Companion forms and weight one forms

In this paper we prove the following theorem. Let L/\Q_p be a finite extension with ring of integers O_L and maximal ideal lambda. Theorem 1. Suppose that p >= 5. Suppose also that \rho:G_\Q -> GL_2(O_L) is a continuous representation satisfying the following conditions. 1. \rho ramifies at only finitely many primes. 2. \rho mod \lambda is modular and absolutely irreducible. 3. \rho is unramified at p and \rho(Frob_p) has eigenvalues \alpha and \beta with distinct reductions modulo \lambda. Then there exists a classical weight one eigenform f = \sum_{n=1}^\infty a_m(f) q^m and an embedding of \Q(a_m(f)) into L such that for almost all primes q, a_q(f)=tr(\rho(\Frob_q)). In particular \rho has finite image and for any embedding i of L in \C, the Artin L-function L(i o \rho, s) is entire.Comment: 15 pages, published version, abstract added in migratio

Digital Genesis: Computers, Evolution and Artificial Life

The application of evolution in the digital realm, with the goal of creating artificial intelligence and artificial life, has a history as long as that of the digital computer itself. We illustrate the intertwined history of these ideas, starting with the early theoretical work of John von Neumann and the pioneering experimental work of Nils Aall Barricelli. We argue that evolutionary thinking and artificial life will continue to play an integral role in the future development of the digital world.Comment: Extended abstract of talk presented at the 7th Munich-Sydney-Tilburg Philosophy of Science Conference: Evolutionary Thinking, University of Sydney, 20-22 March 2014. Presentation slides from talk available at http://www.tim-taylor.com/papers/digital-genesis-presentation.pd

Democracy and Protectionism

Does democracy encourage free trade? It depends. Broadening the franchise involves transferring power from non-elected elites to the wider population, most of whom will be workers. The Hecksher-Ohlin-Stolper-Samuelson logic says that democratization should lead to more liberal trade policies in countries where workers stand to gain from free trade; and to more protectionist policies in countries where workers will benefit from the imposition of tariffs and quotas. We test and confirm these political economy implications of trade theory hypothesis using data on democracy, factor endowments, and protection in the late nineteenth century.

The Effects of Repetition Speed on the Development of Skeletal Muscle Strength

Taylor, K. D. Effect of repetition speed on the development of muscle strength. 1999. The purpose of this study was to determine the effects of repetition protocols on strength. Training was conducted 3 times per week for 8 weeks using 1 set of the free weight bench press in the fast (1 second concentric and 1 second eccentric contractions, N = 15) or slow (2 second concentric and 4 second eccentric contractions, N = 7) speed repetition protocol. Training weight increased from 50% 1 RM weeks 1-2, 75% 1 RM weeks 3-6, and 85% weeks 7-8. Subjects completed 10 repetitions weeks 1-2, and as many as possible weeks 3-8. Testing was done in the protocol used in training (training protocol pre and posttest) and in the protocol not used in training (velocity specificity pre and posttest). Neither group was significantly stronger than the other when tested in the training protocol (F = .220 p \u3e .05). A. velocity specificity effect was not demonstrated (F = .167 fast testing p \u3e .05, F = .055 slow testing p \u3e .05). Female subjects did improve significantly over male subjects in 1 RM strength by percentage. Fast group males = 14,15% increase, fast group females = 23.02% increase (F = 4.51, p \u3c .05 after BMI adjustments). Slow group males = 14.87% increase, slow group females = 25.93% increase (F = 9.25, p \u3c .05 after BMI adjustments). In conclusion, neither fast or slow speed repetitions are superior in developing strength in untrained subjects