Finite reduction and Morse index estimates for mechanical systems

A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur's complement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain.Comment: 13 pages; v2: minor changes, to appear in Nonlinear Differential Equations and Application

Economic performance evaluation of flexible centralised and decentralised blue hydrogen production systems design under uncertainty

Blue hydrogen is viewed as an important energy vector in a decarbonised global economy, but its large-scale and capital-intensive production displays economic performance vulnerabities in the face of increased market and regulatory uncertainty. This study analyses flexible (modular) blue hydrogen production plant designs and evaluates their effectiveness to enhance economic performance under uncertainty. The novelty of this work lies in the development of a comprehensive techno-economic evaluation framework that considers flexible centralised and decentralised blue hydrogen plant design alternatives in the presence of irreducible uncertainty, whilst explicitly considering the time value of money, economies of scale and learning effects. A case study of centralised and decentralised blue hydrogen production for the transport sector in the San Francisco area is developed to highlight the underlying value of flexibility. The proposed methodological framework considers various blue hydrogen plant designs (fixed, phased, and flexible) and compares them using relevant economic indicators (net present value (NPV), capex, value-at-risk/gain, etc.) through a detailed Monte Carlo simulation framework. Results indicate that flexible centralised hydrogen production yields greater economic value than alternative designs, despite the associated cost-premium of modularity. It is also shown that the value of flexibility increases under greater uncertainty, higher learning rates and weaker economies of scale. Moreover, sensitivity analysis reveals that flexible design remains the preferred investment option over a wide range of market and regulatory conditions except for high initial hydrogen demand. Finally, this study demonstrates that major regulatory and market uncertainties surrounding blue hydrogen production can be effectively managed through the application of flexible engineering system design that protects the investment from major downside risks whilst allowing access to favourable upside opportunities

Practical Design and Implementation of a CAVE Environment

CAVE systems are nowadays one of the best Virtual Reality (VR) immersive devices available for rendering virtual environments. Unfortunately, such kind of hardware is extremely expensive, complex and cum-bersome, thus limited in its spread. Several cheaper solutions already exist, but they implement usually only a subset of features of a professional CAVE (like a reduced number of wall-displays, no stereographic at all or with a low-quality support, low brightness, etc.). In this paper we describe how we have built a low cost CAVE with four screens (three walls and a floor), stereographic rendering and user tracking by only using hardware commonly available on the market and free software, we show the different solutions and work-around we implemented to solve the problems we encountered and we conclude with a fair evaluation of our system by using two applications we developed with it

Circular dichroism and 1H NMR studies of Co2+- and Ni2+-substituted concanavalin A and the lentil and pea lectins.

Visible absorption, circular dichroism (CD) and magnetic circular dichroism spectra have been recorded for the Ca2+-Co2+ derivatives of the lentil (CCoLcH) and pea (CCoPSA) lectins (Co2+ at the S1 sites and Ca2+ at the S2 sites) and shown to be very similar for both proteins. The visible absorption and magnetic circular dichroism spectra indicate similar octahedral geometries for high spin Co2+ at S1 in both proteins, as found in the Ca2+-Co2+ complex of concanavalin A (CCoPL) (Richardson, C. E., and Behnke, W. D. (1976) J. Mol. Biol. 102, 441-451). The visible CD data, however, indicate differences in the environment around S1 of CCoLcH and CCoPSA compared to CCoPL. 1H NMR spectra at 90 MHz of the Co2+ and Ni2+ derivatives of the lectins show a number of isotropically shifted signals which arise from protons in the immediate vicinity of the S1 sites. Analysis of the spectra of the Co2+ derivatives in H2O and D2O has permitted resonance assignments of the side chain ring protons of the coordinated histidine at S1 in the lectins. Differences are observed in the H-D exchange rate of the histidine NH proton at S1 in concanavalin A compared to the lentil and pea lectins. NMR data of the Ni2+-substituted proteins, together with spectra of the Co2+ derivatives, also indicate that the side chains of a carboxylate ligand and of the histidine residue at S1 are positioned differently in concanavalin A than in the other two lectins. These results appear to account, in part, for the differences observed in the visible CD spectra of the Co2+-substituted proteins. In addition, binding of monosaccharides does not significantly perturb the spectra of the lectins. An unusual feature in the 1H NMR spectra of all three Co2+-substituted lectins is the presence of two exchangeable downfield shifted resonances which appear to be associated with the two protons of a slowly exchanging water molecule coordinated to the Ca2+ ion at S2. T1 measurements of CCoLcH have provided an estimation of the distances from the Co2+ ion to these two protons of 3.7 and 4.0 A

Generalized Species Sampling Priors with Latent Beta reinforcements

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent family of non-exchangeable species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We compare their theoretical clustering properties with those of the Dirichlet Process and the two parameters Poisson-Dirichlet process. The proposed construction provides a complete characterization of the joint process, differently from existing work. We then propose the use of such process as prior distribution in a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte Carlo sampler for posterior inference. We evaluate the performance of the prior and the robustness of the resulting inference in a simulation study, providing a comparison with popular Dirichlet Processes mixtures and Hidden Markov Models. Finally, we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array CGH data.Comment: For correspondence purposes, Edoardo M. Airoldi's email is [email protected]; Federico Bassetti's email is [email protected]; Michele Guindani's email is [email protected] ; Fabrizo Leisen's email is [email protected]. To appear in the Journal of the American Statistical Associatio

Calibration and validation of high frequency coastal radar waves exploiting in-situ observations and modelled data in the south-west Sicily

This paper describes a calibration procedure for a non-optimally configured High Frequency Radar (HFR) for the period 1 April 2021, to 31 March 2022, to assess sea waves characteristics. The HFR system, a 16.5 MHz WEllen RAdar (WERA), is part of an innovative network for monitoring the state of the sea. The system is installed in the western part of Sicily (Italy) where a wave buoy is positioned. HFR data underestimate the spectral significant wave heights (Hm0), in particular for Hm0 > 2 m, highlighting the need for calibration of the HFR system to ensure its optimal performance for operational purposes. The calibration was performed with both in-situ and modelled data provided by the Copernicus Marine Service. The best results were obtained when the buoy data were used as reference. Encouraging results were achieved as demonstrated by the improvement of the quantitative metrics after the calibration. Indeed, the RMSE decreased from 0.60 to 0.36 m; the correlation R increased slightly from 0.86 to 0.88, the slope from 0.48 to 0.8; whereas intercept from 0.11 to 0.31 m. Moreover, waves higher than > 2 m are well reproduced by the calibrated HFR time series with the RMSE decreasing from 1.3 to 0.53 m

On the birth of limit cycles for non-smooth dynamical systems

The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. In fact, overall results are presented to ensure the existence of limit cycles of such systems. These results may represent new insights in averaging, in particular its relation with non smooth dynamical systems theory. An application is presented in careful detail

Own Song Selectivity in the Songbird Auditory Pathway: Suppression by Norepinephrine

Like human speech, birdsong is a learned behavior that supports species and individual recognition. Norepinephrine is a catecholamine suspected to play a role in song learning. The goal of this study was to investigate the role of norepinephrine in bird's own song selectivity, a property thought to be important for auditory feedback processes required for song learning and maintenance.Using functional magnetic resonance imaging, we show that injection of DSP-4, a specific noradrenergic toxin, unmasks own song selectivity in the dorsal part of NCM, a secondary auditory region.The level of norepinephrine throughout the telencephalon is known to be high in alert birds and low in sleeping birds. Our results suggest that norepinephrine activity can be further decreased, giving rise to a strong own song selective signal in dorsal NCM. This latent own song selective signal, which is only revealed under conditions of very low noradrenergic activity, might play a role in the auditory feedback and/or the integration of this feedback with the motor circuitry for vocal learning and maintenance

Biogeochemical, isotopic and bacterial distributions trace oceanic abyssal circulation

We explore the possibility of tracing routes of dense waters toward and within the ocean abyss by the use of an extended set of observed physical and biochemical parameters. To this purpose, we employ mercury, isotopic oxygen, biopolymeric carbon and its constituents, together with indicators of microbial activity and bacterial diversity found in bottom waters of the Eastern Mediterranean. In this basin, which has been considered as a miniature global ocean, two competing sources of bottom water (one in the Adriatic and one in the Aegean seas) contribute to the ventilation of the local abyss. However, due to a recent substantial reduction of the differences in the physical characteristics of these two water masses it has become increasingly complex a water classification using the traditional approach with temperature, salinity and dissolved oxygen alone. Here, we show that an extended set of observed physical and biochemical parameters allows recognizing the existence of two different abyssal routes from the Adriatic source and one abyssal route from the Aegean source despite temperature and salinity of such two competing sources of abyssal water being virtually indistinguishable. Moreover, as the near-bottom development of exogenous bacterial communities transported by convectively-generated water masses in the abyss can provide a persistent trace of episodic events, intermittent flows like those generating abyssal waters in the Eastern Mediterranean basin may become detectable beyond the availability of concomitant measurements.We explore the possibility of tracing routes of dense waters toward and within the ocean abyss by the use of an extended set of observed physical and biochemical parameters. To this purpose, we employ mercury, isotopic oxygen, biopolymeric carbon and its constituents, together with indicators of microbial activity and bacterial diversity found in bottom waters of the Eastern Mediterranean. In this basin, which has been considered as a miniature global ocean, two competing sources of bottom water (one in the Adriatic and one in the Aegean seas) contribute to the ventilation of the local abyss. However, due to a recent substantial reduction of the differences in the physical characteristics of these two water masses it has become increasingly complex a water classification using the traditional approach with temperature, salinity and dissolved oxygen alone. Here, we show that an extended set of observed physical and biochemical parameters allows recognizing the existence of two different abyssal routes from the Adriatic source and one abyssal route from the Aegean source despite temperature and salinity of such two competing sources of abyssal water being virtually indistinguishable. Moreover, as the near-bottom development of exogenous bacterial communities transported by convectively-generated water masses in the abyss can provide a persistent trace of episodic events, intermittent flows like those generating abyssal waters in the Eastern Mediterranean basin may become detectable beyond the availability of concomitant measurements. © 2016 Rubino et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited