Coexisting chaotic and multi-periodic dynamics in a model of cardiac alternans

The spatiotemporal dynamics of cardiac tissue is an active area of research for biologists, physicists, and mathematicians. Of particular interest is the study of period-doubling bifurcations and chaos due to their link with cardiac arrhythmogenesis. In this paper we study the spatiotemporal dynamics of a recently developed model for calcium-driven alternans in a one dimensional cable of tissue. In particular, we observe in the cable coexistence of regions with chaotic and multi-periodic dynamics over wide ranges of parameters. We study these dynamics using global and local Lyapunov exponents and spatial trajectory correlations. Interestingly, near nodes -- or phase reversals -- low-periodic dynamics prevail, while away from the nodes the dynamics tend to be higher-periodic and eventually chaotic. Finally, we show that similar coexisting multi-periodic and chaotic dynamics can also be observed in a detailed ionic model

The AdS/CFT correspondence and Spectrum Generating Algebras

We list the spectrum generating algebras for string theory and M-theory compactified on various backgrounds of the form $AdS_{d+1} \times S^n$. We identify the representations of these algebras which make up the classical supergravity spectra and argue for the presence of these spectrum generating algebras in the classical string/M-theory. We also discuss the role of the spectrum generating algebras on the conformal field theory side.Comment: 17 pages, 4 Tables, harvma

Polarization-balanced design of AlN/GaN heterostructures: Application to double-barrier structures

Inversion- and depletion-regions generally form at the interfaces between doped leads (cladding layers) and the active region of polar heterostructures like AlN/GaN and other nitride compounds. The band bending in the depletion region sets up a barrier which may seriously impede perpendicular electronic transport. This may ruin the performance of devices such as quantum-cascade lasers and resonant-tunneling diodes. Here we introduce the concepts of polarization balance and polarization-balanced designs: A structure is polarization balanced when the applied bias match the voltage drop arising from spontaneous and piezeolectric fields. Devices designed to operate at this bias have polarization-balanced designs. These concepts offer a systematic approach to avoid the formation of depletion regions. As a test case, we consider the design of AlN/GaN double barrier structures with Al$_{\tilde{x}}$Ga$_{1-\tilde{x}}$N leads. To guide our efforts, we derive a simple relation between the intrinsic voltage drop arising from polar effects, average alloy composition of the active region, and the alloy concentration of the leads. Polarization-balanced designs secure good filling of the ground state for unbiased structures, while for biased structures with efficient emptying of the active structure it removes the depletion barriers

Colored Speech: Cross Burnings, Epistemics, and the Triumph of the Crits?

This Essay examines the Court\u27s recent decision in Virginia v. Black. It argues that Black signifies a different approach to the constitutionality of statutes regulating cross burnings. It shows how the Court\u27s conservatives have essentially accepted the intellectual framework and the mode of analysis suggested previously by the critical race theorists. In particular, this Essay explores the role that Justice Thomas plays in the case. The Essay explains Justice Thomas\u27s active participation as a matter of epistemic authority and epistemic deference

ALLOCATION OF AGRICULTURAL PRODUCTION CAPACITY AMONG COMMERCIAL MARKETS, FOOD AID, AND PRODUCTION CONTROL

Production Economics,

Chasing the Smokestack: Strategic Policymaking With Multiple Instruments

Empirical evidence suggesting that a considerable amount of horizontal strategic interaction exists amongst governments is important in light of recent devolutionary trends of many important public programs. The empirical approach in these studies typically relies on estimating reaction functions in a uni-dimensional policy framework, where a nonzero slope estimate is interpreted as evidence in support of strategic interactions. While this framework is a useful representation within certain contexts, it is potentially too restrictive; for example, in models of resource competition, localities may use multiple instruments in their recruiting pursuits, leading to potential strategic interactions across policy instruments. In this study, we first develop a simple theoretic construct that includes resource competition in a world of three-dimensional policy choice. The model suggests that while a zero-sloped reaction function may exist for any particular policy, this does not necessarily imply the absence of strategic interactions. We examine the implications of the model empirically using US state-level panel data over the period 1977-1994. The results suggest that important cross-policy strategic interactions exist, lending support in favor of the multi-dimensional framework, and indicate that uni-dimensional frameworks may present lower bound estimates of the degree of strategic interaction.