In the framework of the PDE's algebraic topology, previously introduced by A. Pr\'astaro, are considered {\em exotic differential equations}, i.e., differential equations admitting Cauchy manifolds $N$ identifiable with exotic spheres, or such that their boundaries $\partial N$ are exotic spheres. For such equations are obtained local and global existence theorems and stability theorems. In particular the smooth ($4$-dimensional) Poincar\'e conjecture is proved. This allows to complete the previous Theorem 4.59 in \cite{PRA17} also for the case $n=4$.

The Dynamic Source Routing protocol (DSR) is a simple and efficient routing protocol designed specifically for use in multi-hop wireless ad hoc networks of mobile nodes. Preemptive DSR(PDSR) is the modified version of DSR. The main objective of this paper is to analyze and compare the performance of Preemptive DSR and Temporarily Ordered Routing Algorithm(TORA).It discusses the effect of variation in number of nodes and average speed on protocol performance. Simulation results (provided by the instructor) are analyzed to get an insight into the operation of TORA and PDSR in small/large sized networks with slow/fast moving nodes. Results show that PDSR outperforms TORA in terms of the number of MANET control packets used to maintain/erase routes. Also, it is concluded that TORA is a better choice than PDSR for fast moving highly connected set of nodes. It is also observed that DSR provides better data throughput than TORA and that routes can be created faster in PDSR than in TORA. This paper tries to explain the reasons behind the nature of the results.

{p=We obtain uniqueness of additive families { A _ t }_ t >0 of fractional powers of a multi-valued sectorial linear operator A ≡ A _1 in a Banach space, satisfying a certain kind of continuity with respect to the exponent and a spectral property, from uniqueness of the solutions of the second-order incomplete Cauchy problem associated with A . We show the close relationship between the multiplicativity and the uniqueness of fractional powers., h1=Abstract}

We pursued our functional magnetic resonance imaging (fMRI) studies of the neural correlates of romantic love in 24 subjects, half of whom were female (6 heterosexual and 6 homosexual) and half male (6 heterosexual and 6 homosexual). We compared the pattern of activity produced in their brains when they viewed the faces of their loved partners with that produced when they viewed the faces of friends of the same sex to whom they were romantically indifferent. The pattern of activation and de-activation was very similar in the brains of males and females, and heterosexuals and homosexuals. We could therefore detect no difference in activation patterns between these groups.

We study the kinetic and chemical equilibration in 'infinite' parton-hadron matter within the Parton-Hadron-String Dynamics transport approach, which is based on a dynamical quasiparticle model for partons matched to reproduce lattice-QCD results - including the partonic equation of state - in thermodynamic equilibrium. The 'infinite' matter is simulated within a cubic box with periodic boundary conditions initialized at different baryon density (or chemical potential) and energy density. The transition from initially pure partonic matter to hadronic degrees of freedom (or vice versa) occurs dynamically by interactions. Different thermodynamical distributions of the strongly-interacting quark-gluon plasma (sQGP) are addressed and discussed.

In this paper, we apply the sorting network theory to construct an analog rank order filter. We present a voltage mode CMOS two-input sorting element and arrange these to form a rank order filter. The resulting circuit is simpleand is a high-speed, high-precision design. Although the transistor count is moderately higher than other designs, the proposed circuit simultaneously outputs signals of all ranks rather than of just one specified rank. We also develop a slightly modified design which calculates the rank of a given signal. We present reports of simulations to verify the performance of the device.

{p=[Background, The Clock Drawing Test (CDT) is a screening tool for dementia that tests a variety of cognitive domains. The CDT takes a maximum of two minutes to complete and might be helpful in identifying postoperative cognitive disorders at the bedside. The objective of this study was to evaluate the accuracy of the CDT in a population at high risk for postoperative cognitive disorders, Methods, In this prospective observational cohort study, patients were recruited who were ≥ 60 yr of age and scheduled for elective open repair of the abdominal aorta. Delirium was assessed using the Confusion Assessment Method (CAM) on postoperative days (POD) 2 and 4 and at discharge. Cognitive function was assessed with neuropsychometric tests before surgery and at discharge. Postoperative cognitive dysfunction (POCD) was determined using the Reliable Change Index. Clock Drawing Tests were administered at all time points. Agreement between the CDT and test for delirium or POCD was assessed with Cohen’s Kappa statistic., Results, Delirium was noted in 30 of 83 patients (36%; 95% confidence interval [CI] 26 to 46%) during their hospital stay, while POCD was noted in 48 of 78 patients (60%; 95% CI 51 to 72%) at discharge. Agreement between the CDT and CAM was poor at three intervals (Kappa 0.06 to 0.29), as was POCD at discharge (Kappa 0.46). Sensitivity of the CDT was <0.71 for both delirium and POCD at all intervals. False positives and negatives were common., Conclusion, Agreement between CDT and tests for delirium and POCD was poor; sensitivity was inadequate for a screening test. (ClinicalTrials.gov number, NCT00911677)., Contexte, Le test du dessin de l’horloge (CDT) est un outil de dépistage de la démence qui évalue plusieurs domaines cognitifs. Le CDT prend au maximum deux minutes à compléter et pourrait être utile pour identifier les troubles cognitifs postopératoires directement au chevet du patient. L’objectif de cette étude était d’évaluer l’exactitude du CDT chez une population présentant un risque élevé de troubles cognitifs postopératoires., Méthode, Dans cette étude de cohorte prospective et observationnelle, des patients âgés > 60 ans subissant une réparation non urgente ouverte de l’aorte abdominale ont été recrutés. Le delirium a été évalué aux jours postopératoires deux et quatre ainsi qu’au congé à l’aide de la Méthode d’évaluation de la confusion (CAM). Le fonctionnement cognitif a été évalué à l’aide de tests neuropsychométriques avant la chirurgie et lors du congé. Le dysfonctionnement cognitif postopératoire (DCPO) a été déterminé à l’aide d’un indice de changement fiable. Des tests de dessin de l’horloge ont été administrés à tous les points de mesure dans le temps. La correspondance entre le CDT et le test du delirium ou du DCPO a été évaluée à l’aide de l’analyse statistique kappa., Résultats, On a observé du delirium chez 30 des 83 patients (36%; intervalle de confiance [IC] 95%, 26 à 46%) pendant leur séjour à l’hôpital, et le DCPO a été noté chez 48 de 78 patients (60%; IC 95%, 51 à 72%) au moment du congé. La correspondance entre le CDT et le CDT à trois intervalles (kappa 0,06 – 0,29) et le DCPO au moment du congé (kappa 0,46) était médiocre. La sensibilité du CDT était inférieure à 0,71 pour le delirium et le DCPO à tous les intervalles. Les faux positifs et les négatifs étaient fréquents., Conclusion, La correspondance entre le CDT et les tests réalisés pour déterminer la présence de delirium et de DCPO était médiocre; sa sensibilité était inadaptée pour en faire un test de dépistage. (Numéro de ClinicalTrials.gov, NCT00911677).], h1=Résumé}

The topological magnetoelectric effect (TME) is the fundamental quantization effect for topological insulators in units of the fine structure constant $\alpha$. In [Phys. Rev. Lett. 105, 166803(2010)], a topological quantization condition of the TME is given under orthogonal incidence of the optical beam, in which the wave length of the light or the thickness of the TI film must be tuned to some commensurate values. This fine tuning is difficult to realize experimentally. In this article, we give manifestly $SL(2,\mathbb{Z})$ covariant expressions for Kerr and Faraday angles at oblique incidence at a topological insulator thick film. We obtain a generalized quantization condition independent of material details, and propose a more easily realizable optical experiment, in which only the incidence angle is tuned, to directly measure the topological quantization associated with the TME.

We study the boundary-driven asymmetric simple exclusion process (ASEP) in a one-dimensional chain with long-range links. Shortcuts are added to a chain by connecting $pL$ different pairs of sites selected randomly where $L$ and $p$ denote the chain length and the shortcut density, respectively. Particles flow into a chain at one boundary at rate $\alpha$ and out of a chain at the other boundary at rate $\beta$, while they hop inside a chain via nearest-neighbor bonds and long-range shortcuts. Without shortcuts, the model reduces to the boundary-driven ASEP in a one-dimensional chain which displays the low density, high density, and maximal current phases. Shortcuts lead to a drastic change. Numerical simulation studies suggest that there emerge three phases; an empty phase with $ \rho = 0 $, a jammed phase with $ \rho = 1 $, and a shock phase with $ 0<\rho<1$ where $\rho$ is the mean particle density. The shock phase is characterized with a phase separation between an empty region and a jammed region with a localized shock between them. The mechanism for the shock formation and the non-equilibrium phase transition is explained by an analytic theory based on a mean-field approximation and an annealed approximation.

The degrees of freedom (DoF) region of the fast-fading MIMO (multiple-input multiple-output) Gaussian broadcast channel (BC) is studied when there is delayed channel state information at the transmitter (CSIT). In this setting, the channel matrices are assumed to vary independently across time and the transmitter is assumed to know the channel matrices with some arbitrary finite delay. An outer-bound to the DoF region of the general $K$-user MIMO BC (with an arbitrary number of antennas at each terminal) is derived. This outer-bound is then shown to be tight for two classes of MIMO BCs, namely, (a) the two-user MIMO BC with arbitrary number of antennas at all terminals, and (b) for certain three-user MIMO BCs where all three receivers have an equal number of antennas and the transmitter has no more than twice the number of antennas present at each receivers. The achievability results are obtained by developing an interference alignment scheme that optimally accounts for multiple, and possibly distinct, number of antennas at the receivers.