Two- and three-body problem with Floquet-driven zero-range interactions

We study the two-body scattering problem in the zero-range approximation with a sinusoidally driven scattering length and calculate the relation between the mean value and amplitude of the drive for which the effective scattering amplitude is resonantly enhanced. In this manner we arrive at a family of curves along which the effective scattering length diverges but the nature of the corresponding Floquet-induced resonance changes from narrow to wide. Remarkably, on these curves the driving does not induce heating. In order to study the effect of these resonances on the three-body problem we consider one light and two heavy particles with driven heavy-light interaction in the Born-Oppenheimer approximation and find that the Floquet driving can be used to tune the three-body and inelasticity parameters.Comment: 14 pages, 7 figure

Brain-machine interfaces for rehabilitation in stroke: A review

BACKGROUND: Motor paralysis after stroke has devastating consequences for the patients, families and caregivers. Although therapies have improved in the recent years, traditional rehabilitation still fails in patients with severe paralysis. Brain-machine interfaces (BMI) have emerged as a promising tool to guide motor rehabilitation interventions as they can be applied to patients with no residual movement. OBJECTIVE: This paper reviews the efficiency of BMI technologies to facilitate neuroplasticity and motor recovery after stroke. METHODS: We provide an overview of the existing rehabilitation therapies for stroke, the rationale behind the use of BMIs for motor rehabilitation, the current state of the art and the results achieved so far with BMI-based interventions, as well as the future perspectives of neural-machine interfaces. RESULTS: Since the first pilot study by Buch and colleagues in 2008, several controlled clinical studies have been conducted, demonstrating the efficacy of BMIs to facilitate functional recovery in completely paralyzed stroke patients with noninvasive technologies such as the electroencephalogram (EEG). CONCLUSIONS: Despite encouraging results, motor rehabilitation based on BMIs is still in a preliminary stage, and further improvements are required to boost its efficacy. Invasive and hybrid approaches are promising and might set the stage for the next generation of stroke rehabilitation therapies.This study was funded by the Bundesministerium für Bildung und Forschung BMBF MOTORBIC (FKZ13GW0053)andAMORSA(FKZ16SV7754), the Deutsche Forschungsgemeinschaft (DFG), the fortüne-Program of the University of Tübingen (2422-0-0 and 2452-0-0), and the Basque GovernmentScienceProgram(EXOTEK:KK2016/00083). NIL was supported by the Basque Government’s scholarship for predoctoral students

Long-lived states of oscillator chain with dynamical traps

A simple model of oscillator chain with dynamical traps and additive white noise is considered. Its dynamics was studied numerically. As demonstrated, when the trap effect is pronounced nonequilibrium phase transitions of a new type arise. Locally they manifest themselves via distortion of the particle arrangement symmetry. Depending on the system parameters the particle arrangement is characterized by the corresponding distributions taking either a bimodal form, or twoscale one, or unimodal onescale form which, however, deviates substantially from the Gaussian distribution. The individual particle velocities exhibit also a number of anomalies, in particular, their distribution can be extremely wide or take a quasi-cusp form. A large number of different cooperative structures and superstructures made of these formations are found in the visualized time patterns. Their evolution is, in some sense, independent of the individual particle dynamics, enabling us to regard them as dynamical phases.Comment: 8 pages, 5 figurs, TeX style of European Physical Journa

A new weighting scheme and discriminative approach for information retrieval in static and dynamic document collections

This paper introduces a new weighting scheme in information retrieval. It also proposes using the document centroid as a threshold for normalizing documents in a document collection. Document centroid normalization helps to achieve more effective information retrieval as it enables good discrimination between documents. In the context of a machine learning application, namely unsupervised document indexing and retrieval, we compared the effectiveness of the proposed weighting scheme to the 'Term Frequency - Inverse Document Frequency' or TF-IDF, which is commonly used and considered as one of the best existing weighting schemes. The paper shows how the document centroid is used to remove less significant weights from documents and how this helps to achieve better retrieval effectiveness. Most of the existing weighting schemes in information retrieval research assume that the whole document collection is static. The results presented in this paper show that the proposed weighting scheme can produce higher retrieval effectiveness compared with the TF-IDF weighting scheme, in both static and dynamic document collections. The results also show the variation in information retrieval effectiveness that is achieved for static and dynamic document collections by using a specific weighting scheme. This type of comparison has not been presented in the literature before

A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments

In this paper we derive a pore-scale model for permeable biofilm formation in a two-dimensional pore. The pore is divided in two phases: water and biofilm. The biofilm is assumed to consist of four components: water, extracellular polymeric substances (EPS), active bacteria, and dead bacteria. The flow of water is modeled by the Stokes equation whereas a diffusion-convection equation is involved for the transport of nutrients. At the water/biofilm interface, nutrient transport and shear forces due to the water flux are considered. In the biofilm, the Brinkman equation for the water flow, transport of nutrients due to diffusion and convection, displacement of the biofilm components due to reproduction/dead of bacteria, and production of EPS are considered. A segregated finite element algorithm is used to solve the mathematical equations. Numerical simulations are performed based on experimentally determined parameters. The stress coefficient is fitted to the experimental data. To identify the critical model parameters, a sensitivity analysis is performed. The Sobol sensitivity indices of the input parameters are computed based on uniform perturbation by $\pm 10 \%$ of the nominal parameter values. The sensitivity analysis confirms that the variability or uncertainty in none of the parameters should be neglected

Improved unfolding by detrending of statistical fluctuations in quantum spectra

Accepted for publication in Physical Review EA fundamental relation exists between the statistical properties of the fluctuations of the energy level spectrum of a Hamiltonian and the chaotic properties of the physical system it describes. This relationship has been addressed previously as a signature of chaos in quantum dynamical systems. In order to properly analyze these fluctuations, however, it is necessary to separate them from the general tendency, namely, its secular part. Unfortunately this process, called unfolding, is not trivial and can lead to erroneous conclusions about the chaoticity of a system. In this paper we propose a technique to improve the unfolding procedure for the purpose of minimizing the dependence on the particular procedure. This technique is based on detrending the fluctuations of the unfolded spectra through the empirical mode decomposition method

Nonlinear dynamics of coupled transverse-rotational waves in granular chains

The nonlinear dynamics of coupled waves in one-dimensional granular chains with and without a substrate is theoretically studied accounting for quadratic nonlinearity. The multiple time scale method is used to derive the nonlinear dispersion relations for infinite granular chains and to obtain the wave solutions for semiinfinite systems. It is shown that the sum-frequency and difference-frequency components of the coupled transverse-rotational waves are generated due to their nonlinear interactions with the longitudinal wave. Nonlinear resonances are not present in the chain with no substrate where these frequency components have low amplitudes and exhibit beating oscillations. In the chain positioned on a substrate two types of nonlinear resonances are predicted. At resonance, the fundamental frequency wave amplitudes decrease and the generated frequency component amplitudes increase along the chain, accompanied by the oscillations due to the wave numbers asynchronism. The results confirm the possibility of a highly efficient energy transfer between the waves of different frequencies, which could find applications in the design of acoustic devices for energy transfer and energy rectification