Continuous Space Model Research Articles

A Hybrid Framework for Multi-Objective Construction Site Layout Optimization

Effective Construction Site Layout Planning (CSLP) ensures the organized placement and sizing of temporary facilities, enhancing workflow and logistical efficiency. Poorly planned layouts, however, can increase material handling times, create bottlenecks, and reduce productivity, ultimately leading to higher costs. The main objective of this study is to introduce a BIM-based hybrid framework for CSLP that integrates Systematic Layout Planning (SLP) with a Genetic Algorithm (GA), developed through a Design Science Research approach. This Construction Site Optimization Framework (CSOF) addresses CSLP as a multi-objective optimization problem, prioritizing efficient positioning of facilities while accounting for workflow intensity, safety, and manager preferences. The framework’s continuous-space modeling supports a realistic approach, moving beyond fixed-location models. Exploratory case studies demonstrated CSOF’s effectiveness, achieving 30.79% to 40.98% reductions in non-value-adding travel distances and adaptability across varied site conditions. In this way, this research provides a decision-support tool that balances automation with decision-maker input, enhancing layout efficiency and operational flexibility in construction site management.

Establishment of a locally adaptive allele in multidimensional continuous space.

Local adaptation is widely seen when species adapt to spatially heterogeneous environments. Although many theoretical studies have investigated the dynamics of local adaptation using two-population models, there remains a need to extend the theoretical framework to continuous space settings, reflecting the real habitats of species. In this study, we use a multidimensional continuous space model and mathematically analyze the establishment process of local adaptation, with a specific emphasis on the relative roles of mutation and migration. First, the role of new mutations is evaluated by deriving the establishment probability of a locally adapted mutation using a branching process and a diffusion approximation. Next, the contribution of immigrants from a neighboring region with similar environmental conditions is considered. Theoretical predictions of the local adaptation rate agreed with the results of Wright-Fisher simulations in both mutation-driven and migration-driven cases. Evolutionary dynamics depend on several factors, including the strength of migration and selection, population density, habitat size, and spatial dimensions. These results offer a theoretical framework for assessing whether mutation or migration predominantly drives convergent local adaptation in spatially continuous environments in the presence of patchy regions with similar environmental conditions.

Meta-learning-based continuous state-space models for rapid monitoring using heterogeneous grade sources with uneven sampling

In an industrial batch, it is common to produce products with different grades, so only a limited number of data are available for each grade of product. The data are also easily contaminated by external disturbances and noise. The sampling interval would be messy and irregular if contaminated samples were removed. Thus, it is difficult to build models for monitoring the corresponding process. This paper proposes a meta-learning-based functional continuous state space model for fast modeling and monitoring of multi-grade batch processes. It takes advantage of wavelet function properties to effectively handle the irregular sampling issue. In addition, the meta-learning method uses diverse historical multi-grade datasets for modeling. It rapidly establishes an efficient and reliable monitoring model for new running batches with a small number of batch data. The effectiveness of the proposed method is shown through a numerical case and an industrial case in the chemical batch process.

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.

A Continuous Space Model of New Economic Geography with a Quasi-Linear Log Utility Function

A Continuous Space Model of New Economic Geography with a Quasi-Linear Log Utility Function

Making waves: Comparative analysis of gene drive spread characteristics in a continuous space model.

With their ability to rapidly increase in frequency, gene drives can be used to modify or suppress target populations after an initial release of drive individuals. Recent advances have revealed many possibilities for different types of drives, and several of these have been realized in experiments. These drives have advantages and disadvantages related to their ease of construction, confinement and capacity to be used for modification or suppression. Though characteristics of these drives have been explored in modelling studies, assessment in continuous space environments has been limited, often focusing on outcomes rather than fundamental properties. Here, we conduct a comparative analysis of many different gene drive types that have the capacity to form a wave of advance in continuous space using individual-based simulations in continuous space. We evaluate the drive wave speed as a function of drive performance and ecological parameters, which reveals substantial differences between drive performance in panmictic versus spatial environments. In particular, we find that suppression drive waves are uniquely vulnerable to fitness costs and undesired CRISPR cleavage activity in embryos by maternal deposition. Some drives, however, retain robust performance even with widely varying efficiency parameters. To gain a better understanding of drive waves, we compare their panmictic performance and find that the rate of wild-type allele removal is correlated with drive wave speed, though this is also affected by other factors. Overall, our results provide a useful resource for understanding the performance of drives in spatially continuous environments, which may be most representative of potential drive deployment in many relevant scenarios.

Modeling Crossing Behaviors of E-Bikes at Intersection With Deep Maximum Entropy Inverse Reinforcement Learning Using Drone-Based Video Data

The crossing behaviors modeling of non-networked road users can improve Connected and Autonomous Vehicles (CAVs)’s awareness of the imminent hazards in shared space while planning routes. In this study, an agent-based microsimulation model is utilized to simulate the crossing behavior of e-bikes which is difficult to model due to their greater maneuverability. To deeply understand the crossing mechanism of e-bikes, a customized neural network-based nonlinear reward function is developed from five dimensions, including travel efficiency, travel direction, travel destination, risk avoidance, and travel location. A Deep Maximum Entropy Inverse Reinforcement Learning(Deep MEIRL), which can recover the nonlinear reward function, is introduced to predict trajectories of e-bikes from the real drone-based video dataset, collected at the intersection of Jixiangcun, Xi’an (China). The results reveal that the Deep MEIRL can simulate the e-bike crossing trajectory more precisely, particularly in the microscopic behaviors of riders. Comparing Deep MEIRL with the baseline model MEIRL, it can be found that the nonlinear reward function designed in this paper is more advantageous in terms of continuous space modeling, with an improvement of 19.77%. Notably, Deep MEIRL outperforms MEIRL in modeling distance to potentially risk target states for left-and right-turn crossing behavior, improving Mean Absolute Error (MAE) by 71% and 30%, respectively. It means that the Deep MEIRL with a designed neural network is of great value to provide a logical result in modeling e-bike interaction with other road users. Therefore, the research is conducive to CAVs to understand e-bike behaviors in complex traffic scenarios, thereby assisting CAVs in making decisions efficiently.

Come together: A unified description of the escalator capacity.

We investigate a variety of aspects related to the simulation of passenger dynamics on escalators, mainly focusing on the discrepancy between the 'theoretical' and the 'practical' capacity that is observed for these facilities. The structure of the paper is twofold. In the first part, we introduce a space-continuous model to describe the transition of agents from walking on the plain to standing on the escalator. In the second part, we use numerical findings from simulations to study important measures like minimum distances between the standing agents and average occupancies of the escalator steps. One of the most important results obtained in this paper is a generalized analytical formula that describes the escalator capacity. We show that, apart from the conveyor speed, the capacity essentially depends on the time gap between entering passengers which we interpret as human reaction time. Comparing simulation results with corresponding empirical data from field studies and experiments, we deduce a minimum human reaction time in the range of 0.15s-0.30s which is in perfect agreement with results from social psychology. With these findings, it is now possible to determine accurately the relationship between the capacity and the speed of an escalator, allowing a science-based performance evaluation of buildings with escalators.

Recursive identification of a nonlinear state space model

SummaryThe convergence of a recursive prediction error method is analyzed. The algorithm identifies a nonlinear continuous time state space model, parameterized by one right‐hand side component of the differential equation and an output equation with a fixed differential gain, to avoid over‐parametrization. The method minimizes the criterion by simulation using an Euler discretization. A stability analysis of the associated differential equations results in conditions for (local) convergence to a minimum of the criterion function. Simulations verify the theoretical analysis and illustrate the performance in the presence of unmodeled dynamics, by identification of the nonlinear drum boiler dynamics of a power plant model.

Frame-guided assembly from a theoretical perspective.

The molecular self-assembly of various structures such as micelles and vesicles has been the subject of comprehensive studies. Recently, a new approach to design these structures, the frame-guided assembly, has been developed to progress toward fabrics of predefined shape and size, following an initially provided frame of guiding elements. Here, we study the frame-guided assembly in a two-dimensional membrane via computer simulations based on a single-bead coarse grained surfactant model in continuous space. In agreement with the experiment, the assembly process already starts for surfactant concentrations below the critical micelle concentration. Furthermore, upon increasing temperature, the formation process gets more delocalized. Additionally, the assembly process of the resulting membrane plane is modeled by a lattice gas model. It displays a similar phenomenology but additionally allows for the derivation of analytical mean-field predictions. In this way, a fundamental understanding of frame-guided assembly can be gained.

Lower Bound on the Capacity of the Continuous-Space SSFM Model of Optical Fiber

The capacity of a discrete-time model of optical fiber described by the split-step Fourier method (SSFM) as a function of the signal-to-noise ratio SNR and the number of segments in distance K is considered. It is shown that if K ≥ SNR2/3 and SNR → ∞, the capacity of the resulting continuous-space lossless model is lower bounded by 1/2 log2(1 + SNR) - 1/2 + o(1), where o(1) tends to zero with SNR. As K → ∞, the inter-symbol interference (ISI) averages out to zero due to the law of large numbers and the SSFM model tends to a diagonal phase noise model. It follows that, in contrast to the discrete-space model where there is only one signal degree-of-freedom (DoF) at high powers, the number of DoFs in the continuous-space model is at least half of the input dimension n. Intensity-modulation and direct detection achieves this rate. The pre-log in the lower bound when K=δ√SNR is generally characterized in terms of δ. It is shown that if the nonlinearity parameter γ → ∞, the capacity of the continuous-space model is 1/2 log2(1 + SNR) + o(1). The SSFM model when the dispersion matrix does not depend on K is considered. It is shown that the capacity of this model when K=δ√SNR, δ > 3, and SNR → ∞ is 1/2n log2(1 + SNR) + O(1). Thus, there is only one DoF in this model. Finally, it is found that the maximum achievable information rates (AIRs) of the SSFM model with back-propagation equalization obtained using numerical simulation follows a double-ascent curve. The AIR characteristically increases with SNR, reaching a peak at a certain optimal power, and then decreases as SNR is further increased. The peak is attributed to a balance between noise and stochastic ISI. However, if the power is further increased, the AIR will increase again, approaching the lower bound 1/2 log(1 + SNR) - 1/2 + o(1). The second ascent is because the ISI averages out to zero with K → ∞ sufficiently fast.

A spatial stochastic epidemic model: law of large numbers and central limit theorem

We consider an individual-based SIR stochastic epidemic model in continuous space. The evolution of the epidemic involves the rates of infection and recovering of individuals. We assume that individuals move randomly on the two-dimensional torus according to independent Brownian motions. We define the sequences of empirical measures, which describe the evolution of the positions of the susceptible, infected and removed individuals. We prove the convergence in probability, as the size of the population tends to infinity, of those sequences of measures towards the solution of a system of parabolic PDEs. We show that appropriately centrered renormalized sequences of fluctuations around the above limit converge in law, as the size of the population tends to infinity, towards a Gaussian distribution valued process, solution of a system of linear PDEs with highly singular Gaussian driving processes. In the case where the individuals do not move we also define and study the law of large numbers and central limit theorem for the same sequence.

Exact description of SIR-Bass epidemics on 1D lattices

<p style='text-indent:20px;'>This paper is devoted to the study of a stochastic epidemiological model which is a variant of the SIR model to which we add an extra factor in the transition rate from susceptible to infected accounting for the inflow of infection due to immigration or environmental sources of infection. This factor yields the formation of new clusters of infections, without having to specify a priori and explicitly their date and place of appearance.</p><p style='text-indent:20px;'>We establish an exact deterministic description for such stochastic processes on 1D lattices (finite lines, semi-infinite lines, infinite lines) by showing that the probability of infection at a given point in space and time can be obtained as the solution of a deterministic ODE system on the lattice. Our results allow stochastic initial conditions and arbitrary spatio-temporal heterogeneities on the parameters.</p><p style='text-indent:20px;'>We then apply our results to some concrete situations and obtain useful qualitative results and explicit formulae on the macroscopic dynamics and also the local temporal behavior of each individual. In particular, we provide a fine analysis of some aspects of cluster formation through the study of patient-zero problems and the effects of time-varying point sources.</p><p style='text-indent:20px;'>Finally, we show that the space-discrete model gives rise to new space-continuous models, which are either ODEs or PDEs, depending on the rescaling regime assumed on the parameters.</p>

Estimating Causal Peer Influence in Homophilous Social Networks by Inferring Latent Locations

Social influence cannot be identified from purely observational data on social networks, because such influence is generically confounded with latent homophily, that is, with a node’s network partners being informative about the node’s attributes and therefore its behavior. If the network grows according to either a latent community (stochastic block) model, or a continuous latent space model, then latent homophilous attributes can be consistently estimated from the global pattern of social ties. We show that, for common versions of those two network models, these estimates are so informative that controlling for estimated attributes allows for asymptotically unbiased and consistent estimation of social-influence effects in linear models. In particular, the bias shrinks at a rate that directly reflects how much information the network provides about the latent attributes. These are the first results on the consistent nonexperimental estimation of social-influence effects in the presence of latent homophily, and we discuss the prospects for generalizing them.

A weak semantic approach to bisimulation metrics in models with nondeterminism and continuous state spaces

Bisimulation metrics are a successful instrument used to estimate the behavioural distance between probabilistic concurrent systems. They have been defined in both discrete and continuous state space models. However, the weak semantics approach, where non-observable actions are abstracted away, has been adopted only in the discrete case. In this paper we fill this gap and provide a weak bisimulation metric for models with continuous state spaces. A technical difficulty is to provide a suitable notion of weak transition, which requires to lift transitions leaving from states to transitions leaving from a continuous distribution over states. We prove that our weak bisimulation metric is non-expansive, thus allowing for compositional reasoning. We prove that systems at distance zero are equated by a suitable notion of probabilistic weak bisimulation. We apply our theory in a case study where continuous distributions derive from the evolution of the physical environment.

EFFECT OF β ON EFFECTIVE MULTIPLICATION FACTOR IN 1/fβ SPECTRUM RANDOM SYSTEM

We investigated the effect of β on effective multiplication factor(keff) in the 1/fβ spectrum random system. The random system was generated by the 1/fβ noise model. The model is a continuous space model based on the Randomized Weierstrass function and describes the component spatial distribution with a power spectrum of 1/fβ, where f and β are the frequency domain variable and the characteristic parameter related to randomness, respectively. In this work, the two-group Monte Carlo calculations were performed to obtain the keff for a simple cubic geometry that consisted of two materials (fuel burned to 12 GWd/t and concrete). A large number of replicas having different spatial distribution and characterized by the representative β values were generated using the model, and the distribution on keff was analyzed. We found the dependency on β of standard deviation, skewness, and kurtosis of keff distribution. This result is expected to help to predict the keff distribution due to the randomizing model.

A microscopic approach to study the onset of a highly infectious disease spreading

We combine a pedestrian dynamics model with a contact tracking method to simulate the initial spreading of a highly infectious airborne disease in a confined environment. We focus on a medium size population (up to 1000 people) with a small number of infectious people (1 or 2) and the rest of the people are divided between immune and susceptible. We adopt a space-continuous model that represents pedestrian dynamics by the forces acting on them, i.e. a microscopic force-based model. Once discretized, the model results in a high-dimensional system of second order ordinary differential equations. Before adding the contact tracking to the pedestrian dynamics model, we calibrate the model parameters, compare the model results against empirical data, and show that pedestrian self-organization into lanes can be captured. We consider an explicit approach for contact tracking by introducing a sickness domain around a sick person. A healthy but susceptible person who remains in the sickness domain for a certain amount of time may get infected (with a prescribed probability) and become a so-called secondary contact. As a concrete setting to simulate the onset of disease spreading, we consider terminals in two US airports: Hobby Airport in Houston and the Atlanta International Airport. We consider different scenarios and we quantify the increase in average number of secondary contacts as a given terminal becomes more densely populated, the percentage of immune people decreases, the number of primary contacts increases, and areas of high density (such as the boarding buses) are present.

Assortment Optimization over Dense Universe is Easy

Assortment optimization is an important problem in revenue management arising in industries such as online advertising, retailing and airline ticketing. We study assortment optimization under an arbitrary mixture of multi-nomial logit (MNL) models, when the universe of products is dense. In general, it is NP-hard to approximate assortment optimization under mixture of MNLs model within any reasonable factor. However, if the universe of products is dense, we show that assortment optimization has an optimal solution that is well approximated by a nested-by-revenue policy. We argue this by considering an alternate, continuous-space model where product features follow a density on a continuous space, and offer set can be any open subset on the feature space. In this model, we show that there exists a nested-by-revenue policy that is optimal. This characterization holds regardless of the mixture distribution (including discrete and continuous) and the dimension of feature space. Through this characterization and linking the continuous-space to the standard discrete-item model via a fractional relaxation, we also show that, in the finite and discrete item case, nested-by-revenue performs nearly optimally. In particular, we derive an optimality gap, explicitly dependent on the model parameters, that shrinks to zero under suitable scaling as the number of items grows.

Smoothing for continuous dynamical state space models with sampled system coefficients based on sparse kernel learning

A new smoother for a continuous dynamical state space model with sampled system coefficients is proposed. This is completely different from conventional approaches, such as Rauch–Tung–Striebel smoother. In the proposed method, the state vector as a continuous function of time is represented by kernel models. The state process model, namely the differential equation, is treated as part of the measurement model at the sampling instants of the system coefficients. Sparse solution of the kernel weights is obtained through a special regularization strategy called the Lasso estimator. The optimization problem appearing in the Lasso estimation is solved by the fast iterative shrinkage threshold algorithm. The hyperparameters involved, namely the kernel widths and the regularization coefficients, are selected objectively through generalized cross-validation or corrected Akaike information criterion tailored to the Lasso estimator. A simple two-dimension example is employed in the simulation to demonstrate the application and also the performance of the proposed method. It is shown that the proposed method could provide state vector estimates with satisfactory accuracy not only at the sampling instants of the observations but also at any other instants. The sparsity of the solution could also be clearly seen in the experiment. The proposed method can be viewed as an alternative smoothing method, rather than a replacement for conventional smoothers, due to the difficult model tuning and increased computation load.

Multi-step medical image segmentation based on reinforcement learning

Image segmentation technology has made a remarkable effect in medical image analysis and processing, which is used to help physicians get a more accurate diagnosis. Manual segmentation of the medical image requires a lot of effort by professionals, which is also a subjective task. Therefore, developing an advanced segmentation method is an essential demand. We propose an end-to-end segmentation method for medical images, which mimics physicians delineating a region of interest (ROI) on the medical image in a multi-step manner. This multi-step operation improves the performance from a coarse result to a fine result progressively. In this paper, the segmentation process is formulated as a Markov decision process and solved by a deep reinforcement learning (DRL) algorithm, which trains an agent for segmenting ROI in images. The agent performs a serial action to delineate the ROI. We define the action as a set of continuous parameters. Then, we adopted a DRL algorithm called deep deterministic policy gradient to learn the segmentation model in continuous action space. The experimental result shows that the proposed method has 7.24% improved to the state-of-the-art method on three prostate MR data sets and has 3.52% improved on one retinal fundus image data set.