Measurements of motionally averaged heteronuclear dipolar couplings in MAS NMR using R-type recoupling

A novel MAS NMR approach is presented for the determination of heteronuclear dipolar couplings in unoriented materials. The technique is based on the proton-detected local field (PDLF) protocol, and achieves dipolar recoupling by R-type radio-frequency irradiation. The experiment, which is called R-PDLF spectroscopy, is demonstrated on solid and liquid-crystalline systems. For mobile systems, it is shown that the R-PDLF scheme provides better dipolar resolution as compared to techniques combining conventional separated local field (SLF) spectroscopy with R-type recoupling.     

Traffic flow monitoring in software-defined network using modified recursive learning

The recursive network design used in this paper to monitor traffic flow ensures accurate anomaly identification. The suggested method enhances the effectiveness of cyber attacks in SDN. The suggested model achieves a remarkable attack detection performance in the case of distributed denial-of-service (DDoS) attacks by preventing network forwarding performance degradation. The suggested methodology is designed to teach users how to match traffic flows in ways that increase granularity while proactively protecting the SDN data plane from overload. The application of a learnt traffic flow matching control policy makes it possible to obtain the best traffic data for detecting abnormalities obtained during runtime, improving the performance of cyber-attack detection. The accuracy of the suggested model is superior to the MMOS, FMS, DATA, Q-DATA, and DEEP-MC by 19.23%, 16.25%, 47.61%, 16.25%, and 12.04%.     

Determination of the gas chromatographic elution sequences of the (+)- and (−)-enantiomers of stable atropisomeric PCBs on Chirasil-dex

Pure enantiomers of chiral (atropisomeric) polychlorinated biphenyls (PCBs) obtained by high-performance liquid chromatography were used to establish the gas chromatographic elution sequences of the (+)- and (−)-enantiomers of six PCB atropisomers on Chirasil-Dex. The elution order was found to be (−/+) for PCBs 84, 132, 136, and 176 and (+/−) for PCBs 135 and 174. The retention characteristics of all 19 tri- and tetra-ortho atropisomeric PCBs were also investigated. Nine of the atropisomers could be separated using this chiral selector. PCBs 95, 132, and 149 were completely resovled and PCBs 84, 91, 135, 136, 174, and 176 were partially separated (R = 0.7–0.9). All of the separated congeners are 2,3,6-substituted in at least one ring, and conversely – none of the congeners that lacks 2,3,6-substitution could be separated. Thus, chiral recognition and enantiomer separation seems to be strongly governed by 2,3,6-substitution.     

Improvement of the recursive projection method for linear iterative scheme stabilization based on an approximate eigenvalue problem

An algorithm for stabilizing linear iterative schemes is developed in this study. The recursive projection method is applied in order to stabilize divergent numerical algorithms. A criterion for selecting the divergent subspace of the iteration matrix with an approximate eigenvalue problem is introduced. The performance of the present algorithm is investigated in terms of storage requirements and CPU costs and is compared to the original Krylov criterion. Theoretical results on the divergent subspace selection accuracy are established. The method is then applied to the resolution of the linear advection–diffusion equation and to a sensitivity analysis for a turbulent transonic flow in the context of aerodynamic shape optimization. Numerical experiments demonstrate better robustness and faster convergence properties of the stabilization algorithm with the new criterion based on the approximate eigenvalue problem. This criterion requires only slight additional operations and memory which vanish in the limit of large linear systems.     

On a new class of multiplicative pseudo-random number generators

In the computing literature, there are few detailed analytical studies of the global statistical characteristics of a class of multiplicative pseudo-random number generators.We comment briefly on normal numbers and study analytically the approximately uniform discrete distribution or (j,)-normality in the sense of Besicovitch for complete periods of fractional parts {x _{0 1} ⁱ /p} on [0, 1] fori=0, 1,..., (p–1)p^–1–1, i.e. in current terminology, generators given byx _{n+1 1} x _n mod p wheren=0, 1,..., (p–1)p ^–1–1,p is any odd prime, (x ₀,p)=1, ₁ is a primitive root modp ², and 1 is any positive integer.We derive the expectationsE(X, ),E(X ², ),E(X _nX_n+k); the varianceV(X, ), and the serial correlation coefficient k. By means of Dedekind sums and some results of H. Rademacher, we investigate the asymptotic properties of k for various lagsk and integers 1 and give numerical illustrations. For the frequently used case =1, we find comparable results to estimates of Coveyou and Jansson as well as a mathematical demonstration of a so-called rule of thumb related to the choice of ₁ for small k.Due to the number of parameters in this class of generators, it may be possible to obtain increased control over the statistical behavior of these pseudo-random sequences both analytically as well as computationally.     

An alignment-free measure based on physicochemical properties of amino acids for protein sequence comparison

Sequence comparison is an important topic in bioinformatics. With the exponential increase of biological sequences, the traditional protein sequence comparison methods — the alignment methods become limited, so the alignment-free methods are widely proposed in the past two decades. In this paper, we considered not only the six typical physicochemical properties of amino acids, but also their frequency and positional distribution. A 51-dimensional vector was obtained to describe the protein sequence. We got a pairwise distance matrix by computing the standardized Euclidean distance, and discriminant analysis and phylogenetic analysis can be made. The results on the Influenza A virus and ND5 datasets indicate that our method is accurate and efficient for classifying proteins and inferring the phylogeny of species.     

Extended well-posedness of optimization problems

The well-posedness concept introduced in Ref. 1 for global optimization problems with a unique solution is generalized here to problems with many minimizers, under the name of extended well-posedness. It is shown that this new property can be characterized by metric criteria, which parallel to some extent those known about generalized Tikhonov well-posedness.This work was partially supported by MURST, Fondi 40%, Rome, Italy.     

Parameter and state estimation algorithm for single-input single-output linear systems using the canonical state space models

This paper presents a new parameter and state estimation algorithm for single-input single-output systems based on canonical state space models from the given input–output data. Difficulties of identification for state space models lie in that there exist unknown noise terms in the formation vector and unknown state variables. By means of the hierarchical identification principle, those noise terms in the information vector are replaced with the estimated residuals and a new least squares algorithm is proposed for parameter estimation and the system states are computed by using the estimated parameters. Finally, an example is provided.     

Automatic Symmetrization and Energy Estimates Using Local Operators for Partial Differential Equations

We develop a method for automatically symmetrizing Petrowsky well-posed Cauchy problems for constant coefficient linear partial differential equations. The method is rooted in the Sturm sequence technique for establishing the location of the roots of a complex polynomial and can be automated using standard symbolic computation tools. In the special case of homogeneous strictly hyperbolic scalar equations, we show that the resulting estimates are strong enough to control all principal order derivatives and thus can be used in place of the Leray energies. We also illustrate the method by applying it to various problems of mixed type.     

Uncomputability and undecidability in economic theory

Economic theory, game theory and mathematical statistics have all increasingly become algorithmic sciences. Computable Economics, Algorithmic Game Theory[Noam Nisan, Tim Roiughgarden, Éva Tardos, Vijay V. Vazirani (Eds.), Algorithmic Game Theory, Cambridge University Press, Cambridge, 2007] and Algorithmic Statistics[Péter Gács, John T. Tromp, Paul M.B. Vitányi, Algorithmic statistics, IEEE Transactions on Information Theory 47 (6) (2001) 2443-2463] are frontier research subjects. All of them, each in its own way, are underpinned by (classical) recursion theory - and its applied branches, say computational complexity theory or algorithmic information theory - and, occasionally, proof theory. These research paradigms have posed new mathematical and metamathematical questions and, inadvertently, undermined the traditional mathematical foundations of economic theory. A concise, but partial, pathway into these new frontiers is the subject matter of this paper. Interpreting the core of mathematical economic theory to be defined by General Equilibrium Theory and Game Theory, a general - but concise - analysis of the computable and decidable content of the implications of these two areas are discussed. Issues at the frontiers of macroeconomics, now dominated by Recursive Macroeconomic Theory (The qualification ‘recursive’ here has nothing to do with ‘recursion theory’. Instead, this is a reference to the mathematical formalizations of the rational economic agent’s intertemporal optimization problems, in terms of Markov Decision Processes, (Kalman) Filtering and Dynamic Programming, where a kind of ‘recursion’ is invoked in the solution methods. The metaphor of the rational economic agent as a ‘signal processor’ underpins the recursive macroeconomic paradigm.), are also tackled, albeit ultra briefly. The point of view adopted is that of classical recursion theory and varieties of constructive mathematics.