Particle Representation Research Articles

A survey of Particle Swarm Optimization techniques for solving university Examination Timetabling Problem

The university Examination Timetabling Problem is one of the most important scheduling problems that numerous educational organizations have to find out a solution to manage their examinations by assigning these events to particular timeslots, rooms and/or invigilators. This problem is NP-complete due to the number of conflicting constraints that must be considered in the resolution. Particle Swarm Optimization (PSO) technique is a common intelligent method that has been successfully applied to many hard combinatorial optimization problems. The purpose of this paper is to expose a number of articles that appeared this last decade and used the PSO technique to solve the University examination timetabling problem. The overall techniques are described, focusing on the particle representation and updating. This research also offers insight into how well the PSO algorithm performs compared with other algorithms used to solve the same problem and datasets. Finally, a summary of the described algorithms and their most distinguishing features is presented in addition to future research directions.

Multiphase flow patterns in entrained-flow slagging gasifiers: Physical modelling of particle–wall impact at near-ambient conditions

Particle–wall interaction phenomena relevant to multiphase flow in entrained-flow slagging coal gasifiers have been investigated. The micromechanical patterns of particle impingement on the reactor walls have been characterized in a model system by high speed imaging and tracking of wax particles impacted onto a flat surface at near-ambient conditions. The solid/plastic versus fluid state of the wax particles was controlled by proper selection of the particle, ambient and target temperatures. Particle–wall collision was described in terms of normal and lateral restitution coefficients and capture efficiency. The influence of the particle stickiness, impact velocity and angle, and surface properties and structure of the target on the rebound patterns was studied. Results indicate that the elastic–plastic adhesive model provides an adequate representation of the non sticky particle–wall collisions. Moreover, the presence of a powder layer on the target favours energy dissipation and accumulation of particles close to the surface. This pattern promotes the establishment of a dense-dispersed phase in the near-wall zone of entrained-flow slagging gasifiers. Increasing the temperature, particles shift from the solid/plastic to the fluid state and the coefficient of restitution drops to vanishingly small values, confirming that deposition is the prevailing phenomenon during the collision of sticky particles on a wall.

Particle–hole duality, integrability, and Russian doll BCS model

We address a generalized Richardson model (Russian doll BCS model), which is characterized by the breaking of time-reversal symmetry. This model is known to be exactly solvable and integrable. We point out that the Russian doll BCS model, on the level of Hamiltonian, is also particle–hole symmetric. This implies that the same state can be expressed both in the particle and hole representations with two different sets of Bethe roots. We then derive exact relations between Bethe roots in the two representations, which can hardly be obtained staying on the level of Bethe equations. In a quasi-classical limit, similar identities for usual Richardson model, known from literature, are recovered from our results. We also show that these relations for Richardson roots take a remarkably simple form at half-filling and for a symmetric with respect to the middle of the interaction band distribution of one-body energy levels, since, in this special case, the rapidities in the particle and hole representations up to the translation satisfy the same system of equations.

Peridynamic theory of solids from the perspective of classical statistical mechanics

In this paper the classical statistical mechanics has been explored in order to develop statistical mechanical framework for peridynamics. Peridynamic equation of motion is known as upscaled Newton’s equation. The peridynamic system consists of finite number of nonlocally interacting particles at nano and meso scales. This particle representation of peridynamics can be treated in terms of classical statistical mechanics. Hence, in this work the phase space is constructed based on the PD particle from their evolving momentum pi and positions xi. The statistical ensembles are derived by defining appropriate partition functions. The algorithms for NVE and NPH implemented in the classical molecular dynamics are revisited for equilibrium peridynamic models. The current work introduces Langevin dynamics to the peridynamic theory through fluctuation–dissipation principle. This introduces a heat bath to the peridynamic system which eliminates the ambiguity with the role of temperature in a peridynamic system. Finally, it was seen that the homogenization of a peridynamic model with finite number of particles approaches to a conventional continuum model. The upscaled non-equilibrium peridynamics has potential applications in modeling wide variety of multiscale–multiphysics problems from nano to macro scale or vice versa.

Online multi-modal robust non-negative dictionary learning for visual tracking.

Dictionary learning is a method of acquiring a collection of atoms for subsequent signal representation. Due to its excellent representation ability, dictionary learning has been widely applied in multimedia and computer vision. However, conventional dictionary learning algorithms fail to deal with multi-modal datasets. In this paper, we propose an online multi-modal robust non-negative dictionary learning (OMRNDL) algorithm to overcome this deficiency. Notably, OMRNDL casts visual tracking as a dictionary learning problem under the particle filter framework and captures the intrinsic knowledge about the target from multiple visual modalities, e.g., pixel intensity and texture information. To this end, OMRNDL adaptively learns an individual dictionary, i.e., template, for each modality from available frames, and then represents new particles over all the learned dictionaries by minimizing the fitting loss of data based on M-estimation. The resultant representation coefficient can be viewed as the common semantic representation of particles across multiple modalities, and can be utilized to track the target. OMRNDL incrementally learns the dictionary and the coefficient of each particle by using multiplicative update rules to respectively guarantee their non-negativity constraints. Experimental results on a popular challenging video benchmark validate the effectiveness of OMRNDL for visual tracking in both quantity and quality.

The spatial Lambda-Fleming–Viot process: An event-based construction and a lookdown representation

Nous construisons un processus à valeurs mesures équivalent au processus $\varLambda $-Fleming–Viot spatial (SLFV) introduit dans (Banach Center Publ. 80 (2008) 121–144). Contrairement à la construction effectuée dans (Banach Center Publ. 80 (2008) 121–144), nous fixons une réalisation de la suite d’événements de reproduction et obtenons une évolution quenched des diversités génétiques locales. Pour ce faire, nous utilisons une représentation particulaire qui met en avant le rôle des généalogies dans l’attribution des types (ou allèles) aux individus de la population. Cette construction nous permet également de clarifier l’espace d’états du SLFV et d’obtenir plusieurs propriétés trajectorielles du processus à valeurs mesures, ainsi que des arbres étiquetés qui décrivent les relations généalogiques liant un échantillon d’individus. Nous complétons ces résultats avec une construction look-down fournissant un système de particules dont la mesure empirique au temps $t$, vue comme un processus en $t$, a même loi que le SLFV quenched. Dans tous ces résultats, le fait que nous travaillions à configuration d’événements fixée et que les reproductions ne se produisent que localement (en espace) introduisent de sérieuses difficultés techniques qui sont surmontées en contrôlant le nombre d’événements et de particules présentes dans une zone donnée de l’espace pendant un laps de temps macroscopique.

Robust visual multitask tracking via composite sparse model

Recently, multitask learning was applied to visual tracking by learning sparse particle representations in a joint task, which led to the so-called multitask tracking algorithm (MTT). Although MTT shows impressive tracking performances by mining the interdependencies between particles, the individual feature of each particle is underestimated. The utilized L1,q norm regularization assumes all features are shared between all particles and results in nearly identical representation coefficients in nonsparse rows. We propose a composite sparse multitask tracking algorithm (CSMTT). We develop a composite sparse model to formulate the object appearance as a combination of the shared feature component, the individual feature component, and the outlier component. The composite sparsity is achieved via the L1,∞ and L1,1 norm minimization, and is optimized by the alternating direction method of multipliers, which provides a favorable reconstruction performance and an impressive computational efficiency. Moreover, a dynamical dictionary updating scheme is proposed to capture appearance changes. CSMTT is tested on real-world video sequences under various challenges, and experimental results show that the composite sparse model achieves noticeable lower reconstruction errors and higher computational speeds than traditional sparse models, and CSMTT has consistently better tracking performances against seven state-of-the-art trackers.

Visual tracking based on group sparsity learning

We propose a new tracking method based on a group sparsity learning model. Previous work on sparsity tracking rely on a single sparse model to characterize the templates of tracking targets, which is hard to express complex tracking scenes. In this work, we utilize a superposition of multiple simpler sparse models to capture the structural information across templates. More specifically, our tracking method is formulated within particle filter framework and the particle representations are decomposed into two sparsity norms: a $$l_{1,\infty }$$l1,? norm and a $$l_{1,2}$$l1,2 norm, capturing the common and different information across the templates, respectively. To efficiently implement the proposed tracker, we adapt the alternating direction method of multipliers to solve the formulated two-norm optimization problem. The proposed tracking method is compared with seven state-of-the-art trackers using 16 publicly available and challenging video sequences due to appearance changes, heavy occlusions, and pose variations. Experiment results show that our tracker outperforms the five other tracking methods.

A new non-overlapping concept to improve the Hybrid Particle Level Set method in multi-phase fluid flows

A novel non-overlapping concept is augmented to the Hybrid Particle Level Set (HPLS) method to improve its accuracy and suitability for the modelling of multi-phase fluid flows. The concept addresses shortcomings in the reseeding algorithm, which maintains resolution of the surface at runtime. These shortcomings result in the misplacement of newly seeded particles in the opposite signed domain and necessitate a restriction on the distance that a particle can escape without deletion, which reduces the effectiveness of the method. The non-overlapping concept judges the suitability of potential new particles based on information already contained within the particle representation of the surface. By preventing the misplacement of particles it is possible to significantly relax the distance restriction thereby increasing the accuracy of the HPLS method in multi-phase flows. To demonstrate its robustness and efficiency, the concept is examined with a number of challenging test cases, including both level-set-only simulations and two-phase fluid flows.

Modeling and measurement of abraded particles

A novel particle representation is presented that allows the description of particle roundness as an additional measure, aiming at the characterization of entire particle ensembles during an attrition process. The particle representation is based on a combination of a convex polyhedron and a solid sphere which is known as Minkowski addition in the field of convex geometry. An image analysis procedure and a subsequent roundness estimation procedure are presented, utilizing a Hough transformation and a local optimal fit of the proposed shape model. The technique has been verified based on simulated particles and tested in a proof of concept experiment featuring potassium alum which was exposed to high stirring rates resulting in considerable attrition and abrasion. The results demonstrate that the proposed model and image analysis procedure are valuable tools to monitor and study attrition behavior.

Tunneling in polymer quantization and the Quantum Zeno Effect

As an application of the polymer quantization scheme, in this work we investigate the one dimensional quantum mechanical tunneling phenomenon from the perspective of polymer representation of a non-relativistic point particle and derive the transmission and reflection coefficients. Since any tunneling phenomenon inevitably evokes a tunneling time we attempt an analytical calculation of tunneling times by defining an operator well suited in discrete spatial geometry. The results that we come up with hint at appearance of the Quantum Zeno Effect in polymer framework.

A jetlet hierarchy for ideal fluid dynamics

Truncated Taylor expansions of smooth flow maps are used in Hamiltonʼs principle to derive a multiscale Lagrangian particle representation of ideal fluid dynamics. Numerical simulations for scattering of solutions at one level of truncation are found to produce solutions at higher levels. These scattering events to higher levels in the Taylor expansion are interpreted as modeling a cascade to smaller scales.

Optimization of decentralized random field estimation networks under communication constraints through Monte Carlo methods

We propose a new methodology for designing decentralized random field estimation schemes that takes the tradeoff between the estimation accuracy and the cost of communications into account. We consider a sensor network in which nodes perform bandwidth limited two-way communications with other nodes located in a certain range. The in-network processing starts with each node measuring its local variable and sending messages to its immediate neighbors followed by evaluating its local estimation rule based on the received messages and measurements. Local rule design for this two-stage strategy can be cast as a constrained optimization problem with a Bayesian risk capturing the cost of transmissions and penalty for the estimation errors. A similar problem has been previously studied for decentralized detection. We adopt that framework for estimation, however, the corresponding optimization schemes involve integral operators that are impossible to evaluate exactly, in general. We employ an approximation framework using Monte Carlo methods and obtain an optimization procedure based on particle representations and approximate computations. The procedure operates in a message-passing fashion and generates results for any distributions if samples can be produced from, e.g., the marginals. We demonstrate graceful degradation of the estimation accuracy as communication becomes more costly.

Object Tracking via Robust Multitask Sparse Representation

Sparse representation has been applied to the object tracking problem. Mining the self-similarities between particles via multitask learning can improve tracking performance. However, some particles may be different from others when they are sampled from a large region. Imposing all particles share the same structure may degrade the results. To overcome this problem, we propose a tracking algorithm based on robust multitask sparse representation (RMTT) in this letter. When we learn the particle representations, we decompose the sparse coefficient matrix into two parts in our algorithm. Joint sparse regularization is imposed on one coefficient matrix while element-wise sparse regularization is imposed on another matrix. The former regularization exploits self-similarities of particles while the later one considers the differences between them. Experiments on the benchmark data show the superior performance over other state-of-art algorithms.

Hybrid particle swarm optimization for preemptive resource-constrained project scheduling

Abstract In this paper a hybrid particle swarm optimization procedure is proposed to solve the preemptive resource-constrained project scheduling problem in which a maximum of one interruption per activity is allowed. Four types of particle representations are designed and two schedule generation schemes are adopted to decode the particle representations. Particle-updating mechanisms based on the peak crossover operator are designed for all particle representations. Computational experiments have been carried out on standard project scheduling problem sets. Analysis of the computational results has confirmed that introduction of preemption helps to reduce project duration and the proposed particle swarm optimization procedures are effective for preemptive resource-constrained project scheduling.

Electromagnetic Fields on Time-Involute Particles Around Biharmonic Particles and its Lorentz Transformations in Heisenberg Spacetime

In this paper, we obtain the new parametric representation for a time-involute particles in Heisenberg spacetime \( \mathcal {H}_{1}^{4}\). By using the Frenet frame, we derive the necessary and sufficient conditions to construct a biharmonic particle Heisenberg spacetime \(\mathcal {H}_{1}^{4}\). We give a geometrical description of time-involute particles around timelike biharmonic particle in \(\mathcal {H} _{1}^{4}\). Moreover, we obtain Lorentz transformations this particles. Finally, we give the relationship of electromagnetic fields on Heisenberg spacetime.

A triple-moment hail bulk microphysics scheme. Part I: Description and initial evaluation

Hail processes in deep convection can have a substantial impact on precipitation characteristics as well as on dynamic and thermodynamic properties of convective downdrafts and cold pools, yet the realistic representation of hail in many cloud-resolving models employing bulk microphysical schemes is challenging. The limits imposed by fixing one or two of the distribution parameters in many one- and two-moment bulk microphysics schemes often lead to particularly poor representations of particles within the tails of size distribution spectra; an especially important consideration for hail, which covers a broad range of sizes in nature. In order to improve the representation of hail distributions in simulations of deep moist convection in cloud-resolving numerical models, a new triple-moment bulk hail microphysics scheme (3MHAIL) is presented and evaluated. The 3MHAIL scheme predicts the relative dispersion parameter for a gamma distribution function via prognostication of the sixth moment (related to the reflectivity factor) of the distribution in addition to the mass mixing ratio and number concentration (third and zeroeth moments, respectively) thereby allowing for a fully prognostic distribution function. Significant improvement in the representation of sedimentation, melting, and formation processes of hail are achieved with the 3MHAIL scheme compared to lower-order moment schemes.

High gradient magnetic particle separation in a channel with bifurcations

Micro particle separation from solid–liquid suspension under the influence of hydrodynamic and magnetic forces in a channel with bifurcation is studied numerically by applying the Boundary Element Method based fluid flow solver. The particle trajectories are computed using the Lagrangian particle tracking, where the forces on particles are computed based on the point particle representation. In the separator due to the bifurcation channel geometry the magnetic particles experience varying Kelvin force as they travel along the channel, although in the same direction the high gradient magnetic field does not change. In this way, the interplay of hydrodynamic and magnetic forces leads to changes in collection efficiency of the separator. A comparison with magnetic separation in the narrow channel design is done and recommendation for optimal choice of fluid flow rate and magnitude of external magnetic field is discussed.

A small-time coupling between $\Lambda$-coalescents and branching processes

We describe a new general connection between $\Lambda$-coalescents and genealogies of continuous-state branching processes. This connection is based on the construction of an explicit coupling using a particle representation inspired by the lookdown process of Donnelly and Kurtz. This coupling has the property that the coalescent comes down from infinity if and only if the branching process becomes extinct, thereby answering a question of Bertoin and Le Gall. The coupling also offers new perspective on the speed of coming down from infinity and allows us to relate power-law behavior for $N^{\Lambda}(t)$ to the classical upper and lower indices arising in the study of pathwise properties of L\'{e}vy processes.

Mesoscale modeling of shear-thinning polymer solutions

We simulate the linear and nonlinear rheology of two different viscoelastic polymer solutions, a polyisobutylene solution in pristane and an aqueous solution of hydroxypropylcellulose, using a highly coarse-grained approach known as Responsive Particle Dynamics (RaPiD) model. In RaPiD, each polymer has originally been depicted as a spherical particle with the effects of the eliminated degrees of freedom accounted for by an appropriate free energy and transient pairwise forces. Motivated by the inability of this spherical particle representation to entirely capture the nonlinear rheology of both fluids, we extended the RaPiD model by introducing a deformable particle capable of elongation. A Finite-Extensible Non-Linear Elastic potential provides a free energy penalty for particle elongation. Upon disentangling, this deformability allows more time for particles to re-entangle with neighbouring particles. We show this process to be integral towards recovering the experimental nonlinear rheology, obtaining excellent agreement. We show that the nonlinear rheology is crucially dependent upon the maximum elongation and less so on the elasticity of the particles. In addition, the description of the linear rheology has been retained in the process.