Impulse optimization for data association

To address the convergence issues in the natural occupation optimization of reduced density matrix functional theory (RDMFT), we recently proposed the explicit-by-implicit (EBI) idea to handle the ensemble N-representability constraint (Yao et al. J. Phys. Chem. Lett. 2021, 12, 6788). This work continues to focus on these issues that can affect the reliability of the electronic structure description in RDMFT; further explores the combination of EBI, as well as the (augmented) Lagrangian methods (both LM and ALM), with both first- and second-order numerical optimization algorithms; and carefully evaluates their performances in natural occupation optimizations of various systems, including strongly correlated systems and large molecules. By comparing both converged energies and elapsed times, it can be seen that the LM and ALM have serious convergence issues for systems of different sizes. In contrast, the optimizations of EBI can converge to better energies with fewer iterations. However, due to the local convergence nature of the Newton's Method (NM) algorithm, EBI@NM still suffers from the local minimum issue for both strongly correlated systems and large molecules. Overall, the combination of EBI with the simple first-order algorithm of gradient descent (GD), namely EBI@GD, consistently provides the lowest converged energies for different types of systems, with the lowest computational scaling. These tests demonstrate the advantages of EBI in the calculations of transition states, strongly correlated systems, and large molecules. Meanwhile, the insights gained from this work are helpful to further develop more efficient algorithms for RDMFT.

Communication-efficient distributed cubic Newton with compressed lazy Hessian

Feedforward neural networks (FNN's) have been proposed to solve complex problems in pattern recognition and classification and function approximation. Despite the general success of learning methods for FNN's, such as the backpropagation (BP) algorithm, second-order optimization algorithms and layer-wise learning algorithms, several drawbacks remain to be overcome. In particular, two major drawbacks are convergence to a local minima and long learning time. In this paper we propose an efficient learning method for a FNN that combines the BP strategy and optimization layer by layer. More precisely, we construct the layer-wise optimization method using the Taylor series expansion of nonlinear operators describing a FNN and propose to update weights of each layer by the BP-based Kaczmarz iterative procedure. The experimental results show that the new learning algorithm is stable, it reduces the learning time and demonstrates improvement of generalization results in comparison with other well-known methods.

Functional to anatomical brain image registration is needed for accurate localization of brain activation maps. Due to the presence of nonlinear distortions, it is more effective to consider non-rigid transformations to achieve such a registration. In this paper, a non-rigid registration technique based on the B-spline free-form deformation model and mutual information similarity measure is introduced. An optimization formulation is devised to achieve a fast and robust registration. This formulation differs from the previous formulations by utilizing a limited-memory, second-order optimization algorithm instead of the usual first-order gradient-based algorithms. It also enforces hard parameter constraints instead of constraints based upon physics or Jacobian smoothness. The results obtained indicate that this registration technique provides improvements over rigid and affine techniques when registering functional to anatomical magnetic resonance brain images.

The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of second-order subdifferentials of nonsmooth functions with employing the machinery of second-order variational analysis and generalized differentiation. First we develop a globally superlinearly convergent damped Newton-type algorithm for the class of continuously differentiable functions with Lipschitzian gradients, which are nonsmooth of second order. Then we design such a globally convergent algorithm to solve a structured class of nonsmooth quadratic composite problems with extended-real-valued cost functions, which typically arise in machine learning and statistics. Finally, we present the results of numerical experiments and compare the performance of our main algorithm applied to an important class of Lasso problems with those achieved by other first-order and second-order optimization algorithms.

We present an approach for efficient numerical solution of optimization problems governed by parabolic partial differential equations. The main ingredients are: space-time finite element discretization, second-order optimization algorithms, and storage reduction techniques. We discuss the combination of these components for the solution of large-scale optimization problems.

Maneuvering Target Tracking in Dense Clutter Based on Particle Filtering

Bearings-only tracking (BOT) using a single maneuvering platform has been studied extensively in the past. However, only a few studies exist in the open literature that deal with measurement origin uncertainty. Most publications are concerned with finding the best filtering approach, since BOT is inherently nonlinear, or finding the optimal maneuver strategy for the sensor platform to improve observability. We consider measurement origin uncertainty due to the existence of multiple targets in the surveillance region, non-unity detection probability, and false alarms. Our algorithm uses the multiframe assignment (MFA) to solve the data association problem, and filtering is performed using the unscented Kalman filter (UKF). We employ both the modified and log polar coordinate systems. Simulation results show that the proposed algorithm is very effective in terms of tracking accuracy and track maintenance capability, especially when formulated in the log polar coordinate system.

The dynamic programming formulation of the forward principle of optimality in the solution of optimal control problems results in a partial differential equation with initial boundary condition whose solution is independent of terminal cost and terminal constraints. Based on this property, two computational algorithms are described. The first-order algorithm with minimum computer storage requirements uses only integration of a system of differential equations with specified initial conditions and numerical minimization in finite-dimensional space. The second-order algorithm is based on the differential dynamic programming approach. Either of the two algorithms may be used for problems with nondifferentiable terminal cost or terminal constraints, and the solution of problems with complicated terminal conditions (e.g., with free terminal time) is greatly simplified.

A simple and commonly used method for tracking in clutter to deal with measurement origin uncertainty is the so-called Strongest Neighbor Filter (SNF). It uses the measurement with the strongest intensity (amplitude) in the neighborhood of the predicted target measurement location, known as the 'strongest neighbor' measurement, as if it were the true one. Its performance is significantly better than that of the Nearest Neighbor Filter (NNF) but usually worse than that of the Probabilistic Data Association Filter (PDAF), while its computational complexity is the lowest one among the three filters. The SNF is, however, not consistent in the sense that its actual tracking errors are well above its on-line calculated error standard deviations. Based on the theoretical results obtained recently of the SNF for tracking in clutter, a probabilistic strongest neighbor filter is presented here. This new filter is consistent and is substantially superior to the PDAF in both performance and computation. The proposed filter is obtained by modifying the standard SNF to account for the probability that the strongest neighbor is not target-oriented, which is accomplished by using probabilistic weights.

The approximate dynamics of many physical phenomena, including turbulence, can be represented by dissipative systems of ordinary differential equations. One often turns to numerical integration to solve them. There is an incompatibility, however, between the answers it can produce (i.e., specific solution trajectories) and the questions one might wish to ask (e.g., what behavior would be typical in the laboratory?) To determine its outcome, numerical integration requires more detailed initial conditions than a laboratory could normally provide. In place of initial conditions, experiments stipulate how tests should be carried out: only under statistically stationary conditions, for example, or only during asymptotic approach to a final state. Stipulations such as these, rather than initial conditions, are what determine outcomes in the laboratory. This theoretical study examines whether the points of view can be reconciled: What is the relationship between one's statistical stipulations for how an experiment should be carried out--stationarity or asymptotic approach--and the expected results? How might those results be determined without invoking initial conditions explicitly? To answer these questions, stationarity and asymptotic approach conditions are analyzed in detail. Each condition is treated as a statistical constraint on the system--a restriction on the probability density of states that might be occupied when measurements take place. For stationarity, this reasoning leads to a singular, invariant probability density which is already familiar from dynamical systems theory. For asymptotic approach, it leads to a new, more regular probability density field. A conjecture regarding what appears to be a limit relationship between the two densities is presented. By making use of the new probability densities, one can derive output statistics directly, avoiding the need to create or manipulate initial data, and thereby avoiding the conceptual incompatibility mentioned above. This approach also provides a clean way to derive reduced-order models, complete with local and global error estimates, as well as a way to compare existing reduced-order models objectively. The new approach is explored in the context of five separate test problems: a trivial one-dimensional linear system, a damped unforced linear oscillator in two dimensions, the isothermal Rayleigh-Plesset equation, Lorenz's equations, and the Stokes limit of Burgers' equation in one space dimension. In each case, various output statistics are deduced without recourse to initial conditions. Further, reduced-order models are constructed for asymptotic approach of the damped unforced linear oscillator, the isothermal Rayleigh-Plesset system, and Lorenz's equations, and for stationarity of Lorenz's equations.

Key Success Factors in the Revitalization of Distressed Firms: A Case of the Korean Corporate Workouts

There is no doubt that chaotic sequences attracted much attention in recent decades due to its distinctive properties. These distinct properties give the availability for the chaotic sequences to be applied in different fields. One of the fields that exploit the chaos features is the encryption field, in which chaotic sequences can be used to encrypt texts or images. The randomization attitude of the chaotic sequences can be affected by the initial condition, or by the code length. As these parameters optimized, the performance of the chaotic sequences enhanced and improved from many points of view. This paper presents study, analysis and evaluation for different chaotic sequences from the security viewpoint. The study and analysis include the standard NIST statistical test suite for random and pseudo random number generators for cryptography applications. The presented sequences are the traditional and enhanced version of chaotic sequences based on the logistic map. The new contribution of the paper is to perform the statistical tests over a range of the code lengths, and initial conditions in order to study the effect of each parameter, then optimize its values. Moreover, the proposed sequences are evaluated and applied to image encryption to verify its robustness.

One of the most widely used concepts of physics is that of linearity or superposition. From a mathematical point of view, a linear system is described by equations—algebraic, differential, or integral—that are linear in the dependent variables. From a physical point of view, a system is linear or possesses a superposition principle if various modes of behavior of the system that arise from various causes or initial conditions can be added together algebraically to produce the same behavior that would result if the causes or initial conditions were added algebraically and applied to the system. For example, water waves of small amplitude superpose linearly on the surface of a pond, so that the ripples produced by two disturbances at the same time are just the sum of those produced by the separate disturbances. In most cases, the assumption of linearity is believed to be justified either as an exact representation of the situation or as a close approximation to the truth. Thus the water waves referred to above form a linear system only so long as the amplitude is small; otherwise, the shape of the resultant wave is different from that of the component waves, as is apparent when the wave is about to “break”. There are some systems, however, that are not even approximately linear, and yet are commonly described by linear equations for want of more effective mathematical methods.

Dynamic Simulation of a 12 DoF Biped Robot with Newton-Euler Method using Unit Vector Approach