Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)

Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie algebra $\mathfrak{g}_{\bar{0}}$. In an earlier paper the authors demonstrated that for any module $M$ in $\mathcal{F}$ the rate of growth of the minimal projective resolution (i.e., the complexity of $M$) is bounded by the dimension of $\mathfrak{g}_{\bar{1}}$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.Comment: 32 page

The Dissociation between Early and Late Selection in Older Adults

Older adults exhibit a reduced ability to ignore task-irrelevant stimuli; however, it remains to be determined where along the information processing stream the most salient age-associated changes occur. In the current study, ERPs provided an opportunity to determine whether age-related differences in processing task-irrelevant stimuli were uniform across information processing stages or disproportionately affected either early or late selection. ERPs were measured in young and old adults during a color-selective attention task in which participants responded to target letters in a specified color (attend condition) while ignoring letters in a different color (ignore condition). Old participants were matched to two groups of young participants on the basis of neuropsychological test performance: one using age-appropriate norms and the other using test scores not adjusted for age. There were no age-associated differences in the magnitude of early selection (attend–ignore), as indexed by the size of the anterior selection positivity and posterior selection negativity. During late selection, as indexed by P3b amplitude, both groups of young participants generated neural responses to target letters under the attend versus ignore conditions that were highly differentiated. In striking contrast, old participants generated a P3b to target letters with no reliable differences between conditions. Individuals who were slow to initiate early selection appeared to be less successful at executing late selection. Despite relative preservation of the operations of early selection, processing delays may lead older participants to allocate excessive resources to task-irrelevant stimuli during late selection

Universal deformation rings for the symmetric group S_4

Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Let S_4 denote the symmetric group on 4 letters. We determine the universal deformation ring R(S_4,V) for every kS_4-module V which has stable endomorphism ring k and show that R(S_4,V) is isomorphic to either k, or W[t]/(t^2,2t), or the group ring W[Z/2]. This gives a positive answer in this case to a question raised by the first author and Chinburg whether the universal deformation ring of a representation of a finite group with stable endomorphism ring k is always isomorphic to a subquotient ring of the group ring over W of a defect group of the modular block associated to the representation.Comment: 12 pages, 2 figure

Программное обеспечение для обучения в малых группах

This article focuses on the method of group training which represents one of the most actual and perspective forms of the organization of educational process. Authors confirm the theoretical conclusions with the experiment made with students of specialty "Information Systems and Technologies". Besides, article includes the description opportunities of the program adapted for work in small groups.В данной статье рассматривается метод группового обучения, который представляет собой одну из наиболее актуальных и перспективных форм организации учебного процесса. Авторы подтверждают свои теоретические выводы экспериментом, проведенным со студентами старших курсов специальности «Информационные системы и технологии». Кроме того, статья включает описание возможностей программы, адаптированной для выполнения общего задания в группах

Tensor Constructions of Open String Theories I: Foundations

The possible tensor constructions of open string theories are analyzed from first principles. To this end the algebraic framework of open string field theory is clarified, including the role of the homotopy associative A_\infty algebra, the odd symplectic structure, cyclicity, star conjugation, and twist. It is also shown that two string theories are off-shell equivalent if the corresponding homotopy associative algebras are homotopy equivalent in a strict sense. It is demonstrated that a homotopy associative star algebra with a compatible even bilinear form can be attached to an open string theory. If this algebra does not have a spacetime interpretation, positivity and the existence of a conserved ghost number require that its cohomology is at degree zero, and that it has the structure of a direct sum of full matrix algebras. The resulting string theory is shown to be physically equivalent to a string theory with a familiar open string gauge group.Comment: 62 pages, LaTe

Computer simulation of syringomyelia in dogs

Syringomyelia is a pathological condition in which fluid-filled cavities (syringes) form and expand in the spinal cord. Syringomyelia is often linked with obstruction of the craniocervical junction and a Chiari malformation, which is similar in both humans and animals. Some brachycephalic toy breed dogs such as Cavalier King Charles Spaniels (CKCS) are particularly predisposed. The exact mechanism of the formation of syringomyelia is undetermined and consequently with the lack of clinical explanation, engineers and mathematicians have resorted to computer models to identify possible physical mechanisms that can lead to syringes. We developed a computer model of the spinal cavity of a CKCS suffering from a large syrinx. The model was excited at the cranial end to simulate the movement of the cerebrospinal fluid (CSF) and the spinal cord due to the shift of blood volume in the cranium related to the cardiac cycle. To simulate the normal condition, the movement was prescribed to the CSF. To simulate the pathological condition, the movement of CSF was blocked

Implementation of the Projector Augmented Wave LDA+U Method: Application to the Electronic Structure of NiO

The so-called local density approximation plus the multi-orbital mean-field Hubbard model (LDA+U) has been implemented within the all-electron projector augmented-wave method (PAW), and then used to compute the insulating antiferromagnetic ground state of NiO and its optical properties. The electronic and optical properties have been investigated as a function of the Coulomb repulsion parameter U. We find that the value obtained from constrained LDA (U=8 eV) is not the best possible choice, whereas an intermediate value (U=5 eV) reproduces the experimental magnetic moment and optical properties satisfactorily. At intermediate U, the nature of the band gap is a mixture of charge transfer and Mott-Hubbard type, and becomes almost purely of the charge-transfer type at higher values of U. This is due to the enhancement of the oxygen 2p states near the top of the valence states with increasing U value.Comment: 23 pages, 6 figures, submitted to Phys. Rev.

Property (T) and rigidity for actions on Banach spaces

We study property (T) and the fixed point property for actions on $L^p$ and other Banach spaces. We show that property (T) holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient of $L^p$), and that in fact it is independent of $1\leq p<\infty$. We show that the fixed point property for $L^p$ follows from property (T) when 1. For simple Lie groups and their lattices, we prove that the fixed point property for $L^p$ holds for any $1< p<\infty$ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement

A Region-Wide Field Placement Program Built on the Foundation of Mentorship and Professionalism

Background: The Region IV Public Health Training Center (R-IV PHTC) provides public health students from the eight states of HHS Region IV with essential practice experiences that demonstrate the value of working with underserved populations. The Pathways to Practice Scholars field placement program is built on a foundation of mentorship, professionalism, and community. Methods: Sixteen student scholars (13 graduate; 3 undergraduate) were selected to work during May-August 2015 in practiceoriented agencies serving underserved populations. Each scholar received a $1500 living allowance. Seven of 16 accepted an internship outside the state of their university. In conjunction with mentors, Scholars developed work plans based on Council on Linkages Core Competency domains. Requirements included a pre-, mid- and post-assessment, an executive summary/reflection, and a virtual webinar presentation. Results: Student Scholars worked at sites across eight states in state or local health departments, Area Health Education Centers (AHECs), and healthcare settings. Students identified Core Competency domains they developed most during the field placement: Communication, Analytical/Assessment, Leadership/Systems Thinking, and Community Engagement. The R-IV PHTC asked mentors to treat interns as valued employees and include them in activities beyond their specific project. Indicators of successful mentorship included expressed appreciation for student assistance and the desire to enrich the student experience while benefiting the agency mission. Mentors provided clearly defined projects for a short timeframe (10-12 weeks), adjusted to the students’ capacity and readiness, and offered opportunities to apply classroom skills to practice. They helped students develop immediately useful products in collaboration with community stakeholders. Conclusions: Mentors play a crucial role in the development and success of field placement students, but students and mentors share equal responsibility in fostering the relationship. Past case studies from this program demonstrate that some students find employment in these same agencies after graduation, and become mentors for future students, thus, creating a self-perpetuating learning community