A skin detection approach based on the Dempster–Shafer theory of evidence

Skin detection is an important step for a wide range of research related to computer vision and image processing and several methods have already been proposed to solve this problem. However, most of these methods suffer from accuracy and reliability problems when they are applied to a variety of images obtained under different conditions. Performance degrades further when fewer training data are available. Besides these issues, some methods require long training times and a significant amount of parameter tuning. Furthermore, most state-of-the-art methods incorporate one or more thresholds, and it is difficult to determine accurate threshold settings to obtain desirable performance. These problems arise mostly because the available training data for skin detection are imprecise and incomplete, which leads to uncertainty in classification. This requires a robust fusion framework to combine available information sources with some degree of certainty. This paper addresses these issues by proposing a fusion-based method termed Dempster–Shafer-based Skin Detection (DSSD). This method uses six prominent skin detection criteria as sources of information (SoI), quantifies their reliabilities (confidences), and then combines their confidences based on the Dempster–Shafer Theory (DST) of evidence. We use the DST as it offers a powerful and flexible framework for representing and handling uncertainties in available information and thus helps to overcome the limitations of the current state-of-the-art methods. We have verified this method on a large dataset containing a variety of images, and achieved a 90.17% correct detection rate (CDR). We also demonstrate how DSSD can be used when very little training data are available, achieving a CDR as high as 87.47% while the best result achieved by a Bayesian classifier is only 68.81% on the same dataset. Finally, a generalized DSSD (GDSSD) is proposed achieving 91.12% CDR.     

An extension of a data assimilation method based on the application of the Fokker–Planck equation

A data assimilation method based on the Kalman filter theory and on the Fokker–Planck equation is extended to assimilate Atlantic Ocean data into a new version of the well-known Modular Ocean Model (MOM_3) from NOAA/GFDL. This extension enables assimilation of non-uniformly distributed data in space and time. Numerical experiments with Levitus atlas data are carried out with the ocean model configured at a low resolution. Some results of these experiments as well as other possible expansions are discussed.     

A polynomial algorithm for a two parameter extension of Wythoff NIM based on the Perron–Frobenius theory

For any positive integer parameters a and b, Gurvich recently introduced a generalization mex _b of the standard minimum excludant mex = mex₁, along with a game NIM(a, b) that extends further Fraenkel’s NIM = NIM(a, 1), which in its turn is a generalization of the classical Wythoff NIM = NIM(1, 1). It was shown that P-positions (the kernel) of NIM(a, b) are given by the following recursion: $$x_n = {\rm mex}_b(\{x_i, y_i \;|\; 0 \leq i < n\}), \;\; y_n = x_n + an; \;\; n \geq 0,$$ and conjectured that for all a, b the limits ?(a, b) = x _n (a, b)/n exist and are irrational algebraic numbers. In this paper we prove that showing that ${\ell(a,b) = \frac{a}{r-1}}$ , where r > 1 is the Perron root of the polynomial $$P(z) = z^{b+1} - z - 1 - \sum_{i=1}^{a-1} z^{\lceil ib/a \rceil},$$ whenever a and b are coprime; furthermore, it is known that ?(ka, kb) = k?(a, b). In particular, ${\ell(a, 1) = \alpha_a = \frac{1}{2} (2 - a + \sqrt{a^2 + 4})}$ . In 1982, Fraenkel introduced the game NIM(a) = NIM(a, 1), obtained the above recursion and solved it explicitly getting ${x_n = \lfloor \alpha_a n \rfloor, \; y_n = x_n + an = \lfloor (\alpha_a + a) n \rfloor}$ . Here we provide a polynomial time algorithm based on the Perron–Frobenius theory solving game NIM(a, b), although we have no explicit formula for its kernel.     

A Note on the WAP–Compactification and the LUC–Compactification of a Topological Group

Let G be a topological group. Denote by G^LUC and G^WAP the LUC–compactification and the WAP–compactification of G, respectively. G^WAP can be regarded as a quotient of G^LUC and the quotient map denoted by . In this note we shall show that, when $G$ is a SIN--group, there exists a dense open subset of G^LUC\ G$, consisting of points of unicity for , of cardinality at least 2^{2 (G)}, where (G) denotes the compact covering number of G. We give an example to show that this statement does not hold for IN–groups, although G^LUC\ G does contain at least 2^{2 (G)} points if G is an IN–group. We also give characterisations of the completion \tilde{G} of G as a subspace of the uniform compactification uG. A consequence of the first result is an analogue of Veechs theorem for the WAP–compactification of a SIN-group.     

A note on the Chermak–Delgado lattice of a finite group

In this note, we describe the structure of finite groups G whose Chermak–Delgado lattice is the interval [G∕Z(G)] = {H∈L(G)∣Z(G)≤H≤G}.     

A conserved phase-field system based on the Maxwell–Cattaneo law

Our aim in this paper is to study a generalization of the conserved Caginalp phase-field system based on the Maxwell–Cattaneo law for heat conduction and endowed with Neumann boundary conditions. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators.     

A gap in the spectrum of the Neumann–Laplacian on a periodic waveguide

We study a spectral problem related to the Laplace operator in a singularly perturbed periodic waveguide. The waveguide is a quasi-cylinder which contains a periodic arrangement of inclusions. On the boundary of the waveguide, we consider both Neumann and Dirichlet conditions. We prove that provided the diameter of the inclusion is small enough the spectrum of Laplace operator contains band gaps, i.e. there are frequencies that do not propagate through the waveguide. The existence of the band gaps is verified using the asymptotic analysis of elliptic operators.     

A hybrid conjugate gradient method based on a quadratic relaxation of the Dai–Yuan hybrid conjugate gradient parameter

To take advantage of the attractive features of the Hestenes–Stiefel and Dai–Yuan conjugate gradient (CG) methods, we suggest a hybridization of these methods using a quadratic relaxation of a hybrid CG parameter proposed by Dai and Yuan. In the proposed method, the hybridization parameter is computed based on a conjugacy condition. Under proper conditions, we show that our method is globally convergent for uniformly convex functions. We give a numerical comparison of the implementations of our method and two efficient hybrid CG methods proposed by Dai and Yuan using a set of unconstrained optimization test problems from the CUTEr collection. Numerical results show the efficiency of the proposed hybrid CG method in the sense of the performance profile introduced by Dolan and Moré.     

A prediction of the acoustical properties of induction cookers based on an FVM–LES-acoustic analogy method

The FVM–LES-acoustic analogy method (FVM–LES-AAM), which is a hybrid prediction technique for the acoustical property computation, is presented and performed in this paper. The FVM–LES-AAM was developed by combining the finite volume method (FVM), the large eddy simulation (LES), and the Ffowcs Williams-Hawkings analogy algorithm (FWH-AA). To predict the acoustical properties of induction cookers, the FVM is used for discretizing the calculation field and building numerical equations, and the LES and FWH-AA are performed for computing the sound sources and predicting the far-field sound, respectively. Using the FVM with the unstructured grids method to discretize the control equation of Navier–Stokes was introduced for illuminating the above numerical simulation procedure. To prove the FVM–LES-AAM method is feasible for predicting the acoustical property of induction cookers, the simulated results were compared with some measured experimental data. The comparisons suggest that the hybrid method is accurate and reliable for the aeroacoustics analysis of induction cookers. Considering the temperature performance, furthermore, some new configurations for the noise reduction of induction cookers were designed, simulated, and discussed. The FVM–LES-AAM prediction technique shows promise as a feasible and computationally affordable approach for not only noise analysis of induction cookers, but also for other aeroacoustics problems in engineering.     

A note on the global existence of a two-dimensional chemotaxis-Navier–Stokes system

In this short note, we establish the global existence of weak solutions and classical solutions to the two-dimensional chemotaxis-Navier–Stokes system for both the Cauchy problem and the initial-boundary value problem under some suitable small conditions on the initial data. In particular, we improve the recent results obtained by Duan–Li–Xiang (J. Differential Equations, 2017).     

A Remark on the Convergence of the Douglas–Rachford Iteration in a Non-convex Setting

Using a known construction of a Lyapunov function, it is shown that the Douglas–Rachford iteration with respect to a sphere and a line in a Hilbert space converges to the intersection point in a fashion which is stronger than uniform convergence on compact sets.     

A new proof of the cross-rule for the ϵ-algorithm based on Schur-complements

Matrices of the form H — GE⁻¹ F are called Schur-complements. They are closely related to elimination procedures and to determinantal identities. In this paper, the quotient property for Schur-complements is used to establish the ‘Schur-complement-method’, a useful tool for proving certain formulas. As an example, a new proof of the cross-rule for the ϵ-algorithm is presented.     

A Note on the Bondage Number of a Graph

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A model of Cahn—Hilliard equation based on a microforce balance

We derive in this Note a model of Cahn—Hilliard equation that takes into account the effects of internal microforces. This model is based on constitutive equations developed by M. Gurtin in [4]. We then obtain the existence and uniqueness of solutions and the existence of global attractors.     

Bahadur’s efficiency of a test of exponentiality based on the loss-of-memory property

A test of exponentiality of Kolmogorov-Smirnov type based on the loss-of-memory characterization property is under study. The large-deviation asymptotics under the null-hypothesis is calculated. Local Bahadur efficiencies for commonly used parametric alternatives are found. Conditions of the Bahadur local optimality are obtained. Bibliography: 13 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 315–329. Translated by S. Yu. Pilyugin     

Aerodynamic optimisation of a hypersonic reentry vehicle based on solution of the Boltzmann–BGK equation and evolutionary optimisation

Over the past decade there has been a surge in the interest, both academic and commercial, in supersonic and hypersonic passenger transport. This paper outlines an original approach for solving the problem of optimal design and configuration of a space vehicle operating in rarefied hypersonic flow. The approach utilises a novel flow solver based on the solution of the Boltzmann–BGK equation. For the first time this solver has been coupled to an evolutionary optimiser to assist in navigation of the unfamiliar hypersonic design space.The Boltzmann–BGK solver is rigorously tested on a number of examples and is shown to handle rarefied gas dynamics examples across a range of length scales. The examples, presented here for the first time, include: a Riemann-type gas expansion problem, drag prediction of a nano-particle and supersonic flow across an aerofoil. Finally the solver is coupled to the evolutionary optimiser Modified Cuckoo Search approach. The coupled solver-optimiser design tool is then used to explore the optimum configuration of the forebody of a generic space reentry vehicle under a range of design conditions.In all examples considered the flow solver produces valid solutions. It is also found that the evolutionary optimiser is successful in navigating the unfamiliar design space.     

A class of adaptive Dai–Liao conjugate gradient methods based on the scaled memoryless BFGS update

Minimizing the distance between search direction matrix of the Dai–Liao method and the scaled memoryless BFGS update in the Frobenius norm, and using Powell’s nonnegative restriction of the conjugate gradient parameters, a one-parameter class of nonlinear conjugate gradient methods is proposed. Then, a brief global convergence analysis is made with and without convexity assumption on the objective function. Preliminary numerical results are reported; they demonstrate a proper choice for the parameter of the proposed class of conjugate gradient methods may lead to promising numerical performance.