Piecewise Linear Functions Research Articles

An infinite family of chiral, non-slice, non-alternating hyperbolic knots with vanishing Upsilon invariants

For a knot in the 3-sphere, its Upsilon invariant is a continuous, piecewise linear function defined on the interval [0,2]. It is a concordance invariant, so vanishes for slice knots. Since it only changes the sign for the mirror image with reversed orientation, it also vanishes for amphicheiral knots. For alternating knots, more generally, quasi-alternating knots, the Upsilon invariant is determined only by the signature. In particular, it vanishes if such a knot has zero signature. On the other hand, it is known that the Upsilon invariant is a non-zero convex function for L-space knots. In this paper, we construct an infinite family of hyperbolic knots, each of which has zero Upsilon invariant, but is chiral, non-slice, non-alternating. To confirm that the Upsilon invariant vanishes, we calculate the full knot Floer complex.

Nonlinear normal modes and response to random inputs of systems with bilinear stiffness

This work seeks to provide a comprehensive review of the effects that stiffness bilinearity can have on the nonlinear modes of a system, its response in a random vibration environment, and the connection between the two. Stiffness bilinearity here refers to a continuous piecewise linear force vs displacement function that is composed of two linear regions. This work focuses on a bilinear stiffness function that is regularized so there is a smooth transition at the point where the two linear regions meet. A single-degree-of-freedom system (SDOF) and a two-degree-of-freedom (2DOF) system are explored and several interesting behaviors are shown. The SDOF bilinear spring model is characterized by four parameters: the low amplitude frequency, the ratio of the linear stiffnesses on either side of the transition, the displacement at which the transition occurs, and the rate or sharpness of the transition. The effect of each parameter on the shape of the NNM is described. In a 2DOF system, these parameters have similar effects, but modal coupling is found to play a significant role. When a bilinear system is subjected to random excitation, many harmonics appear in the response for both the SDOF and 2DOF cases. The root-mean-square (RMS) response of the bilinear system can be larger or smaller than the corresponding linear case depending on the values of the parameters and the type of forcing (broadband, bandlimited, in the shape of a vibration mode, etc.). However, many cases were observed in which the RMS response of the bilinear system was almost the same as that of a linear system, and hence the response could be predicted well using linear analysis. It is hoped that the results presented herein can assist engineers in helping to determine when linear analysis would be adequate to predict the failure of a system, when a rigorous nonlinear analysis is required, and what phenomena are likely to be observed in the latter case.

Polygonal plate element method for free vibration analysis using an efficient alpha (α)-assumed rotations and shear strains

This paper investigates the performance of a recently proposed polygonal plate element with alpha (α)-assumed rotations and shear strains, referred to as αARS-Poly, in free vibration analysis. The αARS-Poly element utilizes a simple and efficient approach involving a scaling factor (α) to enhance the accuracy of assumed rotations and shear strains. To fully explore the advantages of this element, we undertake a comprehensive analysis of free vibration in plate structures using a range of models with complex geometries. Numerical results demonstrate that the αARS-Poly element offers stability and reliability within smooth mode shapes. Furthermore, it significantly outperforms the previous polygonal Reissner-Mindlin plate element with piecewise-linear shape functions (PRMn-PL), achieving frequencies that closely match reference solutions, thereby validating its accuracy and robustness for dynamic applications.

Econometric approaches to examine the onset and duration of temporal variations in pedestrian and bicyclist injury severity analysis

There is considerable evidence in existing safety literature that the exogenous variable effects are likely to be time-varying in the injury severity analysis. The majority of these earlier studies tested time-varying effects of exogenous variables by crash year. However, there might be variability in the variable effects within a year, while the same effect might carry over in some or all parts of the preceding years. Towards that end, in this study, we propose a flexible framework to identify when the time-varying effect is likely to occur (the onset of temporal variation) and how long such time-varying effect lasts (duration of temporal variation) in the model estimates. In the study design, we assume that the onset of temporal variation can be any quarter of a year under consideration, while the time-varying effect can continue over different quarters after the onset of temporal variation in a variable effect. The injury severity model is estimated by using Correlated Random Parameter Generalized Ordered Logit formulation with piecewise linear functions. The empirical analysis is demonstrated by employing active traveler (pedestrian and bicyclist) crash data from Queensland, Australia for the years 2015 through 2020. The estimation results are further augmented by computing elasticity effects. The results indicate that the time-varying effects are likely to be different across years for several variables, while for other variables, the onset of time-varying effects could be different than the start of a year. Such flexibility in model specification is likely to have significant implications for devising and implementing effective countermeasures since it allows us to understand how road traffic injuries are evolving over time and when a new road safety issue might be arising.

TWO-DIMENSIONAL HYPERCHAOTIC MAP FOR CHAOTIC OSCILLATIONS

This manuscript explores a two-dimensional hyperchaotic map for generating chaotic oscillations. Hyperchaotic maps are finding increasing applications in various scientific and technological fields due to the unique properties of their generated oscillations. The studied map, based on two interconnected piecewise-linear functions, is one of the simplest for generating oscillations with a predetermined distribution of values across a continuous parameter space. This simplicity allows for wide applicability in various contexts. The paper presents simulation results demonstrating control over the parameters of the dynamic modes. Building upon these modeling results, a two-dimensional hyperchaotic system is implemented using an electric circuit. The chosen map is attractive due to its inherent simplicity and ease of parameter control. By adjusting these parameters, the distribution of the generated signal's values can be manipulated. The circuit consists of two symmetrical sections connected via feedback loops, employing four amplifiers with variable gain. The gain values act as the circuit's implementation of the control parameters. Chaotic oscillations are generated by applying a delayed clock signal from an external square wave generator to circuit elements. The obtained experimental results exhibit excellent agreement with the simulation data.

A machine-learning-based column generation heuristic for electric bus scheduling

Bus scheduling in public transit consists in determining a set of bus schedules to cover a set of timetabled trips at minimum cost. This planning process has evolved recently with the advent of electric buses that introduce constraints related to vehicle autonomy and battery charging process. In particular, column-generation algorithms have regained popularity for solving problems similar to the one considered in this paper, namely, the multi-depot electric vehicle scheduling problem (MDEVSP) with a piecewise linear charging function and capacitated charging stations. To tackle large-scale MDEVSP instances, we design a column generation (CG) heuristic that relies on reduced-sized networks to generate the bus schedules. The reduction is achieved by selecting a priori a subset of the arcs. Multiple selection techniques are studied: some are based on a greedy heuristic and others exploit a supervised learning algorithm relying on a graph neural network. It turns out that combining both selection types yields the best computational results. On 405 artificial instances involving between 568 and 1474 trips and generated from real bus lines in Montreal, the network reduction technique produced an average computational time reduction of 71.6% (compared to the same CG heuristic but without network reduction), while deteriorating solution cost by an average of 2.2%. On 8 larger instances containing more than 2500 trips on average, the proposed solution method also provided an average time saving of 52.5% with an average gap of 4.2% thanks to a transfer learning approach.

Comparison of local muscle oxygenation and whole-body VO2 during incremental exercise

The use of near-infrared spectroscopy (NIRS) in sports science has become increasingly important in the past few years (Perrey et al., 2024). One application is to determine thresholds from different NIRS parameters like oxygenated (O2Hb) or deoxygenated (HHb) hemoglobin to distinguish between hard and severe-intensity exercise (Caen et al., 2018). Such applications are frequently validated by comparison to established threshold determination concepts. However, it is not yet known which of the two parameters is more closely related to classical concepts. Therefore, the aim of this project was do analyze which NIRS parameter (oxygenated [O2Hb] or deoxygenated [HHb] hemoglobin) better reflects systemic behavior determined from ventilation (VE). Thirteen physically active participants (4 females, 9 males; mean age: 26.3 ± 4.4 years, height: 176.0 ± 10.3 cm, weight: 71.9 ± 9.3 kg) were included in the study. VE and NIRS data from a major locomotor muscle (vastus lateralis) during a step-incremental single leg cycle ergometer test were recorded. We used a custom MATLAB script to fit piecewise linear continuous functions by regression to estimate NIRS and VE thresholds. We used two distinct segments for NIRS data and three distinct segments for VE data. NIRS thresholds were defined as the point of intersection of the two segments in O2Hb and HHb signals, respectively. The ventilatory threshold was defined as the second increase in VE. We used a resampling strategy to reduce the impact of outliers or peculiar data distributions on threshold estimates. Thresholds from O2Hb and HHb in the active leg and VE were observed at 78.24%, 76.37%, and 84.15% of the maximum power achieved. Both O2Hb (r = 0.85, p < 0.001) and HHb (r = 0.75, p = 0.0051) thresholds were significantly correlated, but mean values were significantly different (p < 0.05) from the respiratory compensation point (RCP) mean value. Correlations between O2Hb and HHb values from the passive leg and the RCP values were in the same range (r = 0.88, p < 0.001 and r = 0.79, p = 0.0023, respectively). The results indicate that, based on the correlations, O2Hb is slightly closer related to the second ventilatory threshold compared to HHb. The present study shows that thresholds from both NIRS parameters are closely related to the second ventilatory threshold which indicates a physiological relationship. However, thresholds cannot be used interchangeably as NIRS parameters derived from the working muscle appear earlier than systemic thresholds that demonstrate a delay in kinetics between the working muscle and the system.

Model Predictive Control of a Stand-Alone Hybrid Battery-Hydrogen Energy System: A Case Study of the PHOEBUS Energy System

Model predictive control is a promising approach to robustly control complex energy systems, such as hybrid battery-hydrogen energy storage systems that enable seasonal storage of renewable energies. However, deriving a mathematical model of the energy system suitable for model predictive control is difficult due to the unique characteristics of each energy system component. This work introduces mixed integer linear programming models to describe the nonlinear multidimensional operational behavior of components using piecewise linear functions. Furthermore, this paper develops a new approach for deriving a strategy for seasonal storage of renewable energies using cost factors in the objective function of the optimization problem while considering degradation effects. An experimentally validated simulation model of the PHOEBUS Energy System is utilized to compare the performance of two model predictive controllers with a hysteresis band controller such as utilized for the real-world system. Furthermore, the sensitivity of the model predictive controller to the prediction horizon length and the temporal resolution is investigated. The prediction horizon was found to have the highest impact on the performance of the model predictive controller. The best-performing model predictive controller with a 14-day prediction horizon and perfect foresight increased the total energy stored at the end of the year by 18.9% while decreasing the degradation of the electrolyzer and the fuel cell.

PMSOMA: optical microscope algorithm based on piecewise linear chaotic mapping and sparse adaptive exploration

The optical microscope algorithm (OMA) is a metaheuristic algorithm that draws inspiration from the magnifying functionality of optical microscopes. This study introduces an enhanced variant of OMA, termed PMSOMA, designed to mitigate the original version's limitations, notably its slow convergence rates and vulnerability to local optima. PMSOMA integrates a piecewise linear chaotic map to refine population initialization and augment diversity, alongside a sparse adaptive exploration mechanism to bolster search efficacy. The performance of PMSOMA was rigorously tested using a suite of 50 benchmark functions, the CEC2017 test suite, feature selection datasets, and three classical engineering challenges. The empirical findings confirm that PMSOMA surpasses both the original OMA and competing algorithms by delivering superior solutions, accelerating convergence, and demonstrating enhanced robustness in convergence.

Accurate and fast quaternion fractional-order Franklin moments for color image analysis

Quaternion type moments (QTM) based on hypergeometric functions and harmonic functions have attracted interest in the imaging field. The Franklin system is a complete orthonormal system consisting of piecewise linear continuous functions with Haar wavelet collocation points. However, due to the lack of efficient computational methods and explicit expressions, research on piecewise polynomials with Haar wavelet collocation points remains underexplored. Furthermore, the impact of magnitude and phase of quaternion on the color image features extracted by QTM has not been comprehensively explored. To address these problems, a fast and accurate computation method for Franklin functions is proposed. Quaternion fractional-order Franklin moments (QFFM) are proposed and using the Minkowski distance as a prior parameter for selecting unit pure quaternions. Experiments are conducted to demonstrate the superior performance of QFFM in image reconstruction and color image classification tasks compared with QTM-based and deep learning-based methods. Moreover, with the help of experiments, it is confirmed the effectiveness of using the Minkowski distance to select magnitude and phase of quaternion.

Nested barycentric coordinate system as an explicit feature map for polyhedra approximation and learning tasks

We introduce a new embedding technique based on a nested barycentric coordinate system. We show that our embedding can be used to transform the problems of polyhedron approximation, piecewise linear classification and convex regression into one of finding a linear classifier or regressor in a higher dimensional (but nevertheless quite sparse) representation. Our embedding maps a piecewise linear function into an everywhere-linear function, and allows us to invoke well-known algorithms for the latter problem to solve the former. We explain the applications of our embedding to the problems of approximating separating polyhedra—in fact, it can approximate any convex body and unions of convex bodies—as well as to classification by separating polyhedra, and to piecewise linear regression.

Real-time estimation of immunological responses against emerging SARS-CoV-2 variants in the UK: a mathematical modelling study.

The emergence of SARS-CoV-2 variants and COVID-19 vaccination have resulted in complex exposure histories. Rapid assessment of the effects of these exposures on neutralising antibodies against SARS-CoV-2 infection is crucial for informing vaccine strategy and epidemic management. We aimed to investigate heterogeneity in individual-level and population-level antibody kinetics to emerging variants by previous SARS-CoV-2 exposure history, to examine implications for real-time estimation, and to examine the effects of vaccine-campaign timing. Our Bayesian hierarchical model of antibody kinetics estimated neutralising-antibody trajectories against a panel of SARS-CoV-2 variants quantified with a live virus microneutralisation assay and informed by individual-level COVID-19 vaccination and SARS-CoV-2 infection histories. Antibody titre trajectories were modelled with a piecewise linear function that depended on the key biological quantities of an initial titre value, time the peak titre is reached, set-point time, and corresponding rates of increase and decrease for gradients between two timing parameters. All process parameters were estimated at both the individual level and the population level. We analysed data from participants in the University College London Hospitals-Francis Crick Institute Legacy study cohort (NCT04750356) who underwent surveillance for SARS-CoV-2 either through asymptomatic mandatory occupational health screening once per week between April 1, 2020, and May 31, 2022, or symptom-based testing between April 1, 2020, and Feb 1, 2023. People included in the Legacy study were either Crick employees or health-care workers at three London hospitals, older than 18 years, and gave written informed consent. Legacy excluded people who were unable or unwilling to give informed consent and those not employed by a qualifying institution. We segmented data to include vaccination events occurring up to 150 days before the emergence of three variants of concern: delta, BA.2, and XBB 1.5. We split the data for each wave into two categories: real-time and retrospective. The real-time dataset contained neutralising-antibody titres collected up to the date of emergence in each wave; the retrospective dataset contained all samples until the next SARS-CoV-2 exposure of each individual, whether vaccination or infection. We included data from 335 participants in the delta wave analysis, 223 (67%) of whom were female and 112 (33%) of whom were male (median age 40 years, IQR 22-58); data from 385 participants in the BA.2 wave analysis, 271 (70%) of whom were female and 114 (30%) of whom were male (41 years, 22-60); and data from 248 participants in the XBB 1.5 wave analysis, 191 (77%) of whom were female, 56 (23%) of whom were male, and one (<1%) of whom preferred not to say (40 years, 21-59). Overall, we included 968 exposures (vaccinations) across 1895 serum samples in the model. For the delta wave, we estimated peak titre values as 490·0 IC50 (95% credible interval 224·3-1515·9) for people with no previous infection and as 702·4 IC50 (300·8-2322·7) for people with a previous infection before omicron; the delta wave did not include people with a previous omicron infection. For the BA.2 wave, we estimated peak titre values as 858·1 IC50 (689·8-1363·2) for people with no previous infection, 1020·7 IC50 (725·9-1722·6) for people with a previous infection before omicron, and 1422·0 IC50 (679·2-3027·3) for people with a previous omicron infection. For the XBB 1.5 wave, we estimated peak titre values as 703·2 IC50 (415·0-3197·8) for people with no previous infection, 1215·9 IC50 (511·6-7338·7) for people with a previous infection before omicron, and 1556·3 IC50 (757·2-7907·9) for people with a previous omicron infection. Our study shows the feasibility of real-time estimation of antibody kinetics before SARS-CoV-2 variant emergence. This estimation is valuable for understanding how specific combinations of SARS-CoV-2 exposures influence antibody kinetics and for examining how COVID-19 vaccination-campaign timing could affect population-level immunity to emerging variants. Wellcome Trust, National Institute for Health Research University College London Hospitals Biomedical Research Centre, UK Research and Innovation, UK Medical Research Council, Francis Crick Institute, and Genotype-to-Phenotype National Virology Consortium.

Augmented multi-agent algorithm utilizing intelligent search range detection heuristic to solve assembly line sequencing problem: A case study in the truck industry

Car sequencing is a widely adopted approach to implicitly enhance the short-term balancing of mixed-model assembly lines in practical applications. In this research, we investigate this problem in the context of a real-world case taken from a truck final assembly line. Our study considers cross-ratio constraints that address limitations related to dependent features of the products. Additionally, to manage the distribution of violation errors in cases where predefined congestion level thresholds (soft rules) exist, we propose a piecewise linear penalty function. To tackle these considerations, we formulate a mathematical programming model aimed at minimizing the total weighted penalty incurred from violating both independent and dependent sequencing rules. As the problem falls into the NP-hard category, we develop a multi-start parallel local search algorithm based on multi-agent approach to efficiently solve it. The algorithm is augmented by incorporating a self-adaptive diversification mechanism and a novel intelligent search range detection heuristic. The proposed heuristic enables the searching agents to intelligently explore the solution space rather than relying on a purely random search. The numerical experiments are conducted using 30 real-world instances from three truck assembly lines to validate the quality of the proposed algorithm. The comparison of the results indicates that our algorithm outperforms state-of-the-art algorithms. Furthermore, computational experiments demonstrate the effectiveness of each proposed mechanism in enhancing the algorithm's performance.

Likelihood-based inference for semi-parametric transformation cure models with interval censored data

A simple yet effective way of modeling survival data with cure fraction is by considering Box-Cox transformation cure model (BCTM) that unifies mixture and promotion time cure models. In this article, we numerically study the statistical properties of the BCTM when applied to interval censored data. Time-to-events associated with susceptible subjects are modeled through proportional hazards structure that allows for non-homogeneity across subjects, where the baseline hazard function is estimated by distribution-free piecewise linear function with varied degrees of non-parametricity. Due to missing cured statuses for right censored subjects, maximum likelihood estimates of model parameters are obtained by developing an expectation-maximization (EM) algorithm. Under the EM framework, the conditional expectation of the complete data log-likelihood function is maximized by considering all parameters (including the Box-Cox transformation parameter α) simultaneously, in contrast to conventional profile-likelihood technique of estimating α. The robustness and accuracy of the model and estimation method are established through a detailed simulation study under various parameter settings, and an analysis of real-life data obtained from a smoking cessation study.

Semi-analytical solutions for land subsidence due to groundwater withdrawal

This paper introduces novel semi-analytical models tailored for estimating land subsidence resulting from groundwater extraction in confined aquifers. These models offer high scalability, allowing them to be applied to various well configurations and pumping schedules. Their development involves the numerical integration of two key analytical solutions: the “nucleus of strain” (NoS) (Mindlin and Chen, 1950), which represents a localised zone within the aquifer where a unit change in pore pressure leads to deformation and subsequent surface displacement, and the classic Theis equation (Theis, 1935) for the pore pressure changes induced by a constant-rate well pumping from a laterally unbounded aquifer. These integrations yield surface displacement components, both horizontal and vertical, expressed as functions of two dimensionless spatial–temporal variables, which encompass aquifer depth, thickness, well placement, pumping schedules, and critical hydro-geomechanical parameters like hydraulic conductivity, porosity, vertical compressibility, and water compressibility. Proposed are two distinct modelling approaches: one employing a lookup table (LT) derived from numerical integration results, and the other providing direct closed-form surface displacement solutions by fitting LT data with “hinge models”, which use piecewise-linear functions linked by sigmoidal curves for computational efficiency. In both cases, surface displacement components are estimated by plugging in the dimensionless variables. Conditions of variable pumping from multiple wells can be addressed by applying superposition of solutions. In essence, these semi-analytical models offer swift computational capabilities for understanding and forecasting land subsidence dynamics. Their scalability makes them adaptable to a wide array of well configurations and scheduling scenarios, rendering them valuable for numerous applications. They are particularly significant for providing preliminary estimates of the impacts of groundwater development, conducting “what-if” tests, and performing sensitivity analyses to identify key factors affecting land subsidence risk. This underscores the importance of these models in sustainable groundwater resource management and in mitigating land subsidence and its associated consequences.

The role of posted speed limit on pedestrian and bicycle injury severities: An investigation into systematic and unobserved heterogeneities

The posted speed limit, as a proxy of actual speed, is one of the most fundamental predictors of active travelers’ (pedestrian and bicyclist) injury outcomes when involved in crashes with motor vehicles. Although earlier studies predominantly considered posted speed limit as an exogenous variable and provided highly insightful findings, majorities of them assume the effects of active traveler behavior to remain the same across different posted speed limits, which in turn neglect the heterogeneity in active traveler behaviors on high-speed roads vs. low-speed roads. This study proposes to develop a latent segmentation-based active traveler injury severity model to relax the homogeneity assumption of the posted speed limit by active traveler behavior. Specifically, this study proposes to estimate a latent segmentation-based correlated random parameters generalized ordered logit model to examine active travel injury severity mechanisms. The proposed model accommodates systematic heterogeneity in the effects of posted speed limit, crash year and active traveler group by using a piecewise linear function in injury severity component of the latent segment model. The model is demonstrated by using active traveler crash data from Queensland, Australia, for the years 2015 through 2019. To demonstrate the implications of the estimated models, a number of hypothetical scenario analyses are performed with a specific focus on active traveler behavior and reduction in posted speed limits. The outcomes from the hypothetical scenario analysis highlighted that a 76 % (73 %) reduction in active traveler fatalities can be achieved by converting 50–60 km/hr roadways to 10–40 km/hr roadways in the urban areas (rural areas) of Queensland. The outcomes of the study will allow us to identify effective speed management strategies while targeting those with high-risk behavior.

Efficient Sleep Stage Identification Using Piecewise Linear EEG Signal Reduction: A Novel Algorithm for Sleep Disorder Diagnosis.

Sleep is a vital physiological process for human health, and accurately detecting various sleep states is crucial for diagnosing sleep disorders. This study presents a novel algorithm for identifying sleep stages using EEG signals, which is more efficient and accurate than the state-of-the-art methods. The key innovation lies in employing a piecewise linear data reduction technique called the Halfwave method in the time domain. This method simplifies EEG signals into a piecewise linear form with reduced complexity while preserving sleep stage characteristics. Then, a features vector with six statistical features is built using parameters obtained from the reduced piecewise linear function. We used the MIT-BIH Polysomnographic Database to test our proposed method, which includes more than 80 h of long data from different biomedical signals with six main sleep classes. We used different classifiers and found that the K-Nearest Neighbor classifier performs better in our proposed method. According to experimental findings, the average sensitivity, specificity, and accuracy of the proposed algorithm on the Polysomnographic Database considering eight records is estimated as 94.82%, 96.65%, and 95.73%, respectively. Furthermore, the algorithm shows promise in its computational efficiency, making it suitable for real-time applications such as sleep monitoring devices. Its robust performance across various sleep classes suggests its potential for widespread clinical adoption, making significant advances in the knowledge, detection, and management of sleep problems.

Divisors and curves on logarithmic mapping spaces

We determine the rational class and Picard groups of the moduli space of stable logarithmic maps in genus zero, with target projective space relative a hyperplane. For the class group we exhibit an explicit basis consisting of boundary divisors. For the Picard group we exhibit a spanning set indexed by piecewise-linear functions on the tropicalisation. In both cases a complete set of boundary relations is obtained by pulling back the WDVV relations from the space of stable curves. Our proofs hinge on a controlled technique for manufacturing test curves in logarithmic mapping spaces, opening up the topology of these spaces to further study.

A contact-based constitutive model for the numerical analysis of masonry structures using the distinct element method

This study presents a robust contact constitutive model in the distinct element method (DEM) framework for simulating the mechanical behavior of masonry structures. The model is developed within the block-based modeling strategy, where the masonry unit is modeled as deformable blocks with potential crack surfaces in the middle of the bricks, while the mortar joints are defined as zero-thickness interfaces. The modeling strategy implements multi-surface plasticity with damage mechanics, including a tension cut-off, Coulomb failure criterion, and an elliptical compressive cap for the damage in tension, shear, and compression, respectively. Two new features are introduced in this contact model: a piecewise linear softening function for strength degradation in tension and shear and a hardening/softening function to phenomenologically define the compressive damage of masonry composite into the unit-mortar interface. The constitutive model is implemented in commercial DEM software using the small displacement configuration and validated against material and experimental tests on masonry walls subjected to constant pre-compression and monotonically increasing in-plane load. The experimental and numerical results regarding the force-displacement relationship and damage pattern produced by the proposed constitutive model are compared and critically discussed, demonstrating the capability of DEM coupled with the suitable constitutive law in simulating the behavior of masonry structures.

Model reduction of dynamical systems with a novel data-driven approach: The RC-HAVOK algorithm.

This paper introduces a novel data-driven approximation method for the Koopman operator, called the RC-HAVOK algorithm. The RC-HAVOK algorithm combines Reservoir Computing (RC) and the Hankel Alternative View of Koopman (HAVOK) to reduce the size of the linear Koopman operator with a lower error rate. The accuracy and feasibility of the RC-HAVOK algorithm are assessed on Lorenz-like systems and dynamical systems with various nonlinearities, including the quadratic and cubic nonlinearities, hyperbolic tangent function, and piece-wise linear function. Implementation results reveal that the proposed model outperforms a range of other data-driven model identification algorithms, particularly when applied to commonly used Lorenz time series data.