On the tensor rank of multiplication in any extension of \F_2

In this paper, we obtain new bounds for the tensor rank of multiplication in any extension of \F_2. In particular, it also enables us to obtain the best known asymptotic bound. In this aim, we use the generalized algorithm of type Chudnovsky with derivative evaluations on places of degree one, two and four applied on the descent over \F_2 of a Garcia-Stichtenoth tower of algebraic function fields defined over \F_{2^4}

Getting Past It's Not For People Like Us: Pacific Northwest Ballet Builds a Following with Teens and Young Adults

This case study examines how the Pacific Northwest Ballet set about trying to cultivate the next generation of ballet-goers. Focusing on teens and adults under the age of 25, the Seattle-based ballet company sought in part to knock down the view of many young people that ballet is stuffy or boring and replace it with the view that ballet could be exciting and meaningful to them. The ballet company attacked the problem on a number of fronts, including revising promotional materials to appeal to younger audiences, posting online videos to familiarize viewers with the ballet, holding teen-only previews, and offering heavily discounted tickets. One result was a doubling over four years of ticket sales to teens

Designing for Ballet Classes: Identifying and Mitigating Communication Challenges Between Dancers and Teachers

Dancer-teacher communication in a ballet class can be challenging: ballet is one of the most complex forms of movements, and learning happens through multi-faceted interactions with studio tools (mirror, barre, and floor) and the teacher. We conducted an interview-based qualitative study with seven ballet teachers and six dancers followed by an open-coded analysis to explore the communication challenges that arise while teaching and learning in the ballet studio. We identified key communication issues, including adapting to multi-level dancer expertise, transmitting and realigning development goals, providing personalized corrections and feedback, maintaining the state of flow, and communicating how to properly use tools in the environment. We discuss design implications for crafting technological interventions aimed at mitigating these communication challenges

Creating Work That Matters: Memphis Choreographs to the Soul of a City

Explores the artistic development of Ballet Memphis -- how it became a thriving company within a community that had not historically supported ballet, and how it continues to evolve artistically while remaining relevant to the community

Lower bounds on the class number of algebraic function fields defined over any finite field

We give lower bounds on the number of effective divisors of degree $\leq g-1$ with respect to the number of places of certain degrees of an algebraic function field of genus $g$ defined over a finite field. We deduce lower bounds and asymptotics for the class number, depending mainly on the number of places of a certain degree. We give examples of towers of algebraic function fields having a large class number.Comment: 24 page

Motor simulation without motor expertise: enhanced corticospinal excitability in visually experienced dance spectators

The human “mirror-system” is suggested to play a crucial role in action observation and execution, and is characterized by activity in the premotor and parietal cortices during the passive observation of movements. The previous motor experience of the observer has been shown to enhance the activity in this network. Yet visual experience could also have a determinant influence when watching more complex actions, as in dance performances. Here we tested the impact visual experience has on motor simulation when watching dance, by measuring changes in corticospinal excitability. We also tested the effects of empathic abilities. To fully match the participants' long-term visual experience with the present experimental setting, we used three live solo dance performances: ballet, Indian dance, and non-dance. Participants were either frequent dance spectators of ballet or Indian dance, or “novices” who never watched dance. None of the spectators had been physically trained in these dance styles. Transcranial magnetic stimulation was used to measure corticospinal excitability by means of motor-evoked potentials (MEPs) in both the hand and the arm, because the hand is specifically used in Indian dance and the arm is frequently engaged in ballet dance movements. We observed that frequent ballet spectators showed larger MEP amplitudes in the arm muscles when watching ballet compared to when they watched other performances. We also found that the higher Indian dance spectators scored on the fantasy subscale of the Interpersonal Reactivity Index, the larger their MEPs were in the arms when watching Indian dance. Our results show that even without physical training, corticospinal excitability can be enhanced as a function of either visual experience or the tendency to imaginatively transpose oneself into fictional characters. We suggest that spectators covertly simulate the movements for which they have acquired visual experience, and that empathic abilities heighten motor resonance during dance observation