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The application of topology optimization methods in architecture, while useful for conceptual design explorations, seems to be limited by the practical realization of continuum-type design outcomes. One way to overcome this limitation is setting up design and fabrication techniques, through which continuum domains become discrete structures. This study investigates to which extent discrete optimized systems can be built using a hybrid approach combining 3D printing and analogue fabrication techniques. The procedure is based on an algorithm in Grasshopper (Rhinoceros) that translates continuum topologies obtained in MATLAB into discrete systems, providing alternatives depending on the targeted volume fraction, the intended surface smoothness of the structural components and building material. The study focuses on fabrication aspects and structural performance of discrete structures using 3D printed nodes. Experimental tests evaluate the compressive strength of different types of filaments with varied infill percentages. Final prototypes are fabricated using a hybrid technique involving the use of 3D printed nodes to assemble bar-arrays comprising wooden members. Results provide a critical appraisal of the limitations and potentialities of 3D printing for hybrid fabrication of real scale structures.

Multicarrier transmission strategy provides great benefits in wireless communication technology. For this reason, all of the waveform contenders proposed for the fifth generation and beyond technologies are built on this strategy. Universal filtered multicarrier (UFMC) is one of the foremost representatives of the related waveform contenders. However, utilizing the multicarrier transmission strategy causes the UFMC to generate transmission signals with high peak-to-average power ratio (PAPR), which leads to serious deteriorations in the communication quality. In order to solve this issue, it is crucial to reduce the PAPR of transmission signal before giving it to the wireless channel. With the aim of developing an efficient PAPR reduction scheme for the UFMC waveform, we first developed a new discrete version of the invasive weed optimization (DIWO) algorithm and integrated it to one of the classical PAPR reduction techniques called partial transmit sequence (PTS) as a phase optimizer. By doing so, we obtained an advanced scheme called DIWO–PTS. The function of DIWO algorithm in this new scheme is to optimize the phase sequences in discrete space. The usage of DIWO as a phase optimizer enables PTS to reach better phase combinations in less number of searches. Thus, it becomes possible to boost the PAPR reduction performance of the PTS scheme to a quite high level. Simulation results support the advantage of DIWO-based phase optimization. In the simulations, neither of the algorithms used for comparison in our paper could reach the performance level achieved by DIWO algorithm due to its efficient optimization capability.

This study aimed to apply the Markovian Model (MM) to obtain optimized operating rules for a hydropower reservoir to maximize its efficiency. In this study, a Markovian Control Model with continuous state space (MCM-CSS) is presented to analyze the climatological effects through stochastic integrals. The MCM-CSS compute the optimal policies of hydropower reservoir system over the Grijalva Hydropower System (GHS). The MCM-CSS can be described as follows: a) Historical data review, b) histograms of variables studied, c) state space analysis, d) action space analysis, e) admissible decision rule, f) expected benefit analysis. As a result, the optimal policy graphs were obtained. The result obtained in this research demonstrated the advantage of having applied a continuous space in reservoir inflow and water demand with the MMC-CSS method to avoid the uncertainness and inaccuracies in simulation results with a discrete space. Modified Svanidze’s Method (MSM) is also employed to investigate their capabilities to predict streamflow over the GHS and mean energy generated. The hydrological monthly simulations were calibrated and validated at GHS station for the period 1952–2018. The main objective of the study is to simulate the optimal policies obtained with the MMC-CSS for continuous states using MSM in GHS.

The discrete topology and sizing optimization of frame structures with compliance constraints is studied using a novel approach, which is capable of finding the theoretical lower bounds and high-quality discrete solutions in an efficient manner. The proposed approach works by reformulating the discrete problem as a relaxed semidefinite programming (SDP) problem. This reformulation is made possible by a linear relaxation of the original discrete space and the elimination of the nonconvex equilibrium equation using a semidefinite constraint. A continuous global optimum is first derived using existing solvers and then the discrete solution is discovered by the neighborhood search. Numerical examples are presented, including the sizing optimization of 2-Bay 6-Story frame and 3-Bay 10-Story frame, the topology and sizing optimization of 2-Bay 6-Story braced frame. A topology and sizing example with multiple load cases is also provided. The proposed approach and three other metaheuristic algorithms are used to solve these examples. Theoretical lower bounds for these examples can be efficiently discovered by the proposed approach. For the sizing problems, the discrete solutions by the proposed approach are all better than the other algorithms. For the topology and sizing problems, the proposed approach achieves discrete solutions better than genetic algorithm, but worse than the other metaheuristics. The computational superiority of the proposed approach is validated in all the examples.

Applying generative adversarial networks (GANs) to text-related tasks is challenging due to the discrete nature of language. One line of research resolves this issue by employing reinforcement learning (RL) and optimizing the next-word sampling policy directly in a discrete action space. Such methods compute the rewards from complete sentences and avoid error accumulation due to exposure bias. Other approaches employ approximation techniques that map the text to continuous representation in order to circumvent the non-differentiable discrete process. Particularly, autoencoder-based methods effectively produce robust representations that can model complex discrete structures. In this article, we propose a novel text GAN architecture that promotes the collaborative training of the continuous-space and discrete-space methods. Our method employs an autoencoder to learn an implicit data manifold, providing a learning objective for adversarial training in a continuous space. Furthermore, the complete textual output is directly evaluated and updated via RL in a discrete space. The collaborative interplay between the two adversarial trainings effectively regularize the text representations in different spaces. The experimental results on three standard benchmark datasets show that our model substantially outperforms state-of-the-art text GANs with respect to quality, diversity, and global consistency.

Feature selection is a challenging step in the field of data mining, because there are many local optimal solutions in a feature space. Feature selection can be considered an optimization problem, which requires as few feature combinations as possible and high accuracy. The binary symbiotic organism search (BSOS) algorithm is proposed in this paper. It maps the symbiotic organism search algorithm from a continuous space to a discrete space using an adaptive S-shaped transfer function and can be used to search for the optimal feature subset in a feature selection space. The proposed BSOS algorithm is evaluated using 19 datasets from the UCI repository. First, the results of four basic S-shaped transfer functions are compared with those of the adaptive S-shaped transfer function. Additionally, the experimental results are compared with the results obtained by the popular binary grasshopper optimization, binary gray wolf optimization, traditional binary particle swarm optimization, and binary differential evolution algorithms, which are also employed for feature selection in the existing literature. The experimental results show that the BSOS algorithm can find the fewest number of features in most datasets and achieve a high classification accuracy. Moreover, the experiments also show that the BSOS algorithm is still at a disadvantage in handling low-dimensional datasets and attains low sensitivity in hyperdimensional datasets.

Humans can communicate emotions through a plethora of facial expressions, each with its own intensity, nuances and ambiguities. The generation of such variety by means of conditional GANs is limited to the expressions encoded in the used label system. These limitations are caused either due to burdensome labelling demand or the confounded label space. On the other hand, learning from inexpensive and intuitive basic categorical emotion labels leads to limited emotion variability. In this paper, we propose a novel GAN-based framework that learns an expressive and interpretable conditional space (usable as a label space) of emotions, instead of conditioning on handcrafted labels. Our framework only uses the categorical labels of basic emotions to learn jointly the conditional space as well as emotion manipulation. Such learning can benefit from the image variability within discrete labels, especially when the intrinsic labels reside beyond the discrete space of the defined. Our experiments demonstrate the effectiveness of the proposed framework, by allowing us to control and generate a gamut of complex and compound emotions while using only the basic categorical emotion labels during training. Our source code is available at https://github.com/stefanodapolito/GANmut.

Graph Convolutional Network (GCN) is adopted to tackle the problem of convolution operation in non-Euclidean space. Previous works on GCN have made some progress, however, one of their limitations is that the design of Adjacency Matrix (AM) as GCN input requires domain knowledge and such process is cumbersome, tedious and error-prone. In addition, entries of a fixed Adjacency Matrix are generally designed as binary values (i.e., ones and zeros) which can not reflect the real relationship between nodes. Meanwhile, many applications require a weighted and dynamic Adjacency Matrix instead of an unweighted and fixed AM, and there are few works focusing on designing a more flexible Adjacency Matrix. To that end, we propose an end-to-end algorithm to improve the GCN performance by focusing on the Adjacency Matrix. We first provide a calculation method called node information entropy to update the matrix. Then, we perform the search strategy in a continuous space and introduce the Deep Deterministic Policy Gradient (DDPG) method to overcome the drawback of the discrete space search. Finally, we integrate the GCN and reinforcement learning into an end-to-end framework. Our method can automatically define the Adjacency Matrix without prior knowledge. At the same time, the proposed approach can deal with any size of the matrix and provide a better AM for network. Four popular datasets are selected to evaluate the capability of our algorithm. The method in this paper achieves the state-of-the-art performance on Cora and Pubmed datasets, with the accuracy of 84.6% and 81.6% respectively.

In CFD modelling, small cells or elements are created to fill the volume to simulate the flow in. They constitute a mesh where each cell represents a discrete space that represents the flow locally. Mathematical equations that represent the flow physics are then applied to each cell of the mesh. Generating a high quality mesh is extremely important to obtain reliable solutions and to guarantee numerical stability. This chapter begins with a basic introduction to a typical workflow and guidelines for generating high quality meshes, and concludes with some more advanced topics, i.e., how to generate meshes in parallel, a discussion on mesh quality, and examples on the application of lattice-Boltzmann methods to simulate flow without any turbulence modelling on highly-resolved meshes.

Active learning for sentence understanding aims at discovering informative unlabeled data for annotation and therefore reducing the demand for labeled data. We argue that the typical uncertainty sampling method for active learning is time-consuming and can hardly work in real-time, which may lead to ineffective sample selection. We propose adversarial uncertainty sampling in discrete space (AUSDS) to retrieve informative unlabeled samples more efficiently. AUSDS maps sentences into latent space generated by the popular pre-trained language models, and discover informative unlabeled text samples for annotation via adversarial attack. The proposed approach is extremely efficient compared with traditional uncertainty sampling with more than 10x speedup. Experimental results on five datasets show that AUSDS outperforms strong baselines on effectiveness., Accepted to EMNLP 2020 Findings

The location check-ins of users through various location-based services such as Foursquare, Twitter and Facebook Places, generate large traces of geo-tagged events. These event-traces often manifest in hidden (possibly overlapping) communities of users with similar interests. Inferring these implicit communities is crucial for forming user profiles for improvements in recommendation and prediction tasks. Given only time-stamped geo-tagged traces of users, can we find out these implicit communities, and characteristics of the underlying influence network? Can we use this network to improve the next location prediction task? In this paper, we focus on the problem of community detection as well as capturing the underlying diffusion process. We propose CoLAB, based on spatio-temporal point processes for information diffusion in continuous time but discrete space of locations. It simultaneously models the implicit communities of users based on their check-in activities, without making use of their social network connections. CoLAB captures the semantic features of the location, user-to-user influence along with spatial and temporal preferences of users. The latent community of users and model parameters are learnt through stochastic variational inference. To the best of our knowledge, this is the first attempt at jointly modeling the diffusion process with activity-driven implicit communities. We demonstrate CoLAB achieves upto 27% improvements in location prediction task over recent deep point-process based methods on geo-tagged event traces collected from Foursquare check-ins.

When facing discrete space learning problems, the traditional reinforcement learning algorithms often have the problems of slow convergence and poor convergence accuracy. Deep reinforcement learning needs a large number of learning samples in its learning process, so it often faces with the problems that the algorithm is difficult to converge and easy to fall into local minimums. In view of the above problems, we apply support vector machines classification to reinforcement learning, and propose an algorithm named Advantage Actor-Critic with Support Vector Machine Classification (SVM-A2C). Our algorithm adopts the actor-critic framework and uses the support vector machine classification as a result of the actor's action output, while Critic uses the advantage function to improve and optimize the parameters of support vector machine. In addition, since the environment is changing all the time in reinforcement learning, it is difficult to find a global optimal solution for the support vector machines, the gradient descent method is applied to optimize the parameters of support vector machine. So that the agent can quickly learn a more precise action selection policy. Finally, the effectiveness of the proposed method is proved by the classical experimental environment of reinforcement learning. It is proved that the algorithm proposed in this paper has shorter episodes to convergence and more accurate results than other algorithms.

Time series motifs were introduced in 2002 and have since become a fundamental tool for time series analytics, finding diverse uses in dozens of domains. In this work, we introduce Time Series Chains, which are related to, but distinct from, time series motifs. Informally, time series chains are a temporally ordered set of subsequence patterns, such that each pattern is similar to the pattern that preceded it, but the first and last patterns can be arbitrarily dissimilar. In the discrete space, this is similar to extracting the text chain “data, date, cate, cade, code” from text stream. The first and last words have nothing in common, yet they are connected by a chain of words with a small mutual difference. Time series chains can capture the evolution of systems, and help predict the future. As such, they potentially have implications for prognostics. In this work, we introduce two robust definitions of time series chains and scalable algorithms that allow us to discover them in massive complex datasets.

Some fault data in an actual system operation has the strong discretization and big data characteristics. Meanwhile, the external factors affect the system reliability, and the change of factors may lead to the change of system reliability. At present, the methods in safety system engineering lack the ability to process the multi-factor influence and fault big data simultaneously. But these are the general problems that the actual system reliability analysis must face to be resolved. In order to solve the problems, on the basis of Discrete Space Fault Tree (DSFT), the Fuzzy Structured Element method is introduced to construct the Fuzzy Structured Element Discrete Space Fault Tree (EDSFT). The method can analyze the multi-factor influence on system reliability with DSFT, and use Fuzzy Structured Element (E) to denote the discrete characteristics of fault big data. The results of EDSFT with E can preserve the characteristics of the original fault data distribution and lay the foundation for the analysis of fault big data. The research is particularly suitable for the analysis of system reliability under the fault big data and multi-factor influence.

An adaptive state aggregation Q-Learning method, with the capability of multi-agent cooperation, is proposed to enhance the efficiency of reinforcement learning (RL) and is applied to box-pushing tasks for humanoid robots. First, a decision tree was applied to partition the state space according to temporary differences in reinforcement learning, so that a real valued action domain could be represented by a discrete space. Furthermore, adaptive state Q-Learning, which is the modification of estimating Q-value by tabular or function approximation, is proposed to demonstrate the efficiency of reinforcement learning in simulations of a humanoid robot pushing a box. The box moves in the direction in which the robot asserts force. To push the box to the target point, the robot needs to learn how to adjust angles, avoid obstacles, and keep balance. Simulation results show the proposed method outperforms Q-Learning without using adaptive states.

Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.

This study addresses the design of ply orientation for a CFRP vehicle door by implementing a Discrete Material Optimization (DMO) method in a general-purpose commercial finite element code (ABAQUS) and mathematical analysis tool (MATLAB). To accommodate multiple loading conditions, the weighted mean compliance of the CFRP vehicle door was taken as the objective function, subject to the constraints on the local displacements, primary natural frequency and manufacturability. The sensitivities of objective and constraints were calculated by using the strain vectors, which is a more general method than using element stiffness matrices and allows extracting local displacements from the commercial finite element code. A gradient-based algorithm was employed in the DMO approach to tackle the large-scale problem. In the discrete topology optimization, four material penalization schemes were attempted in this study. The proposed DMO approach was compared with the empirical design and the existing method in commercial software. The results demonstrated that the proposed method is able to produce a more competent solution than the empirical design and other optimization methods efficiently. Keywords: Ply orientation, Vehicle door, Discrete Material Optimization (DMO), Carbon fiber reinforced plastic (CFRP), Topology optimization

This paper proposes an alternative strategy of finite-control-set model-predictive torque control (MPTC) to reduce the computational burden and the torque ripple and decouple the switching frequency from the controller sampling time. An improved discrete space-vector modulation (DSVM) technique is utilized to synthesize a large number of virtual voltage vectors. The deadbeat (DB) technique is used to optimize the voltage vector selection process, avoiding enumerating all the feasible voltage vectors. With this proposed method, only three voltage vectors are tested in each predictive step. Based on the improved DSVM method, the three candidate voltage vectors are calculated by using a novel algebraic way. This new strategy has the benefits of both the MPTC method and the DB method. The effectiveness of the proposed strategy is validated based on a test bench.

In this letter, a novel method based on discrete space model (DSM) and support vector machines (SVMs) is proposed for hyperspectral image (HSI) classification. The DSM approach transforms continuous spectral signatures into discrete features and constructs a space model with the discrete features. Therefore, the classification capability of SVMs can be improved on account of the discrete feature space. Moreover, a composite kernel model is employed to take advantage of the spectral and spatial features among neighboring pixels. The proposed method is applied to real HSIs for classification. The experimental results confirm that the classification accuracy for the SVMs could be improved using the DSM method prior to classification.

Path planning of polyhedrons by rolling on edges includes arbitrary relocation, obstacle avoidance and goal achievement. These tasks have various applications in robotics fields such as autonomous vehicles, navigation and robotic surgery. This paper reviewed path planning approaches applied to rolling contact with different types of polyhedral parts. The advantages and disadvantages of some mainstream algorithms were analyzed and compared. We further pointed out the directions of future research on rolling polyhedron path planning in discrete space.

Graph clustering has wide applications in different areas such as machine learning, bioinformatics, data mining, social networks and understanding a software. Since it is an NP-hard problem, most approaches use the meta-heuristic and search-based evolutionary methods for solving it. Inspired by optimization algorithms like krill herd (KH) and genetic algorithm (GA), this paper proposes a new graph clustering algorithm. KH is an effective algorithm to solve continuous space optimization problems. It imitates individual and group behavior of krills and, normally, it cannot solve discrete space problems. GA is an evolutionary algorithm that uses search techniques to find near-optimal solutions. However, the main disadvantage of the GA is the lack of strong and effective information flow between generations as well as the lack of local search. In the proposed evolutionary algorithm, we have combined strengths of these two algorithms, e.g., adopting the cycle and GA operators, using swarm intelligence, and inspiring the Krill's movements, we got better results for the graph clustering problem. Initial results of the proposed algorithms on a number of software graphs showed that the clustering results obtained from the proposed algorithm are of higher quality compared to other considered algorithms.

This paper presents a metric-aligned meshing algorithm that relies on the Lp-Centroidal Voronoi Tesselation approach. A prototype of this algorithm was first presented at the Scitech conference of 2018 and this work is an extension to that paper. At the end of the previously presented work, a set of problems were mentioned which we are trying to address in this paper. First, we show a significant improvement in code performance since we were limited to present relatively benign (analytical) test cases. Second, we demonstrate here that we are able to rely on discrete metric data that is delivered by a Computational Fluid Dynamics (CFD) solver. Third, we demonstrate how to generate high-order curved elements that are aligned with the underlying discrete metric field.

To cope with the task scheduling problem under multi-task and transportation consideration in large-scale service oriented manufacturing systems (SOMS), a service allocation optimization mathematical model was established, and then a hybrid discrete particle swarm optimization-genetic algorithm (HDPSOGA) was proposed. In SOMS, each resource involved in the whole life cycle of a product, whether it is provided by a piece of software or a hardware device, is encapsulated into a service. So, the transportation during production of a task should be taken into account because the hard-services selected are possibly provided by various providers in different areas. In the service allocation optimization mathematical model, multi-task and transportation were considered simultaneously. In the proposed HDPSOGA algorithm, integer coding method was applied to establish the mapping between the particle location matrix and the service allocation scheme. The position updating process was performed according to the cognition part, the social part, and the previous velocity and position while introducing the crossover and mutation idea of genetic algorithm to fit the discrete space. Finally, related simulation experiments were carried out to compare with other two previous algorithms. The results indicate the effectiveness and efficiency of the proposed hybrid algorithm.

As digital circuits are approaching the limits of Moore’s law, a great deal of effort has been directed to alternative computing approaches. Among them, the old concept of optical signal processing (OSP) has attracted attention, revisited in the light of metamaterials and nano-photonics. This approach has been successful in realizing basic mathematical operations, such as derivatives and integrals, but it is difficult to be applied to more complex ones. Here, inspired by digital filters, we propose a radically new OSP approach, able to realize arbitrary mathematical operations over a nano-photonic platform. Our concept consists in first sampling an optical signal in space through an array of optical antennas and then realizing the desired mathematical operation in discrete space through a network with a discrete number of input and output ports. The design of such network boils down to the design of a structure with a given scattering matrix, which for arbitrarily complex operations can be accomplished through inverse design algorithms. We demonstrate this concept for the case of spatial differentiation through a heuristic design based on a waveguide with periodic arrays of input/output channels at its opposite walls. Our approach combines the robustness and generality of traditional Fourier-based OSP with the compactness of nano-photonics and has the potential of transforming the design of OSP systems with applications in image processing and analog computing.

Digital camouflage plays an important role in improving the combat performance of vehicles. The reconstruction of the spraying model of the automobile surface can improve the automation level of the digital camouflage painting operation. The surface digital camouflage spraying model construction method is a processing flow that incorporates a variety of technical methods, including surface point cloud data collection technology, point cloud synthesis and segmentation method, surface model reconstruction method and spray pattern fusion technology. Four linear laser sensors are used to scan the vehicle surface to obtain the local point cloud data of the vehicle. The vehicle CAD model and the painting pattern figures are analysed. And the region growing segmentation method is used to subdivide the scanned point cloud data. For the point cloud after partitioning, the point set of the digital camouflage pattern is directly searched by using the constructed discrete metric. Then each point cloud is merged with the 2D camouflage pattern to obtain the digital camouflage spraying model of the vehicle surface.

In recent years, people have combined deep learning with reinforcement learning to solve practical problems. However, due to the characteristics of neural networks, it is very easy to fall into local minima when facing small scale discrete space path planning problems. Traditional reinforcement learning uses continuous updating of a single agent when algorithm executes, which leads to a slow convergence speed. In order to solve the above problems, we combine asynchronous methods with existing tabular reinforcement learning algorithms, propose a parallel architecture to solve the discrete space path planning problems, and present four new variants of asynchronous reinforcement learning algorithms. We apply these algorithms on the standard reinforcement learning environment FrozenLake problem, and the experimental results show that these methods can solve discrete space path planning problems efficiently. One of these algorithms, which is called Asynchronous Dyna-Q, surpasses existing asynchronous reinforcement learning algorithms, can well balance the exploration and exploitation.

Discretization continuous feature is an important task to handle the problems with real values in machine learning. In order to construct a classifier using a discrete space, it is required for many supervised classification algorithms to perform with discretized features. In this paper, we presents the supervised classification model based on Hidden Markov Model (HMM) developed recently and we review several discretization methods reported in the litterature. We take 9 benchmarking study data set to evaluate the performance and study the effect of discretization methods on the assessment of the proposed learning algorithm. Three metrics performance including accuracy, Area under curve and squared loss are used to investigate the powerful class prediction and to show the capability of HMM classifier in presence of available data.

Construction of oil-and-gas pipeline networks is an important topic in the field of oil and gas development. The rationality and economy of pipeline-network construction are becoming increa...

In the next years, the launch of new satellites with Hyperspectral (HS) sensors will guarantee the availability of regular multitemporal HS datasets. In order to exploit the dense sampling of the spectrum of HS sensors to discriminate multiple land-cover changes ad-hoc techniques are required. In this paper we propose a novel method for unsupervised multiple Change Detection (CD) in HS multitemporal images based on binary Spectral Change Vectors (SCVs). In greater detail, the method discriminates between unchanged and changed areas in order to focus only on the latter ones. Then, it converts the real valued SCVs in a binary form to work in a discrete high dimensional space. The binary SCVs are clustered following an hierarchical tree structure where each leaf represent a kind of change. The tree also highlights how the different changes are related among each other. The proposed approach has been tested on a multitemporal dataset acquired over an agricultural area. Experimental results confirmed that the binary SCVs allows us to detect and discriminate multiple changes by working in a simpler discrete space.

In order to overcome the disadvantages of high complexity, low speed and accuracy of selective ensemble algorithm based on genetic algorithm. We proposed a new selective ensemble algorithm based on probability PSO algorithm. First, in order to tackle the converging slowly and easily to partial minimum problems of simplified PSO, we introduce the cloud model and the method of complex; Second, we present the definition of probability PSO and the formula that converting the particle position vector to base learner selection problem, that make the transformation from continuous space to discrete space become true. Finally, we choose integration model generalization error as the adaptive function of PPSOSEN. The numerical results show that, compared with discrete PSO, PPSOSEN improved the recognition precision with the same time consumption, and it is an efficient selective ensemble algorithm.

The power system is a crucial infrastructure which supports computer systems that affect many aspects of our daily lives, and thus a constant target of hackers' malicious attacks. An unidentifiable attack is a new type of bad data injection attack on power systems that confuses the control center software by manipulating measurement data so that there exist multiple feasible solutions for state estimation and thus no deterministic state estimation solution can be produced. To reveal and defend against this type of attacks, these multiple feasible solutions must be solved in advance. This paper proposes a fast and reliable algorithm to reveal such unidentifiable attacks. The algorithm combines the angle modulated particle swarm optimization (AMPSO) and the dormant measurement technique. The AMPSO is employed to reduce the complex high-dimensional binary search problem defined in discrete space to a simple four-dimensional search problem defined in continuous space; the dormant measurement technique is used to avoid repeated computation of state estimation. Simulation results using the IEEE 14-bus and 30-bus systems show that our proposed method produces multiple feasible solutions fast and reliably.

This paper deals with the problem of fitting a discrete polynomial curve to 2D noisy data. We use a discrete polynomial curve model achieving connectivity in the discrete space. We formulate the fitting as the problem to find parameters of this model maximizing the number of inliers i.e., data points contained in the discrete polynomial curve. We propose a method guaranteeing inclusion-wise maximality of its obtained inlier set.

In this chapter, we present a new type of model particularly suited to solving physical problems in non-Euclidean spaces. These spaces may mix the concepts of proximity (such as geographic information systems), topological notions (such as social networks), information concepts and algebraic concepts (such as the invariance of certain local symmetries).

A method of text detection in natural images, to be turned into an effective embedded software on a mobile device, shall be both efficient and lightweight. We observed that a simple method based on the morphological Laplace operator is very appropriate: we can construct in quasi-linear time a hierarchical image decomposition/simplification based on its 0-crossings, and search for some text in the resulting tree. Yet, for this decomposition to be sound, we need “0-crossings” to be Jordan curves, and to that aim, we rely on some discrete topology tools. Eventually, the hierarchical representation is the morphological tree of shapes of the Laplacian sign (ToSL). Moreover, we provide an algorithm with linear time complexity to compute this representation. We expect that the proposed hierarchical representation can be useful in some applications other than text detection.

This paper focuses on human-pose estimation using a stationary depth sensor. The main challenge concerns reducing the feature ambiguity and modeling human poses in high-dimensional human-pose space because of the curse of dimensionality. We propose a 3-D-point-cloud system that captures the geometric properties (orientation and shape) of the 3-D point cloud of a human to reduce the feature ambiguity, and use the result from action classification to discover low-dimensional manifolds in human-pose space in estimating the underlying probability distribution of human poses. In the proposed system, a 3-D-point-cloud feature called viewpoint and shape feature histogram (VISH) is proposed to extract the 3-D points from a human and arrange them into a tree structure that preserves the global and local properties of the 3-D points. A nonparametric action-mixture model (AMM) is then proposed to model human poses using low-dimensional manifolds based on the concept of distributed representation. Since human poses estimated using the proposed AMM are in discrete space, a kinematic model is added in the last stage of the proposed system to model the spatial relationship of body parts in continuous space to reduce the quantization error in the AMM. The proposed system has been trained and evaluated on a benchmark dataset. Computer-simulation results showed that the overall error and standard deviation of the proposed 3-D-point-cloud system were reduced compared with some existing approaches without action classification.

The paper introduces Working mode of brushless doubly-fed machine（BDFM） and mathematical model in the d-q coordinates for BDFM，a strategy of discrete space vector modulation in direct torque control for BDFM has been Proposed 。The paper uses Matlab / Simulink to model and simulate the system of the direct torque control for brush double-fed motor based on discrete Space Vector Modulation.Simulation results prove that the discrete space vector modulation technique can reduce the torque ripple of traditional direct torque control system for BDFM, and improve waveform of current and Flux of Control winding.

In many pattern recognition applications, feature space expansion is a key step for improving the performance of the classifier. In this paper, we (i) expand the discrete feature space by generating all orderings of values of k discrete attributes exhaustively, (ii) modify the well-known decision tree and rule induction classifiers (ID3, Quilan, 1986 [1] and Ripper, Cohen, 1995 [2]) using these orderings as the new attributes. Our simulation results on 15 datasets from UCI repository [3] show that the novel classifiers perform better than the proper ones in terms of error rate and complexity. This work has been supported by the Turkish Scientific Technical Research Council (TUBITAK) EEEAG 107E127 Publisher's Version Author Pre-Print

Generating expressive, naturally sounding, speech from text using a speech synthesis (TTS) system is a highly challenging problem. However for tasks such as audiobooks it is essential if their use is to become widespread. Generating expressive speech from text can be divided into two parts: predicting expressive information from text; and synthesizing the speech with a particular expression. Traditionally these components have been studied separately. This paper proposes an integrated approach, where the training data and representation of expressive synthesis is shared across the two components. There are several advantages to this scheme including: robust handling of automatically generated expressive labels; support for a continuous representation of expressions; and joint training of the expression predictor and speech synthesizer. Synthesis experiments indicated that the proposed approach produced far more expressive speech than both a neutral TTS and one where the expression was randomly selected. The experimental results also show the advantage of a continuous expressive synthesis space over a discrete space.

In this technical note, we propose a novel technique to control the relative motion of multiple mobile agents as they stabilize to a desired configuration. In particular, we focus on the agents' relative velocities and the rate of change of their pairwise distances, and employ constructs from classic navigation functions (NFs) to control these quantities. Controlling agent velocities requires nontrivial extensions of the NF methodology to second-order models. Although in this work we propose a centralized framework to control the relative agent velocities, it adds a new dimension to the control of multi-agent systems with several advantages. In particular, we provide a novel approach to control the transient dynamics of a network that may facilitate the integration of continuous motion planing with discrete topology control. The result is verified theoretically and via computer simulations.

Many data in the classification problem contain a number of additional and irrelevant attributes (genes) that affect the accuracy of the classification. Many evolutionary algorithms are used to determine the feature and reduce dimensional patterns such as particle swarm optimization (PSO), after converting it from continuous space to a discrete space. In this research, a method of gene selection was proposed through two consecutive stages: in the first stage, the fuzzy mutual information (FMI) method is used to determine the most important genes selected through a fuzzy model that was built based on the data size. In the second stage, the BPSO algorithm is used to reduce and determine a specific number of genes affecting the process of classification, which came from the first stage. The proposed algorithm, FMI_BPSO, describes efficiency and effectiveness by obtaining a higher classification accuracy and a small number of selected genes compared to other competitor algorithms.

The Capacitated Vehicle Routing Problem (CVRP) is an NP-Hard problem, which means it is impossible to find a polynomial time solution for it. So researchers try to reach a near optimum solution by using meta-heuristic algorithms. The aim of CVRP is to find optimum route for every vehicle and a sequence of customers, that vehicle serve. This paper proposes a method on how PSO is adjusted for a discrete space problem like CVRP. The process of tweaking solutions is described in detail. At last for evaluation of proposed approach and show the effectiveness of it, the result of running proposed approach over benchmarking data set of capacitated vehicle routing problem is illustrated.

Berth scheduling operation is an important problem in container terminal. The mathematic model of this problem is described in this paper and an improved particle swarm optimization algorithm is introduced to obtain the optimal scheduling solution. A floating-point allocation rule is used to encode the particles in the discrete space. A local search method is combined with PSO to avoid precocity. Finally the experiments are done to prove the improved PSO in this paper can resolve the berth scheduling problem and get better solution and convergence speed than the basic PSO.

Hybrid system for sizing and topology optimisation of cable-truss structures.Nonlinear finite element analysis of cable elements.Hybridisation of fuzzy logic and genetic algorithm.Optimisation of prestressed structures.Computational cost reduction through fuzzy filtering. This paper demonstrates an application of a hybrid fuzzy-genetic system in the optimisation of lightweight cabled-truss structures. These structures are described as a system of cables and triangular bar formations jointed at their ends by hinged connections to form a rigid framework. The optimised lightweight structure is determined through a stochastic discrete topology and sizing optimisation procedure that uses ground structure approach, nonlinear finite element analysis, genetic algorithm, and fuzzy logic. The latter is used to include expertise into the evolutionary search with the aim of filtering individuals with low survival possibility, thereby decreasing the total number of evaluations. This is desired because cables, which are inherently nonlinear elements, demand the use of iterative procedures for computing the structural response. Such procedures are computationally costly since the stiffness matrix is evaluated in each iteration until the structure is in equilibrium. Initially, the proposed system is applied to truss benchmarks. Next, the use of cables is investigated and the system's performance is compared against genetic algorithms. The results indicate that the hybrid system considerably decreased the number of evaluations over genetic algorithms. Also, cabled-trusses showed a significant improvement in structural mass minimisation when compared with trusses.

In this paper, we study the problem of dynamically positioning a team of mobile robots for target tracking. We treat the coordination of mobile robots for target tracking as a joint team optimization to minimize uncertainty in target state estimates over a fixed horizon. The optimization is inherently a function of both the positioning of robots in continuous space and the assignment of robots to targets in discrete space. Thus, the robot team must make decisions over discrete and continuous variables. In contrast to methods that decouple target assignments and robot positioning, our approach avoids the strong assumption that a robot's utility for observing a target is independent of other robots’ observations. We formulate the optimization as a mixed integer nonlinear program and apply integer relaxation to develop an approximate solution in decentralized form. We demonstrate our coordinated multirobot tracking algorithm both in simulation and using a pair of mobile robotic sensor platforms to track moving pedestrians. Our results show that coupling target assignment and robot positioning realizes coordinated behaviors that are not possible with decoupled methods.

The dynamic facility layout problem (DFLP) aims to minimise the sum of handling and re-layout costs by devising an individual layout for each distinctive production period. In this paper, a hybrid particle swarm optimisation (HPSO) algorithm is proposed to find near-optimal solutions of DFLP. We use a coding and decoding technique that permits a one to one mapping of a solution in discrete space of DFLP to a PSO particle position in continuous space. The proposed PSO will further use this coding technique to explore the continuous solution space. For further enhancement, the proposed PSO is hybridised with a simple and fast simulated annealing. The developed algorithm is capable of being extended to more general cases although equal area machines and standardised handling equipments with identical unit costs are assumed for the time being. Computational results show the efficiency of the proposed algorithm compared to other heuristics.

With rapid developments in satellite and sensor technologies, there has been a dramatic increase in the availability of high resolution (HR) remotely sensed images. Hence, the ability to collect images remotely is expected to far exceed our capacity to analyse these images manually. Consequently, techniques that can handle large volumes of data are urgently needed. In many of today's multiscale techniques the underlying representation of objects is still pixel-based, i.e. object entities are still described/accessed via pixelbased descriptors, thereby creating a bottleneck when processing large volumes of data. Also, these techniques do not yet leverage the topological and contextual information present in the image. We propose a framework for Discrete Topology based hierarchical segmentation, addressing both the algorithms and data structures that will be required. The framework consists of three components: 1) Conversion to dart-based representation, 2) Size-Constrained-Region Merging to generate multiple segmentations, and 3) Update of two sparse arrays SIGMA and LAMBDA which together encode the topology of each region in the hierarchy. The results of our representation are demonstrated both on a synthetic and a real high resolution images. Application of this representation to objectdetection is also discussed.

This paper presents a hybrid discrete choice-duration model for work activity scheduling with interactions between workers in a multiple-worker household. The model operates in discrete space with a fine level of temporal resolution. The key innovative feature of the model is the introduction of intra-household interactions through worker schedule synchronization mechanisms. The model was estimated based on a large Household Travel Survey from the San Francisco Bay Area. The estimation results confirmed that individual work schedules for workers in a multiple-worker household are subject to strong synchronization and should be modelled jointly rather than independently. In particular, workers in the same household tend to align their schedules and create time window overlaps for joint activities before and after work. Relative strength of the synchronization mechanisms proved to be a function of the person characteristics and household composition.

With the development of informational construction technology, the shield tunnel three-dimensional visualization has been more and more used. This paper proposes a modeling method of discrete space curve based on coordinates of shield line design, then calculate and generate shield tunneling model. The model data is stored in the form of triangular network. This method has fast modeling speed and low request of storage space, and is relatively easy to imply. It can be combined with GIS in fast simulation to improve work efficiency.

Representation of the surrounding environment is a vital task for a mobile robot. Many applications for mobile robots in urban environments may be considered such as self-driving cars, delivery drones or assistive robots. In contrast to the conventional methods, in this paper a Non Uniform Rational B-Spline (NURBS) based technique is represented for 3D mapping of the surrounding environment. While in the state of the art techniques, the robot's environment is expressed in a discrete space, the proposed method is mainly developed for representation of environment in a continuous space. Exploiting the information theory, the generated representation has much lower complexity and more compression capability in relation to some state of the art techniques. In addition to representation in a lower dimensional space, the NURBS based representation is invariant against 3D geometric transformations. Furthermore, the NURBS based representation can be employed for obstacle avoidance and navigation. The applicability of the proposed algorithm is investigated in some urban environments through some publicly available data sets. It has been shown by some experiments that the proposed method has better visual representation and much better data compression compared to some state-of-the-art methods.

Motivation: Most current research in network evolution focuses on networks that follow a Duplication Attachment model where the network is only allowed to grow. The evolution of metabolic networks, however, is characterized by gain as well as loss of reactions. It would be desirable to have a biologically relevant model of network evolution that could be used to calculate the likelihood of homologous metabolic networks. Results: We describe metabolic network evolution as a discrete space continuous time Markov process and introduce a neighbor-dependent model for the evolution of metabolic networks where the rates with which reactions are added or removed depend on the fraction of neighboring reactions present in the network. We also present a Gibbs sampler for estimating the parameters of evolution without exploring the whole search space by iteratively sampling from the conditional distributions of the paths and parameters. A Metropolis–Hastings algorithm for sampling paths between two networks and calculating the likelihood of evolution is also presented. The sampler is used to estimate the parameters of evolution of metabolic networks in the genus Pseudomonas. Availability: An implementation of the Gibbs sampler in Java is available at http://www.stats.ox.ac.uk/∼mithani/networkGibbs/ Contact: mithani@stats.ox.ac.uk Supplementary information: Supplementary data are available at the Bioinformatics online.