Exact analytical approach to differential equations with variable coefficients

This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the analytical expression presented in the paper. The formalism can be easily extended to the infinite dimensional case such as the quantum time-dependent Hamiltonian problem.Comment: 16 pages, 4 figure

Is there a role for funding in explaining recent US bank failures?

This paper tests the role of different banks’ liquidity funding structures in explaining the bank failures that occurred in the United States between 2007 and 2009. The results highlight that funding is indeed a significant factor in explaining banks’ probability of default. By confirming the role of funding as a driver of banking crisis, the paper also recognizes that the new liquidity framework proposed by the Basel Committee on Banking Supervision appears to have the features needed to strengthen banks’ liquidity conditions and improve financial stability. Its correct implementation, together with closer supervision of banks’ liquidity and funding conditions, appear decisive, however, if such improvements are to be achieved.banks, default, crises, liquidity, funding, brokered deposits, liquidity regulation, deposit insurance, United States

Cerebellum: an explanation for dystonia?

Dystonia is a movement disorder that is characterized by involuntary muscle contractions, abnormal movements and postures, as well as by non-motor symptoms, and is due to abnormalities in different brain areas. In this article, we focus on the growing number of experimental studies aimed at explaining the pathophysiological role of the cerebellum in dystonia. Lastly, we highlight gaps in current knowledge and issues that future research studies should focus on as well as some of the potential applications of this research avenue. Clarifying the pathophysiological role of cerebellum in dystonia is an important concern given the increasing availability of invasive and non-invasive stimulation techniques and their potential therapeutic role in this condition

Response of Complex Systems to Complex Perturbations: the Complexity Matching Effect

The dynamical emergence (and subsequent intermittent breakdown) of collective behavior in complex systems is described as a non-Poisson renewal process, characterized by a waiting-time distribution density $\psi (\tau)$ for the time intervals between successively recorded breakdowns. In the intermittent case $\psi (t)\sim t^{-\mu}$, with complexity index $\mu$. We show that two systems can exchange information through complexity matching and present theoretical and numerical calculations describing a system with complexity index $\mu_{S}$ perturbed by a signal with complexity index $\mu_{P}$. The analysis focuses on the non-ergodic (non-stationary) case $\mu \leq 2$ showing that for $\mu_{S}\geq \mu_{P}$, the system $S$ statistically inherits the correlation function of the perturbation $P$. The condition $\mu_{P}=\mu_{S}$ is a resonant maximum for correlation information exchange.Comment: 4 pages, 1 figur

Non-Poisson processes: regression to equilibrium versus equilibrium correlation functions

We study the response to perturbation of non-Poisson dichotomous fluctuations that generate super-diffusion. We adopt the Liouville perspective and with it a quantum-like approach based on splitting the density distribution into a symmetric and an anti-symmetric component. To accomodate the equilibrium condition behind the stationary correlation function, we study the time evolution of the anti-symmetric component, while keeping the symmetric component at equilibrium. For any realistic form of the perturbed distribution density we expect a breakdown of the Onsager principle, namely, of the property that the subsequent regression of the perturbation to equilibrium is identical to the corresponding equilibrium correlation function. We find the directions to follow for the calculation of higher-order correlation functions, an unsettled problem, which has been addressed in the past by means of approximations yielding quite different physical effects.Comment: 30 page