Tapping Dynamics Research Articles

Entropy-based analysis of rhythmic tapping for the quantitative assessment of cerebellar ataxia

The severity of appendicular ataxia is currently assessed by neurological specialists observing the motor deficits during the performance of bedside tests. These tests are traditionally restricted to discrete subjective scales and prescribed by constraints that may in turn affect the subject's performance. To overcome these limitations and facilitate uniform monitoring of cerebellar ataxia, an instrumented assessment system using a wearable sensor has been developed for the rhythmic finger and foot tapping tasks. Departing from the conventional obligation to spatiotemporal parameters that are described clinically, the proposed approach investigates features based on information theory to evaluate the variability of the tapping dynamics. From a clinical trial of 24 healthy subjects and 34 patients diagnosed with cerebellar ataxia (CA), the findings revealed not only are there more variations in movement patterns and timing of tapping events in CA but that movement complexity was also degraded across multiple entropy scales. The system using combined models of different features was able to achieve an average classification accuracy of 81% and 79% in finger and foot tapping respectively. The outcomes strongly agreed with the clinical scale widely-used for the assessment and rating of ataxia (SARA) to a correlation level of 0.71 (p < 0.001) in finger tapping and 0.59 (p < 0.001) in foot tapping.

Edwards Thermodynamics for a Driven Athermal System with Dry Friction.

We obtain, using semianalytical transfer operator techniques, the Edwards thermodynamics of a one-dimensional model of blocks connected by harmonic springs and subjected to dry friction. The theory is able to reproduce the linear divergence of the correlation length as a function of energy density observed in direct numerical simulations of the model under tapping dynamics. We further characterize analytically this divergence using a Gaussian approximation for the distribution of mechanically stable configurations, and show that it is related to the existence of a peculiar infinite temperature critical point.

Cogntive Consistency Analysis in Adaptive Bio-Metric Authentication System Design

Cognitive consistency analysis aims to continuously monitor one's perception equilibrium towards successful accomplishment of cognitive task. Opposite to cognitive flexibility analysis – cognitive consistency analysis identifies monotone of perception towards successful interaction process (e.g., biometric authentication) and useful in generation of decision support to assist one in need. This study consider fingertip dynamics (e.g., keystroke, tapping, clicking etc.) to have insights on instantaneous cognitive states and its effects in monotonic advancement towards successful authentication process. Keystroke dynamics and tapping dynamics are analyzed based on response time data. Finally, cognitive consistency and confusion (inconsistency) are computed with Maximal Information Coefficient (MIC) and Maximal Asymmetry Score (MAS), respectively. Our preliminary study indicates that a balance between cognitive consistency and flexibility are needed in successful authentication process. Moreover, adaptive and cognitive interaction system requires in depth analysis of user’s cognitive consistency to provide a robust and useful assistance.

Estimation method of finger tapping dynamics using simple magnetic detection system

We have developed the simple estimation method of a finger tapping dynamics model for investigating muscle resistance and stiffness during tapping movement in normal subjects. We measured finger tapping movements of 207 normal subjects using a magnetic finger tapping detection system. Each subject tapped two fingers in time with a metronome at 1, 2, 3, 4, and 5 Hz. The velocity and acceleration values for both the closing and opening tapping data were used to estimate a finger tapping dynamics model. Using the frequency response of the ratio of acceleration to velocity of the mechanical impedance parameters, we estimated the resistance (friction coefficient) and compliance (stiffness). We found two dynamics models for the maximum open position and tap position. In the maximum open position, the extensor muscle resistance was twice as high as the flexor muscle resistance and males had a higher spring constant. In the tap position, the flexor muscle resistance was much higher than the extensor muscle resistance. This indicates that the tapping dynamics in the maximum open position are controlled by the balance of extensor and flexor muscle friction resistances and the flexor stiffness, and the flexor friction resistance is the main component in the tap position. It can be concluded that our estimation method makes it possible to understand the tapping dynamics.

Sensitivity vector fields for atomic force microscopes

The application of the sensitivity vector fields (SVFs) for tip–sample interactions in the context of multi-mode tapping dynamics of atomic-force microscopes (AFM) is presented. SVFs represent a novel approach to accurately determine simultaneous parameter variations by exploiting the geometric features of observed chaotic dynamics. The paper also demonstrates that, in certain operating conditions, higher modes are essential to correctly predict the AFM dynamics, and they cannot be neglected. The accuracy of the SVF approach is discussed as applied to a multi-mode AFM model where mode shapes vary due to multiple parameter variations. The identifiability of various parameters based on SVF reconstruction is investigated. Several calibration issues for parameter reconstruction are observed and resolved by a specialized sample filtering and a novel correction factor.

Nonlinear tapping dynamics of multi-walled carbon nanotube tipped atomic forcemicrocantilevers

The nonlinear dynamics of an atomic force microcantilever (AFM) with an attachedmulti-walled carbon nanotube (MWCNT) tip is investigated experimentally andtheoretically. We present the experimental nonlinear frequency response of a MWCNTtipped microcantilever in the tapping mode. Several unusual features in the responsedistinguish it from those traditionally observed for conventional tips. The MWCNT tippedAFM probe is apparently immune to conventional imaging instabilities related to thecoexistence of attractive and repulsive tapping regimes. A theoretical interactionmodel for the system using an Euler elastica MWCNT model is developed andfound to predict several unusual features of the measured nonlinear response.

Closed model for granular compaction under weak tapping.

A one-dimensional lattice model is formulated to study tapping dynamics and the long time steady distribution in granular media. The dynamics conserves the number of particles in the system, and density changes are associated with the creation and destruction of empty sites. The model is shown to be consistent with Edwards' thermodynamics theory of powders. The relationship with lattice models in which the number of particles is not conserved is discussed.

Edwards measure and the steady-state regime of a model with kinetic constraints under tapping

We study the tapping dynamics of a one dimensional Ising model with symmetric kinetic constraints. We define and test a variant of the Edwards hypothesis that one may build a thermodynamics for the steady state by using a flat measure over the metastable states with several macroscopic quantities fixed. Various types of tapping are compared and the accuracy of this measure becomes quickly excellent when the number of quantities fixed on average increases, independently of the way the system is excited. We attribute the validity of the naive flat measure at weak tapping to the spatial separation of density defects.

Microscopic two-dimensional lattice model of dimer granular compaction with friction.

We study by Monte Carlo simulation the compaction dynamics of hard dimers in two dimensions under the action of gravity, subjected to vertical and horizontal shaking, considering also the case in which a friction force acts for horizontal displacements of the dimers. These forces are modeled by introducing effective probabilities for all kinds of moves of the particles. We analyze the dynamics for different values of the time tau during which the shaking is applied to the system and for different intensities of the forces. It turns out that the density evolution in time follows a stretched exponential behavior if tau is not very large, while a power law tail develops for larger values of tau. Moreover, in the absence of friction, a critical value tau(*) exists, which signals the crossover between two different regimes: for tau<tau(*) the asymptotic density scales with a power law of tau, while for tau>tau(*) it reaches logarithmically a maximal saturation value. Such behavior smears out when a finite friction force is present. In this situation the dynamics is slower and lower asymptotic densities are attained. In particular, for significant friction forces, the final density decreases linearly with the friction coefficient. We also compare the frictionless single tap dynamics to the sequential tapping dynamics, observing in the latter case an inverse logarithmic behavior of the density evolution, as found in the experiments.

Phase transitions in the steady-state behavior of mechanically perturbed spin glasses and ferromagnets

We analyze the steady state regime of systems interpolating between spin glasses and ferromagnets under a tapping dynamics recently introduced by analogy with the dynamics of mechanically perturbed granular media. A crossover from a second order to first order ferromagnetic transition as a function of the spin coupling distribution is found. The flat measure over blocked states introduced by Edwards for granular media is used to explain this scenario. Annealed calculations of the Edwards entropy are shown to qualitatively explain the nature of the phase transitions. A Monte-Carlo construction of the Edwards measure confirms that this explanation is also quantitatively accurate.

Testing the Edwards hypothesis in spin systems under tapping dynamics

The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for abstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by considering two distinct mechanisms of energy injection: thermal and random tapping. We find that ergodicity depends upon the tapping procedure (i.e. the way the blocked configurations are dynamically accessed): for thermal tapping ergodicity is a good approximation, while it fails to describe the asymptotic stationary state reached by the random tapping dynamics.

Glassy dynamics in granular compaction: sand on random graphs.

We discuss the use of a ferromagnetic spin model on a random graph to model granular compaction. A multispin interaction is used to capture the competition between local and global satisfaction of constraints characteristic for geometric frustration. We define an athermal dynamics designed to model repeated taps of a given strength. Amplitude cycling and the effect of permanently constraining a subset of the spins at a given amplitude is discussed. Finally we check the validity of Edwards's hypothesis for the athermal tapping dynamics.

THE STEADY STATE OF THE TAPPED ISING MODEL

We consider a tapping dynamics, analogous to that in experiments on granular media, on the simple one-dimensional ferromagnetic Ising model. When unperturbed, the system undergoes a single spin flip falling dynamics where only energy lowering moves occur. With this dynamics the system has an exponentially large number of metastable states and gets stuck in blocked or jammed configurations as do granular media. When stuck, the system is tapped, in order to make it evolve, by flipping in parallel each spin with probability p (corresponding to the strength of the tapping). Under this dynamics the system reaches a steady state regime characterized by an asymptotic energy per spin E(p), which is determined analytically. Within the steady state regime we compare certain time averaged quantities with the ensemble average of Edwards based on a canonical measure over metastable states of fixed average energy. The ensemble average yields results in excellent agreement with the dynamical measurements.

Tapping spin glasses and ferromagnets on random graphs.

We consider a tapping dynamics, analogous to that in experiments on granular media, on spin glasses and ferromagnets on random thin graphs. Between taps, zero temperature single spin flip dynamics takes the system to a metastable state. Tapping corresponds to flipping simultaneously any spin with probability p. This dynamics leads to a stationary regime with a steady state energy E(p). We analytically solve this dynamics for the one-dimensional ferromagnet and +/-J spin glass. Numerical simulations for spin glasses and ferromagnets of higher connectivity are carried out; in particular, we find a novel first order transition for the ferromagnetic systems.

Tapping thermodynamics of the one-dimensional Ising model

We analyse the steady state regime of a one dimensional Ising model under a tapping dynamics recently introduced by analogy with the dynamics of mechanically perturbed granular media. The idea that the steady state regime may be described by a flat measure over metastable states of fixed energy is tested by comparing various steady state time averaged quantities in extensive numerical simulations with the corresponding ensemble averages computed analytically with this flat measure. The agreement between the two averages is excellent in all the cases examined, showing that a static approach is capable of predicting certain measurable properties of the steady state regime.