Phase transitions in the distribution of the Andreev conductance of superconductor-metal junctions with multiple transverse modes

We compute analytically the full distribution of Andreev conductance G(NS) of a metal-superconductor interface with a large number N(c) of transverse modes, using a random matrix approach. The probability distribution P(G(NS),N(c) in the limit of large N(c) displays a Gaussian behavior near the average value =(2-√2)N(c) and asymmetric power-law tails in the two limits of very small and very large G(NS). In addition, we find a novel third regime sandwiched between the central Gaussian peak and the power-law tail for large G(NS). Weakly nonanalytic points separate these four regimes-these are shown to be consequences of three phase transitions in an associated Coulomb gas problem.     

Equilibrium strategy and population-size effects in lowest unique bid auctions

In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large data set of internet auctions. The theory agrees with the data with striking accuracy for small population-size N, while for larger N a qualitatively different distribution is observed. We interpret this result as the emergence of two different regimes, one in which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.     

A coherence-based approach for the pattern recognition of time series

A pattern recognition approach based on the frequency domain measure of squared coherence is a useful approach to identify linearly related groupings of time series over different periods of time. It is considered in an application to identify similar patterns of the yearly rates of change in the Gross Domestic Product (GDP) of twenty two highly developed countries in an econophysics context. The approach is also tested in simulation studies using linearly related time series, and it is shown to have a very good success rate of correct pattern matching.     

Structure-property interplay of proton conducting membranes based on PBI5N, SiO2-Im and H3PO4 for high temperature fuel cells

Polybenzimidazoles (PBIs) are among the polymers of choice to prepare membranes for high temperature polymer fuel cells. Poly-2,2'(2,6-pyridine)-5,5'-bibenzimidazole (PBI5N), doped with H(3)PO(4), and acid-doped PBI5N containing 10 wt% of imidazole-functionalized silica membranes were studied with thermogravimetric analysis, differential scanning calorimetry, dynamic-mechanical analysis, infrared spectroscopy, and broadband electric spectroscopy to examine the structure-property relationships. Key results show that: (1) doped PBI5N membranes show thermal decomposition starting at 120 °C, while pristine PBI5N is stable up to 300 °C; (2) the presence of filler increases the acid uptake and decreases the crystallinity of PBI5N; (3) the addition of phosphoric acid reduces the mechanical properties of the membrane, while the addition of filler has the opposite effect; (4) acid-doped membranes have conductivity values on the order of 10(-2)-10(-3) S cm(-1); and (5) membranes exhibit a Vogel-Tamman-Fulcher (VTF) type proton conduction mechanism, where proton hopping is coupled with the segmental motion of the polymer chain. Infrared spectroscopy combined with DFT quantum mechanical calculations was used to assign the experimental spectrum of PBI5N.     

Application of a Low Transition Temperature Mixture for the Dispersive Liquid–Liquid Microextraction of Illicit Drugs from Urine Samples

The use of psychoactive substances is a serious problem in today’s society and reliable methods of analysis are necessary to confirm their occurrence in biological matrices. In this work, a green sample preparation technique prior to HPLC-MS analysis was successfully applied to the extraction of 14 illicit drugs from urine samples. The isolation procedure was a dispersive liquid–liquid microextraction based on the use of a low transition temperature mixture (LTTM), composed of choline chloride and sesamol in a molar ratio 1:3 as the extracting solvent. This mixture was classified as LTTM after a thorough investigation carried out by FTIR and DSC, which recorded a glass transition temperature at −71 °C. The extraction procedure was optimized and validated according to the main Food and Drug Administration (FDA) guidelines for bioanalytical methods, obtaining good figures of merit for all parameters: the estimated lower limit of quantitation (LLOQ) values were between 0.01 µg L⁻¹ (bk-MMBDB) and 0.37 µg L⁻¹ (PMA); recoveries, evaluated at very low spike levels (in the ng-µg L⁻¹ range), spanned from 55% (MBDB) to 100% (bk-MMBDB and MDPV); finally, both within-run and between-run precisions were lower than 20% (LLOQ) and 15% (10xLLOQ).     

Interior estimates for some semilinear elliptic problem with critical nonlinearity

We study compactness properties for solutions of a semilinear elliptic equation with critical nonlinearity. For high dimensions, we are able to show that any solutions sequence with uniformly bounded energy is uniformly bounded in the interior of the domain. In particular, singularly perturbed Neumann equations admit pointwise concentration phenomena only at the boundary.     

Working Memory Decline in Alzheimer’s Disease Is Detected by Complexity Analysis of Multimodal EEG-fNIRS

Alzheimer’s disease (AD) is characterized by working memory (WM) failures that can be assessed at early stages through administering clinical tests. Ecological neuroimaging, such as Electroencephalography (EEG) and functional Near Infrared Spectroscopy (fNIRS), may be employed during these tests to support AD early diagnosis within clinical settings. Multimodal EEG-fNIRS could measure brain activity along with neurovascular coupling (NC) and detect their modifications associated with AD. Data analysis procedures based on signal complexity are suitable to estimate electrical and hemodynamic brain activity or their mutual information (NC) during non-structured experimental paradigms. In this study, sample entropy of whole-head EEG and frontal/prefrontal cortex fNIRS was evaluated to assess brain activity in early AD and healthy controls (HC) during WM tasks (i.e., Rey–Osterrieth complex figure and Raven’s progressive matrices). Moreover, conditional entropy between EEG and fNIRS was evaluated as indicative of NC. The findings demonstrated the capability of complexity analysis of multimodal EEG-fNIRS to detect WM decline in AD. Furthermore, a multivariate data-driven analysis, performed on these entropy metrics and based on the General Linear Model, allowed classifying AD and HC with an AUC up to 0.88. EEG-fNIRS may represent a powerful tool for the clinical evaluation of WM decline in early AD.     

Concentrating solutions for the Hénon equation in ℝ2

We consider the boundary value problem Δu+⋎x⋎^2α u ^p =0, α>0, in the unit ballB with homogeneous Dirichlet boundary condition andp a large exponent. We find a condition which ensures the existence of a positive solutionu _p concentrating outside the origin atk symmetric points asp goes to +∞. The same techniques lead also to a more general result on general domains. In particular, we find that concentration at the origin is always possible, provided α⊄IN. The first author is supported by M.U.R.S.T., project “Variational methods and nonlinear differential equations” and a PIMS Postdoctoral Fellowship. The second author is supported by M.U.R.S.T., project “Metodi variazionali e topologici nello studio di fenomeni non lineari.” The third author is supported by an Earmarked Grant from RGC of HK.     

A quasi-Newton method for solving fixed point problems in Hilbert spaces

Summary We study the convergence properties of a projective variant of Newton's method for the approximation of fixed points of completely continuous operators in Hilbert spaces. We then discuss applications to nonlinear integral equations and we produce some numerical examples.