Stability Properties of 1-Dimensional Hamiltonian Lattices with Non-analytic Potentials

We investigate the local and global dynamics of two 1-Dimensional (1D) Hamiltonian lattices whose inter-particle forces are derived from non-analytic potentials. In particular, we study the dynamics of a model governed by a "graphene-type" force law and one inspired by Hollomon's law describing "work-hardening" effects in certain elastic materials. Our main aim is to show that, although similarities with the analytic case exist, some of the local and global stability properties of non-analytic potentials are very different than those encountered in systems with polynomial interactions, as in the case of 1D Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Our approach is to study the motion in the neighborhood of simple periodic orbits representing continuations of normal modes of the corresponding linear system, as the number of particles $N$ and the total energy $E$ are increased. We find that the graphene-type model is remarkably stable up to escape energy levels where breakdown is expected, while the Hollomon lattice never breaks, yet is unstable at low energies and only attains stability at energies where the harmonic force becomes dominant. We suggest that, since our results hold for large $N$, it would be interesting to study analogous phenomena in the continuum limit where 1D lattices become strings.Comment: Accepted for publication in the International Journal of Bifurcation and Chao

PRINCIPLES OF POLITICAL ECONOMY AND THE TAXATION OF NATIONS: ECONOMETRIC AND MACHINE-LEARNING EVALUATION OF TARIFFS

Demography affects the ability of countries to manage their debt levels and to make macroeconomic policy. By the same token, the demographic attributes of labor influence political decisions among nations, including international trade policy. In particular, the free movement of labor is a bedrock principle of the European Union. That legal guarantee has prompted one country to leave the Union, even as it inspires other countries to join. This Article investigates the influence of (labor) demographics on tariffs in forty-five OECD and non-OECD countries. A series of econometric models reveals evidence that the population and labor force may influence tariff levels. By contrast, migration does not. Income per capita and consumption affect tariff rates. Machinelearning methods confirm conclusions reached through conventional econometrics and shed further light on the relationship between tariff levels and their hypothesized predictors. The absence of a significant relationship between tariffs and migration undermines the common political assumption that tariff and immigration policy are mutually reinforcing levers of international policy

Mitochondrial respiratory chain deficiency correlates with the severity of neuropathology in sporadic Creutzfeldt-Jakob disease

Mitochondrial dysfunction has been implicated in multiple neurodegenerative diseases but remains largely unexplored in Creutzfeldt-Jakob disease. Here, we characterize the mitochondrial respiratory chain at the individual neuron level in the MM1 and VV2 common molecular subtypes of sporadic Creutzfeldt-Jakob disease. Moreover, we investigate the associations between the mitochondrial respiratory chain and neuropathological markers of the disease. Brain tissue from individuals with sporadic Creutzfeldt-Jakob disease and age-matched controls were obtained from the brain collection of the Austrian Creutzfeldt-Jakob Surveillance. The mitochondrial respiratory chain was studied through a dichotomous approach of immunoreactivities in the temporal cortex and the hippocampal subregions of CA4 and CA3. We show that profound deficiency of all mitochondrial respiratory complexes (I-V) occurs in neurons of the severely affected temporal cortex of patients with Creutzfeldt-Jakob disease. This deficiency correlates strongly with the severity of neuropathological changes, including vacuolation of the neuropil, gliosis and disease associated prion protein load. Respiratory chain deficiency is less pronounced in hippocampal CA4 and CA3 regions compared to the temporal cortex. In both areas respiratory chain deficiency shows a predilection for the MM1 molecular subtype of Creutzfeldt-Jakob disease. Our findings indicate that aberrant mitochondrial respiration could be involved early in the pathogenesis of sporadic Creutzfeldt-Jakob disease and contributes to neuronal death, most likely via ATP depletion. Based on these results, we propose that the restricted MRI diffusion profile seen in the brain of patients with sporadic Creutzfeldt-Jakob disease might reflect cytotoxic changes due to neuronal respiratory chain failure and ATP loss.publishedVersio