Original Problem Research Articles

Cylin-Painting: Seamless 360° Panoramic Image Outpainting and Beyond.

Image outpainting gains increasing attention since it can generate the complete scene from a partial view, providing a valuable solution to construct 360° panoramic images. As image outpainting suffers from the intrinsic issue of unidirectional completion flow, previous methods convert the original problem into inpainting, which allows a bidirectional flow. However, we find that inpainting has its own limitations and is inferior to outpainting in certain situations. The question of how they may be combined for the best of both has as yet remained under-explored. In this paper, we provide a deep analysis of the differences between inpainting and outpainting, which essentially depends on how the source pixels contribute to the unknown regions under different spatial arrangements. Motivated by this analysis, we present a Cylin-Painting framework that involves meaningful collaborations between inpainting and outpainting and efficiently fuses the different arrangements, with a view to leveraging their complementary benefits on a seamless cylinder. Nevertheless, straightforwardly applying the cylinder-style convolution often generates visually unpleasing results as it discards important positional information. To address this issue, we further present a learnable positional embedding strategy to incorporate the missing component of positional encoding into the cylinder convolution, which significantly improves the panoramic results. It is noted that while developed for image outpainting, the proposed algorithm can be effectively extended to other panoramic vision tasks, such as object detection, depth estimation, and image super-resolution. Code will be made available at https://github.com/KangLiao929/Cylin-Painting.

Douglas–Rachford algorithm for control-constrained minimum-energy control problems

Splitting and projection-type algorithms have been applied to many optimization problems due to their simplicity and efficiency, but the application of these algorithms to optimal control is less common. In this paper we utilize the Douglas–Rachford (DR) algorithm to solve control-constrained minimum-energy optimal control problems. Instead of the traditional approach where one discretizes the problem and solves it using large-scale finite-dimensional numerical optimization techniques we split the problem in two subproblems and use the DR algorithm to find an optimal point in the intersection of the solution sets of these two subproblems hence giving a solution to the original problem. We derive general expressions for the projections and propose a numerical approach. We obtain analytic closed-form expressions for the projectors of pure, under-, critically- and over-damped harmonic oscillators. We illustrate the working of our approach to solving not only these example problems but also a challenging machine tool manipulator problem. Through numerical case studies, we explore and propose desirable ranges of values of an algorithmic parameter which yield smaller number of iterations.

One-Click-Based Perception for Interactive Image Segmentation.

Existing deep learning-based interactive image segmentation methods have significantly reduced the user's interaction burden with simple click interactions. However, they still require excessive numbers of clicks to continuously correct the segmentation for satisfactory results. This article explores how to harvest accurate segmentation of interested targets while minimizing the user interaction cost. To achieve the above goal, we propose a one-click-based interactive segmentation approach in this work. For this particularly challenging problem in the interactive segmentation task, we build a top-down framework dividing the original problem into a one-click-based coarse localization followed by a fine segmentation. A two-stage interactive object localization network is first designed, which aims to completely enclose the target of interest based on the supervision of object integrity (OI). Click centrality (CC) is also utilized to overcome the overlapping problem between objects. This coarse localization helps to reduce the search space and increase the focus of the click at a higher resolution. A principled multilayer segmentation network is then designed by a progressive layer-by-layer structure, which aims to accurately perceive the target with extremely limited prior guidance. A diffusion module is also designed to enhance the information flow between layers. Besides, the proposed model can be naturally extended to multiobject segmentation task. Our method achieves the state-of-the-art performance under one-click interaction on several benchmarks.

AoI-Driven Power Allocation and Batch Sampling Control for V2V Status Update Communications

This paper focuses on power allocation and sampling rate control in a spectrum-sharing vehicle-to-vehicle (V2V) status update network, where data packets are sampled in batches at the transmitter of the V2V links. In particular, we aim to minimize the overall power consumption while satisfying the age of information (AoI) requirement of all links. Firstly, we analyze the average AoI of the resulting queueing system with periodical packet batch arrivals and geometrically distributed packet service time. Then, the primal problem is decomposed into two subproblems, i.e., sampling rate optimization and transmit power optimization. Finally, a computationally efficient algorithm with polynomial-time complexity is developed that optimally solves the two subproblems and thus solves the original problem with global optimality. Simulation results validate our average AoI analysis and the proposed algorithm.

Reconstruction-driven motion estimation for motion-compensated MR CINE imaging.

In cardiac CINE, motion-compensated MR reconstruction (MCMR) is an effective approach to address highly undersampled acquisitions by incorporating motion information between frames. In this work, we propose a novel perspective for addressing the MCMR problem and a more integrated and efficient solution to the MCMR field. Contrary to state-of-the-art (SOTA) MCMR methods which break the original problem into two sub-optimization problems, i.e. motion estimation and reconstruction, we formulate this problem as a single entity with one single optimization. Our approach is unique in that the motion estimation is directly driven by the ultimate goal, reconstruction, but not by the canonical motion-warping loss (similarity measurement between motion-warped images and target images). We align the objectives of motion estimation and reconstruction, eliminating the drawbacks of artifacts-affected motion estimation and therefore error-propagated reconstruction. Further, we can deliver high-quality reconstruction and realistic motion without applying any regularization/smoothness loss terms, circumventing the non-trivial weighting factor tuning. We evaluate our method on two datasets: 1) an in-house acquired 2D CINE dataset for the retrospective study and 2) the public OCMR cardiac dataset for the prospective study. The conducted experiments indicate that the proposed MCMR framework can deliver artifact-free motion estimation and high-quality MR images even for imaging accelerations up to 20x, outperforming SOTA non-MCMR and MCMR methods in both qualitative and quantitative evaluation across all experiments.

Recovering sign bits of DCT coefficients in digital images as an optimization problem

Recovering unknown, missing, damaged, distorted, or lost information in DCT coefficients is a common task in multiple applications of digital image processing, including image compression, selective image encryption, and image communication. This paper investigates the recovery of sign bits in DCT coefficients of digital images, by proposing two different approximation methods to solve a mixed integer linear programming (MILP) problem, which is NP-hard in general. One method is a relaxation of the MILP problem to a linear programming (LP) problem, and the other splits the original MILP problem into some smaller MILP problems and an LP problem. We considered how the proposed methods can be applied to JPEG-encoded images and conducted extensive experiments to validate their performances. The experimental results showed that the proposed methods outperformed other existing methods by a substantial margin, both according to objective quality metrics and our subjective evaluation.

Robust ISAC Localization in Smart Cities: A Hybrid Network Approach for NLOS Challenges with Uncertain Parameters

Accurate localization holds paramount importance across many applications within the context of smart cities, particularly in vehicular communication systems, the Internet of Things, and Integrated Sensing and Communication (ISAC) technologies. Nonetheless, achieving precise localization remains a persistent challenge, primarily attributed to the prevalence of non-line-of-sight (NLOS) conditions and the presence of uncertainties surrounding key wireless transmission parameters. This paper presents a comprehensive framework tailored to address the intricate task of localizing multiple nodes within ISAC systems significantly impacted by pervasive NLOS conditions and the ambiguity of transmission parameters. The proposed methodology integrates received signal strength (RSS) and time-of-arrival (TOA) measurements as a strategic response to effectively overcome these substantial challenges, even in situations where the precise values of transmitting power and temporal information remain elusive. An approximation approach is judiciously employed to facilitate the inherent non-convex and NP-hard nature of the original estimation problem, resulting in a notable transformation, rendering the problem amenable to a convex optimization paradigm. The comprehensive array of simulations conducted within this study corroborates the efficacy of the proposed hybrid cooperative localization method by underscoring its superior performance relative to conventional approaches relying solely on RSS or TOA measurements. This enhancement in localization accuracy in ISAC systems holds promise in the intricate urban landscape of smart cities, offering substantial contributions to infrastructure optimization and service efficiency.

Quenching for discretizations of a semilinear parabolic equation with nonlinear boundary outflux

In this paper, we study numerical approximations of a semilinear parabolic problem in one-dimension, of which the nonlinearity appears both in source term and in Neumann boundary condition. By a semidiscretization using finite difference method, we obtain a system of ordinary differential equations which is an approximation of the original problem. We obtain some conditions under which the positive solution of our system quenches in a finite time and estimate its semidiscrete quenching time. Convergence of the numerical quenching time to the theoretical one is established. Next, we show that the quenching rate of the numerical scheme is different from the continuous one. Finally, we give some numerical results to illustrate our analysis.

Разностная схема повышенного порядка аппроксимации для уравнения Аллера с переменными коэффициентами

The initial boundary value problem for the one-dimensional Aller’s equation with variable coefficients and boundary conditions of the first kind is studied. The problem under study describes the processes of heat transfer in a heterogeneous environment, moisture transfer in soils, and fluid filtration in fractured porous media. To numerically solve the problem posed, a difference scheme of high order of accuracy was constructed - fourth order of accuracy in h and second order of accuracy in τ. Using the method of energy inequalities, an a priori estimate of the solution in a difference treatment is obtained. From this estimate it follows that the solution is unique and stable with respect to the right-hand side and initial data. Under the assumption of the existence of an exact solution to the original differential problem in the class of sufficiently smooth functions, and also due to the linearity of the problem under consideration, the obtained a priori estimate implies that the solution of the constructed difference problem converges to the solution of the original differential problem at a rate equal to the order of approximation of the difference scheme. The goal and scientific novelty of the work is to obtain a new numerical scheme of a higher order of approximation when solving the Dirichlet problem for the Aller’s equation with variable coefficients.

Стационарная вращательно-симметричная конвекция при изотахофорезе в круговой цилиндрической области с недеформируемой свободной непроницаемой боковой поверхностью

The results of a study of the isotachophoresis process convective stability are presented. Isotachophoresis is the method of separation of a multicomponent mixture to individual components by an external electric field. It is assumed that the process of isotachophoresis occur in an infinite vertical circular cylinder with free side boundaries. The problem of the stationary (monotonic, neutral) concentration gravitational convection occurrence is transform to the study of the solution stability for the problem linearized on the solution of the original problem corresponding to the mechanical equilibrium of the final stage of the isotachophoresis process, in which the zones of the individual components of the mixture move with the identical constant velocity in a stationary flow. It is indicated that the main contribution to the stability/instability of the equilibrium is made by concentration gradients in the vicinity of the boundaries between the zones of individual components. Due to the complexity of constructing an exact solution corresponding to mechanical equilibrium, the exact solution replaced by an asymptotic solution (piecewise constant concentration distribution), which, in turn, is an exact solution of the asymptotic version of the transport under action of an electric field component equations (diffusion-free model). The choice of piecewise constant mechanical equilibrium leads to concentration gradients in the form of delta functions and a linear boundary value problem with delta-like coefficients to determine the critical parameters of instability. An exact solution of the problem (a system of ordinary differential equations with boundary conditions) and, using the method of one-dimensional perturbations, an exact dispersion relation for determining critical parameters (in the case of vanishingly small diffusion) is constructed.

Robust Optimization of Large-Scale Wind–Solar Storage Renewable Energy Systems Considering Hybrid Storage Multi-Energy Synergy

With the rapid integration of renewable energy sources, such as wind and solar, multiple types of energy storage technologies have been widely used to improve renewable energy generation and promote the development of sustainable energy systems. Energy storage can provide fast response and regulation capabilities, but multiple types of energy storage involve different energy conversion relationships. How to fully utilize the advantages of multiple energy storage and coordinate the multi-energy complementarity of multiple energy storage is the key to maintaining a stable operation of the power system. To this end, this paper proposes a robust optimization method for large-scale wind–solar storage systems considering hybrid storage multi-energy synergy. Firstly, the robust operation model of large-scale wind–solar storage systems considering hybrid energy storage is built. Secondly, the column constraint generation (CCG) algorithm is adopted to transform the original problem into a two-stage master problem and sub-problem for solving to obtain the optimal strategy of system operation with robustness. Finally, the validity of the proposed method is verified through case tests. The results show that the proposed method can effectively coordinate the multi-energy complementary and coordinated operation of multiple hybrid energy storage, and the obtained operation strategy of large-scale wind–solar storage systems can well balance the economy and robustness of the system.

Joint Beamforming and Phase Shifts Design for RIS-Aided Multi-User Full-Duplex Systems in Smart Cities.

Full-duplex (FD) and reconfigurable intelligent surface (RIS) are potential technologies for achieving wireless communication effectively. Therefore, in theory, the RIS-aided FD system is supposed to enhance spectral efficiency significantly for the ubiquitous Internet of Things devices in smart cities. However, this technology additionally induces the loop-interference (LI) of RIS on the residual self-interference (SI) of the FD base station, especially in complicated urban outdoor environments, which will somewhat counterbalance the performance benefit. Inspired by this, we first establish an objective and constraints considering the residual SI and LI in two typical urban outdoor scenarios. Then, we decompose the original problem into two subproblems according to the variable types and jointly design the beamforming matrices and phase shifts vector methods. Specifically, we propose a successive convex approximation algorithm and a soft actor-critic deep reinforcement learning-related scheme to solve the subproblems alternately. To prove the effectiveness of our proposal, we introduce benchmarks of RIS phase shifts design for comparison. The simulation results show that the performance of the low-complexity proposed algorithm is only slightly lower than the exhaustive search method and outperforms the fixed-point iteration scheme. Moreover, the proposal in scenario two is more outstanding, demonstrating the application predominance in urban outdoor environments.

The origin, conditions and mechanism for the formation of alpine-type hyperbasites of the Lesser Caucasus

The problem of hyperbasites origin is one of the widely discussed topics in geology. This is because they often appear when no expected. Their development does not correspond to the general regularities of the geological complexes’ development. Therefore, when problematic instances of hyperbasites appear, discussion is inevitable. This is due to the imperfections of existing concepts, which are not without flaws. The essence of this concept lies in the fact that during the rotation of the Earth around its axis, geodynamic forces are formed. The hyperbasites complex by its nature belongs to deep igneous formations formed at the initial stage of development of volcano-plutonic processes, where the composition of magmatic products was not subject to decomposition. In general, the origin of igneous rocks is associated with deep anomalous processes, which were formed under the influence of geodynamic forces, where decompression of mantle matter occurs, causing a catastrophic increase in the volume of mantle matter, as well as the associated development of volcanoplutonic processes. Hyperbasites are formed both in divergent and convergent zones of the Earth’s crust. The main factor for their formation is high pressure – deep thermodynamic conditions, where there are no favorable thermodynamic conditions for the complete separation of magmatic melts by composition. The emergence of hypermafic rocks on the surface is associated with geotectonic or denudation processes. Denudation processes can expose only those hypermafic formations that are located at the site of formation. These zones include ancient platforms, sheets, terranes, etc., which were cut by deep erosion processes. As for those hyperbasic formations that are classified as alpinotype hyperbasites, they were moved to the structure of the Alps-Himalayan folded zone from the basement with a collision with subsequent geotectonic processes, where they formed in the bed of the Paleotethys Ocean, both in the process of divergence and convergence. The noted pattern of formation and the mechanism of formation of alpine-type hyperbasites clearly corresponds to the patterns of development of geodynamic forces in the face of the Earth, also with natural laws, which are the main factors in the evolution of the Earth’s crust. From the standpoint of KDEZK, the origin, mechanism of formation, as well as the form of distribution of alpinotype hypermafic rocks of the Lesser Caucasus occurred in the Paleotethys bed, under different thermodynamic conditions and at depths. Further, as a result of the collision, it participated in the formation of folded zones of the Lesser Caucasus. Within the Lesser Caucasus, two genetic types of hypermafic rocks are exposed. Some of them correspond to the convergent zone of the Tethys paleocean, while others correspond to divergent zones. In terms of ore content, the most promising are those hypermafic rocks that are genetically related to convergent zones.

Convolution kernel determination problem in the third order Moore–Gibson–Thompson equation

This article is concerned with the study of the inverse problem of determining the difference kernel in a Volterra type integral term function in the third-order Moore–Gibson–Thompson (MGT) equation. First, the initial-boundary value problem is reduced to an equivalent problem. Using the Fourier spectral method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution to the integral equations are proved. The obtained solution to the integral equations of Volterra-type is also the unique solution to the equivalent problem. Based on the equivalence of the problems, the theorem of the existence and uniqueness of the classical solutions of the original inverse problem is proved.

A non-zero-sum investment and reinsurance game between two mean–variance insurers with dynamic CVaR constraints

This paper is devoted to investigating a non-zero-sum game between two competing insurers. The insurers can diversify their insurance risks by purchasing proportional reinsurance and investing their collected premiums into a financial market composed of one risk-free asset and one stock. The reinsurance premiums charged by the reinsurer follow the generalized mean–variance premium principle. Moreover, the dynamic CVaR constraints are incorporated in the game problem to control risks. With the dynamic mean–variance objective, we introduce two forward deterministic auxiliary processes to represent the expectations of the insurers’ wealth processes and transform the original time inconsistent game problem into a standard time consistent game problem with two state variables for each insurer. By adopting the dynamic programming principle and the Lagrange duality method, we derive the Nash equilibrium investment–reinsurance strategies for the two insurers. Finally, the effects of several important model parameters on the optimal policies are analyzed by numerical examples.

An efficient Legendre-Galerkin approximation for the fourth-order equation with singular potential and SSP boundary condition

Abstract In this article, we develop an efficient Legendre-Galerkin approximation based on a reduced-dimension scheme for the fourth-order equation with singular potential and simply supported plate (SSP) boundary conditions in a circular domain. First, we deduce the equivalent reduced-dimension scheme and essential pole condition associated with the original problem, based on which a class of weighted Sobolev spaces are defined and a weak formulation and its discrete scheme are also established for each reduced one-dimensional problem. Second, the existence and uniqueness of the weak solution and the approximation solutions are given using the Lax-Milgram theorem. Then, we construct a class of projection operators, give their approximation properties, and then prove the error estimates of the approximation solutions. In addition, we construct a set of effective basis functions in approximate space using orthogonal property of Legendre polynomials and derive the equivalent matrix form of the discrete scheme. Finally, a large number of numerical examples are performed, and the numerical results illustrate the validity and high accuracy of our algorithm.

Secularism under Dispute: Towards Agonistic, Pluralistic, and Democratic Politics. A Latin American Perspective

Abstract This article introduces some discussion on the limitations of the distinction between laicidad and secularization in Latin America (and to a lesser extent, the notion of religious freedom), mainly highlighting the problem of the colonial origin of these conceptions and their relationship with the liberal hegemonic political framework of the field. The paper’s thesis is that the boundaries for achieving a secular context in the region are not only connected to the lack of secular policies but to the application of limited concepts on the separation between church and state, and the impact of this emphasis on a reductionist vision of the religious diversity phenomenon and its link with the socio-political processes of the region. Our propose, finally, is to review these ideas in the light of the concept of radical democracy, and the contribution of this category in the broadening of the processes of institutionalization of religious identity configurations. We will take as an example of application the debates raised by the Pavez vs. Chile case in the Inter-American Court, resolved in the year 2021.

A constraint dissolving approach for nonsmooth optimization over the Stiefel manifold

Abstract This paper focuses on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox-friendly objective functions. We propose a constraint dissolving function named NCDF and show that it has the same first-order stationary points and local minimizers as the original problem in a neighborhood of the Stiefel manifold. Furthermore, we show that the Clarke subdifferential of NCDF is easy to achieve from the Clarke subdifferential of the objective function. Therefore, various existing approaches for unconstrained nonsmooth optimization can be directly applied to nonsmooth optimization problems over the Stiefel manifold. We propose a framework for developing subgradient-based methods and establishing their convergence properties based on prior works. Furthermore, based on our proposed framework, we can develop efficient approaches for optimization over the Stiefel manifold. Preliminary numerical experiments further highlight that the proposed constraint dissolving approach yields efficient and direct implementations of various unconstrained approaches to nonsmooth optimization problems over the Stiefel manifold.

Topological belief space planning for active SLAM with pairwise Gaussian potentials and performance guarantees

Determining a globally optimal solution of belief space planning (BSP) in high-dimensional state spaces directly is computationally expensive, as it involves belief propagation and objective function evaluation for each candidate action. However, many problems of interest, such as active SLAM, exhibit structure that can be harnessed to expedite planning. Also, in order to choose an optimal action, an exact value of the objective function is not required as long as the actions can be sorted in the same way. In this paper we leverage these two key aspects and present the topological belief space planning (t-bsp) concept that uses topological signatures to perform this ranking for information-theoretic cost functions, considering only topologies of factor graphs that correspond to future posterior beliefs. In particular, we propose a highly efficient topological signature based on the von Neumann graph entropy that is a function of graph node degrees and supports an incremental update. We analyze it in the context of active pose SLAM and derive error bounds between the proposed topological signature and the original information-theoretic cost function. These bounds are then used to provide performance guarantees for t-bsp with respect to a given solver of the original information-theoretic BSP problem. Realistic and synthetic simulations demonstrate drastic speed-up of the proposed method with respect to the state-of-the-art methods while retaining the ability to select a near-optimal solution. A proof of concept of t-bsp is given in a small-scale real-world active SLAM experiment.

Modular hierarchical reinforcement learning for multi-destination navigation in hybrid crowds

Real-world robot applications usually require navigating agents to face multiple destinations. Besides, the real-world crowded environments usually contain dynamic and static crowds that implicitly interact with each other during navigation. To address this challenging task, a novel modular hierarchical reinforcement learning (MHRL) method is developed in this paper. MHRL is composed of three modules, i.e., destination evaluation, policy switch, and motion network, which are designed exactly according to the three phases of solving the original navigation problem. First, the destination evaluation module rates all destinations and selects the one with the lowest cost. Subsequently, the policy switch module decides which motion network to be used according to the selected destination and the obstacle state. Finally, the selected motion network outputs the robot action. Owing to the complementary strengths of a variety of motion networks and the cooperation of modules in each layer, MHRL is able to deal with hybrid crowds effectively. Extensive simulation experiments demonstrate that MHRL achieves better performance than state-of-the-art methods.