Binary Constraints Research Articles

Planar #CSP Equality Corresponds to Quantum Isomorphism – A Holant Viewpoint

Recently, Mančinska and Roberson proved that two graphs G and \(G^{\prime }\) are quantum isomorphic if and only if they admit the same number of homomorphisms from all planar graphs. We extend this result to planar #CSP with any pair of sets \(\mathcal {F}\) and \(\mathcal {F}^{\prime }\) of real-valued, arbitrary-arity constraint functions. Graph homomorphism is the special case, in which each of \(\mathcal {F}\) and \(\mathcal {F}^{\prime }\) contains a single symmetric 0-1-valued binary constraint function. Our treatment uses the framework of planar Holant problems. To prove that quantum isomorphic constraint function sets give the same value on any planar #CSP instance, we apply a novel form of holographic transformation of Valiant, using the quantum permutation matrix \(\mathcal {U}\) defining the quantum isomorphism. Due to the noncommutativity of \(\mathcal {U}\) ’s entries, it turns out that this form of holographic transformation is only applicable to planar Holant. To prove the converse, we introduce the quantum automorphism group \(Qut(\mathcal {F})\) of a set \(\mathcal {F}\) of constraint functions/tensors and characterize the intertwiners of \(Qut(\mathcal {F})\) as the signature matrices of planar \(\text{Holant}{\mathcal {F}\,|\,\mathcal {EQ})\) quantum gadgets. Then, we define a new notion of (projective) connectivity for constraint functions and reduce their arity while preserving their inclusion in the original intertwiner space. Finally, to address the challenges posed by generalizing from 0-1 valued to real-valued constraint functions, we adapt a technique of Lovász in the classical setting for isomorphisms of real-weighted graphs to the setting of quantum isomorphisms.

Evolving scientific discovery by unifying data and background knowledge with AI Hilbert

The discovery of scientific formulae that parsimoniously explain natural phenomena and align with existing background theory is a key goal in science. Historically, scientists have derived natural laws by manipulating equations based on existing knowledge, forming new equations, and verifying them experimentally. However, this does not include experimental data within the discovery process, which may be inefficient. We propose a solution to this problem when all axioms and scientific laws are expressible as polynomials and argue our approach is widely applicable. We model notions of minimal complexity using binary variables and logical constraints, solve polynomial optimization problems via mixed-integer linear or semidefinite optimization, and prove the validity of our scientific discoveries in a principled manner using Positivstellensatz certificates. We demonstrate that some famous scientific laws, including Kepler’s Law of Planetary Motion and the Radiated Gravitational Wave Power equation, can be derived in a principled manner from axioms and experimental data.

SBHA: Sensitive Binary Hashing Autoencoder for Image Retrieval.

Binary hashing is an effective approach for content-based image retrieval, and learning binary codes with neural networks has attracted increasing attention in recent years. However, the training of hashing neural networks is difficult due to the binary constraint on hash codes. In addition, neural networks are easily affected by input data with small perturbations. Therefore, a sensitive binary hashing autoencoder (SBHA) is proposed to handle these challenges by introducing stochastic sensitivity for image retrieval. SBHA extracts meaningful features from original inputs and maps them onto a binary space to obtain binary hash codes directly. Different from ordinary autoencoders, SBHA is trained by minimizing the reconstruction error, the stochastic sensitive error, and the binary constraint error simultaneously. SBHA reduces output sensitivity to unseen samples with small perturbations from training samples by minimizing the stochastic sensitive error, which helps to learn more robust features. Moreover, SBHA is trained with a binary constraint and outputs binary codes directly. To tackle the difficulty of optimization with the binary constraint, we train the SBHA with alternating optimization. Experimental results on three benchmark datasets show that SBHA is competitive and significantly outperforms state-of-the-art methods for binary hashing.

Encoding Constraints as Binary Constraint Networks Satisfying BTP

Recently, the Binary Constraint Tree (BCT), a tree structured Binary Constraint Network (BCN), has been shown to be more succinct than various ad-hoc constraints. In this paper, we investigate the modelling power of a well-known tractable hybrid class generalizing BCT, i.e. the class of BCNs satisfying Broken Triangle Property (BTP) called BTP Networks (BTPNs). We show that the consistency checker of BTPN can be computed by polysize monotone circuit, thus, some global constraints cannot be encoded as polysize BTPN, such as the AllDifferent and Linear constraints. Then our study reveals that BTPN is strictly more succinct than the DNNF constraint and all 14 ad-hoc constraints discussed in (Wang and Yap 2023), such as the context-free grammar, BCT and smart table constraints. Furthermore, we also show that BTPN is as powerful as DNNF in terms of computing various operations and queries. In addition, we prove that it is NP-hard to determine the minimum sized BTPN encoding a constraint.

Optimal classification trees with leaf-branch and binary constraints

Using empirical models to predict whether sections within pipes have defects can save inspection costs and, potentially, avoid oil spills. Optimal Classification Tree (OCT) formulations offer potentially desirable combinations of interpretability and prediction accuracy on unseen pipes. Approaches based on powerful state-of-the-art OCT formulations have enabled researchers to solve decision tree problems optimally instead of using traditional sub-optimal greedy approaches. Yet, the recently proposed formulations also have limitations. Some of the most recent formulations require a large number of decision variables and constraints leading to computational inefficiencies. Previous formulations have optimal solutions with undesirable or invalid tree structures which may depend on the particular software implementation. Additionally, some formulations always grow a full tree even when desirable parsimonious tree options are available. This article proposes the Modified Optimal Classification Tree (M-OCT) formulation with novel leaf-branch-interaction constraints, which could stabilize the previous formulation and reduce the chance of invalid tree structures when generating optimal trees. By incorporating the idea of binary encoding of thresholds from a previous article, we reduce the total number of binary variables. We then extend M-OCT to construct a novel formulation called Binary Node Penalty Optimal Classification Tree (BNP-OCT) with binary splits and node complexity constraints, which support efficiency in standard branch-and-cut solvers and prevents the overfitting issue when learning the optimal tree models. We compare the proposed methods with alternatives including standard formulations using 15 standard data sets. In addition, we use 750 test cases to compare the computational stability of pre-existing formulations to those involving the proposed leaf-branch constraints. We demonstrate that the proposed formulation offers advantages in accuracy, computational efficiency, and structural stability. We also describe how the proposed methods are able to achieve 94% classification accuracy on balanced test sets for unseen pipes.

On Enforcing Dyadic-type Homogeneous Binary Function Product Constraints in MatBase

Homogeneous binary function products are often encountered in the sub-universes modeled by databases, from genealogical trees to sports, from education to healthcare, etc. Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility. The (Elementary) Mathematical Data Model provides 17 dyadic-type homogeneous binary function product constraint types. MatBase, an intelligent data and knowledge base management system prototype, allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them. This paper describes the algorithms that MatBase uses for enforcing all these 17 homogeneous binary function product constraint types, which may also be used by developers not having access to MatBase.

A 1-bit DACs precoding for MU-MIMO based on binary equilibrium constraint: An alternating direction method

High power consumption is one of the main problems in the practical application of massive multi-user multi-input-multi-output (MU-MIMO) systems, and using 1-bit digital-to-analog converters (DACs) instead of high-resolution DACs is an effective way to reduce the power consumption of massive MU-MIMO systems. How to design efficient precoding schemes to improve the performance of 1-bit MU-MIMO systems has become a hot research field. This paper mainly studies the precoding problem of 1-bit DACs based on minimum mean squared error (MMSE). We first transform the non-convex constraints of the traditional optimization problem using binary equilibrium constraints. Then, to solve the transformed objective problem, we establish a framework based on the alternating direction method (ADM), use the fast projection gradient (FPG) method, and propose an alternating maximum minimum (AMM) algorithm to solve the optimization variables alternately. We have verified the convergence of the proposed algorithm and analyzed the accuracy of the proposed ADM framework and the computational complexity of the proposed algorithm in detail. In the simulation section, we analyze the uncoded bit error rate (BER) performance of the proposed algorithm in phase-shift keying (PSK) modulation and quadrature amplitude modulation (QAM) modes. The simulation results show that compared with existing advanced algorithms, the proposed algorithm can achieve performance advantages of about 1 dB and 2 dB in QPSK modulation mode and 16QAM modulation mode, respectively.

The NANOGrav 12.5 yr Data Set: A Computationally Efficient Eccentric Binary Search Pipeline and Constraints on an Eccentric Supermassive Binary Candidate in 3C 66B

The radio galaxy 3C 66B has been hypothesized to host a supermassive black hole binary (SMBHB) at its center based on electromagnetic observations. Its apparent 1.05 yr period and low redshift (∼0.02) make it an interesting testbed to search for low-frequency gravitational waves (GWs) using pulsar timing array (PTA) experiments. This source has been subjected to multiple searches for continuous GWs from a circular SMBHB, resulting in progressively more stringent constraints on its GW amplitude and chirp mass. In this paper, we develop a pipeline for performing Bayesian targeted searches for eccentric SMBHBs in PTA data sets, and test its efficacy by applying it to simulated data sets with varying injected signal strengths. We also search for a realistic eccentric SMBHB source in 3C 66B using the NANOGrav 12.5 yr data set employing PTA signal models containing Earth term-only as well as Earth+pulsar term contributions using this pipeline. Due to limitations in our PTA signal model, we get meaningful results only when the initial eccentricity e 0 < 0.5 and the symmetric mass ratio η > 0.1. We find no evidence for an eccentric SMBHB signal in our data, and therefore place 95% upper limits on the PTA signal amplitude of 88.1 ± 3.7 ns for the Earth term-only and 81.74 ± 0.86 ns for the Earth+pulsar term searches for e 0 < 0.5 and η > 0.1. Similar 95% upper limits on the chirp mass are (1.98 ± 0.05) × 109 and (1.81 ± 0.01) × 109 M ☉. These upper limits, while less stringent than those calculated from a circular binary search in the NANOGrav 12.5 yr data set, are consistent with the SMBHB model of 3C 66B developed from electromagnetic observations.

On the Parameterized Intractability of Determinant Maximization

In the Determinant Maximization problem, given an n×n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n \ imes n$$\\end{document} positive semi-definite matrix A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf {A}} $$\\end{document} in Qn×n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Q}^{n \ imes n}$$\\end{document} and an integer k, we are required to find a k×k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k \ imes k$$\\end{document} principal submatrix of A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf {A}} $$\\end{document} having the maximum determinant. This problem is known to be NP-hard and further proven to be W[1]-hard with respect to k by Koutis (Inf Process Lett 100:8–13, 2006); i.e., a f(k)nO(1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(k)n^{{{\\,\\mathrm{\\mathcal {O}}\\,}}(1)}$$\\end{document}-time algorithm is unlikely to exist for any computable function f. However, there is still room to explore its parameterized complexity in the restricted case, in the hope of overcoming the general-case parameterized intractability. In this study, we rule out the fixed-parameter tractability of Determinant Maximization even if an input matrix is extremely sparse or low rank, or an approximate solution is acceptable. We first prove that Determinant Maximization is NP-hard and W[1]-hard even if an input matrix is an arrowhead matrix; i.e., the underlying graph formed by nonzero entries is a star, implying that the structural sparsity is not helpful. By contrast, Determinant Maximization is known to be solvable in polynomial time on tridiagonal matrices (Al-Thani and Lee, in: LAGOS, 2021). Thereafter, we demonstrate the W[1]-hardness with respect to the rankr of an input matrix. Our result is stronger than Koutis’ result in the sense that any k×k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k \ imes k$$\\end{document} principal submatrix is singular whenever k>r\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k > r$$\\end{document}. We finally give evidence that it is W[1]-hard to approximate Determinant Maximization parameterized by k within a factor of 2-ck\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^{-c\\sqrt{k}}$$\\end{document} for some universal constant c>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c > 0$$\\end{document}. Our hardness result is conditional on the Parameterized Inapproximability Hypothesis posed by Lokshtanov et al. (in: SODA, 2020), which asserts that a gap version of Binary Constraint Satisfaction Problem is W[1]-hard. To complement this result, we develop an ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-additive approximation algorithm that runs in ε-r2·rO(r3)·nO(1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon ^{-r^2} \\cdot r^{{{\\,\\mathrm{\\mathcal {O}}\\,}}(r^3)} \\cdot n^{{{\\,\\mathrm{\\mathcal {O}}\\,}}(1)}$$\\end{document} time for the rank r of an input matrix, provided that the diagonal entries are bounded.

LCEMH: Label Correlation Enhanced Multi-modal Hashing for efficient multi-modal retrieval

Supervised multi-modal hashing can effectively improve the discriminative power of hash codes by leveraging semantic label information. However, most existing supervised multi-modal hashing models generally rely on discrete labels for supervision. They only provide limited guidance and may not fully capture the potential semantic similarity between multi-modal data. Moreover, the binary constraints of hash codes further restrict their ability to fully capture the rich semantic information embedded in the labels. To address these limitations, we propose a Label Correlation Enhanced Multi-modal Hashing (LCEMH) approach for efficient multi-modal retrieval. Specifically, our proposed model can effectively expand the inter-class boundaries of discrete labels to further enrich the supervision of similarity. Additionally, we directly transform the acquired richer label information into hash codes simply and effectively, thus retaining more comprehensive information in the labels with minimal quantization loss, and enhancing the discriminant ability of the generated hash codes. Experimental results on three public multimedia retrieval datasets demonstrate the superiority of LCEMH in performance. The source code of LCEMH is available online at: https://github.com/ChaoqunZheng/LCEMH.

Robust Data-Driven Automation Based on Relaxed Supervised Hashing With Self-Optimized Labels

Recently, the Visual Internet of Things (VIoT) has been widely used in data-driven automation, where VIoT devices are used to monitor environmental dynamics and to trigger corresponding actuators after examining event signatures (e.g., hashes). Nonetheless, VIoT devices may collect partially observed data, e.g., largely occluded images, which cause biased labeling and oversensitivity during modeling. Moreover, in typical methods, class labels are rigid and fixed categorical variables, where marginal space between different classes is fixed and equal. In fact, margins may be unequally spaced. Such nonflexibility in class labels inevitably causes fitting difficulty. In light of such, this study proposes relaxed robust supervised hashing (Relaxed RSH) for generating reliable signatures that can simultaneously conquer the above problems caused by incomplete data and rigid margins. To accommodate oversensitivity, this study proposes measuring hash learning loss by robust half quadratic (HQ) functions for modeling incomplete data. In the initial label matrix, slack variables are added to relax binary constraints. Such slack variables can be self-optimized during the learning process and can be used to automatically adjust margins between different classes. Decorrelation, balancing, and normalization constraints based on Relaxed RSH are also devised to provide discriminant and compact codes. Experimental results based on open datasets showed that the proposed method yielded higher mAP and F1 than the baselines. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the problems caused by incomplete data and rigid class margins during event signature (e.g., hash) learning, where hashes are used to trigger automation systems. In existing hashing methods, incomplete data (e.g., continuous occlusion, missing values, and sample-specific outliers) along with rigid class margins cause fitting biases, thereby challenging data-driven automation. This study proposes Relaxed RSH by designing robust HQ loss, self-optimized label learning, and corresponding constraints for generating discriminant hashes. This prevents actuators from being mistriggered by corrupted data. Experiments were conducted on various data corruption. Future research will address the design for incremental/decentralized hash learning.

Disperse Asymmetric Subspace Relation Hashing for Cross-Modal Retrieval

In cross-modal retrieval, the hashing technique has sparked a great revolution because of its competitive query speed and minimal storage. However, existing approaches may have critical limitations: 1) Label Intrinsic Relations. They barely explore category information inherent in labels and only consider labels as distinct entities, losing rich latent semantic information. 2) Modality-specific and Modality-coherence Semantics. They often construct a common subspace and an affinity matrix to learn modality-specific features and modality-coherence correlations, respectively. The former will lead to considerable quantization errors because the subspaces should be approximate rather than exactly equal. The latter is not scalable due to its high computational costs. 3) Non-relaxation Optimization Strategy. To solve constraints, some approaches relax the binary constraints to continuous, rising significant quantization errors. To mitigate these problems, we propose Disperse Asymmetric Subspace Relation Hashing, termed DASRH. In particular, it first embeds modality-specific kernel features into dispersed latent spaces, which can effectively fuse heterogeneous patterns. Additionally, it exploits fine-grained categories from labels by reconstructing collective semantic representations, making discriminative binary codes. Furthermore, it constructs an asymmetric consistent relation integration, preserving both inter-modal disparities and intra-class differences. In the optimization process, an effective alternative iterative optimization scheme is established. Theoretical analysis and comprehensive experiments highlight the advantages of our DASRH against cutting-edge technology.

A hybrid approach for unit commitment with splitting technique and local search

In the modern electricity market, solving the unit commitment (UC) problem becomes more challenging due to its large number of binary variables and coupling constraints. Therefore, the goal of this paper is to obtain nearly optimal solutions for such complex UC problems within specific time limits. To achieve this, a hybrid approach is presented in this paper, which incorporates a splitting technique and a local search for UC. The hybrid approach involves two steps. In the first step, the augmented Lagrange function (ALF) of UC is decomposed using a splitting technique based on the alternating direction method of multipliers (ADMM). The resulting sub-problems can be effectively solved in a distributed manner by utilizing Lagrange duality theory and binary variable characteristics. Additionally, the penalty parameters of the ALF are updated effectively with the sub-gradient method to diminish the influence of the initial penalty parameters on the algorithm. In the second step, the appropriate relaxation unit is selected using the binary variable characteristics in the current solution of ADMM. Further, the high-quality feasibility of the final solution is ensured through local search. The hybrid approach utilizes ADMM to quickly fix most binary variables in the UC model and then leverages the CPLEX solver to solve the mixed-integer linear programming (MILP) formulation of UC by fixing a large number of binary variables. Consequently, the CPLEX solver needs to branch fewer binary variables, reducing the local search time. The hybrid approach is applied to solve several power systems consisting of up to 1000 units. Compared with the CPLEX solver, the solution of the hybrid approach is found to be stable, and the relative gap of the solution is less than 1 %, demonstrating the effectiveness and performance of the proposed approach while meeting the time limit requirements of the power industry dispatching.

Deep Adaptive Quadruplet Hashing With Probability Sampling for Large-Scale Image Retrieval

With the preferable efficiency in storage and computation, hashing has shown potential application in large-scale multimedia retrieval. Compared with traditional hashing algorithms using hand-crafted characteristics, deep hashing inherits the representational capacity of deep neural networks to jointly learn semantic features and hash functions, encoding raw data into compact binary codes with significant discrimination. Generally, most of the current multi-wise hashing methods view the similarity margins between image pairs as constant values in training process. When the distance between sample pairs exceeds the fixed margin, the hashing network would not learn anything. Besides, available hashing methods commonly introduce the random sampling strategy to build training batches and ignore the sample distribution, which is harmful to parameter optimization. In this paper, we propose a novel Deep Adaptive Quadruplet Hashing with probability sampling (DAQH) for discriminative binary code learning. Specifically, with exploring the distribution relationship of raw samples, a non-uniform probability sampling strategy is proposed to build more informative and representative training batches, while maintaining the diversity of training samples. By introducing the prior similarity of sample pairs to calculate corresponding margins, an adaptive margin quadruplet loss is designed to dynamically preserve the underlying semantic relationships with its neighbors. To tune the attributes of binary codes, by combining quadruple regularization and orthogonality optimization, binary code constraint is developed to make the learned embedding with significant discrimination. Extensive experimental results on various benchmark datasets demonstrate our proposed DAQH framework achieves state-of-the-art visual similarity search performance.

The Binary Distributed Observer Approach to the Cooperative Output Regulation of Linear Multiagent Systems

In this note, the cooperative output regulation problem of general heterogeneous linear multi-agent systems with binary constraints is studied. To speed up the convergence rate, the binary distributed observer is proposed only utilizing sign of the relative state instead of using full relative information. Under some mild conditions, the binary distributed observer can estimate the state of the leader system exponentially in finite time sense. The leader system can generate various reference signals such as step functions, sinusoidal functions or their combinations. Furthermore, both state and output feedback control protocols are synthesized to solve the problem. An illustrative example is presented to support the feasibility of the proposed framework.

Task-Oriented Compact Representation of 3D Point Clouds via A Matrix Optimization-Driven Network

This paper explores the task-oriented compact representation of 3D point clouds, which should maintain the performance of subsequent applications applied to such compact point clouds as much as possible. Designing from the perspective of matrix optimization, we propose MOPS-Net, a novel deep learning-based method that is distinguishable from existing approaches due to its interpretability and flexibility. The matrix optimization problem is challenging due to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">discrete</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">combinatorial</i> nature of the sampling matrix. Therefore, we tackle the challenges by relaxing the binary constraint of the sampling matrix and formulating a constrained and differentiable optimization problem. We then design a deep neural network to mimic the matrix optimization by exploring both the local and global structures of the input data. MOPS-Net can be end-to-end trained with a task network and is permutation-invariant, making it robust to the input. We also extend MOPS-Net such that a single network after one-time training is capable of handling arbitrary downsampling ratios. Extensive experimental results show that MOPS-Net can achieve favorable performance against state-of-the-art deep learning-based methods over various tasks, including classification, reconstruction, and registration. Besides, we validate the robustness of MOPS-Net on noisy data.

A design of experiments based on the Normal‐boundary‐intersection method to identify optimum machine settings in manufacturing processes

AbstractFinding the appropriate machine settings for a given manufacturing process is an important issue in industrial production. A set of minimum and maximum machine settings correspond to the lower and upper quality limits that are specified for the produced product, and by this define the boundaries of all appropriate machine settings. This paper shows that these boundaries are the solution of a multi‐objective optimisation problem, which is called the optimum machine settings problem. However, for most processes there is no mathematical model of the manufacturing process available, which maps the setting parameters on the quality key figures in a way that allows to compute the optimisation problem. In this case, experiments may provide the required empirical data simultaneously while executing the optimisation procedure. Using a case study on heat sealing in industrial packaging, the paper shows, how to develop a design of experiments based on the Normal‐boundary‐intersection method (NBI), and how to generate the Pareto‐frontier by executing test according to this test plan. It addresses the specific limitations inherent in solving an optimisation problem by experiments. The behaviour of the method towards discrete and binary objectives and constraints is discussed.

Constraint reranking in diachronic OT: binary-feet and word-minimum phenomena in Austronesian

AbstractLanguages throughout the Malayo-Polynesian branch of Austronesian exhibit a range of sound changes which all appear to be triggered by the presence of a schwa in an open penultimate syllable. These changes are gemination of the final-syllable onset, deletion of penultimate schwa in three-or-more syllable words, and the shift of schwa to a full vowel in open penultimate syllables only. The changes are analyzed as a product of drift, whereby changes in daughter languages are motivated by some property of the proto-language. In this case, it is argued that schwa was a zero-mora vowel in Proto-Austronesian and Proto-Malayo-Polynesian, and that these changes worked to add a mora to a word which would otherwise contain a degenerate single-mora foot. The observed changes are then analyzed as a product of constraint promotion modeled in Diachronic Optimality Theory, whereby constraint movement over time may explain historical sound change. In the case of Malayo-Polynesian, it is shown that the promotion of the Binary Foot constraint (Ft-Bin) can explain all three of the attested schwa-triggered sound changes.

Bicriteria Sparse Nonnegative Matrix Factorization via Two-Timescale Duplex Neurodynamic Optimization.

In this article, sparse nonnegative matrix factorization (SNMF) is formulated as a mixed-integer bicriteria optimization problem for minimizing matrix factorization errors and maximizing factorized matrix sparsity based on an exact binary representation of l0 matrix norm. The binary constraints of the problem are then equivalently replaced with bilinear constraints to convert the problem to a biconvex problem. The reformulated biconvex problem is finally solved by using a two-timescale duplex neurodynamic approach consisting of two recurrent neural networks (RNNs) operating collaboratively at two timescales. A Gaussian score (GS) is defined as to integrate the bicriteria of factorization errors and sparsity of resulting matrices. The performance of the proposed neurodynamic approach is substantiated in terms of low factorization errors, high sparsity, and high GS on four benchmark datasets.

Weighted Sum-Rate Maximization in Multi-IRS-Aided Multi-Cell mmWave Communication Systems for Suppressing ICI

Intelligent reflecting surface (IRS) has been envisioned as a disruptive technology with the capability of reconfiguring the wireless transmission environment. Hence, the IRS is used to assist the communication system, however, the impacts of inter-cell interference (ICI) on cell-edge users are severe in multi-cell communications but have been ignored in most literature about IRS-assisted communication systems. In this paper, we consider the downlink transmission of cell-edge users in multi-cell millimeter wave (mmWave) communication systems with the aid of multiple IRSs deployed at the cell boundary. To suppress the ICI, we maximize the weighted sum-rate (WSR) by jointly optimizing the IRS-user association matrix, the transmit beamforming of mmWave base stations (MBSs), and the phase shifts of IRSs, subject to the power limits of MBSs, the reflection constraints of IRSs, and the association constraints. Then, a joint IRS-user association and beamforming algorithm with alternating optimization (AO) framework is developed to tackle the mixed-integer non-convex problem. Specifically, a simplified objective function with respect to the association variables is derived and the non-convex binary constraints are handled by the relaxation operation and the first-order Taylor expansion, while the arithmetic-geometric mean inequality (AGMI)-based rank-one relaxation algorithm and the ring-based penalty convex-concave procedure (CCP) method are proposed for obtaining the transmit beamforming matrix of MBSs and the phase shifts of IRSs, respectively. Simulation results demonstrate the superiority of the proposed algorithm over the benchmark schemes. The useful insights into the optimization of IRS-user association and design of the number of elements of IRSs are also presented for future networks.