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The diffusion of a Brownian particle exploring a meta-stable potential energy landscape with fluctuations is studied theoretically and numerically. The inverse harmonic part of the potential is replaced by a Gaussian approximated curve in the neighborhood of the saddle point and a new type of Monte-Carlo simulation algorithm is presented to simulate the random fluctuations of the potential energy. The probability of successful barrier surmounting and terminal arrival was calculated and compared with previous results. It is shown that, the replacement we have made is reasonable for the study of diffusion, which is primarily affected by the fluctuation of the barrier height, while other variations have little influence on the diffusion process. The Gaussian permutation and random Gaussian algorithms proposed here are expected to bring new ideas to the research of more complex problems.

We have considered the problem of dynamic propagation of the three-dimensional few-cycle optical pulses of Gaussian and super-Gaussian cross-section inside the Bragg medium with carbon nanotubes. The system has dissipation and additional energy “pumping”. We have shown that the pulse propagation is stable inside the considered environment. The special aspect of the pulse evolution of different cross-sections has been determined.

Novel features and weak classifiers are proposed for face detection within the AdaBoost learning framework. Features are histograms computed from a set of spatial templates in filtered images. The filter banks consist of Intensity, Laplacian of Gaussian (Difference of Gaussians), and Gabor filters, aiming to capture spatial and frequency properties of faces at different scales and orientations. Features selected by AdaBoost learning, each of which corresponds to a histogram with a pair of filter and template, can thus be interpreted as boosted marginal distributions of faces. We fit the Gaussian distribution of each histogram feature only for positives (faces) in the sample set as the weak classifier. The results of the experiment demonstrate that classifiers with corresponding features are more powerful in describing the face pattern than haar-like rectangle features introduced by Viola and Jones.

Clustering by fast search and finding of Density Peaks (called as DPC) introduced by Alex Rodríguez and Alessandro Laio attracted much attention in the field of pattern recognition and artificial intelligence. However, DPC still has a lot of defects that are not resolved. Firstly, the local density ${\rho }_i$ of point $i$ is affected by the cutoff distance $d_c$, which can influence the clustering result, especially for small real-world cases. Secondly, the number of clusters is still found intuitively by using the decision diagram to select the cluster centers. In order to overcome these defects, this paper proposes an automatic density peaks clustering approach using DNA genetic algorithm optimized data field and Gaussian process (referred to as ADPC-DNAGA). ADPC-DNAGA can extract the optimal value of threshold with the potential entropy of data field and automatically determine the cluster centers by Gaussian method. For any data set to be clustered, the threshold can be calculated from the data set objectively rather than the empirical estimation. The proposed clustering algorithm is benchmarked on publicly available synthetic and real-world datasets which are commonly used for testing the performance of clustering algorithms. The clustering results are compared not only with that of DPC but also with that of several well-known clustering algorithms such as Affinity Propagation, DBSCAN and Spectral Cluster. The experimental results demonstrate that our proposed clustering algorithm can find the optimal cutoff distance $d_c$, to automatically identify clusters, regardless of their shape and dimension of the embedded space, and can often outperform the comparisons.

The classification of images using regular or geometric moment functions suffers from two major problems. First, odd orders of central moments give zero value for images with symmetry in the x and/or y directions and symmetry at centroid. Secondly, these moments are very sensitive to noise especially for higher order moments. In this paper, a single solution is proposed to solve both these problems. The solution involves the computation of the moments from a reference point other than the image centroid. The new reference centre is selected such that the invariant properties like translation, scaling and rotation are still maintained. In this paper, it is shown that the new proposed moments can solve the symmetrical problem. Next, we show that the new proposed moments are less sensitive to Gaussian and random noise as compared to two different types of regular moments derived by Hu.⁶ Extensive experimental study using a neural network classification scheme with these moments as inputs are conducted to verify the proposed method.

We present a quasi-analytic perturbation expansion for multivariate N-dimensional Gaussian integrals. The perturbation expansion is an infinite series of lower-dimensional integrals (one-dimensional in the simplest approximation). This perturbative idea can also be applied to multivariate Student-t integrals. We evaluate the perturbation expansion explicitly through 2nd order, and discuss the convergence, including enhancement using Padé approximants. Brief comments on potential applications in finance are given, including options, models for credit risk and derivatives, and correlation sensitivities.

The generator of a Gaussian quantum Markov semigroup on the algebra of bounded operator on a $d$-mode Fock space is represented in a generalized GKLS form with an operator $G$ quadratic in creation and annihilation operators and Kraus operators $L_1,\dots ,L_m$ linear in creation and annihilation operators. Kraus operators, commutators $[G,L_{\ell }]$ and iterated commutators $[G,[G,L_{\ell }]],\dots$ up to the order $2d-m$, as linear combinations of creation and annihilation operators determine a vector in ${ℂ}^{2d}$. We show that a Gaussian quantum Markov semigroup is irreducible if such vectors generate ${ℂ}^{2d}$, under the technical condition that the domains of $G$ and the number operator coincide. Conversely, we show that this condition is also necessary if the linear space generated by Kraus operators and their iterated commutator with $G$ is fully non-commutative.

We give a characterization of QMSs on the Bosonic Fock Space $\mathrm{\Gamma }({ℂ}^d)$ whose predual preserves the set of gaussian states. We show they can be obtained via certain generalized GKLS generators and they satisfy an explicit formula for their action on Weyl operators.

Gaussian quantum Markov semigroup on the algebra of bounded operator on a $d$-mode Fock space is characterized either by the property of their predual that preserves quantum Gaussian states. In this paper, show that gaussian QMSs can have only Gaussian invariant states if the spectrum of the drift matrix does not contain points on the imaginary axis. Moreover, in this case, any initial state converges in trace norm toward a unique gaussian invariant state.

To many, high-frequency (HF) radio communications is obsolete in this age of long-distance satellite communications and undersea optical fiber. Yet despite this, the HF band is used by defense agencies for backup communications and spectrum surveillance, and is monitored by spectrum management organizations to enforce licensing. Such activity usually requires systems capable of locating distant transmitters, separating valid signals from interference and noise, and recognizing signal modulation. Our research targets the latter issue. The ultimate aim is to develop robust algorithms for automatic modulation recognition of real HF signals. By real, we mean signals propagating by multiple ionospheric modes with co-channel signals and non-Gaussian noise. However, many researchers adopt Gaussian noise for their modulation recognition algorithms for the sake of convenience at the cost of accuracy. Furthermore, literature describing the probability density function (PDF) of HF noise does not abound. So we describe a simple empirical technique, not found in the literature, that supports our work by showing that the probability density function (PDF) for HF noise is generally not Gaussian. In fact, the probability density function varies with the time of day, electro-magnetic environment, and state of the ionosphere.

The impetus for investigating the probability density function of high-frequency (HF) noise arises from the requirement for a better noise model for automatic modulation recognition techniques. Many current modulation recognition methods still assume Gaussian noise models for the transmission medium. For HF communications this can be an incorrect assumption. Whereas a previous investigation [1] focuses on the noise density function in an urban area of Adelaide Australia, this work studies the noise density function in a remote country location east of Adelaide near Swan Reach, South Australia. Here, the definition of HF noise is primarily of natural origins – it is therefore impulsive – and excludes man-made noise sources. A new method for measuring HF noise is introduced that is used over a 153 kHz bandwidth at various frequencies across the HF band. The method excises man-made signals and calculates the noise PDF from the residue. Indeed, the suitability of the Bi-Kappa distribution at modeling HF noise is found to be even more compelling than suggested by the results of the earlier investigation.

The notion of an Ohm–Rush algebra, and its associated content map, has connections with prime characteristic algebra, polynomial extensions, and the Ananyan–Hochster proof of Stillman’s conjecture. As further restrictions are placed (creating the increasingly more specialized notions of weak content, semicontent, content, and Gaussian algebras), the construction becomes more powerful. Here we settle the question in the affirmative over a Noetherian ring from [N. Epstein and J. Shapiro, The Ohm-Rush content function, J. Algebra Appl.15(1) (2016) 1650009, 14 pp.] of whether a faithfully flat weak content algebra is semicontent (and over an Artinian ring of whether such an algebra is content), though both questions remain open in general. We show that in content algebra maps over Prüfer domains, heights are preserved and a dimension formula is satisfied. We show that an inclusion of nontrivial valuation domains is a content algebra if and only if the induced map on value groups is an isomorphism, and that such a map induces a homeomorphism on prime spectra. Examples are given throughout, including results that show the subtle role played by properties of transcendental field extensions.

The main goal of this paper is to introduce a new procedure for a naïve Bayes classifier, namely alpha skew Gaussian naïve Bayes (ASGNB), which is based on a flexible generalization of the Gaussian distribution applied to continuous variables. As a direct advantage, this method can accommodate the possibility to handle with asymmetry in the uni or bimodal behavior. We provide the estimation procedure of this method, and we check the predictive performance when compared to other traditional classification methods using simulation studies and many real datasets with different application fields. The ASGNB is a powerful alternative to classification tasks when lie the presence of asymmetry of bimodality in the data and outperforms well when compared to other traditional classification methods in most of the cases analyzed.

Nowadays, hybridization of different algorithms for the optimization of non-conventional machining processes tries to accomplish better results. The paper consists of experimental evolutionary-particle Swarm Optimization (PSO), Quantum-PSO and Gaussian Quantum Particle Swarm Optimization (G-QPSO)-based ANN modeling and comparative investigation on performances such as material removal rate (MRR), machining depth (MD), roughness of surface and overcut (OC) for machining of silica by ECDM process using mixed electrolyte. The paper also shows the co-efficient of NN models for different machining criteria and G-QPSO and also the comparative study of MD, roughness (SR), overcut (OC) as well as MRR using different algorithms and convergence test for fitness of experimental results also propounded to achieve cross-validation of models and multi-response optimal results for micro-machining of Silica by ECDM using PSO, QPSO and GQPSO. It is found that Gaussian Quantum Particle Swarm Optimization (G-QPSO)-ANN is more efficient for ECDM and achieves optimal results at 55-volt, pulse on time 52.3 s, inter-electrode gap (IEG) 30 mm, duty ratio 0.475 and electrolytic concentration 30 (wt.%).

We have recently shown that the output field in the Braunstein–Kimble protocol of teleportation is a superposition of two fields: the input one and a field created by Alice's measurement and by displacement of the state at Bob's station by using the classical information provided by Alice. We study here the noise added by teleportation and compare its influence in the Gaussian and non-Gaussian settings.

We consider the most general Gaussian quantum Markov semigroup on a one-mode Fock space, discuss its construction from the generalized GKSL representation of the generator. We prove the known explicit formula on Weyl operators, characterize irreducibility and its equivalence to a Hörmander type condition on commutators and establish necessary and sufficient conditions for existence and uniqueness of normal invariant states. We illustrate these results by applications to the open quantum oscillator and the quantum Fokker-Planck model.

We study the behavior of the number of votes cast for different electoral subjects in majority elections, and in particular, the Albanian elections of the last 10 years, as well as the British, Russian, and Canadian elections. We report the frequency of obtaining a certain percentage (fraction) of votes versus this fraction for the parliamentary elections. In the distribution of votes cast in majority elections we identify two regimes. In the low percentiles we see a power law distribution, with exponent about -1.7. In the power law regime we find over 80% of the data points, while they relate to 20% of the votes cast. Votes of the small electoral subjects are found in this regime. The other regime includes percentiles above 20%, and has Gaussian distribution. It corresponds to large electoral subjects. A similar pattern is observed in other first past the post (FPP) elections, such as British and Canadian, but here the Gaussian is reduced to an exponential. Finally we show that this distribution can not be reproduced by a modified "word of mouth" model of opinion formation. This behavior can be reproduced by a model that comprises different number of zealots, as well as different campaign strengths for different electoral subjects, in presence of preferential attachment of voters to candidates.

Having long been the realm of molecular chemistry, astronomy, and plasma diagnostics, the upper millimeter-wave band (∼100 to 300 GHz) and the THz region above it have recently become the subject of heightened activity in the engineering community because of exciting new technology (e.g., sub-picosecond optoelectronics) and promising new “terrestrial” applications (e.g., counter-terrorism and medical imaging). The most challenging of these applications are arguably those that demand remote sensing at a stand-off of roughly 10 m or more between the target and the sensor system. As in any other spectral region, remote sensing in the THz region brings up the complex issues of sensor modality and architecture, free-space electromagnetic effects and components, transmit and receive electronics, signal processing, and atmospheric propagation. Unlike other spectral regions, there is not much literature that addresses these issues from a conceptual or system-engineering viewpoint. So a key theme of this chapter is to review or derive the essential engineering concepts in a comprehensive fashion, starting with fundamental principles of electromagnetics, quantum mechanics, and signal processing, and building up to trade-off formulations using system-level metrics such as noiseequivalent power and receiver operating characteristics. A secondary theme is to elucidate aspects of the THz region and its incumbent technology that are unique, whether advantageous or disadvantageous, relative to other spectral regions. The end goal is to provide a useful tutorial for graduate students or practicing engineers considering the upper mm-wave or THz regions for system research or development.