Operating Model of Knowledge Quantum Engineering for Decision-Making in Conditions of Indeterminacy

The operating model of knowledge quantum engineering for identification and prognostic decision- making in conditions of α-indeterminacy is suggested in the article. The synthesized operating model solves three basic tasks: Аt-task to formalize tk-knowledge; Вt-task to recognize (identify) objects according to observed results; Сt-task to extrapolate (prognosticate) the observed results. Operating derivation of identification and prognostic decisions using authentic different-level algorithmic knowledge quantum (using tRAKZ-method) assumes synthesis of authentic knowledge quantum database (BtkZ) using induction operator as a system of implicative laws, and then using deduction operator according to the observed tk-knowledge and BtkZ a derivation of identification or prognostic decisions in a form of new tk-knowledge.

Travelling waves in a complex Ginzburg-Landau equation with time-delay feedback

One of the simplest ways to create nonlinear oscillations is the Hopf bifurcation. The spatiotemporal dynamics observed in an extended medium with diffusion (e.g., a chemical reaction) undergoing this bifurcation is governed by the complex Ginzburg-Landau equation, one of the best-studied generic models for pattern formation, where besides uniform oscillations, spiral waves, coherent structures and turbulence are found. The presence of time delay terms in this equation changes the pattern formation scenario, and different kind of travelling waves have been reported. In particular, we study the complex Ginzburg-Landau equation that contains local and global time-delay feedback terms. We focus our attention on plane wave solutions in this model. The first novel result is the derivation of the plane wave solution in the presence of time-delay feedback with global and local contributions. The second and more important result of this study consists of a linear stability analysis of plane waves in that model. Evaluation of the eigenvalue equation does not show stabilisation of plane waves for the parameters studied. We discuss these results and compare to results of other models.

An international round-robin calibration protocol for nanoindentation measurements

Nanoindentation has become a common technique for measuring the hardness and elastic-plastic properties of materials, including coatings and thin films. In recent years, different nanoindenter instruments have been commercialised and used for this purpose. Each instrument is equipped with its own analysis software for the derivation of the hardness and reduced Young's modulus from the raw data. These data are mostly analysed through the Oliver and Pharr method. In all cases, the calibration of compliance and area function is mandatory. The present work illustrates and describes a calibration procedure and an approach to raw data analysis carried out for six different nanoindentation instruments through several round-robin experiments. Three different indenters were used, Berkovich, cube corner, spherical, and three standardised reference samples were chosen, hard fused quartz, soft polycarbonate, and sapphire. It was clearly shown that the use of these common procedures consistently limited the hardness and reduced the Young's modulus data spread compared to the same measurements performed using instrument-specific procedures. The following recommendations for nanoindentation calibration must be followed: (a) use only sharp indenters, (b) set an upper cut-off value for the penetration depth below which measurements must be considered unreliable, (c) perform nanoindentation measurements with limited thermal drift, (d) ensure that the load-displacement curves are as smooth as possible, (e) perform stiffness measurements specific to each instrument/indenter couple, (f) use Fq and Sa as calibration reference samples for stiffness and area function determination, (g) use a function, rather than a single value, for the stiffness and (h) adopt a unique protocol and software for raw data analysis in order to limit the data spread related to the instruments (i.e. the level of drift or noise, defects of a given probe) and to make the H and E r data intercomparable. © 2011 Elsevier Ltd.

Applications of Nonclassical Logic Methods for Purposes of Knowledge Discovery and Data Mining

* The work is partially supported by Grant no. NIP917 of the Ministry of Science and Education – Republic of Bulgaria.

Free energy functional expansion as the generalized approach to the equation of state of dense fluids

A version of the thermodynamic perturbation theory based on a scaling transformation of the partition function has been applied to the statistical derivation of the equation of state in a highpressure region. Two modifications of the equations of state have been obtained on the basis of the free energy functional perturbation series. The comparative analysis of the experimental PV T- data on the isothermal compression for the supercritical fluids of inert gases has been carried out. © 2012.

Representing Autoepistemic Logic in Modal Logic

The nonmonotonic logic called Autoepistemic Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Autoepistemic Logic with an initial set of axioms if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meaning of that initial set of sentences. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and unlike the original Autoepistemic Logic, it is easily generalized to the case where quantified variables may be shared across the scope of modal expressions thus allowing the derivation of quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan formula and its converse hold.

Evaluation of Pareto/D/1/k Queue by Simulation

The finding that Pareto distributions are adequate to model Internet packet interarrival times has motivated the proposal of methods to evaluate steady-state performance measures of Pareto/D/1/k queues. Some limited analytical derivation for queue models has been proposed in the literature, but their solutions are often of a great mathematical challenge. To overcome such limitations, simulation tools that can deal with general queueing system must be developed. Despite certain limitations, simulation algorithms provide a mechanism to obtain insight and good numerical approximation to parameters of queues. In this work, we give an overview of some of these methods and compare them with our simulation approach, which are suited to solve queues with Generalized-Pareto interarrival time distributions. The paper discusses the properties and use of the Pareto distribution. We propose a real time trace simulation model for estimating the steady-state probability showing the tail-raising effect, loss probability, delay of the Pareto/D/1/k queue and make a comparison with M/D/1/k. The background on Internet traffic will help to do the evaluation correctly. This model can be used to study the long- tailed queueing systems. We close the paper with some general comments and offer thoughts about future work.

Adaptive SOA Infrastructure Based on Variability Management

In order to exploit the adaptability of a SOA infrastructure, it becomes necessary to provide platform mechanisms that support a mapping of the variability in the applications to the variability provided by the infrastructure. The approach focuses on the configuration of the needed infrastructure mechanisms including support for the derivation of the infrastructure variability model.

Hamilton’s Principle with Variable Order Fractional Derivatives

MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

Generalised Riccati solution and pinning control of complex stochastic networks

This paper considers the global synchronisation of a stochastic version of coupled map lattices networks through an innovative stochastic adaptive linear quadratic pinning control methodology. In a stochastic network, each state receives only noisy measurement of its neighbours' states. For such networks we derive a generalised Riccati solution that quantifies and incorporates uncertainty of the forward dynamics and inverse controller in the derivation of the stochastic optimal control law. The generalised Riccati solution is derived using the Lyapunov approach. A probabilistic approximation type algorithm is employed to estimate the conditional distributions of the state and inverse controller from historical data and quantifying model uncertainties. The theoretical derivation is complemented by its validation on a set of representative examples.

A Note on Elementary Derivations

2000 Mathematics Subject Classification: Primary: 14R10. Secondary: 14R20, 13N15.

On the Range and the Kernel of Derivations

2000 Mathematics Subject Classification: Primary 47B47, 47B10; Secondary 47A30.

On Supra-Bayesian Weighted Combination of Available Data Determined by Kerridge Inaccuracy and Entropy

2010 Mathematics Subject Classification: 94A17.

Efficient algorithm for routing optimization via statistical mechanics

Many practical routing algorithms are heuristic, adhoc and centralized, rendering generic and optimal path configurations difficult to obtain. Here we study a scenario whereby selected nodes in a given network communicate with fixed routers and employ statistical physics methods to obtain optimal routing solutions subject to a generic cost. A distributive message-passing algorithm capable of optimizing the path configuration in real instances is devised, based on the analytical derivation, and is greatly simplified by expanding the cost function around the optimized flow. Good algorithmic convergence is observed in most of the parameter regimes. By applying the algorithm, we study and compare the pros and cons of balanced traffic configurations to that of consolidated traffic, which provides important implications to practical communication and transportation networks. Interesting macroscopic phenomena are observed from the optimized states as an interplay between the communication density and the cost functions used. © 2013 IEEE.

Generalized D-Symmetric Operators I

2000 Mathematics Subject Classification: Primary: 47B47, 47B10; secondary 47A30.