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

Towards a continuous modeling of natural language domains

Humans continuously adapt their style and language to a variety of domains. However, a reliable definition of `domain' has eluded researchers thus far. Additionally, the notion of discrete domains stands in contrast to the multiplicity of heterogeneous domains that humans navigate, many of which overlap. In order to better understand the change and variation of human language, we draw on research in domain adaptation and extend the notion of discrete domains to the continuous spectrum. We propose representation learning-based models that can adapt to continuous domains and detail how these can be used to investigate variation in language. To this end, we propose to use dialogue modeling as a test bed due to its proximity to language modeling and its social component.Comment: 5 pages, 3 figures, published in Uphill Battles in Language Processing workshop, EMNLP 201

Modified teleparallel theories of gravity

We investigate modified theories of gravity in the context of teleparallel geometries. It is well known that modified gravity models based on the torsion scalar are not invariant under local Lorentz transformations while modifications based on the Ricci scalar are. This motivates the study of a model depending on the torsion scalar and the divergence of the torsion vector. We derive the teleparallel equivalent of $f(R)$ gravity as a particular subset of these models and also show that this is the unique theory in this class that is invariant under local Lorentz transformation. Furthermore one can show that $f(T)$ gravity is the unique theory admitting second order field equations.Comment: 9 pages, 1 figure; some typos fixed, slightly improved notatio

Geometrically nonlinear Cosserat elasticity in the plane: applications to chirality

Modelling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become non-chiral. Various approaches have been suggested to overcome this problem. We propose a new approach to this problem by formulating an intrinsically two-dimensional model which does not require references to a higher dimensional one. We are able to model planar chiral materials starting from a geometrically non-linear Cosserat type elasticity theory. Our results are in agreement with previously derived equations of motion but can contain additional terms due to our non-linear approach. Plane wave solutions are briefly discussed within this model.Comment: 22 pages, 1 figure; v2 updated versio

New classes of modified teleparallel gravity models

New classes of modified teleparallel theories of gravity are introduced. The action of this theory is constructed to be a function of the irreducible parts of torsion $f(T_{\rm ax},T_{\rm ten},T_{\rm vec})$, where $T_{\rm ax},T_{\rm ten}$ and $T_{\rm vec}$ are squares of the axial, tensor and vector components of torsion, respectively. This is the most general (well-motivated) second order teleparallel theory of gravity that can be constructed from the torsion tensor. Different particular second order theories can be recovered from this theory such as new general relativity, conformal teleparallel gravity or $f(T)$ gravity. Additionally, the boundary term $B$ which connects the Ricci scalar with the torsion scalar via $R=-T+B$ can also be incorporated into the action. By performing a conformal transformation, it is shown that the two unique theories which have an Einstein frame are either the teleparallel equivalent of general relativity or $f(-T+B)=f(R)$ gravity, as expected.Comment: v2: 10 pages, accepted for publication in PLB; for a detailed derivation of the field equations see Appendix A in v

Trends in tariff reforms and trends in wage inequality

The authors provide new evidence on the impacts of trade reforms on wages and wage inequality in developing countries. While most of the current literature on the topic achieves identification by comparing outcomes before and after one episode of trade liberalization across industries, they propose a stronger identifying strategy. The authors explore the recent historical record of policy changes adopted by Argentina: from significant protection in the early 1970s, to the first episode of liberalization during the late 1970s, back to a slowdown of reforms during the 1980s, to the second episode of liberalization in the 1990s. These swings in trade policy comprise broken trends in trade reforms that they can compare with observed trends in wages and wage inequality. After setting up unusual historical data sets of trends in tariffs, trends in wages, and trends in wage inequality, the evidence supports two well-known hypotheses: trade liberalization, other things being equal, (1) has reduced wages, and (2) has increased wage inequality.Free Trade,Economic Theory&Research,Trade Policy,Export Competitiveness,Labor Markets