Binary Constraints Research Articles

A Framework for One-Bit and Constant-Envelope Precoding Over Multiuser Massive MISO Channels

Consider the following problem: A multi-antenna base station (BS) sends multiple symbol streams to multiple single-antenna users via precoding. However, unlike conventional multiuser precoding, the transmitted signals are subjected to binary, unit-modulus, or even discrete unit-modulus constraints. Such constraints arise in the one-bit and constant-envelope (CE) massive MIMO scenarios, wherein high-resolution digital-to-analog converters (DACs) are replaced by one-bit DACs and phase shifters, respectively, for cutting down hardware cost and energy consumption. Multiuser precoding under one-bit and CE restrictions poses significant design difficulty. In this paper we establish a framework for designing multiuser precoding under the one-bit, continuous CE and discrete CE scenarios---all within one theme. We first formulate a precoding design that focuses on minimizations of symbol-error probabilities (SEPs), assuming quadrature amplitude modulation (QAM) constellations. We then devise an algorithm for our SEP-based design. The algorithm combines i) a novel penalty method for handling binary, unit-modulus and discrete unit-modulus constraints; and ii) a first-order non-convex optimization recipe custom-built for the design. Specifically, the latter is an inexact majorization-minimization method via accelerated projected gradient, which, as shown by simulations, runs very fast and can handle a large number of decision variables. Simulation results indicate that the proposed design offers significantly better bit-error rate performance than the existing designs.

Binary constraint satisfaction problems defined by excluded topological minors

The binary Constraint Satisfaction Problem (CSP) is to decide whether there exists an assignment to a set of variables which satisfies specified constraints between pairs of variables. A binary CSP instance can be presented as a labelled graph encoding both the forms of the constraints and where they are imposed. We consider subproblems defined by restricting the allowed form of this graph. One type of restriction is to forbid certain specified substructures (patterns). This captures some tractable classes of the CSP, but does not capture classes defined by language restrictions, or the well-known structural property of acyclicity.We extend the notion of pattern and introduce the notion of a topological minor of a binary CSP instance. By forbidding a finite set of patterns from occurring as topological minors we obtain a compact mechanism for expressing novel tractable subproblems of the CSP, including new generalisations of the class of acyclic instances.

The Morita Theory of Quantum Graph Isomorphisms

We classify instances of quantum pseudo-telepathy in the graph isomorphism game, exploiting the recently discovered connection between quantum information and the theory of quantum automorphism groups. Specifically, we show that graphs quantum isomorphic to a given graph are in bijective correspondence with Morita equivalence classes of certain Frobenius algebras in the category of finite-dimensional representations of the quantum automorphism algebra of that graph. We show that such a Frobenius algebra may be constructed from a central type subgroup of the classical automorphism group, whose action on the graph has coisotropic vertex stabilisers. In particular, if the original graph has no quantum symmetries, quantum isomorphic graphs are classified by such subgroups. We show that all quantum isomorphic graph pairs corresponding to a well-known family of binary constraint systems arise from this group-theoretical construction. We use our classification to show that, of the small order vertex-transitive graphs with no quantum symmetry, none is quantum isomorphic to a non-isomorphic graph. We show that this is in fact asymptotically almost surely true of all graphs.

Uplift Allocation of Voltage and Local Reliability Constraints

Centralized electricity markets currently do not optimize reactive power and voltage in the market clearing software. Voltage and local reliability (VLR) commitment requirements are mostly identified through out of market operational procedures. Failure to maintain VLR may incur voltage collapse, generation, transformer loss, or even blackout. Midcontinent Independent System Operator (MISO) employs binary constraints, minimum/maximum generation constraints, interface constraints, and manual commitments to address VLR requirement in the market clearing process and ensure adequate commitment for reliability. This paper integrates binary VLR constraints in day-ahead security constrained unit commitment to improve market efficiency. However, VLR constraints may cause uplift cost, and sometimes the associated uplift cost can be significant. An uplift cost allocation method with the consideration of resources commitment reasons is developed in this paper. The proposed approach is considered for implementation in MISO market clearing process and a MISO test case is used to validate the effectiveness of the proposed approach.

Dual-UAV-Enabled Secure Communications: Joint Trajectory Design and User Scheduling

In this paper, we investigate a novel unmanned aerial vehicle (UAV)-enabled secure communication system. Two UAVs are applied in this system where one UAV moves around to communicate with multiple users on the ground using orthogonal time-division multiple access while the other UAV in the area jams the eavesdroppers on the ground to protect communications of the desired users. Specifically, we maximize the minimum worst-case secrecy rate among the users within each period by jointly adjusting UAV trajectories and user scheduling under the maximum UAV speed constraints, the UAV return constraints, the UAV collision avoidance constraints, and the discrete binary constraints on user scheduling variables. Since the resulting optimization problem is very difficult to solve due to its highly nonlinear objective function and nonconvex constraints, we first equivalently transform it into a more tractable problem. In particular, the binary constraints are equivalently converted to a number of equality constraints. Then, we develop a novel joint optimization algorithm to handle the converted problem. In order to further improve the secrecy rate performance, we also extend the developed algorithm to the case with multiple jamming UAVs. The simulation results show that the proposed joint optimization algorithm achieves significantly better performance than the conventional algorithms.

Classically and Asteroseismically Constrained 1D Stellar Evolution Models of α Centauri A and B Using Empirical Mixing Length Calibrations

Abstract The bright, nearby binary α Centauri provides an excellent laboratory for testing stellar evolution models, because it is one of the few stellar systems for which we have high-precision classical (mass, radius, luminosity) and asteroseismic (p-mode) observations. Stellar models are created and fit to the classical and seismic observations of both stars by allowing for the free variation of the convective mixing length parameter α MLT. This system is modeled using five different sets of assumptions about the physics governing the stellar models. There are 31 pairs of tracks (out of ∼150,000 generated) that fit the classical, binary, and seismic observational constraints of the system within 3σ. Models with each tested choice of input physics are found to be viable, but the optimal mixing lengths for α Cen A and α Cen B remain the same regardless of the physical prescription. The optimal mixing lengths are α MLT,A/α ⊙ = 0.932 and α MLT,B/α ⊙ = 1.095. That α Cen A and α Cen B require subsolar and supersolar mixing lengths, respectively, to fit the observations is a trend consistent with recent findings, such as those of Kervella et al., Joyce & Chaboyer, and Viani et al. The optimal models find an age for α Centauri of 5.3 ± 0.3 Gyr.

A Bayesian framework for molecular strain identification from mixed diagnostic samples

We provide a mathematical formulation and develop a computational framework for identifying multiple strains of microorganisms from mixed samples of DNA. Our method is applicable in public health domains where efficient identification of pathogens is paramount, e.g. for the monitoring of disease outbreaks. We formulate strain identification as an inverse problem that aims at simultaneously estimating a binary matrix (encoding presence or absence of mutations in each strain) and a real-valued vector (representing the mixture of strains) such that their product is approximately equal to the measured data vector. The problem at hand has a similar structure to blind deconvolution, except for the presence of binary constraints, which we enforce in our approach. Following a Bayesian approach, we derive a posterior density. We present two computational methods for solving the non-convex maximum a posteriori estimation problem. The first one is a local optimization method that is made efficient and scalable by decoupling the problem into smaller independent subproblems, whereas the second one yields a global minimizer by converting the problem into a convex mixed-integer quadratic programming problem. The decoupling approach also provides an efficient way to integrate over the posterior. This provides useful information about the ambiguity of the underdetermined problem and, thus, the uncertainty associated with numerical solutions. We evaluate the potential and limitations of our framework in silico using synthetic and experimental data with available ground truths.

Quadratic Combinatorial Optimization Using Separable Underestimators

Binary programs with a quadratic objective function are NP-hard in general, even if the linear optimization problem over the same feasible set is tractable. In this paper, we address such problems by computing quadratic global underestimators of the objective function that are separable but not necessarily convex. Exploiting the binary constraint on the variables, a minimizer of the separable underestimator over the feasible set can be computed by solving an appropriate linear minimization problem over the same feasible set. Embedding the resulting lower bounds into a branch-and-bound framework, we obtain an exact algorithm for the original quadratic binary program. The main practical challenge is the fast computation of an appropriate underestimator, which in our approach reduces to solving a series of semidefinite programs. We exploit the special structure of the resulting problems to obtain a tailored coordinate-descent method for their solution. Our extensive experimental results on various quadratic combinatorial optimization problems show that our approach outperforms both CPLEX and the related QCR method as well as the SDP-based software BiqCrunch on instances of the quadratic shortest path problem and the quadratic assignment problem.

Solving the patient appointment scheduling problem in outpatient chemotherapy clinics using clustering and mathematical programming

Abstract The patient appointment scheduling problem in outpatient chemotherapy clinics is one of the most important and challenging problems due to large numbers of binary variables and thus unrealistic computation times. In this paper, we propose a new approach inspired from cellular manufacturing to reduce the number of binary variables and constraints. The proposed approach consists of two stages: the clustering stage and the mathematical programming stage. In the clustering stage, current clustering algorithms are used to find the optimum cluster members for a given patient mix. The resulted clusters are used in the second stage, namely the mathematical programming stage to optimally assign every nurse to a cluster of patients and a group of chairs at the optimum time slot. The objective function of the mathematical programming model is to achieve the minimum total completion time of all treatments. Compared to the previous models, the proposed approach has the advantage of giving the optimum solution for real problems in much fewer computation time. Another advantage is that a nurse is assigned to each cluster of patients along their treatment durations instead of assigning a nurse just to start up the treatment.

Parameter-Free <inline-formula> <tex-math notation="LaTeX">$\ell_p$ </tex-math> </inline-formula>-Box Decoding of LDPC Codes

The alternating direction method of multipliers (ADMMs) decoding of low-density parity-check codes has received many attentions due to its excellent performance at the error floor region. In this letter, we develop a parameter-free decoder based on linear program decoding by replacing the binary constraint with the intersection of a box and an $\ell _{p}$ sphere. An efficient $\ell _{2}$ -box ADMM is designed to handle this model in a distributed fashion. Numerical experiments demonstrate that our decoder attains better adaptability to different signal-to-noise ratio and channels.

Binary image deblurring with automatic binary value estimation

We propose a total variation-based variational model for nonblind binary image deblurring. The binary constraint is considered using the double-well function as the penalty term. We show the existence of a minimizer for the proposed model. By using operator splitting and alternating split Bregman, we get an effective numerical algorithm for the proposed model. Different from the existing methods in which the binary values are assumed to be known, our method can estimate the binary values automatically in the iteration process. Numerical results and comparisons demonstrate that the proposed algorithm is promising.

Masculine exposure: Transgressive representations of the male nude in contemporary dance and editorial fashion photography

Abstract The male body as subject/object has taken various forms across artistic disciplines, cultures and points throughout history. Previously, the image of a virile, muscled Adonis prevailed as an idealized hegemonic masculinity. A look at contemporary visual and performing arts of the twenty-first century reveals a progressive shift towards a more inclusive range of multiple masculinities and representations of maleness, queering conventional depictions of the male form. This creative interrogation of normative gender expression on the stage and screen and in print has the potential to challenge binary constraints on gender and expand the visibility of queer, marginalized expressions of masculinity. This article employs queer gaze theory and close readings of performance as text to examine works by fashion photographer Steven Klein and choreographer John Jasperse to evaluate how the personal history, creative methodology and artistic outlook of each contemporary artist play a role in questioning traditional masculine representations via the transgressive nude male body.

Deep Discrete Cross-Modal Hashing for Cross-Media Retrieval

Cross-modal hashing has drawn increasing research interests in multimedia retrieval due to the explosive growth of multimedia big data. It is such a challenging topic due to the heterogeneity gap and high storage cost. However, most of the previous methods based on conventional linear projections and relaxation scheme fail to capture the nonlinear relationship among samples and suffers from large quantization loss, which result in an unsatisfactory performance of cross-modal retrieval. To address these issues, this paper is dedicated to learning discrete nonlinear hash functions by deep learning. A novel framework of cross-modal deep neural networks is proposed to learn binary codes directly. We formulate the similarity preserving in the framework, and also bit-independent as well as binary constraints are imposed on the hash codes. Specifically, we consider intra-modality similarity preserving at each hidden layer of the networks. Inter-modality similarity preserving is formulated by the output of each individual network. By so doing, the cross correlation can be encoded into the network training (i.e. hash functions learning) by back propagation algorithm. The final objective is solved by alternative optimization in an iterative fashion. Experimental results on four datasets i.e. NUS-WIDE, MIR Flickr, Pascal VOC, and LabelMe demonstrate the effectiveness of the proposed method, which is significantly superior to state-of-the-art cross-modal hashing approaches.

Optimization for Roads' Construction: Selection, Prioritization, and Scheduling

AbstractLimited resources (budget, labor, machinery) have a significant toll on the roads' construction. The question of interest is: given variations of resources over a lengthy construction time, what would be the best construction scheduling plan, or how to optimize the Gantt chart while considering two highly challenging features (1) prerequisite conditions and (2) the interdependency of the benefit of the projects’ completions. We formulate it as a bilevel problem where the objective function is to minimize generalized costs and the lower level accounts for the drivers’ route choice. We employ a solution algorithm based on a supervised learning technique (a linear regression model of machine‐learning) and an integer programming problem and it is applied to the datasets of Winnipeg and Chicago. The regression model was found to be a tight approximation which resulted in an efficient algorithm (the CPU time is almost a linear function of the number of iterations). Moreover, the proposed methodology can render promising results (at least locally optimal solutions). This article is the first to formulate the Gantt chart using linear binary constraints and optimize it tailored to real‐life case studies.

A GPU-Outperforming FPGA Accelerator Architecture for Binary Convolutional Neural Networks

FPGA-based hardware accelerators for convolutional neural networks (CNNs) have received attention due to their higher energy efficiency than GPUs. However, it is challenging for FPGA-based solutions to achieve a higher throughput than GPU counterparts. In this article, we demonstrate that FPGA acceleration can be a superior solution in terms of both throughput and energy efficiency when a CNN is trained with binary constraints on weights and activations. Specifically, we propose an optimized fully mapped FPGA accelerator architecture tailored for bitwise convolution and normalization that features massive spatial parallelism with deep pipelines stages. A key advantage of the FPGA accelerator is that its performance is insensitive to data batch size, while the performance of GPU acceleration varies largely depending on the batch size of the data. Experiment results show that the proposed accelerator architecture for binary CNNs running on a Virtex-7 FPGA is 8.3× faster and 75× more energy-efficient than a Titan X GPU for processing online individual requests in small batch sizes. For processing static data in large batch sizes, the proposed solution is on a par with a Titan X GPU in terms of throughput while delivering 9.5× higher energy efficiency.

SqueezedText: A Real-Time Scene Text Recognition by Binary Convolutional Encoder-Decoder Network

A new approach for real-time scene text recognition is proposed in this paper. A novel binary convolutional encoder-decoder network (B-CEDNet) together with a bidirectional recurrent neural network (Bi-RNN). The B-CEDNet is engaged as a visual front-end to provide elaborated character detection, and a back-end Bi-RNN performs character-level sequential correction and classification based on learned contextual knowledge. The front-end B-CEDNet can process multiple regions containing characters using a one-off forward operation, and is trained under binary constraints with significant compression. Hence it leads to both remarkable inference run-time speedup as well as memory usage reduction. With the elaborated character detection, the back-end Bi-RNN merely processes a low dimension feature sequence with category and spatial information of extracted characters for sequence correction and classification. By training with over 1,000,000 synthetic scene text images, the B-CEDNet achieves a recall rate of 0.86, precision of 0.88 and F-score of 0.87 on ICDAR-03 and ICDAR-13. With the correction and classification by Bi-RNN, the proposed real-time scene text recognition achieves state-of-the-art accuracy while only consumes less than 1-ms inference run-time. The flow processing flow is realized on GPU with a small network size of 1.01 MB for B-CEDNet and 3.23 MB for Bi-RNN, which is much faster and smaller than the existing solutions.

Comprehensive smart home energy management system using mixed-integer quadratic-programming

Handling of varying energy sources and flexible connection to smart grids is a current challenge. Minimizing the overall monetary cost and maximizing the use of renewable energy sources are not the exclusive optimization goals, but also guaranteeing the thermal comfort is an important goal. This paper deals with a comprehensive approach of a mixed-integer quadratic-programming model predictive control scheme based on the thermal building model and the building energy management system. Calculating the global optima while handling continuous and binary constraints as well as variables and considering both the thermal and electrical part of a smart home are the key aspect of the proposed model predictive controller. By inclusion of disturbance forecasts, occupancy prediction, and individual user weights the control scheme is optimally suited for implementation in real buildings. Furthermore, the occupancy prediction in this research is based on an unsupervised method, which is useful for an effective implementation. This work demonstrates the optimal management of appliances such as heating, a battery storage, a freezer, a dishwasher, a photo-voltaic system, and the opportunities to buy from and sell to the smart grid. Optimal utilization of the building’s thermal storage capacity helps to minimize necessary battery capacity. Simulation results underline the efficient global optimization while demonstrating all proposed features of the complex control scheme.

Bilinear Bäcklund transformations, kink periodic solitary wave and lump wave solutions of the Bogoyavlenskii–Kadomtsev–Petviashvili equation

This paper investigates the Bogoyavlenskii–Kadomtsev– Petviashvili equation by using the binary Bell polynomials method and differential constraint technique. Several kinds of more general bilinear representations and Bäklund transformations are presented. At the same time, multiple wave solutions including the kink periodic solitary wave and bright–dark lump wave solutions are constructed. The resonant interactions between two kink solitary waves are investigated and exhibited mathematically and graphically. Lump wave solutions, a kind of rational function localized in all directions of the space, are obtained by the Taylor expansion of the kink periodic solitary wave. Also, we discuss the dynamical behavior of the lump wave solutions and their structures.

A synchronous game for binary constraint systems

Recently, Slofstra proved that the set of quantum correlations is not closed. We prove that the set of synchronous quantum correlations is not closed, which implies his result, by giving an example of a synchronous game that has a perfect quantum approximate strategy but no perfect quantum strategy. We also exhibit a graph for which the quantum independence number and the quantum approximate independence number are different. We prove new characterisations of synchronous quantum approximate correlations and synchronous quantum spatial correlations. We solve the synchronous approximation problem of Dykema and the second author, which yields a new equivalence of Connes’ embedding problem in terms of synchronous correlations.

Unsupervised Deep Hashing with Similarity-Adaptive and Discrete Optimization.

Recent vision and learning studies show that learning compact hash codes can facilitate massive data processing with significantly reduced storage and computation. Particularly, learning deep hash functions has greatly improved the retrieval performance, typically under the semantic supervision. In contrast, current unsupervised deep hashing algorithms can hardly achieve satisfactory performance due to either the relaxed optimization or absence of similarity-sensitive objective. In this work, we propose a simple yet effective unsupervised hashing framework, named Similarity-Adaptive Deep Hashing (SADH), which alternatingly proceeds over three training modules: deep hash model training, similarity graph updating and binary code optimization. The key difference from the widely-used two-step hashing method is that the output representations of the learned deep model help update the similarity graph matrix, which is then used to improve the subsequent code optimization. In addition, for producing high-quality binary codes, we devise an effective discrete optimization algorithm which can directly handle the binary constraints with a general hashing loss. Extensive experiments validate the efficacy of SADH, which consistently outperforms the state-of-the-arts by large gaps.