Lower Bounds for L1L_1 Discrepancy

We find the best asymptotic lower bounds for the coefficient of the leading term of the $L_1$ norm of the two-dimensional (axis-parallel) discrepancy that can be obtained by K.Roth's orthogonal function method among a large class of test functions. We use methods of combinatorics, probability, complex and harmonic analysis.Comment: a slightly different version of the article is accepted to "Mathematika

Herman's Theory Revisited

We prove that a $C^{2+\alpha}$-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class $D_\delta$, $0<\delta<\alpha\le1$, is $C^{1+\alpha-\delta}$-smoothly conjugate to a rigid rotation. We also derive the most precise version of Denjoy's inequality for such diffeomorphisms.Comment: 10 page

Policy Space and Voting Coalitions in Congress: The Bearing of Policy on Politics, 1930-1954

The question of how the substance of politics helps shape legislative coalitions and bases of support has been displaced from the center of studies of Congress since the publication of pioneering work in the 1960s and early 1970s. Seeking to revive this research program, the authors apply an original coding scheme in tandem with a factor analytic analysis of voting and policy space to the period spanning the last years of the Hoover presidency to the start of Eisenhower's. Investigating legislator parameters—the dimensions of voting space—and roll call parameters—the dimensions of policy space—the paper confirms the strong independent impact of the substance of policy on the political decisions of legislators and reveals an issue-specific concatenation of party and region that altered over the course of the period

Fundamental Limits on the Speed of Evolution of Quantum States

This paper reports on some new inequalities of Margolus-Levitin-Mandelstam-Tamm-type involving the speed of quantum evolution between two orthogonal pure states. The clear determinant of the qualitative behavior of this time scale is the statistics of the energy spectrum. An often-overlooked correspondence between the real-time behavior of a quantum system and the statistical mechanics of a transformed (imaginary-time) thermodynamic system appears promising as a source of qualitative insights into the quantum dynamics.Comment: 6 pages, 1 eps figur

On the Validity of the 0-1 Test for Chaos

In this paper, we present a theoretical justification of the 0-1 test for chaos. In particular, we show that with probability one, the test yields 0 for periodic and quasiperiodic dynamics, and 1 for sufficiently chaotic dynamics