Continuous Operator Authentication for Teleoperated Systems Using Hidden Markov Models

In this article, we present a novel approach for continuous operator authentication in teleoperated robotic processes based on Hidden Markov Models (HMM). While HMMs were originally developed and widely used in speech recognition, they have shown great performance in human motion and activity modeling. We make an analogy between human language and teleoperated robotic processes (i.e., words are analogous to a teleoperator’s gestures, sentences are analogous to the entire teleoperated task or process) and implement HMMs to model the teleoperated task. To test the continuous authentication performance of the proposed method, we conducted two sets of analyses. We built a virtual reality (VR) experimental environment using a commodity VR headset (HTC Vive) and haptic feedback enabled controller (Sensable PHANToM Omni) to simulate a real teleoperated task. An experimental study with 10 subjects was then conducted. We also performed simulated continuous operator authentication by using the JHU-ISI Gesture and Skill Assessment Working Set (JIGSAWS). The performance of the model was evaluated based on the continuous (real-time) operator authentication accuracy as well as resistance to a simulated impersonation attack. The results suggest that the proposed method is able to achieve 70% (VR experiment) and 81% (JIGSAWS dataset) continuous classification accuracy with as short as a 1-second sample window. It is also capable of detecting an impersonation attack in real-time.

A novel adaptive method for operator inclusions

A novel splitting algorithm for solving operator inclusion with the sum of the maximal monotone operator and the monotone Lipschitz continuous operator in the Banach space is proposed and studied. The proposed algorithm is an adaptive variant of the forward-reflected-backward algorithm, where the rule used to update the step size does not require knowledge of the Lipschitz constant of the operator. For operator inclusions in 2-uniformly convex and uniformly smooth Banach space, the theorem on the weak convergence of the method is proved.

Continuous operator method application for direct and inverse scattering problems

We describe the continuous operator method for solution nonlinear operator equations and discuss its application for investigating direct and inverse scattering problems. The continuous operator method is based on the Lyapunov theory stability of solutions of ordinary differential equations systems. It is applicable to operator equations in Banach spaces, including in cases when the Frechet (Gateaux) derivative of a nonlinear operator is irreversible in a neighborhood of the initial value. In this paper, it is applied to the solution of the Dirichlet and Neumann problems for the Helmholtz equation and to determine the wave number in the inverse problem. The internal and external problems of Dirichlet and Neumann are considered. The Helmholtz equation is considered in domains with smooth and piecewise smooth boundaries. In the case when the Helmholtz equation is considered in domains with smooth boundaries, the existence and uniqueness of the solution follows from the classical potential theory. When solving the Helmholtz equation in domains with piecewise smooth boundaries, the Wiener regularization is carried out. The Dirichlet and Neumann problems for the Helmholtz equation are transformed by methods of potential theory into singular integral equations of the second kind and hypersingular integral equations of the first kind. For an approximate solution of singular and hypersingular integral equations, computational schemes of collocation and mechanical quadrature methods are constructed and substantiated. The features of the continuous method are illustrated with solving boundary problems for the Helmholtz equation. Approximate methods for reconstructing the wave number in the Helmholtz equation are considered.

Analysis of the spectral symbol associated to discretization schemes of linear self-adjoint differential operators

Given a linear self-adjoint differential operator $$\mathscr {L}$$ L along with a discretization scheme (like Finite Differences, Finite Elements, Galerkin Isogeometric Analysis, etc.), in many numerical applications it is crucial to understand how good the (relative) approximation of the whole spectrum of the discretized operator $$\mathscr {L}\,^{(n)}$$ L ( n ) is, compared to the spectrum of the continuous operator $$\mathscr {L}$$ L . The theory of Generalized Locally Toeplitz sequences allows to compute the spectral symbol function $$\omega $$ ω associated to the discrete matrix $$\mathscr {L}\,^{(n)}$$ L ( n ) . Inspired by a recent work by T. J. R. Hughes and coauthors, we prove that the symbol $$\omega $$ ω can measure, asymptotically, the maximum spectral relative error $$\mathscr {E}\ge 0$$ E ≥ 0 . It measures how the scheme is far from a good relative approximation of the whole spectrum of $$\mathscr {L}$$ L , and it suggests a suitable (possibly non-uniform) grid such that, if coupled to an increasing refinement of the order of accuracy of the scheme, guarantees $$\mathscr {E}=0$$ E = 0 .

On linear continuous operators on C_p-spaces

The paper describes the structure of a linear continuous operator on the space of continuous functions in the topology of pointwise convergence. The corresponding theorem is a generalization of A.V.Arkhangel'skii's theorem on the general form of a continuous linear functional on such spaces.

Perturbation and Stability of Continuous Operator Frames in Hilbert C ∗ -Modules

Frame theory has a great revolution in recent years. This theory has been extended from the Hilbert spaces to Hilbert C ∗ -modules. In this paper, we consider the stability of continuous operator frame and continuous K -operator frames in Hilbert C ∗ -modules under perturbation, and we establish some properties.

Solvability for a Fully Elastic Beam Equation with Left-End Fixed and Right-End Simply Supported

The aim of the present paper is to consider a fully elastic beam equation with left-end fixed and right-end simply supported, i.e., u 4 t = f t , u t , u ′ t , u ″ t , u ‴ t , t ∈ 0,1 u 0 = u ′ 0 = u 1 = u ″ 1 = 0 , where f : 0,1 × ℝ 4 ⟶ ℝ is a continuous function. By applying Leray–Schauder fixed point theorem of the completely continuous operator, the existence and uniqueness of solutions are obtained under the conditions that the nonlinear function satisfies the linear growth and superlinear growth. For the case of superlinear growth, a Nagumo-type condition is introduced to limit that f t , x 0 , x 1 , x 2 , x 3 is quadratical growth on x 3 at most.

A Method for Quantitative Interpretation of Stationary Thermal Fields for Layered Media

A new method to solve thermal conjugacy problems is presented for layered models with a thermal conductivity jump at their boundaries. The purpose of this method is to approximate the inverse thermal conductivity coefficient, which has breaks, by using a combination of step functions. A generalized continuous operator is constructed in a continuous space of piecewise–homogeneous media. We obtained an analytical solution for the stationary problem of heat conjugacy in the layered model with finite thickness and with Dirichlet–Neumann conditions at the external boundaries. An algorithm was constructed for downward continuation of the heat flux to depths that correspond to the top of the mantle layer. The advantages of this method are illustrated by testing the crustal seismic, gravity and geothermal data of a study area in the Urals and neighboring regions of Russia. We examined statistical relations between density and thermal parameters and determined heat flux components for the crust and the mantle. The method enables a downward continuation of the heat flux to the base of the upper mantle and allows us to determine the thermal effects of the lateral and vertical features of deep tectonic structures.

Existence and Uniqueness Theorems for a Fractional Differential Equation with Impulsive Effect under Band-Like Integral Boundary Conditions

In this paper, we consider a class of nonlinear Caputo fractional differential equations with impulsive effect under multiple band-like integral boundary conditions. By constructing an available completely continuous operator, we establish some criteria for judging the existence and uniqueness of solutions. Finally, an example is presented to demonstrate our main results.