Neural networks in Fréchet spaces

We propose a neural network architecture in infinite dimensional spaces for which we can show the universal approximation property. Indeed, we derive approximation results for continuous functions from a Fréchet space X into a Banach space Y. The approximation results are generalising the well known universal approximation theorem for continuous functions from Rn to R, where approximation is done with (multilayer) neural networks Cybenko (1989) Math. Cont. Signals Syst. 2, 303–314 and Hornik et al. (1989) Neural Netw., 2, 359–366 and Funahashi (1989) Neural Netw., 2, 183–192 and Leshno (1993) Neural Netw., 6, 861–867. Our infinite dimensional networks are constructed using activation functions being nonlinear operators and affine transforms. Several examples are given of such activation functions. We show furthermore that our neural networks on infinite dimensional spaces can be projected down to finite dimensional subspaces with any desirable accuracy, thus obtaining approximating networks that are easy to implement and allow for fast computation and fitting. The resulting neural network architecture is therefore applicable for prediction tasks based on functional data.acceptedVersio

Evaluation of protein pattern changes in roots and leaves of Zea mays plants in response to nitrate availability by two-dimensional gel electrophoresis analysis

<p>Abstract</p> <p>Background</p> <p>Nitrogen nutrition is one of the major factors that limit growth and production of crop plants. It affects many processes, such as development, architecture, flowering, senescence and photosynthesis. Although the improvement in technologies for protein study and the widening of gene sequences have made possible the study of the plant proteomes, only limited information on proteome changes occurring in response to nitrogen amount are available up to now. In this work, two-dimensional gel electrophoresis (2-DE) has been used to investigate the protein changes induced by NO₃^-concentration in both roots and leaves of maize (<it>Zea mays </it>L.) plants. Moreover, in order to better evaluate the proteomic results, some biochemical and physiological parameters were measured.</p> <p>Results</p> <p>Through 2-DE analysis, 20 and 18 spots that significantly changed their amount at least two folds in response to nitrate addition to the growth medium of starved maize plants were found in roots and leaves, respectively. Most of these spots were identified by Liquid Chromatography Electrospray Ionization Tandem Mass Spectrometry (LC-ESI-MS/MS). In roots, many of these changes were referred to enzymes involved in nitrate assimilation and in metabolic pathways implicated in the balance of the energy and redox status of the cell, among which the pentose phosphate pathway. In leaves, most of the characterized proteins were related to regulation of photosynthesis. Moreover, the up-accumulation of lipoxygenase 10 indicated that the leaf response to a high availability of nitrate may also involve a modification in lipid metabolism.</p> <p>Finally, this proteomic approach suggested that the nutritional status of the plant may affect two different post-translational modifications of phosphoenolpyruvate carboxylase (PEPCase) consisting in monoubiquitination and phosphorylation in roots and leaves, respectively.</p> <p>Conclusion</p> <p>This work provides a first characterization of the proteome changes that occur in response to nitrate availability in leaves and roots of maize plants. According to previous studies, the work confirms the relationship between nitrogen and carbon metabolisms and it rises some intriguing questions, concerning the possible role of NO and lipoxygenase 10 in roots and leaves, respectively. Although further studies will be necessary, this proteomic analysis underlines the central role of post-translational events in modulating pivotal enzymes, such as PEPCase.</p

Physical Activity Classification for Elderly People in Free-Living Conditions

Physical activity is strongly linked with mental and physical health in the elderly population and accurate monitoring of activities of daily living (ADLs) can help improve quality of life and well-being. This study presents and validates an inertial sensors-based physical activity classification system developed with older adults as the target population. The dataset was collected in free-living conditions without placing constraints on the way and order of performing ADLs. Four sensor locations (chest, lower back, wrist, and thigh) were explored to obtain the optimal number and combination of sensors by finding the best tradeoff between the system's performance and wearability. Several feature selection techniques were implemented on the feature set obtained from acceleration and angular velocity signals to classify four major ADLs (sitting, standing, walking, and lying). A support vector machine was used for the classification of the ADLs. The findings show the potential of different solutions (single sensor or multisensor) to correctly classify the ADLs of older people in free-living conditions. Considering a minimal set-up of a single sensor, the sensor worn at the L5 achieved the best performance. A two-sensor solution (L5 + thigh) achieved a better performance with respect to a single-sensor solution. By contrast, considering more than two sensors did not provide further improvements. Finally, we evaluated the computational cost of different solutions and it was shown that a feature selection step can reduce the computational cost of the system and increase the system performance in most cases. This can be helpful for real-time applications.<br/

Performance Evaluation of State of the Art Systems for Physical Activity Classification of Older Subjects Using Inertial Sensors in a Real Life Scenario: A Benchmark Study

The popularity of using wearable inertial sensors for physical activity classification has dramatically increased in the last decade due to their versatility, low form factor, and low power requirements. Consequently, various systems have been developed to automatically classify daily life activities. However, the scope and implementation of such systems is limited to laboratory-based investigations. Furthermore, these systems are not directly comparable, due to the large diversity in their design (e.g., number of sensors, placement of sensors, data collection environments, data processing techniques, features set, classifiers, cross-validation methods). Hence, the aim of this study is to propose a fair and unbiased benchmark for the field-based validation of three existing systems, highlighting the gap between laboratory and real-life conditions. For this purpose, three representative state-of-the-art systems are chosen and implemented to classify the physical activities of twenty older subjects (76.4 \ub1 5.6 years). The performance in classifying four basic activities of daily life (sitting, standing, walking, and lying) is analyzed in controlled and free living conditions. To observe the performance of laboratory-based systems in field-based conditions, we trained the activity classification systems using data recorded in a laboratory environment and tested them in real-life conditions in the field. The findings show that the performance of all systems trained with data in the laboratory setting highly deteriorates when tested in real-life conditions, thus highlighting the need to train and test the classification systems in the real-life setting. Moreover, we tested the sensitivity of chosen systems to window size (from 1 s to 10 s) suggesting that overall accuracy decreases with increasing window size. Finally, to evaluate the impact of the number of sensors on the performance, chosen systems are modified considering only the sensing unit worn at the lower back. The results, similarly to the multi-sensor setup, indicate substantial degradation of the performance when laboratory-trained systems are tested in the real-life setting. This degradation is higher than in the multi-sensor setup. Still, the performance provided by the single-sensor approach, when trained and tested with real data, can be acceptable (with an accuracy above 80%)

Proteome changes in the skin of the grape cultivar Barbera among different stages of ripening

<p>Abstract</p> <p>Background</p> <p>Grape ripening represents the third phase of the double sigmoidal curve of berry development and is characterized by deep changes in the organoleptic characteristics. In this process, the skin plays a central role in the synthesis of many compounds of interest (<it>e.g</it>. anthocyanins and aroma volatiles) and represents a fundamental protective barrier against damage by physical injuries and pathogen attacks. In order to improve the knowledge on the role of this tissue during ripening, changes in the protein expression in the skin of the red cultivar Barbera at five different stages from <it>véraison </it>to full maturation were studied by performing a comparative 2-DE analysis.</p> <p>Results</p> <p>The proteomic analysis revealed that 80 spots were differentially expressed throughout berry ripening. Applying a two-way hierarchical clustering analysis to these variations, a clear difference between the first two samplings (up to 14 days after <it>véraison</it>) and the following three (from 28 to 49 days after <it>véraison</it>) emerged, thus suggesting that the most relevant changes in protein expression occurred in the first weeks of ripening. By means of LC-ESI-MS/MS analysis, 69 proteins were characterized. Many of these variations were related to proteins involved in responses to stress (38%), glycolysis and gluconeogenesis (13%), C-compounds and carbohydrate metabolism (13%) and amino acid metabolism (10%).</p> <p>Conclusion</p> <p>These results give new insights to the skin proteome evolution during ripening, thus underlining some interesting traits of this tissue. In this view, we observed the ripening-related induction of many enzymes involved in primary metabolism, including those of the last five steps of the glycolytic pathway, which had been described as down-regulated in previous studies performed on whole fruit. Moreover, these data emphasize the relevance of this tissue as a physical barrier exerting an important part in berry protection. In fact, the level of many proteins involved in (a)biotic stress responses remarkably changed through the five stages taken into consideration, thus suggesting that their expression may be developmentally regulated.</p

Stochastic Modeling of Wind Derivatives in Energy Markets

We model the logarithm of the spot price of electricity with a normal inverse Gaussian (NIG) process and the wind speed and wind power production with two Ornstein\u2013Uhlenbeck processes. In order to reproduce the correlation between the spot price and the wind power production, namely between a pure jump process and a continuous path process, respectively, we replace the small jumps of the NIG process by a Brownian term. We then apply our models to two different problems: first, to study from the stochastic point of view the income from a wind power plant, as the expected value of the product between the electricity spot price and the amount of energy produced; then, to construct and price a European put-type quanto option in the wind energy markets that allows the buyer to hedge against low prices and low wind power production in the plant. Calibration of the proposed models and related price formulas is also provided, according to specific datasets

Chemical Characterization of a Collagen-Derived Protein Hydrolysate and Biostimulant Activity Assessment of Its Peptidic Components

Protein hydrolysates (PHs) are plant biostimulants consisting of oligopeptides and free amino acids exploited in agriculture to increase crop productivity. This work aimed to fractionate a commercial collagen-derived protein hydrolysate (CDPH) according to the molecular mass of the peptides and evaluate the bioactivity of different components. First, the CDPH was dialyzed and/or filtrated and analyzed on maize, showing that smaller compounds were particularly active in stimulating lateral root growth. The CDPH was then fractionated through fast protein liquid chromatography and tested on in vitro grown tomatoes proving that all the fractions were bioactive. Furthermore, these fractions were characterized by liquid chromatography-electrospray ionization- tandem mass spectrometry revealing a consensus sequence shared among the identified peptides. Based on this sequence, a synthetic peptide was produced. We assessed its structural similarity with the CDPH, the collagen, and polyproline type II helix by comparing the respective circular dichroism spectra and for the first time, we proved that a signature peptide was as bioactive as the whole CDPH

Structural characterization and K–Ar illite dating of reactivated, complex and heterogeneous fault zones: lessons from the Zuccale Fault, Northern Apennines

We studied the Zuccale Fault (ZF) on Elba, part of the Northern Apennines, to unravel the complex deformation history that is responsible for the remarkable architectural complexity of the fault. The ZF is characterized by a patchwork of at least six distinct, now tightly juxtaposed brittle structural facies (BSF), i.e. volumes of deformed rock characterized by a given fault rock type, texture, colour, composition, and age of formation. ZF fault rocks vary from massive cataclasite to foliated ultracataclasite, from clay-rich gouge to highly sheared talc phyllonite. Understanding the current spatial juxtaposition of these BSFs requires tight constraints on their age of formation during the ZF lifespan to integrate current fault geometries and characteristics over the time dimension of faulting. We present new K–Ar gouge dates obtained from three samples from two different BSFs. Two top-to-the-east foliated gouge and talc phyllonite samples document faulting in the Aquitanian (ca. 22 Ma), constraining east-vergent shearing along the ZF already in the earliest Miocene. A third sample constrains later faulting along the exclusively brittle, flat-lying principal slip surface t