Locked and Unlocked Polygonal Chains in 3D

In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain are maintained throughout the movement. The analogous concept for closed chains is convexification: reconfiguration to a planar convex polygon. Chains that cannot be straightened or convexified are called locked. While there are open chains in 3D that are locked, we show that if an open chain has a simple orthogonal projection onto some plane, it can be straightened. For closed chains, we show that there are unknotted but locked closed chains, and we provide an algorithm for convexifying a planar simple polygon in 3D with a polynomial number of moves.Comment: To appear in Proc. 10th ACM-SIAM Sympos. Discrete Algorithms, Jan. 199

The Automorphism Group of a Finite p-Group is Almost Always a p-Group

Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups whose automorphism group is a p-group. Yet the goal of this paper is to prove that the automorphism group of a finite p-group is almost always a p-group. The asymptotics in our theorem involve fixing any two of the following parameters and letting the third go to infinity: the lower p-length, the number of generators, and p. The proof of this theorem depends on a variety of topics: counting subgroups of a p-group; analyzing the lower p-series of a free group via its connection with the free Lie algebra; counting submodules of a module via Hall polynomials; and using numerical estimates on Gaussian coefficients.Comment: 38 pages, to appear in the Journal of Algebra; improved references, changes in terminolog

Locked and Unlocked Polygonal Chains in Three Dimensions

This paper studies movements of polygonal chains in three dimensions whose links are not allowed to cross or change length. Our main result is an algorithmic proof that any simple closed chain that initially takes the form of a planar polygon can be made convex in three dimensions. Other results include an algorithm for straightening open chains having a simple orthogonal projection onto some plane, and an algorithm for making convex any open chain initially configured on the surface of a polytope. All our algorithms require only O (n) basic moves.

Branch Rings, Thinned Rings, Tree Enveloping Rings

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which (1) is finitely generated and infinite-dimensional, but has only finite-dimensional quotients; (2) has a subalgebra of finite codimension, isomorphic to $M_2(K)$; (3) is prime; (4) has quadratic growth, and therefore Gelfand-Kirillov dimension 2; (5) is recursively presented; (6) satisfies no identity; (7) contains a transcendental, invertible element; (8) is semiprimitive if k has characteristic $\neq2$; (9) is graded if k has characteristic 2; (10) is primitive if k is a non-algebraic extension of GF(2); (11) is graded nil and Jacobson radical if k is an algebraic extension of GF(2).Comment: 35 pages; small changes wrt previous versio

Normal-superconducting transition induced by high current densities in YBa2Cu3O7-d melt-textured samples and thin films: Similarities and differences

Current-voltage characteristics of top seeded melt-textured YBa2Cu3O7-d are presented. The samples were cut out of centimetric monoliths. Films characteristics were also measured on microbridges patterned on thin films grown by dc sputtering. For both types of samples, a quasi-discontinuity or quenching was observed for a current density J* several times the critical current density Jc. Though films and bulks much differ in their magnitude of both Jc and J*, a proposal is made as to a common intrinsic origin of the quenching phenomenon. The unique temperature dependence observed for the ratio J*/Jc, as well as the explanation of the pre-quenching regime in terms of a single dissipation model lend support to our proposal.Comment: 10 pages, 10 figures, submitted to Physical Review

The Sound Sensation of Apical Electric Stimulation in Cochlear Implant Recipients with Contralateral Residual Hearing

BACKGROUND: Studies using vocoders as acoustic simulators of cochlear implants have generally focused on simulation of speech understanding, gender recognition, or music appreciation. The aim of the present experiment was to study the auditory sensation perceived by cochlear implant (CI) recipients with steady electrical stimulation on the most-apical electrode. METHODOLOGY/PRINCIPAL FINDINGS: Five unilateral CI users with contralateral residual hearing were asked to vary the parameters of an acoustic signal played to the non-implanted ear, in order to match its sensation to that of the electric stimulus. They also provided a rating of similarity between each acoustic sound they selected and the electric stimulus. On average across subjects, the sound rated as most similar was a complex signal with a concentration of energy around 523 Hz. This sound was inharmonic in 3 out of 5 subjects with a moderate, progressive increase in the spacing between the frequency components. CONCLUSIONS/SIGNIFICANCE: For these subjects, the sound sensation created by steady electric stimulation on the most-apical electrode was neither a white noise nor a pure tone, but a complex signal with a progressive increase in the spacing between the frequency components in 3 out of 5 subjects. Knowing whether the inharmonic nature of the sound was related to the fact that the non-implanted ear was impaired has to be explored in single-sided deafened patients with a contralateral CI. These results may be used in the future to better understand peripheral and central auditory processing in relation to cochlear implants

Sociodemographic variables, clinical features, and the role of preassessment cross-sex hormones in older trans people

Introduction: As referrals to gender identity clinics have increased dramatically over the last few years, no studies focusing on older trans people seeking treatment are available. Aims: The aim of this study was to investigate the sociodemographic and clinical characteristics of older trans people attending a national service and to investigate the influence of cross-sex hormones (CHT) on psychopathology. Methods: Individuals over the age of 50 years old referred to a national gender identity clinic during a 30-month period were invited to complete a battery of questionnaires to measure psychopathology and clinical characteristics. Individuals on cross-sex hormones prior to the assessment were compared with those not on treatment for different variables measuring psychopathology. Main Outcome Measures: Sociodemographic and clinical variables and measures of depression and anxiety (Hospital Anxiety and Depression Scale), self-esteem (Rosenberg Self-Esteem Scale), victimization (Experiences of Transphobia Scale), social support (Multidimensional Scale of Perceived Social Support), interpersonal functioning (Inventory of Interpersonal Problems), and nonsuicidal self-injury (Self-Injury Questionnaire). Results: The sex ratio of trans females aged 50 years and older compared to trans males was 23.7:1. Trans males were removed for the analysis due to their small number (n ¼ 3). Participants included 71 trans females over the age of 50, of whom the vast majority were white, employed or retired, and divorced and had children. Trans females on CHT who came out as trans and transitioned at an earlier age were significantly less anxious, reported higher levels of self-esteem, and presented with fewer socialization problems. When controlling for socialization problems, differences in levels of anxiety but not self-esteem remained. Conclusion: The use of cross-sex hormones prior to seeking treatment is widespread among older trans females and appears to be associated with psychological benefits. Existing barriers to access CHT for older trans people may need to be re-examined