Discrete-continuous Model Research Articles

Modelling the complementarity and flexibility between different shared modes available in smart electric mobility hubs (eHUBS)

eHUBS are physical locations that integrate two or more electric shared mobility modes. As they provide transport users easier access to a wide range of transport modes, multimodal behaviour is expected to be more common. However, this issue has not been addressed in previous stated preference studies on mode choices involving innovative transport modes. In this study, multimodal behaviour is explicitly addressed both in measurement and in modelling by adopting the multiple discrete–continuous (MDC) modelling framework in contrast to discrete choice models. Instead of asking transport users to indicate the most preferred alternative, they were allowed to choose more than one alternative by allocating trips between several modes. This study aims to answer two questions: 1) whether there is complementarity between the multiple shared modes offered in eHUBS and 2) how would transport users adapt when one of the shared modes that they plan to use becomes unavailable. Using stated mode choice data of non-commuting trips from transport users whose current mode is driving a private car in Manchester, UK, several models under the MDC framework were estimated including Multiple Discrete-Continuous Extreme Value (MDCEV) model, mixed MDCEV model, and the extended Multiple Discrete Continuous (eMDC) model. The results show that there is complementarity between shared electric vehicle (EV) and electric bike (e-bike) offered in the eHUBS. In addition, the research show that the flexibility between those two shared modes is stronger than assumed in the MDCEV model, and common preference heterogeneity cannot fully account for this phenomenon.

Modelling daisy quorum drive: A short-term bridge across engineered fitness valleys.

Engineered gene-drive techniques for population modification and/or suppression have the potential for tackling complex challenges, including reducing the spread of diseases and invasive species. Gene-drive systems with low threshold frequencies for invasion, such as homing-based gene drive, require initially few transgenic individuals to spread and are therefore easy to introduce. The self-propelled behavior of such drives presents a double-edged sword, however, as the low threshold can allow transgenic elements to expand beyond a target population. By contrast, systems where a high threshold frequency must be reached before alleles can spread-above a fitness valley-are less susceptible to spillover but require introduction at a high frequency. We model a proposed drive system, called "daisy quorum drive," that transitions over time from a low-threshold daisy-chain system (involving homing-based gene drive such as CRISPR-Cas9) to a high-threshold fitness-valley system (requiring a high frequency-a "quorum"-to spread). The daisy-chain construct temporarily lowers the high thresholds required for spread of the fitness-valley construct, facilitating use in a wide variety of species that are challenging to breed and release in large numbers. Because elements in the daisy chain only drive subsequent elements in the chain and not themselves and also carry deleterious alleles ("drive load"), the daisy chain is expected to exhaust itself, removing all CRISPR elements and leaving only the high-threshold fitness-valley construct, whose spread is more spatially restricted. Developing and analyzing both discrete patch and continuous space models, we explore how various attributes of daisy quorum drive affect the chance of modifying local population characteristics and the risk that transgenic elements expand beyond a target area. We also briefly explore daisy quorum drive when population suppression is the goal. We find that daisy quorum drive can provide a promising bridge between gene-drive and fitness-valley constructs, allowing spread from a low frequency in the short term and better containment in the long term, without requiring repeated introductions or persistence of CRISPR elements.

How immune dynamics shape multi-season epidemics: a continuous-discrete model in one dimensional antigenic space

We extend a previously published model for the dynamics of a single strain of an influenza-like infection. The model incorporates a waning acquired immunity to infection and punctuated antigenic drift of the virus, employing a set of coupled integral equations within a season and a discrete map between seasons. The long term behaviour of the model is demonstrated by examples where immunity to infection depends on the time since a host was last infected, and where immunity depends on the number of times that a host has been infected. The first scenario leads to complicated dynamics in some regions of parameter space, and to regions of parameter space with more than one attractor. The second scenario leads to a stable fixed point, corresponding to an identical epidemic each season. We also examine the model with both paradigms in combination, almost always but not exclusively observing a stable fixed point or periodic solution. Adding stochastic perturbations to the between season map fails to destroy the model’s qualitative dynamics. Our results suggest that if the level of host immunity depends on the elapsed time since the last infection then the epidemiological dynamics may be unpredictable.

Pseudo-spin polarized one-way elastic wave eigenstates in one-dimensional phononic superlattices

We use a one-dimensional discrete binary elastic superlattice bridging continuous models of superlattices that showcase one-way propagation character and the discrete elastic Su-Schrieffer-Heeger model that does not. By considering Bloch wave solutions of the superlattice wave equation, we demonstrate conditions supporting elastic eigenmodes that do not satisfy translational invariance of Bloch waves over the entire Brillouin zone, unless their amplitude vanishes for some wave number. These modes are characterized by a pseudo-spin, and occur only on one side of the Brillouin zone for given spin, leading to spin-selective one-way wave propagation. We demonstrate how these features result from the interplay of translational invariance of Bloch waves, pseudo-spin, and a Fabry-Pérot resonance condition in the superlattice unit cell.

Pseudo-Spin Polarized One-Way Elastic Wave Eigenstates in One-Dimensional Phononic Superlattices

We investigate a one-dimensional discrete binary elastic superlattice bridging continuous models of superlattices that showcase a one-way propagation character, as well as the discrete elastic Su–Schrieffer–Heeger model, which does not exhibit this character. By considering Bloch wave solutions of the superlattice wave equation, we demonstrate conditions supporting elastic eigenmodes that do not satisfy the translational invariance of Bloch waves over the entire Brillouin zone, unless their amplitude vanishes for a certain wave number. These modes are characterized by a pseudo-spin and occur only on one side of the Brillouin zone for a given spin, leading to spin-selective one-way wave propagation. We demonstrate how these features result from the interplay of the translational invariance of Bloch waves, pseudo-spins, and a Fabry–Pérot resonance condition in the superlattice unit cell.

Discrete-continuous models of residential energy demand: A comprehensive review

This paper reviews forty years of research applying econometric models of discrete-continuous choice to analyze residential demand for energy. The review is primarily from the perspective of economic theory. We examine how well the utility-theoretic models developed in the literature match data that is commonly available on residential energy use, and we highlight the modeling challenges that have arisen through efforts to match theory with data. The literature contains two different formalizations of a corner solution. The first, by Dubin and McFadden (1984) and Hanemann (1984), models an extreme corner solution, in which only one of the discrete choice alternatives is chosen. While those papers share similarities, they also have some differences which have not been noticed or exposited in the literature. Subsequently, a formulation first implemented by Wales and Woodland (1983) and extended by Kim et al. (2002) and Bhat (2008) models a general corner solution, where several but not all of the discrete choice alternatives are chosen. Seventeen papers have employed one or another of these models to analyze residential demand for fuels and/or energy end uses in a variety of countries. We review issues that arose in these applications and identify some alternative model formulations that can be used in future work on residential energy demand.

Discrete-continuous model for facility location problem with capacity-cost relation constraints

The facility location problem (FLP) involves optimally locating a set of facilities that must satisfy the demands of a group of customers distributed in a planar area. Traditionally, various FLP models have been applied to find new facilities by considering already-existing facilities, and choosing new locations among a given set of discrete candidates. These are unreasonable because a limited set of candidates may not include the optimal locations. In this study, we developed a mathematical model based on mixed-integer linear programming (MILP) for FLP. In this model, the locations of existing facilities are known and categorized as discrete. On the other hand, the locations of new facilities to be found are categorized as continuous and discrete. In addition, the optimal number of new facilities is determined by a judgment formula. The cost of facilities is also considered, including fixed opening costs and variable capacity-related costs. To make the model closer to reality, the entire area is divided into several zones with varying costs. We developed a greedy multiphase location method for the proposed MILP (MPL-MILP) that efficiently determines the exact locations of new facilities in a stepwise manner. For large-scale problems, we developed a two-variable-based dynamic iterative partial optimization (TVB-DIPO) to obtain near-optimal solutions within a given time limit. Computational experiments were conducted to test the performance of the proposed MPL-MILP and TVB-DIPO. The results indicate that MPL-MILP is suitable for small- and medium-sized problems with exact solutions, while TVB-DIPO is more suitable for large-scale problems with higher solution efficiencies.

Identifying the relationship between intention to use flat-rate public transport and trip frequency by a discrete-continuous model

Identifying the relationship between intention to use flat-rate public transport and trip frequency by a discrete-continuous model

Fractional discrete-continuous model of heat transfer process

Fractional discrete-continuous model of heat transfer process

Self-force of high-speed dislocation in anisotropic media based on configurational mechanics

Subsonic, transonic, and supersonic dislocations play a critical role during super high strain rate (>105/s) deformation. For these high-speed dislocations, the self-force is history dependent, which is different from and much more complex than the quasi-static dislocations. Solutions to the self-force of high-speed dislocation in continuum media are only known for some special cases, i.e., subsonic dislocation moving in isotropic infinite crystals with a constant speed. However, metals are generally anisotropic, and high-speed dislocations may have complicated histories and interact with the free surface. How crystal anisotropy, complicated motion history and free surface influence their self-force has so far received little attention. In the current work, we proposed an effective calculation method of self-force on high-speed dislocation based on the discrete-continuous model of three-dimensional dislocation elastodynamics and the dynamic J-integral of configurational mechanics. It is applicable to arbitrarily moving subsonic, transonic and supersonic dislocation, in both isotropic and anisotropic crystals, and can automatically consider the image force if the dislocation is close to the free surface. The effectiveness of the method is carefully verified by comparing it with the existing theoretical solutions and the molecular dynamics results. The effect of crystal anisotropy on the elastodynamic stress field, as well as the self-force of high-speed dislocation close to or far from free surface are studied.

On derivative-free extended Kalman filtering and its Matlab-oriented square-root implementations for state estimation in continuous-discrete nonlinear stochastic systems

Recent research in nonlinear filtering and signal processing has suggested an efficient derivative-free Extended Kalman filter (EKF) designed for discrete-time stochastic systems. Such approach, however, has failed to address the estimation problem for continuous-discrete models. In this paper, we develop a novel continuous-discrete derivative-free EKF methodology by deriving the related moment differential equations (MDEs) and sample point differential equations (SPDEs). Additionally, we derive their Cholesky-based square-root MDEs and SPDEs and obtain several numerically stable derivative-free EKF methods. Finally, we propose the MATLAB-oriented implementations for all continuous-discrete derivative-free EKF algorithms derived. They are easy to implement because of the built-in fashion of the MATLAB numerical integrators utilized for solving either the MDEs or SPDEs in use, which are the ordinary differential equations (ODEs). More importantly, these are accurate derivative-free EKF implementations because any built-in MATLAB ODE solver includes the discretization error control that bounds the discretization error arisen and makes the implementation methods accurate. Besides, this is done in automatic way and no extra coding is required from users. The new filters are particularly effective for working with stochastic systems with highly nonlinear and/or nondifferentiable drift and observation functions, i.e. when the calculation of Jacobian matrices are either problematical or questionable. The performance of the novel filtering methods is demonstrated on several numerical tests.

Probit-Based Discrete-Continuous Choice Model to Explore the Relationship Between Car Ownership and Commuters’ Non-Work Activity Durations in Xiaoshan District of Hangzhou, China

In China, a developing country, the car ownership level is much lower than that in developed countries, but transportation policies have been implemented to discourage car ownership and mitigate traffic congestion. However, car ownership (considered as car availability in this paper, meaning that an individual has access to a household private car) may influence travelers’ well-being. To highlight the interrelation between car ownership and travelers’ well-being, this paper develops a probit-based discrete-continuous model to analyze the relationship between car ownership and the duration of commuters’ three major non-work outdoor activities (Act1: shopping and dining; Act2: leisure and entertainment; and Act3: visiting relatives or friends) in Xiaoshan District, Hangzhou, China. Empirical results indicate strong effects of individual and household socio-demographics, built environment attributes, and work-related characteristics on the car ownership decision and the duration of three non-work activities. The analysis shows positive correlations in unobserved factors between the car ownership decision and the duration of Acts1–3, indicating a mutually promotive relationship. Similarly, negative correlations among the duration of Acts1–3 show that non-work activities’ duration is mutually substitutive. These findings will help to better understand commuters’ car ownership decisions and non-work outdoor activity behavior restricted by fixed work schedules in developing countries, which can, in turn, better evaluate the impact of transportation policies (such as car ownership restriction) on travel demand as well as well-being, and provide decision support for the formulation of transportation policies.

Generation Expansion Planning Considering Discrete Storage Model and Renewable Energy Uncertainty: A Bi-Interval Optimization Approach

Both discrete storage model (DSM) and continuous storage model (CSM) have been used in the power system planning literature. In this article, we conduct a sizing-error analysis for the use of CSM in generation expansion planning (GEP), which shows more reasonable storage sizing decisions are offered by the DSM in comparison to the CSM. However, when the DSM is considered in the context of interval optimization, the discrete status variables in mutually exclusive constraints and the strong temporal coupling in state-of-charge constraints create significant challenges. To tackle this, a tailored interval optimization approach is proposed to consider both DSM and renewable energy uncertainty in GEP. Our approach is proved to cover all worst cases in a given uncertainty set, meanwhile running in an iteration-free manner. Moreover, to reduce the conservativeness of investment decisions, a bi-interval policy is designed to achieve a better tradeoff between investment cost and system security.

Synchronization coexistence in a Rulkov neural network based on locally active discrete memristor

At present, many neuron models have been proposed, which can be divided into discrete neuron models and continuous neuron models. Discrete neuron models have the advantage of faster simulation speed and the ease of understanding complex dynamic phenomena. Due to the properties of memorability, nonvolatility, and local activity, locally active discrete memristors (LADMs) are also suitable for simulating synapses. In this paper, we use an LADM to mimic synapses and establish a Rulkov neural network model. It is found that the change of coupling strength and the initial state of the LADM leads to multiple firing patterns of the neural network. In addition, considering the influence of neural network parameters and the initial state of the LADM, numerical analysis methods such as phase diagram and timing diagram are used to study the phase synchronization. As the system parameters and the initial states of the LADM change, the LADM coupled Rulkov neural network exhibits synchronization transition and synchronization coexistence.

Investigating the Self-Force and Evolution of High-Speed Dislocations in Impacted Metals: A Discrete-Continuous Model and Configurational Mechanics Analysis

Investigating the Self-Force and Evolution of High-Speed Dislocations in Impacted Metals: A Discrete-Continuous Model and Configurational Mechanics Analysis

Efficient Estimation of Time-Dependent Brain Functional Connectivity Using Anatomical Connectivity Constraints

There is ongoing interest in the dynamics of resting state brain networks (RSNs) as potential predictors of cognitive and behavioural states. Multivariate Autoregressors (MAR) are used to model regional brain activity as a linear combination of past activity in other regions. The coefficients of the MAR are taken as estimates of effective brain connectivity. However, assumption of stationarity, and the large number of coefficients renders the MAR impractical for estimating brain networks from standard neuroimaging time-series of limited durations. We propose HsMM-MAR-AC, a novel sparse hybrid discrete-continuous model for the efficient estimation of time-dependent effective brain networks from non-stationary brain activity time-series. Discrete quasi-stationary Brain States, and the fast switching between them, are modelled by a Hidden semi-Markov Model whose continuous emissions are drawn from a sparse MAR. The coefficients of the MAR are restricted by Anatomical Brain Connectivity information in two ways: 1) Effective direct connectivity between two brain regions is only considered if the corresponding anatomical connection exists; and 2) the autoregressors lag associated with each connection is based on the fiber length between the two regions, such that only one lag per connection is estimated. We test the accuracy of HsMM-MAR-AC in recovering simulated resting state networks of various durations, and at different thresholds of anatomical restrictions. We demonstrate that HsMM-MAR-AC recovers the RSNs more accurately than the benchmark method of the sliding window, with as little as 4 minutes of data. We also show that when the anatomical restrictions are relaxed, longer time-series are needed to estimate the networks, and became computationally unfeasible without anatomical restrictions. HsMM-MAR-AC offers an efficient model for estimating time-dependent Effective Connectivity from neuroimaging data that exploits the advantages of Hidden Markov and MAR models without identifiability problems, excessive demand on data collection, or unnecessary computational effort.

SubZero: A Sea Ice Model With an Explicit Representation of the Floe Life Cycle

AbstractSea ice dynamics exhibit granular behavior as individual floes and fracture networks become particularly evident at length scales O(10–100) km and smaller. However, climate models do not resolve floes and represent sea ice as a continuum, while existing floe‐scale sea ice models tend to oversimplify floes using discrete elements of predefined simple shapes. The idealized nature of climate and discrete element sea ice models presents a challenge of comparing the model output with floe‐scale sea ice observations. Here we present SubZero, a conceptually new sea ice model geared to explicitly simulate the life cycles of individual floes by using complex discrete elements with time‐evolving shapes. This unique model uses parameterizations of floe‐scale processes, such as collisions, fractures, ridging, and welding, to simulate a wide range of evolving floe shapes and sizes. We demonstrate the novel capabilities of the SubZero model in idealized experiments, including uniaxial compression, the summer‐time sea ice flow through the Nares Strait, and winter‐time sea ice growth. The model naturally reproduces the statistical behavior of the observed sea ice, such as the power‐law appearance of the floe size distribution and the long‐tailed ice thickness distribution. The SubZero model could provide a valuable alternative to existing discrete element and continuous sea ice models for simulations of floe interactions.

A panel data-based discrete-continuous modelling framework to analyze longitudinal driver behavior in homogeneous and heterogeneous disordered traffic conditions

ABSTRACT We propose a panel data-based discrete-continuous modeling framework to analyze driver behavior in two disparatetrajectory datasets – one from a heterogeneous disorderly (HD) traffic streamin India and another from a homogeneous traffic stream in the United States. Thepanel data-based framework allows the analyst to isolate the subject vehicle-and driver-specific unobserved factors that influence driver behavior. Doing sohelps reduce the confounding effects of such unobserved factors on analyzingthe influence of observed factors, such as relative speeds and spacing betweenthe subject vehicle and other vehicles, on driver behavior. The empiricalresults reveal both similarities and differences in driver behavior between thetwo trajectory datasets. In addition, the analysis sheds light on the suitability of different lengthsof influence zones on driver behavior in the two datasets. The insights from this study can help improve driver behavior modelsand traffic simulation frameworks for both traffic conditions..

Discrete-Continuous Smoothing and Mapping

We describe a general approach for maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> (MAP) inference in a class of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">discrete-continuous factor graphs</i> commonly encountered in robotics applications. While there are openly available tools providing flexible and easy-to-use interfaces for specifying and solving inference problems formulated in terms of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">either</i> discrete <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">or</i> continuous graphical models, at present, no similarly general tools exist enabling the same functionality for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hybrid</i> discrete-continuous problems. We aim to address this problem. In particular, we provide a library, DC-SAM, extending existing tools for inference problems defined in terms of factor graphs to the setting of discrete-continuous models. A key contribution of our work is a novel solver for efficiently recovering approximate solutions to discrete-continuous inference problems. The key insight to our approach is that while joint inference over continuous and discrete state spaces is often hard, many commonly encountered discrete-continuous problems can naturally be split into a “discrete part” and a “continuous part” that can individually be solved easily. Leveraging this structure, we optimize discrete and continuous variables in an alternating fashion. In consequence, our proposed work enables straightforward representation of and approximate inference in discrete-continuous graphical models. We also provide a method to approximate the uncertainty in estimates of both discrete and continuous variables. We demonstrate the versatility of our approach through its application to distinct robot perception applications, including robust pose graph optimization, and object-based mapping and localization.

New continuous-discrete model for wireless sensor networks security

A wireless sensor network (WSN) is a group of "smart" sensors with a wireless infrastructure designed to monitor the environment. This technology is the basic concept of the Internet of Things (IoT). The WSN can transmit confidential information while working in an insecure environment. Therefore, appropriate security measures must be considered in the network design. However, computational node constraints, limited storage space, an unstable power supply, and unreliable communication channels, and unattended operations are significant barriers to the application of cybersecurity techniques in these networks. This paper considers a new continuous-discrete model of malware propagation through wireless sensor network nodes, which is based on a system of so-called dynamic equations with impulsive effect on time scales.