Bilinear structure and Schlesinger transforms of the qq-PIII_{\rm III} and qq-PVI_{\rm VI} equations

We show that the recently derived ($q$-) discrete form of the Painlev\'e VI equation can be related to the discrete P$_{\rm III}$, in particular if one uses the full freedom in the implementation of the singularity confinement criterion. This observation is used here in order to derive the bilinear forms and the Schlesinger transformations of both $q$-P$_{\rm III}$ and $q$-P$_{\rm VI}$.Comment: 10 pages, Plain Te

Effect of moisture on the fatigue behavior of graphite/epoxy composite laminates

The form of the moisture distribution in the specimen (gradient and flat profile) was considered to establish the influence of accelerated moisture conditioning on fatigue behavior. For the gradient specimens having an average moisture content of 1.4 percent, fatigue life was reduced by a factor of 8 at all stress levels investigated. Corresponding reduction in fatigue life for the flat moisture profile specimens at the same average moisture content was comparatively smaller, being about a factor of 5 from the value in dry specimens. X-ray radiographic analysis of damage accumulation in compression-compression fatigue revealed interlaminar cracking to be the dominant mode of failure responsible for the observed enhanced cyclic degradation of moisture-conditioned specimens. This finding was corroborated by the observed systematic reduction in interlaminar shear strength as a function of moisture content, which, in turn, increased the propensity for delamination under cyclic compressive loads. Residual strength measurements on cycled specimens indicated significant strength reductions at long lives, particularly in moisture conditioned specimens

Riccati Solutions of Discrete Painlev\'e Equations with Weyl Group Symmetry of Type E8(1)E_8^{(1)}

We present a special solutions of the discrete Painlev\'e equations associated with $A_0^{(1)}$, $A_0^{(1)*}$ and $A_0^{(1)**}$-surface. These solutions can be expressed by solutions of linear difference equations. Here the $A_0^{(1)}$-surface discrete Painlev\'e equation is the most generic difference equation, as all discrete Painlev\'e equations can be obtained by its degeneration limit. These special solutions exist when the parameters of the discrete Painlev\'e equation satisfy a particular constraint. We consider that these special functions belong to the hypergeometric family although they seems to go beyond the known discrete and $q$-discrete hypergeometric functions. We also discuss the degeneration scheme of these solutions.Comment: 22 page

Riemann zeros, prime numbers and fractal potentials

Using two distinct inversion techniques, the local one-dimensional potentials for the Riemann zeros and prime number sequence are reconstructed. We establish that both inversion techniques, when applied to the same set of levels, lead to the same fractal potential. This provides numerical evidence that the potential obtained by inversion of a set of energy levels is unique in one-dimension. We also investigate the fractal properties of the reconstructed potentials and estimate the fractal dimensions to be $D=1.5$ for the Riemann zeros and $D = 1.8$ for the prime numbers. This result is somewhat surprising since the nearest-neighbour spacings of the Riemann zeros are known to be chaotically distributed whereas the primes obey almost poisson-like statistics. Our findings show that the fractal dimension is dependent on both the level-statistics and spectral rigidity, $\Delta_3$, of the energy levels.Comment: Five postscript figures included in the text. To appear in Phys. Rev.

Update on the clinical utility of sildenafil in the treatment of pulmonary arterial hypertension

Sildenafil is an orally administered phosphodiesterase type 5 inhibitor that is approved for the treatment of pulmonary arterial hypertension (PAH). The hemodynamic effects of sildenafil are mitigated primarily via potentiating the effects of endogenous nitric oxide, leading to smooth muscle cell relaxation and reductions in pulmonary arterial pressures and pulmonary vascular resistance. When added to standard background therapy in patients with idiopathic or associated PAH from congenital heart disease, anorexigen use, or connective tissue disease, sildenafil treatment results in improved exercise capacity as measured by 6 minute walk distance, improved hemodynamics, and favorable changes in quality of life. Sildenafil use is contraindicated with concomitant nitrate administration, and caution should be exercised when used in combination with antihypertensive agents due to risks of precipitating hypotension. Side effects are generally mild, and include flushing, headaches, and epistaxis. The combination of sildenafil with intravenous epoprostenol is safe and well tolerated, and further improves exercise capacity. Sildenafil is approved only for treatment of PAH, and although emerging data suggest a potential role in treating other types of pulmonary hypertension, larger trials are required to confirm these findings

On a q-difference Painlev\'e III equation: I. Derivation, symmetry and Riccati type solutions

A q-difference analogue of the Painlev\'e III equation is considered. Its derivations, affine Weyl group symmetry, and two kinds of special function type solutions are discussed.Comment: arxiv version is already officia

Fast Computation of Kernel Estimators

The computational complexity of evaluating the kernel density estimate (or its derivatives) at m evaluation points given n sample points scales quadratically as O(nm)—making it prohibitively expensive for large datasets. While approximate methods like binning could speed up the computation, they lack a precise control over the accuracy of the approximation. There is no straightforward way of choosing the binning parameters a priori in order to achieve a desired approximation error. We propose a novel computationally efficient ε-exact approximation algorithm for the univariate Gaussian kernel-based density derivative estimation that reduces the computational complexity from O(nm) to linear O(n+m). The user can specify a desired accuracy ε. The algorithm guarantees that the actual error between the approximation and the original kernel estimate will always be less than ε. We also apply our proposed fast algorithm to speed up automatic bandwidth selection procedures. We compare our method to the best available binning methods in terms of the speed and the accuracy. Our experimental results show that the proposed method is almost twice as fast as the best binning methods and is around five orders of magnitude more accurate. The software for the proposed method is available online

Real-time QoS Routing Scheme in SDN-based Robotic Cyber-Physical Systems

Industrial cyber-physical systems (CPS) have gained enormous attention of manufacturers in recent years due to their automation and cost reduction capabilities in the fourth industrial revolution (Industry 4.0). Such an industrial network of connected cyber and physical components may consist of highly expensive components such as robots. In order to provide efficient communication in such a network, it is imperative to improve the Quality-of-Service (QoS). Software Defined Networking (SDN) has become a key technology in realizing QoS concepts in a dynamic fashion by allowing a centralized controller to program each flow with a unified interface. However, state-of-the-art solutions do not effectively use the centralized visibility of SDN to fulfill QoS requirements of such industrial networks. In this paper, we propose an SDN-based routing mechanism which attempts to improve QoS in robotic cyber-physical systems which have hard real-time requirements. We exploit the SDN capabilities to dynamically select paths based on current link parameters in order to improve the QoS in such delay-constrained networks. We verify the efficiency of the proposed approach on a realistic industrial OpenFlow topology. Our experiments reveal that the proposed approach significantly outperforms an existing delay-based routing mechanism in terms of average throughput, end-to-end delay and jitter. The proposed solution would prove to be significant for the industrial applications in robotic cyber-physical systems