A Unified Toolbox for Multipartite Entanglement Certification

Adaptive approximation of signed distance fields through piecewise continuous interpolation

This paper presents a new adaptive post-processing algorithm for ringing artifact reduction after image interpolation (up sampling). The algorithm is based on the concept of total variation (TV) for ringing control. It uses known TV of the blocks of the low-resolution image. Conditional gradient, subgradient and projection subgradient methods for this algorithm are considered and analyzed. A test set of 181300 overlapping 11times11 blocks of real images was used for local algorithm optimization and analysis. Local conditional gradient method shows the best objective and subjective results.

The paper is devoted to mathematical methods of planning in systems consisting of rational agents. An agent is an autonomous object that has sources of information about the environment and influences this environment. A rational agent is an agent who has a goal and uses optimal behavioral strategies to achieve it. It is assumed that there is a utility function, which is defined on the set of possible sequences of actions of the agent and takes values in the set of real numbers. A rational agent acts to maximize the utility function. If rational agents form a system, then they have a common goal and act in an optimal way to achieve it. Agents use the optimal solution of the extreme problem, which corresponds to the goal of the system. The problem of linear programming is considered, in which the number of product sets produced by the system is maximized. To solve the nonlinear problem of optimizing the production plan, the conditional gradient method is used, which at each iteration allows a posteriori estimation of the error of the solution and allows stopping the calculation process after reaching the required accuracy. Since the rational agents that are part of the system can have separate optimality criteria, multi-criteria optimization problems appear. The article considers a humanmachine procedure for solving such problems, which is connected with the conditional gradient method and uses information from the decision-maker (DM) at each iteration. The difficulties of this approach are that the DM is not able to make decisions many times under the condition of a significant number of iterations of the nonlinear programming method. The article proposes to replace OPR with an artificial neural network. Nonlinear and stochastic programming methods are used to find optimal parameters of this network.

We construct a numerical solution of an optimal control problem for Oskolkov's equations system. The system models the dynamics of Kelvin‐Voigt viscoelastic fluid. Solutions of the original boundary problem and of the conjugate problem are found numerically by means of the difference schemes method. We apply the approach of the research of evolution systems that are not solvable with respect to the time derivative. The optimization is performed using the conditional gradient method. We present the numerical experiment.

We propose a simple rule for the step-size choice in the conditional gradient method, which does not require any line-search procedure. It takes into account the current behavior of the method. Its convergence is established under the same assumptions as those for the previously known methods.

Secant-inexact projection algorithms for solving a new class of constrained mixed generalized equations problems

Infinite-dimensional optimization problems occur in various applications such as optimal control problems and parameter identification problems. If these problems are solved numerically the methods require a discretization which can be viewed as a perturbation of the data of the optimization problem. In this case the expected convergence behavior of the numerical method used to solve the problem does not only depend on the discretized problem but also on the original one. Algorithms which are analyzed include the gradient projection method, conditional gradient method, Newton's method and quasi-Newton methods for unconstrained and constrained problems with simple constraints.

In this paper, we consider a class of optimal control problems involving linear first boundary value problems of parabolic type. A conditional gradient method is used to devise a computational algorithm for solving this class of problems. The convergence property of this algorithm is investigated by using a topology arising in the study of relaxed controls.

The paper develops a second-order Newton algorithm for finding local solutions of rank-constrained LMI problems in robust synthesis. The algorithm is based on a quadratic approximation of a suitably defined merit function and generates sequences of LMI feasible iterates. The main thrust of the algorithm is that it inherits the good local convergence properties of Newton methods and thus overcomes the difficulties encountered with earlier methods such as the Frank and Wolfe or conditional gradient methods which tend to be very slow in the neighborhood of a local solution. Moreover, it is easily implemented using available Semi-Definite Programming (SDP) codes. Proposed algorithms have proven global and local convergence properties and thus represent improvements over classically used D-K iteration schemes but also outperform earlier conditional gradient algorithms. Reported computational results demonstrate these facts.

In this work, time-depended Schrodinger equation described particles at matter (crystal, catalysis, metal) surface could be considered as propose of numerical control of quantum system. Accessing existing physical experimental results on the motion of particles (molecules, atoms) at surface, based on variational method of quantum control theory in Hilbert space, using density function theory (DFT), time-depended Schrodinger equation to proceed the investigation of computational approach. To do quantum calculation at surface, physically, first needs a concept as control goal: such as breaking a chemical bond as target; reducing energy of high intensity shaped laser pulse. Particles at surface is a kind of constrain control for spatial variable. Optimal control is to find and characterize the quantum optima for minimizing or maximizing the cost functional. Control methods contain selecting chemical reagent, designing chemical reaction, making control scope for a quantized system: time varying Schrodinger equation. Precisely, for general quadratic cost function, in two or three dimensional cases, a semi discrete (time continuous, spatial discrete) algorithm consisting of finite element method and conjugate gradient method, would be utilized for solving a numerical solution of state system, and obtaining quantum optimal control from a initial guess of control input. It is quite curious: what is the difference of control particles occurred at surface than control free particles? whether one can develop a suit of theory or methodology for quantum surface control? It is certainly expected to connect theoretical control, to numerical or computational control, and to experimental control as carrying out quantum system control of particles on the surface. It is desired that quantum control theory (QCT) for quantum dot at surface would be evidenced in visualization method, and attained confidential verification in the guidance of real-time computer-aided experiments in the viewpoint of chemistry and physics.

In this paper, we consider constrained optimization problems subject to a convex set C. Stochastic gradient descent (SGD) is a simple and popular stochastic optimization algorithm that has been the workhorse of machine learning for many years. We show a new and surprising fact about SGD, in that depending on the constraint set C, one can operate SGD with much lower-dimensional stochastic gradients without affecting its performance. In particular, we design an optimization algorithm that operates with the lower-dimensional (compressed) stochastic gradients, and establish that with the right set of parameters it has the exact same dimension-free convergence guarantees as that of regular SGD for popular convex and nonconvex optimization settings. We also present two applications of these bounds, one for improving the empirical risk minimization bounds in differentially private nonconvex optimization, and other for reducing communication costs with distributed SGD. Additionally, we also show that this connection between constraint set structure and gradient compression also extends beyond SGD to the conditional gradient (Frank-Wolfe) method. The geometry of the constraint set, captured by its Gaussian width, plays an important role in all our results.

In this paper, we consider the application of several gradient methods to the traffic assignment problem: we search equilibria in the stable dynamics model (Nesterov and De Palma, 2003) and the Beckmann model. Unlike the celebrated Frank–Wolfe algorithm widely used for the Beckmann model, these gradients methods solve the dual problem and then reconstruct a solution to the primal one. We deal with the universal gradient method, the universal method of similar triangles, and the method of weighted dual averages and estimate their complexity for the problem. Due to the primal-dual nature of these methods, we use a duality gap in a stopping criterion. In particular, we present a novel way to reconstruct admissible flows in the stable dynamics model, which provides us with a computable duality gap.

Fault detection and diagnosis are critical challenges in Very Large Scale Integration (VLSI) circuits, where even minor defects can cause significant performance degradation or system failure. Traditional fault detection methods often struggle with scalability and real-time analysis as circuits grow increasingly complex. This paper proposes an AI-augmented framework that leverages machine learning algorithms and neural networks to enhance the fault detection process in VLSI circuits. The proposed model not only identifies and classifies faults with high accuracy but also provides root-cause diagnostics, significantly reducing testing time and maintenance costs. Simulation results demonstrate the effectiveness of the AI-based approach in comparison with conventional techniques, showcasing improved fault coverage, faster detection, and scalability for modern chip designs. This study serves as a step toward the integration of intelligent diagnostics into chip manufacturing, paving the way for more robust and self-healing electronic systems.

Inferring molecular structure from Nuclear Magnetic Resonance (NMR) measurements requires an accurate forward model that can predict chemical shifts from 3D structure. Current forward models are limited to specific molecules like proteins and state-of-the-art models are not differentiable. Thus they cannot be used with gradient methods like biased molecular dynamics. Here we use graph neural networks (GNNs) for NMR chemical shift prediction. Our GNN can model chemical shifts accurately and capture important phenomena like hydrogen bonding induced downfield shift between multiple proteins, secondary structure effects, and predict shifts of organic molecules. Previous empirical NMR models of protein NMR have relied on careful feature engineering with domain expertise. These GNNs are trained from data alone with no feature engineering yet are as accurate and can work on arbitrary molecular structures. The models are also efficient, able to compute one million chemical shifts in about 5 seconds. This work enables a new category of NMR models that have multiple interacting types of macromolecules.

Evaluating a function by approximating it in a rather large domain may require polynomial or rational functions of large degrees. This may lead to long delays of computation, and this may also make the numerical error control difficult. A natural way to deal with this problem is to split the interval where the function is to be approximated into several smaller subintervals. It suffices to store in a table, for each subinterval, the coefficients of a low-degree approximation that is valid in that interval. Such a method is not new (a PDP-9 implementation is reported in [7]), but it becomes very attractive nowadays, since memory is less and less expensive.KeywordsDouble PrecisionMinimax ApproximationMachine NumberTarget PrecisionRepresentable NumberThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.