Higher-order Constraints Research Articles

The consequence of higher-order curvature-based constraints on [formula omitted] gravity

In this investigation, we perform an observational statistical analysis in the theory of f(R,Lm) gravity. The proposed theoretical model is based on the Ricci scalar’s non-linear contribution. We use a distinct parametrization for the deceleration parameter and constrain the model parameters by using various observational data. To determine the best-fit model for the cosmological parameters, we use different observational datasets such as the Hubble Space Telescope, the Pantheon Supernova Survey, the Gold dataset, the Gamma-Ray Burst (GRB), and the Baryon Acoustic Oscillations (BAO). Furthermore, we study the late-time cosmic evolution of the Universe in detail and examine the implications of the constraint values on cosmological parameters. Additionally, we conduct a thorough comparison with the standard cosmological model ΛCDM and other standard models obtained by Odintsov et al. (2024); Odintsov et al. (2023) to examine the validity of our proposed model in the low-redshift regimes. Finally, we find that the proposed model encapsulates an intriguing transition from early deceleration at high redshift to acceleration at low redshift, a quintessence dark energy scenario, and convergence towards the well-established ΛCDM model in late-time Universe’s evolution.

Decoupled variational retinex for reconstruction and fusion of underwater shallow depth-of-field image with parallax and moving objects

Underwater imaging often suffers from poor quality due to the complex underwater environment and limitations of hardware equipment, leading to images with shallow depth of field and moving objects, which pose a challenge for information fusion of image sequences from the same underwater scene. To effectively address these problems, we propose a decoupled variational Retinex method for reconstructing and fusing underwater shallow depth of field images. Specifically, we first construct a module that adopts the decoupled variational Retinex model to adjust pixel dynamic range and luminance components, enhance non-local properties’ extraction with higher-order data constraints, and significantly improve image quality. Then, we develop a precision alignment strategy for image sequences by calculating and correcting control point deviations in the overlapping areas, achieving accurate registration of the image sequences, and effectively reconstructing scenes with parallax. Moreover, scenes with moving objects within the image sequence are reconstructed by redistributing overlapping areas. We design a novel cost function based on the neighborhood information of seams, which facilitates iterative optimization of these solved seams. This process improves the segmentation accuracy within these regions, achieving more precise scene reconstruction. Compared with state-of-the-art approaches, our method demonstrates superior performance in rectifying degraded image quality and reconstructing visually appealing images, with the resulting reconstructed images showing enhanced subjective visual quality.

Different effects of visual occlusion on interpersonal coordination of head and body movements during dyadic conversations.

In recent decades, interpersonal coordination and synchrony have been extensively examined in the field of psychology and cognitive science. Studies suggest that perceptual information enables interpersonal coordination and that perceptual noise may even enhance coordination. However, how these perceptual factors influence interpersonal coordination dynamics between head and body movements remains unclear. This study investigated the effect of visual information on the interpersonal coordination of head and body movements during dyadic conversations. The availability of visual information was manipulated by positioning a partition halfway between a pair of participants, and the conversations were recorded using a video camera. A video-based human pose estimation software (OpenPose) was used to quantify each interlocutor's head and body movements, which were submitted for cross-recurrence quantification analysis (CRQA), to assess the degree of coordination between the interlocutors. The results showed different effects between head- and body-movement coordination (i.e., a CRQA measure, maximum line length). The occlusion of visual information increased head-movement coordination, whereas it decreased body-movement coordination. The results suggest that a distinct mechanism may be present at the head- and body-movement coordination level and this study observed differing appearances of compensatory behaviors. Further studies should be conducted to investigate the complex relationships between interpersonal coordination dynamics and various kinds of communication constraints, such as long-term or short-term, and lower-order (perceptual-motor) or higher-order (cognitive-social) level constraints.

Path-Constrained Time-Optimal Motion Planning for Robot Manipulators With Third-Order Constraints

Planning time-optimal motions of robot manipulators is important for maximizing productivity in industry and has attracted much attention in academia. Time-optimal time scaling (TOTS) of specified paths subject to second-order constraints is a well-studied problem in robotics. However, there is still a lack of effective approaches for computing TOTS with higher order constraints. This article proposes a novel method for TOTS subject to third-order constraints. The proposed method formulates the third-order TOTS as a four-stage optimization involving only linear programming by exploiting the special structure of the problem. The proposed method first performs a backward pass and a forward pass to generate the second-order optimal velocity profile. Then, the points violating the third-order constraints are identified, and the constraint violations are eliminated through numerical integration around the violating points. A bisection search algorithm is proposed to quickly determine the switching points at which the elimination process begins. The proposed method is verified through numerical examples and experimental tests. The results indicate that the proposed method outperforms the state-of-the-art approaches in terms of solution quality and computation time.

Continual Image Deraining With Hypergraph Convolutional Networks.

Image deraining is a challenging task since rain streaks have the characteristics of a spatially long structure and have a complex diversity. Existing deep learning-based methods mainly construct the deraining networks by stacking vanilla convolutional layers with local relations, and can only handle a single dataset due to catastrophic forgetting, resulting in a limited performance and insufficient adaptability. To address these issues, we propose a new image deraining framework to effectively explore nonlocal similarity, and to continuously learn on multiple datasets. Specifically, we first design a patchwise hypergraph convolutional module, which aims to better extract the nonlocal properties with higher-order constraints on the data, to construct a new backbone and to improve the deraining performance. Then, to achieve better generalizability and adaptability in real-world scenarios, we propose a biological brain-inspired continual learning algorithm. By imitating the plasticity mechanism of brain synapses during the learning and memory process, our continual learning process allows the network to achieve a subtle stability-plasticity tradeoff. This it can effectively alleviate catastrophic forgetting and enables a single network to handle multiple datasets. Compared with the competitors, our new deraining network with unified parameters attains a state-of-the-art performance on seen synthetic datasets and has a significantly improved generalizability on unseen real rainy images.

Social Relation Reasoning Based on Triangular Constraints

Social networks are essentially in a graph structure where persons act as nodes and the edges connecting nodes denote social relations. The prediction of social relations, therefore, relies on the context in graphs to model the higher-order constraints among relations, which has not been exploited sufficiently by previous works, however. In this paper, we formulate the paradigm of the higher-order constraints in social relations into triangular relational closed-loop structures, i.e., triangular constraints, and further introduce the triangular reasoning graph attention network (TRGAT). Our TRGAT employs the attention mechanism to aggregate features with triangular constraints in the graph, thereby exploiting the higher-order context to reason social relations iteratively. Besides, to acquire better feature representations of persons, we introduce node contrastive learning into relation reasoning. Experimental results show that our method outperforms existing approaches significantly, with higher accuracy and better consistency in generating social relation graphs.

Midpoint projection algorithm for stochastic differential equationson manifolds.

Stochastic differential equationsprojected onto manifolds occur in physics, chemistry, biology, engineering, nanotechnology, and optimization, with interdisciplinary applications. Intrinsic coordinate stochastic equationson the manifold are sometimes computationally impractical, and numerical projections are therefore useful in many cases. In this paper a combined midpoint projection algorithm is proposed that uses a midpoint projection onto a tangent space, combined with a subsequent normal projection to satisfy the constraints. We also show that the Stratonovich form of stochastic calculus is generally obtained with finite bandwidth noise in the presence of a strong enough external potential that constrains the resulting physical motion to a manifold. Numerical examples are given for a wide range of manifolds, including circular, spheroidal, hyperboloidal, and catenoidal cases, higher-order polynomial constraints that give a quasicubical surface, and a ten-dimensional hypersphere. In all cases the combined midpoint method has greatly reduced errors compared to other methods used for comparison, namely, a combined Euler projection approach and a tangential projection algorithm. We derive intrinsic stochastic equationsfor spheroidal and hyperboloidal surfaces for comparison purposes to verify the results. Our technique can handle multiple constraints, which allows manifolds that embody several conserved quantities. The algorithm is accurate, simple, and efficient. A reduction of an order of magnitude in the diffusion distance error is found compared to the other methods and an up to several orders of magnitude reduction in constraint function errors.

Quantum Many-Body Theory from a Solution of the N-Representability Problem.

Here we present a many-body theory based on a solution of the N-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an equation that re-expresses physical constraints on higher-order RDMs to generate direct constraints on the 2-RDM, which are required for its derivation from an N-particle density matrix, known as N-representability conditions. The approach produces a complete hierarchy of 2-RDM constraints that do not depend explicitly upon the higher RDMs or the wave function. By using the two-particle part of a unitary decomposition of higher-order constraint matrices, we can solve the energy minimization by semidefinite programming in a form where the low-rank structure of these matrices can be potentially exploited. We illustrate by computing the ground-state electronic energy and properties of the H_{8} ring.

Higher-Order MSL Horn Constraints

The monadic shallow linear (MSL) class is a decidable fragment of first-order Horn clauses that was discovered and rediscovered around the turn of the century, with applications in static analysis and verification. We propose a new class of higher-order Horn constraints which extend MSL to higher-order logic and develop a resolution-based decision procedure. Higher-order MSL Horn constraints can quite naturally capture the complex patterns of call and return that are possible in higher-order programs, which make them well suited to higher-order program verification. In fact, we show that the higher-order MSL satisfiability problem and the HORS model checking problem are interreducible, so that higher-order MSL can be seen as a constraint-based approach to higher-order model checking. Finally, we describe an implementation of our decision procedure and its application to verified socket programming.

Generalized Lie symmetries and almost regular Lagrangians: a link between symmetry and dynamics

The generalized Lie symmetries of almost regular Lagrangians are studied, and their impact on the evolution of dynamical systems is determined. It is found that if the action has a generalized Lie symmetry, then the Lagrangian is necessarily singular; the converse is not true, as we show with a specific example. It is also found that the generalized Lie symmetry of the action is a Lie subgroup of the generalized Lie symmetry of the Euler–Lagrange equations of motion. The converse is once again not true, and there are systems for which the Euler–Lagrange equations of motion have a generalized Lie symmetry while the action does not, as we once again show through a specific example. Most importantly, it is shown that each generalized Lie symmetry of the action contributes one arbitrary function to the evolution of the dynamical system. The number of such symmetries gives a lower bound to the dimensionality of the family of curves emanating from any set of allowed initial data in the Lagrangian phase space. Moreover, if second- or higher-order Lagrangian constraints are introduced during the application of the Lagrangian constraint algorithm, these additional constraints could not have been due to the generalized Lie symmetry of the action.

A jerk-limited heuristic feedrate scheduling method based on particle swarm optimization for a 5-DOF hybrid robot

Compared with machine tools, five degrees-of-freedom (DOFs) hybrid robots have been widely concerned in the manufacturing of large complex surface parts due to their characteristics of high flexibility and large workspace. It is of great significance to schedule the time-optimal feedrate that satisfies the high-order constraints (e.g., jerk or jounce) in the toolpath and joint systems to achieve the high-precision and high-efficiency machining of the robot. To overcome the complexity of five-axis feedrate scheduling and improve the optimality of machining time, this paper proposes a jerk-limited heuristic feedrate scheduling (HFS) method with near-optimal time. Firstly, the analytical equations between all constraints and the parametric feedrate are derived, and the mathematical model for control points optimization of the parametric feedrate profile expressed by a B-spline curve is established. Then, combined with the global search particle swarm optimization (GSPSO) algorithm, a proposed moving window planning method optimizes a small number of control points so that the feedrate curve has enough rising space. Subsequently, to obtain the near time-optimal feedrate, the local search PSO (LSPSO) algorithm within the moving window is developed to locally adjust the non-uniformly inserted control points. Compared with the existing methods, the HFS method is beneficial to further optimize the machining time with a faster computation speed, and ensure the stability of the robot machining. Finally, simulations and experiments on the developed TriMule-800 hybrid robot verify the effectiveness of this method.

Efficient Global MOT Under Minimum-Cost Circulation Framework.

We developed a minimum-cost circulation framework for solving the global data association problem, which plays a key role in the tracking-by-detection paradigm of multi-object tracking (MOT). The global data association problem was extensively studied under the minimum-cost flow framework, which is theoretically attractive as being flexible and globally solvable. However, the high computational burden has been a long-standing obstacle to its wide adoption in practice. While enjoying the same theoretical advantages and maintaining the same optimal solution as the minimum-cost flow framework, our new framework has a better theoretical complexity bound and leads to orders of practical efficiency improvement. This new framework is motivated by the observation that minimum-cost flow only partially models the data association problem and it must be accompanied by an additional and time-consuming searching scheme to determine the optimal object number. By employing a minimum-cost circulation framework, we eliminate the searching step and naturally integrate the number of objects into the optimization problem. By exploring the special property of the associated graph, that is, an overwhelming majority of the vertices are with unit capacity, we designed an implementation of the framework and proved it has the best theoretical computational complexity so far for the global data association problem. We evaluated our method with 40 experiments on five MOT benchmark datasets. Our method was always the most efficient in every single experiment and averagely 53 to 1,192 times faster than the three state-of-the-art methods. When our method served as a sub-module for global data association methods utilizing higher-order constraints, similar running time improvement was attained. We further illustrated through several case studies how the improved computational efficiency enables more sophisticated tracking models and yields better tracking accuracy. We made the source code publicly available on GitHub with both Python and MATLAB interfaces.

Non-holonomic and quasi-integrable deformations of the AB equations

For the first time both non-holonomic and quasi-integrable deformations are obtained for the AB system of coupled equations. The AB system models geophysical and atmospheric fluid motion along with ultra-short pulse propagation in nonlinear optics, and serves as a generalization of the well-known sine-Gordon equation. The non-holonomic deformation retains integrability subjected to higher-order differential constraints whereas the quasi-AB system, which is partially deviated from integrability, is characterized by an infinite subset of quantities (charges) that are conserved only asymptotically given the solution possesses definite space–time parity properties. Particular localized solutions to both these deformations of the AB system are obtained, some of which are qualitatively unique to the corresponding deformation, displaying similarities with physically observed excitations.

Convex optimization of nonlinear inequality with higher order derivatives

This paper is devoted to the Mayer problem on the optimization of nonlinear inequalities containing higher-order derivatives. We formulate the conditions of optimality for discrete and differential problems with higher-order inequality constraints. Discrete and differential problems play a substantial role in the formulation of optimal conditions in the form of Euler–Lagrange inclusions and ‘transversality’ conditions. The basic concept of obtaining optimal conditions is the proposed discretization method and equivalence results. Combining this approach and passing to the limit in the discrete-approximation problem, we establish sufficient optimality conditions for higher-order differential inequality. Moreover, to demonstrate this approach, the optimization of second-order polyhedral differential inequality is considered and a numerical example is given to illustrate the theoretical results.

On the motion of an Earth satellite after fixing the magnitude of its acceleration as a problem with nonholonomic third-order constraint

The motion of an artificial Earth satellite with constant absolute value of the acceleration is considered. This requirement is equivalent to imposing a second-order nonlinear nonholonomic constraint or a third-order linear nonholonomic constraint. Two theories of motion of nonholonomic systems with high-order constraints are used for solving this problem. According to the first theory, a consistent system of differential equations is constructed with respect to the generalized coordinates and the Lagrange multipliers; the second theory is based on the application of the generalized Gauss principle. The results are different, although the constraints are satisfied in both theories. It turns out that infinitely many solutions can be built, but using these theories one can find two specific solutions. The question of the difference of these two solutions from the set of all other possible solutions is raised. We also simplify the previously obtained differential equations. The transition to dimensionless variables is made. Three parameters of motion prior to imposition of the constraint are single out, which control the motion after the application of the constraint. The solutions obtained from these theories of motion of nonholonomic systems are compared.

Temporal Reasoning with Kinodynamic Networks

Temporal reasoning is central to Artificial Intelligence (AI) and many of its applications. However, the existing algorithmic frameworks for temporal reasoning are not expressive enough to be applicable to robots with complex kinodynamic constraints typically described using differential equations. For example, while minimum and maximum velocity constraints can be encoded in Simple Temporal Networks (STNs), higher-order kinodynamic constraints cannot be represented in existing frameworks. In this paper, we present a novel framework for temporal reasoning called Kinodynamic Networks (KDNs). KDNs combine elements of existing temporal reasoning frameworks with the idea of Bernstein polynomials. The velocity profiles of robots are represented using Bernstein polynomials; and dynamic constraints on these velocity profiles can be converted to linear constraints on the to-be-determined coefficients of their Bernstein polynomials. We study KDNs for their attractive theoretical properties and apply them to the Multi-Agent Path Finding (MAPF) problem with higher-order kinodynamic constraints. We show that our approach is not only scalable but also yields smooth velocity profiles for all robots that can be executed by their controllers.

Online Reentry Trajectory Optimization Using Modified Sequential Convex Programming for Hypersonic Vehicle

In this article, a highly nonlinear trajectory optimization problem for reentry vehicles is rapidly solved by the proposed modified sequential convex programming (MSCP) method. A logarithm linearization approach is proposed to decouple the dynamics of high order and nonconvex path constraints of heat rate, dynamic pressure, and normal load. Next, the model including the no-fly zone constraint, and the nonconvex objective function are convexified with first-order Taylor series expansion. Subsequently, the continuous-time optimal problem is converted to an equivalent finite-dimensional sequential convex programming (SCP) problem. Moreover, a compensation term is added to the state equations to maintain the feasibility of the reformulated problem. Consequently, to guarantee the optimality of the solution, a penalty term with respect to the compensation term is added to the objective function. In the end, an online optimization scheme with MSCP is proposed. Compared to a general proposed optimal control solver, numerical simulations are conducted to verify the optimality and fast convergence of MSCP. Furthermore, online optimization simulations demonstrate the validity of the proposed online scheme for pop-up no-fly zone and mission temporary changes.

Hamiltonian constraints and unfree gauge symmetry

We study Hamiltonian form of unfree gauge symmetry where the gauge parameters have to obey differential equations. We consider the general case such that the Dirac-Bergmann algorithm does not necessarily terminate at secondary constraints, and tertiary and higher order constraints may arise. Given the involution relations for the first-class constraints of all generations, we provide explicit formulas for unfree gauge transformations in the Hamiltonian form, including the differential equations constraining gauge parameters. All the field theories with unfree gauge symmetry share the common feature: they admit sort of "global constants of motion" such that do not depend on the local degrees of freedom. The simplest example is the cosmological constant in the unimodular gravity. We consider these constants as modular parameters rather than conserved quantities. We provide a systematic way of identifying all the modular parameters. We demonstrate that the modular parameters contribute to the Hamiltonian constraints, while they are not explicitly involved in the action. The Hamiltonian analysis of the unfree gauge symmetry is precessed by a brief exposition for the Lagrangian analogue, including explicitly covariant formula for degrees of freedom number count. We also adjust the BFV-BRST Hamiltonian quantization method for the case of unfree gauge symmetry. The main distinction is in the content of the non-minimal sector and gauge fixing procedure. The general formalism is exemplified by traceless tensor fields of irreducible spin $s$ with the gauge symmetry parameters obeying transversality equations.

Efficient phase coding in hippocampal place cells.

Neural codes have been postulated to build efficient representations of the external world. The hippocampus, an encoding system, employs neuronal firing rates and spike phases to encode external space. Although the biophysical origin of such codes is at a single neuronal level, the role of neural components in efficient coding is not understood. The complexity of this problem lies in the dimensionality of the parametric space encompassing neural components, and is amplified by the enormous biological heterogeneity observed in each parameter. A central question that spans encoding systems therefore is how neurons arrive at efficient codes in the face of widespread biological heterogeneities. To answer this, we developed a conductance-based spiking model for phase precession, a phase code of external space exhibited by hippocampal place cells. Our model accounted for several experimental observations on place cell firing and electrophysiology: the emergence of phase precession from exact spike timings of conductance-based models with neuron-specific ion channels and receptors; biological heterogeneities in neural components and excitability; the emergence of subthreshold voltage ramp, increased firing rate, enhanced theta power within the place field; a signature reduction in extracellular theta frequency compared to its intracellular counterpart; and experience-dependent asymmetry in firing-rate profile. We formulated phase-coding efficiency, using Shannon's information theory, as an information maximization problem with spike phase as the response and external space within a single place field as the stimulus. We employed an unbiased stochastic search spanning an 11-dimensional neural space, involving thousands of iterations that accounted for the biophysical richness and neuron-to-neuron heterogeneities. We found a small subset of models that exhibited efficient spatial information transfer through the phase code, and investigated the distinguishing features of this subpopulation at the parametric and functional scales. At the parametric scale, which spans the molecular components that defined the neuron, several nonunique parametric combinations with weak pairwise correlations yielded models with similar high phase-coding efficiency. Importantly, placing additional constraints on these models in terms of matching other aspects of hippocampal neural responses did not hamper parametric degeneracy. We provide quantitative evidence demonstrating this parametric degeneracy to be a consequence of a many-to-one relationship between the different parameters and phase-coding efficiency. At the functional scale, involving the cellular-scale neural properties, our analyses revealed an important higher-order constraint that was exclusive to models exhibiting efficient phase coding. Specifically, we found a counterbalancing negative correlation between neuronal gain and the strength of external synaptic inputs as a critical functional constraint for the emergence of efficient phase coding. These observations implicate intrinsic neural properties as important contributors in effectuating such counterbalance, which can be achieved by recruiting nonunique parametric combinations. Finally, we show that a change in afferent statistics, manifesting as input asymmetry onto these neuronal models, induced an adaptive shift in the phase code that preserved its efficiency. Together, our analyses unveil parametric degeneracy as a mechanism to harness widespread neuron-to-neuron heterogeneity towards accomplishing stable and efficient encoding, provided specific higher-order functional constraints on the relationship of neural gain to external inputs are satisfied.

Developing an Understanding of Science

Young children are adept at several types of scientific reasoning, yet older children and adults have difficulty mastering formal scientific ideas and practices. Why do “little scientists” often become scientifically illiterate adults? We address this question by examining the role of intuition in learning science, both as a body of knowledge and as a method of inquiry. Intuition supports children's understanding of everyday phenomena but conflicts with their ability to learn physical and biological concepts that defy firsthand observation, such as molecules, forces, genes, and germs. Likewise, intuition supports children's causal learning but provides little guidance on how to navigate higher-order constraints on scientific induction, such as the control of variables or the coordination of theory and data. We characterize the foundations of children's intuitive understanding of the natural world, as well as the conceptual scaffolds needed to bridge these intuitions with formal science.