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

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

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

Dynamics of Dynamics within a Single Data Acquisition Session: Variation in Neocortical Alpha Oscillations in Human MEG

Background Behavioral paradigms applied during human recordings in electro- and magneto- encephalography (EEG and MEG) typically require 1–2 hours of data collection. Over this time scale, the natural fluctuations in brain state or rapid learning effects could impact measured signals, but are seldom analyzed. Methods and Findings We investigated within-session dynamics of neocortical alpha (7–14 Hz) rhythms and their allocation with cued-attention using MEG recorded from primary somatosensory neocortex (SI) in humans. We found that there were significant and systematic changes across a single ~1 hour recording session in several dimensions, including increased alpha power, increased differentiation in attention-induced alpha allocation, increased distinction in immediate time-locked post-cue evoked responses in SI to different visual cues, and enhanced power in the immediate cue-locked alpha band frequency response. Further, comparison of two commonly used baseline methods showed that conclusions on the evolution of alpha dynamics across a session were dependent on the normalization method used. Conclusions These findings are important not only as they relate to studies of oscillations in SI, they also provide a robust example of the type of dynamic changes in brain measures within a single session that are overlooked in most human brain imaging/recording studies.National Institutes of Health (U.S.) (P41RR14075)National Institutes of Health (U.S.) (K25MH072941)National Institutes of Health (U.S.) (K01AT003459)National Institutes of Health (U.S.) (1RO1-NS045130-01)National Institutes of Health (U.S.) (T32GM007484)National Science Foundation (U.S.) (0316933)Osher Lifelong Learning Institute

Pairwise assembly of organopalladium(II) units with cyanurato(3-) and trithiocyanurato(3-) ligands: formation of chiral Pd12, Pd10 and Pd9 cage-molecules

The o-palladated, chloro-bridged dimers [Pd{2-phenylpyridine(-H)}-μ-Cl]2 and [Pd{N,N-dimethylbenzylamine(-H)}-μ-Cl]2 react with cyanuric acid in the presence of base to afford closed, chiral cage-molecules in which twelve organo-Pd(II) centers, located in pairs at the vertices of an octahedron, are linked by four tetrahedrally-arranged cyanurato(3-) ligands. Incomplete (Pd10) cages, having structures derived from the corresponding Pd12 cages by replacing one pair of organopalladium centers with two protons, have also been isolated. Reaction of [Pd{2-phenylpyridine(-H)}-μ-Cl]2 with trithiocyanuric acid gives an entirely different and more open type of cage-complex, comprising only nine organopalladium centers and three thiocyanurato(3-) ligands: cage-closure in this latter system appears to be inhibited by steric crowding of the thiocarbonyl groups

Analysing the impact of rescheduling time in hybrid manufacturing control

Hybrid manufacturing control architectures merge the benefits of hierarchical and heterarchical approaches. Disturbances can be handled at upper or lower decision levels, depending on the type of disturbance, its impact and the time the control system has to react. This paper focuses particularly on a disturbance handling mechanism at upper decision levels using a rescheduling manufacturing method. Such rescheduling is more complex that the offline scheduling since the control system must take into account the current system status, obtain a satisfactory performance under the new conditions, and also come up with a new schedule in a restricted amount of time. Then, this paper proposes a simple and generic rescheduling method which, based on the satisfying principle, analyses the trade-off between the rescheduling time and the performance achieved after a perturbation. The proposed approach is validated on a simulation model of a realistic assembly cell and results demonstrate that adaptation of the rescheduling time might be beneficial in terms of overall performance and reactivity.info:eu-repo/semantics/publishedVersio

Cortical fast-spiking parvalbumin interneurons enwrapped in the perineuronal net express the metallopeptidases Adamts8, Adamts15 and Neprilysin.

The in situ hybridization Allen Mouse Brain Atlas was mined for proteases expressed in the somatosensory cerebral cortex. Among the 480 genes coding for protease/peptidases, only four were found enriched in cortical interneurons: Reln coding for reelin; Adamts8 and Adamts15 belonging to the class of metzincin proteases involved in reshaping the perineuronal net (PNN) and Mme encoding for Neprilysin, the enzyme degrading amyloid β-peptides. The pattern of expression of metalloproteases (MPs) was analyzed by single-cell reverse transcriptase multiplex PCR after patch clamp and was compared with the expression of 10 canonical interneurons markers and 12 additional genes from the Allen Atlas. Clustering of these genes by K-means algorithm displays five distinct clusters. Among these five clusters, two fast-spiking interneuron clusters expressing the calcium-binding protein Pvalb were identified, one co-expressing Pvalb with Sst (PV-Sst) and another co-expressing Pvalb with three metallopeptidases Adamts8, Adamts15 and Mme (PV-MP). By using Wisteria floribunda agglutinin, a specific marker for PNN, PV-MP interneurons were found surrounded by PNN, whereas the ones expressing Sst, PV-Sst, were not

Noninvasive optical inhibition with a red-shifted microbial rhodopsin

Optogenetic inhibition of the electrical activity of neurons enables the causal assessment of their contributions to brain functions. Red light penetrates deeper into tissue than other visible wavelengths. We present a red-shifted cruxhalorhodopsin, Jaws, derived from Haloarcula (Halobacterium) salinarum (strain Shark) and engineered to result in red light–induced photocurrents three times those of earlier silencers. Jaws exhibits robust inhibition of sensory-evoked neural activity in the cortex and results in strong light responses when used in retinas of retinitis pigmentosa model mice. We also demonstrate that Jaws can noninvasively mediate transcranial optical inhibition of neurons deep in the brains of awake mice. The noninvasive optogenetic inhibition opened up by Jaws enables a variety of important neuroscience experiments and offers a powerful general-use chloride pump for basic and applied neuroscience.McGovern Institute for Brain Research at MIT (Razin Fellowship)United States. Defense Advanced Research Projects Agency. Living Foundries Program (HR0011-12-C-0068)Harvard-MIT Joint Research Grants Program in Basic NeuroscienceHuman Frontier Science Program (Strasbourg, France)Institution of Engineering and Technology (A. F. Harvey Prize)McGovern Institute for Brain Research at MIT. Neurotechnology (MINT) ProgramNew York Stem Cell Foundation (Robertson Investigator Award)National Institutes of Health (U.S.) (New Innovator Award 1DP2OD002002)National Institute of General Medical Sciences (U.S.) (EUREKA Award 1R01NS075421)National Institutes of Health (U.S.) (Grant 1R01DA029639)National Institutes of Health (U.S.) (Grant 1RC1MH088182)National Institutes of Health (U.S.) (Grant 1R01NS067199)National Science Foundation (U.S.) (Career Award CBET 1053233)National Science Foundation (U.S.) (Grant EFRI0835878)National Science Foundation (U.S.) (Grant DMS0848804)Society for Neuroscience (Research Award for Innovation in Neuroscience)Wallace H. Coulter FoundationNational Institutes of Health (U.S.) (RO1 MH091220-01)Whitehall FoundationEsther A. & Joseph Klingenstein Fund, Inc.JPB FoundationPIIF FundingNational Institute of Mental Health (U.S.) (R01-MH102441-01)National Institutes of Health (U.S.) (DP2-OD-017366-01)Massachusetts Institute of Technology. Simons Center for the Social Brai