion associated with braiding plaiting) hair. We show how to achieve this optimal braiding motion straightforwardly: one stirring rod is driven in a figure-of-eight motion, while the other two rods are baffles, which rotate episodically about their common centre. We also explore the extent to which the physical baffles may be replaced by flow structures (such as periodic islands).

46,XX Male - Testicular Disorder of Sexual Differentiation (DSD): hormonal, molecular and cytogenetic studies

The XX male syndrome - Testicular Disorder of Sexual Differentiation (DSD) is a rare condition characterized by a spectrum of clinical presentations, ranging from ambiguous to normal male genitalia. We report hormonal, molecular and cytogenetic evaluations of a boy presenting with this syndrome. Examination of the genitalia at age of 16 months, showed: penis of 3.5 cm, proximal hypospadia and scrotal testes. Pelvic ultrasound did not demonstrate Mullerian duct structures. Karyotype was 46,XX. Gonadotrophin stimulation test yielded insufficient testosterone production. Gonadal biopsy showed seminiferous tubules without evidence of Leydig cells. Molecular studies revealed that SRY and TSPY genes and also DYZ3 sequences were absent. In addition, the lack of deletions or duplications of SOX9, NR5A1, WNT4 and NROB1 regions was verified. The infant was heterozygous for all microsatellites at the 9p region, including DMRT1 gene, investigated. Only 10% of the patients are SRY-negative and usually they have ambiguous genitalia, as the aforementioned patient. The incomplete masculinization suggests gain of function mutation in one or more genes downstream to SRY gene.

Floquet stability analysis of the flow around an oscillating cylinder

This investigative work is concerned with the flow around a circular cylinder submitted to forced transverse oscillations. The goal is to investigate how the transition to turbulence is initiated in the wake for cases with different Reynolds numbers (Re) and displacement amplitudes (A). For each Re the motion frequency is kept constant, close to the Strouhal number of the flow around a fixed cylinder at the same Re. Stability analysis of two-dimensional periodic flows around a forced-oscillating cylinder is carried out with respect to three-dimensional infinitesimal perturbations. The procedure consists of performing a Floquet type analysis of time-periodic base flows, computed using the spectral/hp element method. With the results of the Floquet calculations, considerations regarding the stability of the system are drawn, and the form of the instability at its onset is obtained. The critical Reynolds number is observed to change with the amplitude of oscillation. With respect to instabilities, unstable modes with the same symmetry as mode A of a fixed cylinder are observed; however, they present different wavelengths. Also, the instabilities observed for the oscillating cylinder are distinctively stronger in the braid shear layers. Other unstable modes similar to mode B are found. Quasi-periodic modes are observed in the 2S wake, and subharmonic mode occurrences are reported in P + S wakes. (C) 2009 Elsevier Ltd. All rights reserved.

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.

Introducing resistance genes against ToMV, TYLCV and TSWV infections in two tomato varieties (Muchamiel and De la Pera)

Dissertação de mestrado em Biologia Molecular, Biotecnologia e Bioempreendedorismo em Plantas

Varões entrançados de material compósito com capacidade de monitorização

Dissertação de mestrado integrado em Engenharia Civil

Hipnose para controle de claustrofobia em exames de ressonância magnética

OBJETIVO: Testar a eficácia da hipnose para o controle de claustrofobia em pacientes submetidos a exames de ressonância magnética. MATERIAIS E MÉTODOS: Vinte pacientes claustrofóbicos, com indicação de sedação para ressonância magnética, foram submetidos a hipnose pela técnica de Braid. Os pacientes suscetíveis à hipnose foram encaminhados para realização do exame em estado de transe hipnótico, sem uso de medicamentos para sedação. RESULTADOS: Da amostra estudada, 18 casos (90%) foram suscetíveis à técnica. Dos 16 pacientes sensíveis à hipnose que compareceram para a ressonância magnética, 15 (93,8%) realizaram o exame em transe hipnótico, sem ocorrência de crise de claustrofobia e sem necessitar de medicamentos para sedação. CONCLUSÃO: Hipnose é uma alternativa para a sedação medicamentosa em pacientes claustrofóbicos que necessitam realizar ressonância magnética.

ONKI-projektin ontologiaeditorien vertailuraportti

Kansalliskirjastossa maaliskuussa 2013 käynnistynyt ONKI-projekti vastaa yleisen suomalaisen ontologian (YSO) sekä kansallisen ONKI-ontologiapalvelun kehityksestä ja ylläpidosta. ONKI-projektia rahoittavat valtiovarainministeriö sekä opetus- ja kulttuuriministeriö. Projektin alkuvaiheen ensimmäisiä tavoitteita on ollut vertailla tällä hetkellä tarjolla olevia ontologioiden muokkaukseen käytettäviä ohjelmistoja, joista tästedes käytämme nimeä ontologiaeditori. Vertailun perusteella annetaan yhteenveto ja suositus vertailussa olleista vaihtoehdoista. Ontologia- editori on keskeisin työväline projektin jatkovaiheessa ja vastaavia työkaluja käyttävät myös Kansalliskirjaston ulkopuoliset, ONKI-projektiin liittyvät yhteistyötahot. Raportissa esitellään projektin taustaa ja ontologiaeditorien käyttöä ja merkitystä ontologiatyössä sekä niihin liittyvät perusvaatimukset. Vertailussa olleet editorit, Top Braid Composer eri versioineen, Protégé 4.3, TopBraid EVN, PoolParty Thesaurus Server, VocBench, IQvoc sekä TemaTres esitellään kukin erikseen. Lopuksi esitetään yhteenveto ja suositus.

Bone properties and skeletal maturity in adolescent males, as assessed by quantitative ultrasound

ABSTRACT Background: Previous studies have implied that weight-bearing, intense and prolonged physical activities optimize bone accretion during the grow^ing years. The majority of past inquiries have used dual-energy X-ray absorptiometry (DXA) to examine bone strength and hand-wrist radiography to determine skeletal maturity in children. Recently, quantitative ultrasound (QUS) technologies have been developed to examine bone properties and skeletal maturity in a safe, noninvasive and cost-effective manner. Objective: The purpose of this study was to compare bone properties and skeletal maturity in competitive male child and adolescent athletes with minimallyactive, age-matched controls, using QUS technology. >. Methods: In total, 224 males were included in the study. The 115 pre-pubertal boys aged 10-12 years consisted of control, minimally-active children (n=34), soccer players (n=26), gymnasts (n=25) and hockey players (n=30). In addition, the 109 late-pubertal boys aged 14-16 years consisted of control, minimally-active adolescents (n=31), soccer players (n=30), gymnasts (n=17) and hockey players (n=31). The athletic groups were elite level players that predominantly trained year-round. Physical activity, nutrition and sports participation were assessed with various questionnaires. Anthropometries, such as height, weight and relative body fat percentage (BF%) were assessed using standard measures. Skeletal strength and age were evaluated using bone QUS. Lastly, salivary testosterone (sT) concentration was measured using Radioimmunoassay (RIA). Results: Within each age group, there were no significant differences between the activity groups in age and pubertal stage. An age effect was apparent in all variables, as expected. A sport effect was noted in all physical characteristics: the child and adolescent gymnasts were shorter and lighter than other sports groups. Adiposity was greater in the controls and in the hockey players. All child subjects were pubertal stage (fanner) I or II, while adolescent subjects were pubertal stage IV or V. There were no differences in daily energy and mineral intakes between sports groups. In both age groups, gymnasts had a higher training volume than other athletic groups. Bone speed of sound (50s) was higher in adolescents compared with the children. Gymnasts had signifieantly higher radial 50S than controls, hockey and soccer players in both age cohorts. Hockey athletes also had higher radial 50S than controls and soccer players in the child and adolescent groups, respectiyely. Child gymnasts and soccer players had greater tibial 50S compared with the hockey players and control groups. Likewise, adolescent gymnasts and soccer players had higher tibial SoS compared with the control group. No interaction was apparent between age and type of activity in any of the bone measures. » Lastly, maturity as assessed by sT and secondary sex characteristics (Tanner stage) was not different between sports group within each age group. Despite the similarity in chronological age, androgen levels and sexual maturity, differences between activity groups were noted in skeletal maturity. In the younger group, hockey players had the highest bone age while the soccer players had the lowest bone age. In the adolescent group, gymnasts and hockey players were characterized by higher skeletal maturity compared with controls. An interaction between the age and sport type effects was apparent in skeletal maturity, reflecting the fact that among the children, the soccer players were significantly less mature than the rest of the groups, while in the adolescents, the controls were the least skeletally mature. Summary and Conclusions: In summary, radial and tibial SOS are enhanced by the unique loading pattern in each sport (i.e, upper and lower extremities in gymnastics, lower extremities in soccer), with no cumulative effect between childhood and adolescence. That is, the effect of sport participation on bone SOS was apparent already among the young athletes. Enhanced bone properties among athletes of specific sports suggest that participation in these sports can improve bone strength and potential bone health.

Distinguishing links up to link-homotopy by algebraic methods

In this paper we provide a complete algebraic invariant of link-homotopy, that is, an algebraic invariant that distinguishes two links if and only if they are link-homotopic. The paper establishes a connection between the ""peripheral structures"" approach to link-homotopy taken by Milnor, Levine and others, and the string link action approach taken by Habegger and Lin. (C) 2009 Elsevier B.V. All rights reserved.