Rational points on X_0^+ (p^r)

We show how the recent isogeny bounds due to \'E. Gaudron and G. R\'emond allow to obtain the triviality of X_0^+ (p^r)(Q), for r>1 and p a prime exceeding 2.10^{11}. This includes the case of the curves X_split (p). We then prove, with the help of computer calculations, that the same holds true for p in the range 10 < p < 10^{14}, p\neq 13. The combination of those results completes the qualitative study of such sets of rational points undertook in previous papers, with the exception of p=13.Comment: 16 pages, no figur

AN INVESTIGATION OF CONCENTRATED AND DISTRIBUTED STRAIN INDUCING CONSTRAINTS FOR TRAINING SHAPE MEMORY ALLOYS

This research explores concentrated and distributed strain inducing constraints for Two Way Shape Memory (TWSM) training of cantilevered NiTiNOL shape memory alloy strips via the constrained thermal cycling of deformed Martensite training method. The goal is to evaluate the performance of a tip-moment trained sample actuator, which is characterized by constant strain along the sample length, and compare it with the performance of tip-force trained sample actuators, which have root concentrated strain. The shape and net tip displacement of trained specimens is expected to vary with training constraint type and training load magnitude, rendering it uncertain which sample will have greater work potential. A training structure and systems for introducing thermal and mechanical loads were developed to provide the explored training constraints and induce TWSM. The work performance was evaluated by measuring vertical displacement of tip weights. The experimental results indicate that samples subject to strain distributing constraints during training have higher work potential than samples subject to concentrated strain inducing constraints

Network structure determines patterns of network reorganization during adult neurogenesis

New cells are generated throughout life and integrate into the hippocampus via the process of adult neurogenesis. Epileptogenic brain injury induces many structural changes in the hippocampus, including the death of interneurons and altered connectivity patterns. The pathological neurogenic niche is associated with aberrant neurogenesis, though the role of the network-level changes in development of epilepsy is not well understood. In this paper, we use computational simulations to investigate the effect of network environment on structural and functional outcomes of neurogenesis. We find that small-world networks with external stimulus are able to be augmented by activity-seeking neurons in a manner that enhances activity at the stimulated sites without altering the network as a whole. However, when inhibition is decreased or connectivity patterns are changed, new cells are both less responsive to stimulus and the new cells are more likely to drive the network into bursting dynamics. Our results suggest that network-level changes caused by epileptogenic injury can create an environment where neurogenic reorganization can induce or intensify epileptic dynamics and abnormal integration of new cells.Comment: 28 pages, 10 figure

Concise Review: Exciting Cells: Modeling Genetic Epilepsies with Patient‐Derived Induced Pluripotent Stem Cells

Human induced pluripotent stem cell (iPSC) models of epilepsy are becoming a revolutionary platform for mechanistic studies and drug discovery. The skyrocketing pace of epilepsy gene discovery is vastly outstripping the development of in vivo animal models. Currently, antiepileptic drug prescribing to patients with specific genetic epilepsies is based on small‐scale clinical trials and empiricism; however, rapid production of patient‐derived iPSC models will allow for precision therapy. We review iPSC‐based studies that have already afforded novel discoveries in diseases with epileptic phenotypes, as well as challenges to using iPSC‐based neurological disease models. We also discuss iPSC‐derived cardiomyocyte studies of arrhythmia‐inducing ion channelopathies that exemplify novel drug discovery and use of multielectrode array technology that can be translated to epilepsy research. Beyond initial studies of Rett, Timothy, Phelan‐McDermid, and Dravet syndromes, the stage is set for groundbreaking iPSC‐based mechanistic and therapeutic discoveries in genetic epilepsies with the potential to impact patient treatment and quality of life. Stem Cells 2016;34:27–33Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134416/1/stem2203_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134416/2/stem2203.pd