Separation Constraints Research Articles

On maximum bipartite matching with separation

Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two vertices that are close to each other are not allowed to be matched simultaneously. We show that the problem is hard to approximate even for paths, and provide constant-factor approximation algorithms for both paths and grids.

Nominal Compounds in Old English Meter and Prosody

What is the lexicon’s role in licensing the selection of phonologically-marked structures in Old English verse? Specifically, what is its role in the avoidance of certain nominal compounds in verse, even though the same compounds are used apparently freely in prose (Terasawa 1994)? Using a simulation of the Old English lexicon, we offer a statistical analysis of the poetic use of nominal compounds compared to the availability of relevant prosodic structures in the ambient language. In the process, we unify Terasawa’s separate constraints and demonstrate a new way of addressing the complex interplay between Old English prosody and the structure of Old English alliterative meter. Our results endorse Terasawa’s position: We find that the dispreference for nominal compounds of the XX-LX type is a general but noncategorical property of Old English. We attribute their highly restricted usage in verse to the demands of poetic diction and their incompatibility with the metrical templates that scops and scribes replicate. Additionally, while syllable weight factors into metrical organization, it does so less for stress placement, which remains morphologically grounded; this asymmetry in the ranking value of weight between poetry and prose is considered briefly in the context of the Old English monastic scribal training.

Robust cooperative train trajectory optimization with stochastic delays under virtual coupling

AbstractVirtual coupling technology was recently proposed in railways, which separates trains by a relative braking distance (or even shorter distance) and moves trains synchronously to increase capacity at bottlenecks. This study proposes a real‐time cooperative train trajectory planning algorithm for coordinating train movements under virtual coupling by considering stochastic initial delays. The algorithm uses mixed‐integer programming models to estimate the delay propagation among trains, detect feasible coupled‐running locations, and optimize the trajectories of the two trains such that they coordinate their speeds to achieve energy‐efficient, punctual movements, as well as a safe coupled‐running process. A robust optimization method is proposed to capture the stochastic delays as an uncertainty set, which is reformulated to its dual problem. Case studies of planning train trajectories for the classical virtual‐coupling scenario suggest that (1) the coupled‐running distance is greatly affected by the coordination of train timetables, delays, and safe separation constraints at switches; (2) the coordination of train movements for a coupled‐running process imposes extra energy costs; and (3) the proposed method can detect feasible coupled‐running locations and produce cooperative speed profiles in short computational times.

Parallel MPC for Linear Systems With State and Input Constraints

This letter proposes a parallelizable algorithm for linear-quadratic model predictive control (MPC) problems with state and input constraints. The algorithm itself is based on a parallel MPC scheme that has originally been designed for systems with input constraints. In this context, one contribution of this letter is the construction of time-varying yet separable constraint margins ensuring recursive feasibility and asymptotic stability of sub-optimal parallel MPC in a general setting, which also includes state constraints. Moreover, it is shown how to tradeoff online run-time guarantees versus the conservatism that is introduced by the tightened state constraints. The corresponding performance of the proposed method as well as the cost of the recursive feasibility guarantees is analyzed in the context of controlling a large-scale mechatronic system. This is illustrated by numerical experiments for a large-scale control system with more than 100 states and 60 control inputs leading to run-times in the millisecond range.

ULD-Net: 3D unsupervised learning by dense similarity learning with equivariant-crop.

Although many recent deep learning methods have achieved good performance in point cloud analysis, most of them are built upon the heavy cost of manual labeling. Unsupervised representation learning methods have attracted increasing attention due to their high label efficiency. How to learn more useful representations from unlabeled 3D point clouds is still a challenging problem. Addressing this problem, we propose a novel unsupervised learning approach for point cloud analysis, named ULD-Net, consisting of an equivariant-crop (equiv-crop) module to achieve dense similarity learning. We propose dense similarity learning that maximizes consistency across two randomly transformed global-local views at both the instance level and the point level. To build feature correspondence between global and local views, an equiv-crop is proposed to transform features from the global scope to the local scope. Unlike previous methods that require complicated designs, such as negative pairs and momentum encoders, our ULD-Net benefits from the simple Siamese network that relies solely on stop-gradient operation preventing the network from collapsing. We also utilize the feature separability constraint for more representative embeddings. Experimental results show that our ULD-Net achieves the best results of context-based unsupervised methods and comparable performances to supervised models in shape classification and segmentation tasks. On the linear support vector machine classification benchmark, our ULD-Net surpasses the best context-based method spatiotemporal self-supervised representation learning (STRL) by 1.1% overall accuracy. On tasks with fine-tuning, our ULD-Net outperforms STRL under fully supervised and semisupervised settings, in particular, 0.1% accuracy gain on the ModelNet40 classification benchmark, and 0.6% medium intersection of union gain on the ShapeNet part segmentation benchmark.

Heterogeneous treatment effects analysis for social scientists: A review

Social scientists have long been interested in the varying responses to a specific intervention, motivating the enterprise of heterogeneous treatment effects (HTE) analysis. Over the past five decades, the rapid development of HTE methods, from conventional multiplicative interactions in linear models to explorations based on machine learning techniques, has been witnessed. This article presents a systematic review of major HTE methods, including multiplicative interaction modeling, generalized additive modeling, propensity-score-based methods, marginal treatment effect, separate LASSO constraints, causal trees, causal forests, Bayesian additive regression trees, and meta-learners (i.e., the S-learner, T-learner, X-learner, and R-learner). These methods, as described roughly in a chronological order to emphasize methodological developments, are addressed to highlight their respective strengths and limitations. Following an illustrative example, this article reflects on future methodological developments.

Hyperspectral image denoising and destriping based on sparse representation, graph Laplacian regularization and stripe low-rank property

During the acquisition of a hyperspectral image (HSI), it is easily corrupted by many kinds of noises, which limits the subsequent applications. For decades, numerous HSI denoising methods have been proposed. However, these methods rarely consider the stripe noise as an independent component, thus cannot effectively remove the stripe noise. In this paper, we propose a mixed noise removal algorithm to destripe an HSI by taking advantage of the low-rank property of stripe noise. In the meantime, sparse representation and graph Laplacian regularization are utilized to remove Gaussian and sparse noise. Roughly speaking, the sparse representation helps achieve the approximation of the original image. A graph Laplacian regularization term can ensure the non-local spatial similarity of an HSI. Separate constraints on the sparse coefficient matrix and stripe noise components can help remove different types of noises. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed method for HSI restoration.

Online cooperative airspace conflict resolution of unmanned aerial vehicles by space mapping based iterative search method

This paper presents an investigation into the locally centralized conflict resolution problem of unmanned aerial vehicles (UAVs), in which the headings are adjustable variables. Firstly, the geometric characteristics of the conflict resolution problem in two-dimensional space are studied, and the problem is reduced into a nonlinear programing model. Secondly, the nonlinear safe separation constraint is transferred into linear style in the sine value space using the space mapping method. The feasible region of two conflict-related UAVs is transformed into a half-space in the sine value space. The minimum adjustment vector and the maximum adjustable vector are obtained in this space. Thirdly, to search for the local optimal conflict-free solution, a two-layered optimization method is given. In the first layer, feasible conflict-free solutions are obtained by iterative search in virtue of the minimum adjustment vector and the maximum adjustable vector. In the second layer, the local optimal solution is generated using the sequential quadratic programing (SQP) method. The effectiveness of the proposed method is verified by numerical simulations. Compared with the existing geometric guidance theory based methods, the proposed method could effectively generate conflict-free solutions that lead to fewer detours, through which UAVs could coordinate online in highly crowded airspace.

Explicit Solutions to the 3D Incompressible Euler Equations in Lagrangian Formulation

We introduce many families of explicit solutions to the three dimensional incompressible Euler equations for nonviscous fluid flows using the Lagrangian framework. Almost no exact Lagrangian solutions exist in the literature prior to this study. We search for solutions where the time component and the spatial component are separated, applying the same ideas we used previously in the two dimensional case. We show a general method to derive separate constraint equations for the spatial component and the time component. Using this provides us with a plenty of solution sets exhibiting several different types of fluid behaviour, but since they are computationally heavy to analyze, we have to restrict deeper analysis to the most interesting cases only. It is also possible and perhaps even probable that there exist more solutions of the separation of variables type beyond what we have found.

Peter Bergmann on observables in Hamiltonian General Relativity: A historical-critical investigation

The problem of observables and their supposed lack of change has been significant in Hamiltonian quantum gravity since the 1950s. This paper considers the unrecognized variety of ideas about observables in the thought of constrained Hamiltonian dynamics co-founder Peter Bergmann, who trained many students at Syracuse and invented observables. Whereas initially Bergmann required a constrained Hamiltonian formalism to be mathematically equivalent to the Lagrangian, in 1953 Bergmann and Schiller introduced a novel postulate, motivated by facilitating quantum gravity. This postulate held that observables were invariant under transformations generated by each individual first-class constraint. While modern works rely on Bergmann's authority and sometimes speak of “Bergmann observables,” he had much to say about observables, generally interesting and plausible but not all mutually consistent and much of it neglected.On occasion he required observables to be locally defined (not changeless and global); at times he wanted observables to be independent of the Hamiltonian formalism (implicitly contrary to a definition involving separate first-class constraints). But typically he took observables to have vanishing Poisson bracket with each first-class constraint and took this result to be justified by the example of electrodynamics. He expected observables to be analogous to the transverse true degrees of freedom of electromagnetism. Given these premises, there is no coherent concept of observables which he reliably endorsed, much less established.A revised definition of observables that satisfies the requirement that equivalent theories should have equivalent observables using the Rosenfeld–Anderson–Bergmann–Castellani gauge generator G, a tuned sum of first-class constraints that changes the canonical action ∫dt(pq̇−H) by a boundary term. Bootstrapping from theory formulations with no first-class constraints, one finds that the “external” coordinate gauge symmetry of GR calls for covariance (a transformation rule and hence a 4-dimensional Lie derivative for the Poisson bracket), not invariance (0 Poisson bracket), under G (not each first-class constraint separately).

Gradient-echo-train-based sub-millisecond periodic event encoded dynamic imaging with random (k, t)-space undersampling: k-t get-SPEEDI.

PurposeThe gradient‐echo‐train‐based Sub‐millisecond Periodic Event Encoded Dynamic Imaging (get‐SPEEDI) technique provides ultrahigh temporal resolutions (∼0.6 ms) for detecting rapid physiological activities, but its practical adoption can be hampered by long scan times. This study aimed at developing a more efficient variant of get‐SPEEDI for reducing the scan time without degrading temporal resolution or image quality.MethodsThe proposed pulse sequence, named k‐t get‐SPEEDI, accelerated get‐SPEEDI acquisition by undersampling the k‐space phase‐encoding lines semi‐randomly. At each time frame, k‐space was fully sampled in the central region whereas randomly undersampled in the outer regions. A time‐series of images was reconstructed using an algorithm based on the joint partial separability and sparsity constraints. To demonstrate the performance of k‐t get‐SPEEDI, images of human aortic valve opening and closing were acquired with 0.6‐ms temporal resolution and compared with those from conventional get‐SPEEDI.Resultsk‐t get‐SPEEDI achieved a 2‐fold scan time reduction over the conventional get‐SPEEDI (from ∼6 to ∼3 min), while achieving comparable SNRs and contrast‐to‐noise ratio (CNRs) for visualizing the dynamic process of aortic valve: SNR/CNR ≈ 70/38 vs. 73/39 in the k‐t and conventional get‐SPEEDI scans, respectively. The time courses of aortic valve area also matched well between these two sequences with a correlation coefficient of 0.86.ConclusionsThe k‐t get‐SPEEDI pulse sequence was able to half the scan time without compromising the image quality and ultrahigh temporal resolution. Additional scan time reduction may also be possible, facilitating in vivo adoptions of SPEEDI techniques.

Multicriteria Optimization for Dynamic Demers Cartograms.

Cartograms are popular for visualizing numerical data for administrative regions in thematic maps. When there are multiple data values per region (over time or from different datasets) shown as animated or juxtaposed cartograms, preserving the viewer's mental map in terms of stability between multiple cartograms is another important criterion alongside traditional cartogram criteria such as maintaining adjacencies. We present a method to compute stable stable Demers cartograms, where each region is shown as a square scaled proportionally to the given numerical data and similar data yield similar cartograms. We enforce orthogonal separation constraints using linear programming, and measure quality in terms of keeping adjacent regions close (cartogram quality) and using similar positions for a region between the different data values (stability). Our method guarantees the ability to connect most lost adjacencies with minimal-length planar orthogonal polylines. Experiments show that our method yields good quality and stability on multiple quality criteria.

A Multi-Criteria Allocation Strategy for Provisioning Cloud Resources

The adoption of the Business Process outsourcing strategy has been accentuated with the advent of Cloud computing that brings a new model for consuming and paying resources. Nevertheless, companies hesitate between a high distribution allowing to combine several Cloud offers adapted for process fragments and guarantee a good level of obfuscation or a weak distribution to minimize the data transfer which is charged by most suppliers and which may slow down the execution of processes. Hence, this paper proposes a novel selection method based on a heuristic algorithm that aims to find the right balance by optimizing the cost and performance while ensuring the protection of outsourced processes. To this end, several criteria are considered such as data transfer, task separation constraints and tolerated delay margins. The results obtained through a case study and comparisons with other selection methods show that the configurations selected by the algorithm meet companies’ requirements and are at the same time inexpensive, efficient and secure.

Non-negative matrix factorization improves the efficiency of recording frequency-following responses in normal-hearing adults and neonates

Objective One challenge in extracting the scalp-recorded frequency-following response (FFR) is related to its inherently small amplitude, which means that the response cannot be identified with confidence when only a relatively small number of recording sweeps are included in the averaging procedure. Design This study examined how the non-negative matrix factorisation (NMF) algorithm with a source separation constraint could be applied to improve the efficiency of FFR recordings. Conventional FFRs elicited by an English vowel/i/with a rising frequency contour were collected. Study sample: Fifteen normal-hearing adults and 15 normal-hearing neonates were recruited. Results The improvements of FFR recordings, defined as the correlation coefficient and root-mean-square differences across a sweep series of amplitude spectrograms before and after the application of the source separation NMF (SSNMF) algorithm, were characterised through an exponential curve fitting model. Statistical analysis of variance indicated that the SSNMF algorithm was able to enhance the FFRs recorded in both groups of participants. Conclusions Such improvements enabled FFR extractions in a relatively small number of recording sweeps, and opened a new window to better understand how speech sounds are processed in the human brain. KEYWORDS

An integrated rolling horizon and adaptive-refinement approach for disjoint trajectories optimization

Planning for multiple commodities simultaneously is a challenging task arising in divers applications, including robot motion or various forms of traffic management. Separation constraints between commodities frequently have to be considered to ensure safe trajectories, i.e., paths over time. Discrete decisions to ensure at least one of often multiple possible separation conditions renders planning of best possible continuous trajectories even more complex. Hence, the resulting disjoint trajectories optimization problems are mostly solved sequentially or with restricted planning space, potentially leading to losses in the usage of sparse resources and system capacities. To tackle these drawbacks, we develop a graph-based model for disjoint trajectories optimization with general separation requirements. We present a novel technique to derive a discretization for the full available space of motion. This can depict arbitrary, potentially non-convex, restricted areas. This necessitates solving an integer linear optimization program whose size scales with the number of discretization points. Thus, even for moderately sized instances a sufficiently detailed representation of space and time leads to models too large for state of the art hard- and software. To overcome this issue, we develop an adaptive-refinement algorithm: Starting from an optimal solution to the integer program in a coarse discretization, the algorithm re-optimizes trajectories in an adaptively-refined discretized neighborhood of the current solution. This is further integrated into a rolling horizon approach. We apply our approach to the integrated trajectory optimization and runway scheduling in the surrounding of airports. Computational experiments with realistic instances demonstrate the efficiency of the method.

Mountain railway alignment optimization integrating layouts of large‐scale auxiliary construction projects

AbstractMountain railway alignment design is an important but complex civil engineering problem. To overcome the drastically undulating terrain, long tunnels and high bridges are major structures used along a mountain railway, which poses great challenges for railway design and construction. Unfortunately, despite being studied for many years, the crucial construction factors of complex structures have received slight attention in alignment optimization. In this paper, for the first time, the layout of large‐scale auxiliary construction projects (LACPs), including tunnel shafts and access roads, is incorporated into the alignment design process in order to consider construction practicability and economy. Primarily, an alignment–LACPs concurrent optimization model is built. After defining the comprehensive design variables, the alignment–LACPs total construction cost is formulated as the objective function. Besides, the separate constraints for designing the alignment and LACPs are considered. Also, a construction duration computation is proposed for constraining the alignment–LACPs integration. To solve the model, a four‐step hybrid solution method is developed. Specifically, the alignment is first generated with a particle swarm optimization (PSO). Afterward, a new divide and conquer approach is devised to search for shaft alternatives along the alignment. Then, a customized Dijkstra algorithm is developed to search for complex access roads. Finally, a novel polynomial mechanism for time‐varying acceleration coefficients (TVAC) is designed for PSO to evolve the alignment–LACPs solutions. The above model and methods have been applied to two complex actual mountain railway examples. Their effectiveness is demonstrated through detailed analysis of resulting railway solutions and control experiments with contemporary TVAC‐based methods.

Multi-Beam Multi-Hop Routing for Intelligent Reflecting Surfaces Aided Massive MIMO

Intelligent reflecting surface (IRS) is envisioned to play a significant role in future wireless communication systems as an effective means of reconfiguring the radio signal propagation environment. In this paper, we study a new multi-IRS aided massive multiple-input multiple-output (MIMO) system, where a multi-antenna BS transmits independent messages to a set of remote single-antenna users using orthogonal beams that are subsequently reflected by different groups of IRSs via their respective multi-hop passive beamforming over pairwise line-of-sight (LoS) links. We aim to select optimal IRSs and their beam routing path for each of the users, along with the active/passive beamforming at the BS/IRSs, such that the minimum received signal power among all users is maximized. This problem is particularly difficult to solve due to a new type of path separation constraints for avoiding the IRS-reflected signal induced interference among different users. To tackle this difficulty, we first derive the optimal BS/IRS active/passive beamforming solutions based on their practical codebooks given the reflection paths. Then we show that the resultant multi-beam multi-hop routing problem can be recast as an equivalent graph-optimization problem, which is however NP-complete. To solve this challenging problem, we propose an efficient recursive algorithm to partially enumerate the feasible routing solutions, which is able to effectively balance the performance-complexity trade-off. Numerical results demonstrate that the proposed algorithm achieves near-optimal performance with low complexity and outperforms other benchmark schemes. Useful insights into the optimal multi-beam multi-hop routing design are also drawn under different setups of the multi-IRS aided massive MIMO network.

On Landscape of Nonconvex Regularized Least Squares for Sparse Support Recovery

Exact sparse support recovery from noisy deterministic Fourier measurements is studied in this paper. The ideal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{0}$</tex-math></inline-formula> -regularized least squares (LS) program is known to have strict local minimizers for multiple sparse supports. By applying a specific non-convex surrogate of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{0}$</tex-math></inline-formula> -regularizer, we show that, under certain conditions, the set of local minimizers with particularly separated supports is a singleton. Thus, any converging algorithms that can enforce the corresponding separation constraint will lead to the true support as the unique solution. In this regard, we construct a novel optimal mapping operator that can fulfill the separation condition, and several empirically effective algorithms are developed. The simulation results demonstrate the theoretical claims made in this paper.

Separable Coupled Dictionary Learning for Large-Scene Precise Classification of Multispectral Images

Large-scene precise classification of multispectral images (MSIs) has become one of the hot topics in remote sensing field. MSIs usually have wide swath and a meter or even submeter level of spatial resolution, which make large-scene observation possible. However, the limited number of spectral bands leads to the confusion of land covers in classification, especially for the large-scene conditions with abundant land cover types. Therefore, overlapped hyperspectral images (HSIs) can be used to improve the precision degree of classification. To achieve this purpose, coupled dictionary learning has been proposed as a major means. Aiming at separating the class-specific characteristics and mutual patterns among different land covers, this paper proposed a separable coupled dictionary learning (SCDL) method, which converts the separation of mutual features into the construction of separable coupled dictionaries and learns both class-specific coupled dictionaries and mutual coupled dictionaries simultaneously with the aid of label information. More specifically, the proposed method uses the labels of training samples to construct class-specific reconstruction error constraint, class-specificity constraint and separable dictionary incoherence constraint as regularization terms, to make sure that the learned coupled dictionaries to be both compact and discriminative. The learned separable coupled dictionaries facilitate pixels belong to the same category to be represented by the mutual dictionary and the class-specific sub-dictionary of corresponding class. The experiments compared with several state-of-the-art methods on three pairs of HSI and MSI have shown better classification performance.

Decentralized Trajectory Optimization for Multiple UASs under Uncertainty of Intent and Wind

To guarantee the operational safety of unmanned aircraft systems (UASs) in short time scales, it is important to adopt the systems for planning conflict-free trajectories which are robust against the uncertainty of the tactical flight intent of neighboring UASs and the wind conditions. Thus, the present paper proposes a new decentralized trajectory optimization method that enables to track the strategic four-dimensional trajectories as much as possible while maintaining the necessary separation from the neighboring UASs under the above-stated uncertainty. The proposed method adopts a fully decentralized formulation for separation constraints which is enabled by the worst-case estimate of the uncertainty of the neighboring UAS's decision and wind. The effectiveness of the method is demonstrated through numerical simulations.