Extreme Value Theory for Piecewise Contracting Maps with Randomly Applied Stochastic Perturbations

We consider globally invertible and piecewise contracting maps in higher dimensions and we perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process: in this framework we develop an extreme value theory for a few classes of observables and we show how to get the (usual) limiting distributions together with an extremal index depending on the strength of the noise.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1407.041

Environmental and genetic influences on neurocognitive development: the importance of multiple methodologies and time-dependent intervention

Genetic mutations and environmental factors dynamically influence gene expression and developmental trajectories at the neural, cognitive, and behavioral levels. The examples in this article cover different periods of neurocognitive development—early childhood, adolescence, and adulthood—and focus on studies in which researchers have used a variety of methodologies to illustrate the early effects of socioeconomic status and stress on brain function, as well as how allelic differences explain why some individuals respond to intervention and others do not. These studies highlight how similar behaviors can be driven by different underlying neural processes and show how a neurocomputational model of early development can account for neurodevelopmental syndromes, such as autism spectrum disorders, with novel implications for intervention. Finally, these studies illustrate the importance of the timing of environmental and genetic factors on development, consistent with our view that phenotypes are emergent, not predetermined

Regulatory Taking: A Contract Approach

This Article begins by defining the parameters of the fifth amendment\u27s taking clause. The Article then reviews the various tests used in determining whether governmental action constitutes a taking, and discusses the recent Supreme Court decisions within the framework of case law as it has evolved since the Court\u27s 1922 landmark decision, Pennsylvania Coal Co. v. Mahon. Finally, the Article suggests a formula based on well-established contract principles for analyzing the impact of land use regulation on private property interests

Transverse intrafascicular multichannel electrode (TIME) system for treatment of phantom limb pain in amputees

International audienceAIM: Phantom limb pain (PLP) develops in the lost limb in 50-80% of amputees. Today, it is not completely understood why the pain occurs, and no effective treatments are available. The favorable effect of electrical stimulation on PLP has been demonstrated. Our aim is to develop a novel system for manipulation of sensations by application of multi-channel microstimulation to the nerve stump of an amputee and explore this method as a treatment for clinched fist PLP (see figure). RESULTS: 1) Electrode design. Non-corrugated TIME electrodes with different dimensions and 8-12 active sites have been manufactued and tested in vivo and in vitro testing in the rat and pig. Methods for corrugated prototypes were developed and the first prototypes were realized. 2) Electrode selectivity modeling. A peripheral nerve model is under development to evaluate the electrode's selective stimulation properties and to optimize electrode design. Simulated currents and neural activity generated were qualitatively assessed using experimental data obtained from rat nerves. 3) Implant modeling. To optimize the implantation procedure, a theoretical peripheral nervous tissue model and a 3D FEM was implemented. Both models closely reproduce the experimental peripheral nervous tissue behaviour and simulate the insertion forces transmitted to the electrode during implantation. 4) Multi-channel stimulators and connectors. A 12-pole prototype, bench-top stimulator has been implemented and successfully tested in animal experiments. A high-count, implantable connector between stimulator and electrode has been designed. 5) Biocompatibility. Electrode materials were evaluated and did not induce immune rejection and significant inflammatory reaction after in vivo implantation in the rat. Electrode implantation will require an understanding of the fascicular characteristics of the target nerve. Morphological characteristics of the rat, pig and human nerves are currently evaluated and compared. 6) Animal testing. First TIME electrodes test were carried out in the acute rat and acute pig. Results indicated selective stimulation of different fascicles with graded recruitment. 7) Clinical evaluation: To quantify the location of artificially evoked sensations and evaluate the strength of artificially evoked sensations a psychophysical testing platform is under development. Main inclusion criteria for patient recruitment have been identified and protocols have been defined. CONCLUSION: The feasibility of the corrugated version of the TIME electrode has yet to be explored. Further work designing, optimizing and testing the TIME electrode and all technological developments will be carried out including theoretical stimulations and animal experimental work before the optimal electrode for human implant will be chosen

On Hilberg's Law and Its Links with Guiraud's Law

Hilberg (1990) supposed that finite-order excess entropy of a random human text is proportional to the square root of the text length. Assuming that Hilberg's hypothesis is true, we derive Guiraud's law, which states that the number of word types in a text is greater than proportional to the square root of the text length. Our derivation is based on some mathematical conjecture in coding theory and on several experiments suggesting that words can be defined approximately as the nonterminals of the shortest context-free grammar for the text. Such operational definition of words can be applied even to texts deprived of spaces, which do not allow for Mandelbrot's ``intermittent silence'' explanation of Zipf's and Guiraud's laws. In contrast to Mandelbrot's, our model assumes some probabilistic long-memory effects in human narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic

Evidence for surface uplift of the Atlas Mountains and the surrounding peripheral plateaux: Combining apatite fission-track results and geomorphic indicators in the Western Moroccan Meseta (coastal Variscan Paleozoic basement)

This work represents an initial attempt to link the evolution of the topography in relation to the general tectonic framework of western Morocco. For this purpose, in a section of the Western Moroccan Meseta different tools are combined in order to attain the general objective. Apatite fission-track (AFT) data of granitic rocks of the Rabat–Khenifra area give ages around 200 Ma with track length distributions which are compatible with the thermal models already established for the area. An inverse correlation between AFT ages and elevation is observed which is compatible with previous models indicating northward tilting of the whole Western Moroccan Meseta which is younger than 20–25 Ma. In order to test this possibility a detailed analysis of the topography at different scales in the Western Moroccan Meseta has been performed. Results indicate that two open folds with different amplitudes are recognized and that the one with wider wavelength could correspond to a lithospheric fold as previously stated by other authors on the basis of independent geological arguments. The northward tilting proposed based on the AFT data agrees with the results obtained in the analysis of the topography which reinforces the presence of a very open fold with a wavelength of 200–300 km in the north-western limb of the Western Moroccan Meseta

One-carbon metabolism, cognitive impairment and CSF measures of Alzheimer pathology: homocysteine and beyond.

Hyperhomocysteinemia is a risk factor for cognitive decline and dementia, including Alzheimer disease (AD). Homocysteine (Hcy) is a sulfur-containing amino acid and metabolite of the methionine pathway. The interrelated methionine, purine, and thymidylate cycles constitute the one-carbon metabolism that plays a critical role in the synthesis of DNA, neurotransmitters, phospholipids, and myelin. In this study, we tested the hypothesis that one-carbon metabolites beyond Hcy are relevant to cognitive function and cerebrospinal fluid (CSF) measures of AD pathology in older adults. Cross-sectional analysis was performed on matched CSF and plasma collected from 120 older community-dwelling adults with (n = 72) or without (n = 48) cognitive impairment. Liquid chromatography-mass spectrometry was performed to quantify one-carbon metabolites and their cofactors. Least absolute shrinkage and selection operator (LASSO) regression was initially applied to clinical and biomarker measures that generate the highest diagnostic accuracy of a priori-defined cognitive impairment (Clinical Dementia Rating-based) and AD pathology (i.e., CSF tau phosphorylated at threonine 181 [p-tau181]/β-Amyloid 1-42 peptide chain [Aβ1-42] >0.0779) to establish a reference benchmark. Two other LASSO-determined models were generated that included the one-carbon metabolites in CSF and then plasma. Correlations of CSF and plasma one-carbon metabolites with CSF amyloid and tau were explored. LASSO-determined models were stratified by apolipoprotein E (APOE) ε4 carrier status. The diagnostic accuracy of cognitive impairment for the reference model was 80.8% and included age, years of education, Aβ1-42, tau, and p-tau181. A model including CSF cystathionine, methionine, S-adenosyl-L-homocysteine (SAH), S-adenosylmethionine (SAM), serine, cysteine, and 5-methyltetrahydrofolate (5-MTHF) improved the diagnostic accuracy to 87.4%. A second model derived from plasma included cystathionine, glycine, methionine, SAH, SAM, serine, cysteine, and Hcy and reached a diagnostic accuracy of 87.5%. CSF SAH and 5-MTHF were associated with CSF tau and p-tau181. Plasma one-carbon metabolites were able to diagnose subjects with a positive CSF profile of AD pathology in APOE ε4 carriers. We observed significant improvements in the prediction of cognitive impairment by adding one-carbon metabolites. This is partially explained by associations with CSF tau and p-tau181, suggesting a role for one-carbon metabolism in the aggregation of tau and neuronal injury. These metabolites may be particularly critical in APOE ε4 carriers

On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids

This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation type, being automatic, and being biautomatic are investigated for this class of monoids. The first main result shows that for any consistent combination of these properties and their negations, there is a homogeneous monoid with exactly this combination of properties. We then introduce the new concept of abstract Rees-commensurability (an analogue of the notion of abstract commensurability for groups) in order to extend this result to show that the same statement holds even if one restricts attention to the class of n-ary homogeneous monoids (where every side of every relation has fixed length n). We then introduce a new encoding technique that allows us to extend the result partially to the class of n-ary multihomogenous monoids

Bringing sensation to prosthetic hands—chronic assessment of implanted thin-film electrodes in humans

Direct stimulation of peripheral nerves with implantable electrodes successfully provided sensory feedback to amputees while using hand prostheses. Longevity of the electrodes is key to success, which we have improved for the polyimide-based transverse intrafascicular multichannel electrode (TIME). The TIMEs were implanted in the median and ulnar nerves of three trans-radial amputees for up to six months. We present a comprehensive assessment of the electrical properties of the thin-film metallization as well as material status post explantationem. The TIMEs stayed within the electrochemical safe limits while enabling consistent and precise amplitude modulation. This lead to a reliable performance in terms of eliciting sensation. No signs of corrosion or morphological change to the thin-film metallization of the probes was observed by means of electrochemical and optical analysis. The presented longevity demonstrates that thin-film electrodes are applicable in permanent implant systems