A diagrammatic approach to study the information transfer in weakly non-linear channels

In a recent work we have introduced a novel approach to study the effect of weak non-linearities in the transfer function on the information transmitted by an analogue channel, by means of a perturbative diagrammatic expansion. We extend here the analysis to all orders in perturbation theory, which allows us to release any constraint concerning the magnitude of the expansion parameter and to establish the rules to calculate easily the contribution at any order. As an example we explicitly compute the information up to the second order in the non-linearity, in presence of random gaussian connectivities and in the limit when the output noise is not small. We analyze the first and second order contributions to the mutual information as a function of the non-linearity and of the number of output units. We believe that an extensive application of our method via the analysis of the different contributions at distinct orders might be able to fill a gap between well known analytical results obtained for linear channels and the non trivial treatments which are required to study highly non-linear channels.Comment: 17 pages, 3 figure

A perturbative approach to non-linearities in the information carried by a two layer neural network

We evaluate the mutual information between the input and the output of a two layer network in the case of a noisy and non-linear analogue channel. In the case where the non-linearity is small with respect to the variability in the noise, we derive an exact expression for the contribution to the mutual information given by the non-linear term in first order of perturbation theory. Finally we show how the calculation can be simplified by means of a diagrammatic expansion. Our results suggest that the use of perturbation theories applied to neural systems might give an insight on the contribution of non-linearities to the information transmission and in general to the neuronal dynamics.Comment: Accepted as a preprint of ICTP, Triest

On the reliability and repeatability of surface electromyography factorization by muscle synergies in daily life activities

Muscle synergy theory is a new appealing approach for different research fields. This study is aimed at evaluating the robustness of EMG reconstruction via muscle synergies and the repeatability of muscle synergy parameters as potential neurophysiological indices. Eight healthy subjects performed walking, stepping, running, and ascending and descending stairs' trials for five repetitions in three sessions. Twelve muscles of the dominant leg were analyzed. The “nonnegative matrix factorization” and “variability account for” were used to extract muscle synergies and to assess EMG goodness reconstruction, respectively. Intraclass correlation was used to quantify methodology reliability. Cosine similarity and coefficient of determination assessed the repeatability of the muscle synergy vectors and the temporal activity patterns, respectively. A 4-synergy model was selected for EMG signal factorization. Intraclass correlation was excellent for the overall reconstruction, while it ranged from fair to excellent for single muscles. The EMG reconstruction was found repeatable across sessions and subjects. Considering the selection of neurophysiological indices, the number of synergies was not repeatable neither within nor between subjects. Conversely, the cosine similarity and coefficient of determination values allow considering the muscle synergy vectors and the temporal activity patterns as potential neurophysiological indices due to their similarity both within and between subjects. More specifically, some synergies in the 4-synergy model reveal themselves as more repeatable than others, suggesting focusing on them when seeking at the neurophysiological index identification

Permittivity of wood as a function of moisture for cultural heritage applications: A preliminary study

In this work, the evaluation of moisture content in historic wooden objects starting from permittivity measurements is investigated. For this purpose, a WR430 waveguide with a 1.7-2.6 GHz range was used to estimate the complex permittivity correlated to different moisture levels. Experimental tests were carried out on poplar (Populus nigra L.), a wood typically used in central Italy in the thirteenth-sixteenth centuries as a painting support. For the considered measurement system, experimental results and calibration curves are reported

Permittivity-Based Water Content Calibration Measurement in Wood-Based Cultural Heritage: A Preliminary Study

In this work, the dielectric permittivity of four kinds of wood (Fir, Poplar, Oak, and Beech Tree), used in Italian Artworks and structures, was characterized at different humidity levels. Measurements were carried out using three different probes connected to a bench vector network analyzer: a standard WR90 X-band waveguide, a WR430 waveguide, and an open-ended coaxial probe. In particular, we investigated the dispersion model for the four wood species, showing how a log-fit model of the open-ended data presents a determination coefficient R2 > 0.990 in the 1–12 GHz frequency range. This result has proven helpful to fill the frequency gap between the measurements obtained at different water contents with the two waveguide probes showing an R2 > 0.93. Furthermore, correlating the log-fit vertical shift with the water content, it was possible to find a calibration curve with a linear characteristic. These experimental results will be helpful for on-site non-invasive water monitoring of wooden artworks or structures. Moreover, the final results show how the open-ended coaxial probe, with a measurement deviation lower than 7% from the waveguide measurements, may be used directly as a non-invasive sensor for on-site measurements

Replica symmetric evaluation of the information transfer in a two-layer network in presence of continuous+discrete stimuli

In a previous report we have evaluated analytically the mutual information between the firing rates of N independent units and a set of multi-dimensional continuous+discrete stimuli, for a finite population size and in the limit of large noise. Here, we extend the analysis to the case of two interconnected populations, where input units activate output ones via gaussian weights and a threshold linear transfer function. We evaluate the information carried by a population of M output units, again about continuous+discrete correlates. The mutual information is evaluated solving saddle point equations under the assumption of replica symmetry, a method which, by taking into account only the term linear in N of the input information, is equivalent to assuming the noise to be large. Within this limitation, we analyze the dependence of the information on the ratio M/N, on the selectivity of the input units and on the level of the output noise. We show analytically, and confirm numerically, that in the limit of a linear transfer function and of a small ratio between output and input noise, the output information approaches asymptotically the information carried in input. Finally, we show that the information loss in output does not depend much on the structure of the stimulus, whether purely continuous, purely discrete or mixed, but only on the position of the threshold nonlinearity, and on the ratio between input and output noise.Comment: 19 pages, 4 figure

Quantifying age-related differences of ankle mechanical properties using a robotic device

A deep analysis of ankle mechanical properties is a fundamental step in the design of an exoskeleton, especially if it is to be suitable for both adults and children. This study aims at assessing age-related differences of ankle properties using pediAnklebot. To achieve this aim, we enrolled 16 young adults and 10 children in an experimental protocol that consisted of the evaluation of ankle mechanical impedance and kinematic performance. Ankle impedance was measured by imposing stochastic torque perturbations in dorsi-plantarflexion and inversion-eversion directions. Kinematic performance was assessed by asking participants to perform a goal-directed task. Magnitude and anisotropy of impedance were computed using a multiple-input multiple-output system. Kinematic performance was quantified by computing indices of accuracy, smoothness, and timing. Adults showed greater magnitude of ankle impedance in both directions and for all frequencies, while the anisotropy was higher in children. By analyzing kinematics, children performed movements with lower accuracy and higher smoothness, while no differences were found for the duration of the movement. In addition, adults showed a greater ability to stop the movement when hitting the target. These findings can be useful to a proper development of robotic devices, as well as for implementation of specific training programs

A device to characterize optical fibres

ATLAS is a general purpose experiment approved for the LHC collider at CERN. An important component of the detector is the central hadronic calorimeter; for its construction more than 600,000 Wave Length Shifting (WLS) fibres (corresponding to a total length of 1,120 Km) have been used. We have built and put into operation a dedicated instrument for the measurement of light yield and attenuation length over groups of 20 fibres at a time. The overall accuracy achieved in the measurement of light yield (attenuation length) is 1.5% (3%). We also report the results obtained using this method in the quality control of a large sample of fibres.Comment: 17 pages 20 figeres submitted to NIM journa

Optimal force evaluation for isotonic fatigue characterization in mouse Tibialis Anterior muscle

Skeletal muscle fatigue is most often studied as a response to repeated stimulations in isometric conditions and it is usually quantified as the progressive loss of force generating capability over time. However, physical dynamic activity is based on the shortening of skeletal muscles. Therefore, the condition that best mimics body movements is the isotonic one, in which muscle is allowed to shorten against a constant load. In the literature, the isotonic fatigue test is performed allowing the muscle to lift a load corresponding to one-third of the maximal isometric force (reference optimal force), as best representative of the force at which the tissue develops its maximum power. The goal of this study was to devise a new testing protocol in which each muscle was tested for isotonic fatigue by shortening against its own optimal force, i.e. the force at which it really developed the maximum power. Our hypothesis was that testing all the muscle at a standard reference value would introduce significant errors in the parameters associated to muscle fatigue and in their variance. The proposed protocol was based on the real-time measurement of the maximum power a muscle was able to generate through the application of the after-load technique and a mathematical interpolation to the Hill's equation, that therefore allowed to determine the experimental optimal force to be applied during the fatigue test. Experimental results showed that the muscles tested with the experimental optimal force had a fatigue time significantly lower than the control muscles tested with the reference optimal force. A decrease, even if not statistically significant, was also measured for the power and work generated during the fatigue test. Of note, for all these parameters a huge decrease in the measurement variance was reported, confirming that a precise assessment of the muscle experimental optimal force was needed to increase the accuracy of the measurements. On the other hand, the application of the protocol proposed in this work required an increase in the test duration, due to the application of the after-load technique, and a real time measurement of the power generated by the tissue