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Intraday electricity markets play an increasingly important role in balancing the intermittent generation of renewable energy resources, which creates a need for accurate probabilistic price forecasts. However, research to date has focused on univariate approaches, while in many European intraday electricity markets all delivery periods are traded in parallel. Thus, the dependency structure between different traded products and the corresponding cross‐product effects cannot be ignored. We aim to fill this gap in the literature by using copulas to model the high‐dimensional intraday price return vector. We model the marginal distribution as a zero‐inflated Johnson's SU$$ {S}_U $$ distribution with location, scale, and shape parameters that depend on market and fundamental data. The dependence structure is modeled using copulas, accounting for the particular market structure of the intraday electricity market, such as overlapping but independent trading sessions for different delivery days and allowing the dependence parameter to be time‐varying. We validate our approach in a simulation study for the German intraday electricity market and find that modeling the dependence structure improves the forecasting performance. Additionally, we shed light on the impact of the single intraday coupling on the trading activity and price distribution and interpret our results in light of the market efficiency hypothesis. The approach is directly applicable to other European electricity markets. [ABSTRACT FROM AUTHOR]

—In state of the art high-precision motion systems, which utilize magnetic levitation, a quasi-zero stiffness gravity compensation is one of the essentials to improve dynamic performance, eliminate position dependency and thus simplify controller design. Special configurations of permanent magnets, such as Halbach magnet arrays, can realize magnetic levitation as a form of magnetic spring. However, unlike conventional permanent magnet machines with large stiffness, the quasi-zero stiffness magnetic spring requires higher modeling accuracy for force estimation, which is affected by the nonlinear reluctance effect of permanent magnets. In this study, we propose an accurate magnetic modeling method for the quasi-zero stiffness magnetic spring. By correcting the reluctance effect of magnets, the proposed magnetic model achieves superior accuracy estimating levitation force and stiffness to the conventional surface current model. Using the reluctance-corrected magnetic model, tolerance analysis was performed to identify dominant geometric parameters affecting the uncertainty of the Halbach array magnetic spring performance. A Monte-Carlo simulation was used to estimate the overall tolerance of magnetic forces and stiffness. The experimental results fit in the tolerances. • Accurate analytical model for Halbach array linear magnetic spring (HMS) considering magnet's reluctance. • The model estimates the level of quasi-zero stiffness of the HMS accurately. • Performance variations were quantitatively estimated with some dominant tolerances identified. • Overall uncertainties were evaluated using the Monte-Carlo method. [ABSTRACT FROM AUTHOR]

Computer simulations are a powerful tool in many fields of research. This also applies to the broadly understood analysis of experimental data, which are frequently burdened with multiple imperfections. Often the underlying imprecision or vagueness can be suitably described in terms of fuzzy numbers which enable also the capture of subjectivity. On the other hand, due to the random nature of the experimental data, the tools for their description must take into account their statistical nature. In this way, we come to random fuzzy numbers that model fuzzy data and are also solidly formalized within the probabilistic setting. In this contribution, we introduce the so-called LR random fuzzy numbers that can be used in various Monte-Carlo simulations on fuzzy data. The proposed method of generating fuzzy numbers with membership functions given by probability densities is both simple and rich, well-grounded mathematically, and has a high application potential. [ABSTRACT FROM AUTHOR]

Public investment in Big Science generates social benefits that can ultimately support economic growth. This paper implements a model for the social Cost – Benefit Analysis (CBA) of Big Science and relies on Monte Carlo methods to quantify the uncertainty of long-term projections. We evaluate social costs and benefits of the High Luminosity upgrade of the Large Hadron Collider (HL-LHC) at CERN up to 2038. Monte Carlo simulations show that there is a 94% chance to observe a positive net present value for society. The attractiveness of CERN for Early Stage Researchers and technological spillovers for collaborating firms are key for a positive CBA result. Cultural effects, especially those related to onsite visitors, also contribute to generating societal benefits. [ABSTRACT FROM AUTHOR]

Recently, extropy as an alternative measure of uncertainty has been widely used in statistical procedures. In this article, we present some properties of the negative cumulative residual extropy and then propose a test for uniformity. An approximation of distribution of the test statistic is derived. The mean, variance and the asymptotic null distribution of the test statistic is presented. Percentage points and power against seven alternatives are reported. The results of a simulation study show the test is competitive in terms of power. Moreover, the proposed statistic is easy to compute and can approximate by the beta distribution. [ABSTRACT FROM AUTHOR]

The paper investigates optimal reinsurance-investment strategies with the assumption that the insurers can purchase proportional reinsurance contracts and invest their wealth in a financial market consisting of one risk-free asset and one risky asset whose price process obeys the rough Heston model. The problem is formulated as a utility maximization problem with a minimum guarantee under an S-shaped utility. Since the rough Heston model is non-Markovian and non-semimartingale, the utility maximization problem cannot be solved by the classical dynamical programming principle and related approaches. This paper uses semi-martingale approximation techniques to approximate the utility maximization problem and proves the rates of convergence for the optimal strategies. The approximate problem is a kind of classical stochastic control problem under multi-factor stochastic volatility models. As the approximate control problem still cannot be solved analytically, a dual-control Monte-Carlo method is developed to solve it. Numerical examples and implementations are provided. [ABSTRACT FROM AUTHOR]

Decarbonization requires new energy systems components to mitigate fossil fuel dependency, for instance electric vehicles and heat pumps, forming a sector integrated energy system. Energy management is a promising approach to integrate these devices more efficiently by orchestrating the respective consumption and generation. This study investigates the advantage of an advanced energy management algorithm that is applied to varying energy system scenarios. The energy management algorithm is based on economic principles and the system topology is represented by a rooted tree. Grid elements form parents, which act as auctioneers and devices act according to type specific demand and supply functions. This algorithm is compared to an approach where devices are not coordinated, at a system scale of six households. In order to account for different characteristics of the energy system, the different scenarios are defined according to a morphological analysis and are analysed by means of Monte-Carlo simulation. These scenarios vary the PV generation, heating technology, and building insulation. It is shown that the algorithm reduces peak loads across all scenarios by around 15 kW. Other key performance indicators, such as own consumption and self-sufficiency show a dependency on the scenarios, although the algorithm outperforms the reference in each one, achieving an increase in own consumption of at least 13 p.p. and 22 p.p. in terms of self-sufficiency.

This paper analyses the problem of the kinematic singularity of 6 DOF serial robots by extending the use of Monte-Carlo numerical methods to visualize singularity configurations. To achieve this goal, first, forward kinematics and D-H parameters have been derived for the manipulator. Second, the derived equations are used to generate and visualize a workspace that gives a good intuition of the motion shape of the manipulator. Third, the Jacobian matrix is computed using graphical methods, aiming to locate positions that cause singularity. Finally, the data obtained are processed in order to visualize the singularity and to design a trajectory free of singularity. MATLAB robotics toolbox, Symbolic toolbox, and curve fitting toolbox are the MATLAB toolboxes used in the calculations. The results of the surface and contour plots of the determinate of the Jacobian matrix behavior lead to design a manipulator’s trajectory free of singularity and show the parameters that affect the manipulator’s singularity and its behavior in the workspace.

A rough volatility model contains a stochastic Volterra integral with a weakly singular kernel. The classical Euler-Maruyama algorithm is not very efficient for simulating this kind of model because one needs to keep records of all the past path-values and thus the computational complexity is too large. This paper develops a fast two-step iteration algorithm using an approximation of the weakly singular kernel with a sum of exponential functions. Compared to the Euler-Maruyama algorithm, the complexity of the fast algorithm is reduced from O (N 2) to O (N log ⁡ N) or O (N log 2 ⁡ N) for simulating one path, where N is the number of time steps. Further, the fast algorithm is developed to simulate rough Heston models with (or without) regime switching, and multi-factor approximation algorithms are also studied and compared. The convergence rates of the Euler-Maruyama algorithm and the fast algorithm are proved. A number of numerical examples are carried out to confirm the high efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

An investigation of runaway electron (RE) kinetics under the influence of a strongly inhomogeneous electric field was carried out by means of 2-D analytical and 2-D numerical Monte–Carlo approaches. Several shapes of cathodes generating an inhomogeneous electric field were studied. Within the developed 2-D analytical model, blade-shaped and cone-shaped cathodes were considered. The voltage values which allow electrons to scatter at large angles close to $\pi $ /2 near a blade-shaped cathode were determined. Also, it was shown that the RE scatter angles are larger for the blade (in comparison with the ones for the cone) due to the electric field defocusing effect. Within the framework of the numerical 2-D Monte–Carlo model, a cathode was assumed to have a parabolic shape. Inapplicability of the classical runaway criterion in strongly inhomogeneous electric fields was demonstrated. Also, it was shown that the cathode surface domain of electron emission and an initial direction of electron motion have a strong influence on their energy balance and, hence, on the probability for electrons to transit into the continuous accelerating regime. Energy losses of REs were estimated. A correlation between the full-width at half-maximum of the RE energy spectrum and an inelastic energy loss value was proposed. [ABSTRACT FROM AUTHOR]

A large proportion of market making models derive from the seminal model of Avellaneda and Stoikov. The numerical approximation of the value function and the optimal quotes in these models remains a challenge when the number of assets is large. In this article, we propose closed-form approximations for the value functions of many multi-asset extensions of the Avellaneda–Stoikov model. These approximations or proxies can be used (i) as heuristic evaluation functions, (ii) as initial value functions in reinforcement learning algorithms, and/or (iii) directly to design quoting strategies through a greedy approach. Regarding the latter, our results lead to new and easily interpretable closed-form approximations for the optimal quotes, both in the finite-horizon case and in the asymptotic (ergodic) regime. [ABSTRACT FROM AUTHOR]

The optimal stopping investment is a kind of mixed expected utility maximization problems with optimal stopping time. The aim of this paper is to develop the least-squares Monte-Carlo methods to solve the optimal stopping investment under the constant elasticity of variance (CEV) model. Such a problem has no closed-form solutions for the value functions, optimal strategies and optimal exercise boundaries due to the early exercised feature. The dual optimal stopping problem is first derived and then the strong duality between the dual and prime problems is established. The least-squares Monte-Carlo methods based on the dual control theory are developed and numerical simulations are provided. Both the power and non-HARA utilities are studied. [ABSTRACT FROM AUTHOR]

We study random submatrices of a large matrix A. We show how to approximately compute A from its random submatrix of the smallest possible size O(r log r ) with a small error in the spectral norm, where r = ||A||²F/||A||²2 is the numerical rank of A. The numerical rank is always bounded by, and is a stable relaxation of, the rank of A. This yields an asymptotically optimal guarantee in an algorithm for computing low-rank approximations of A. We also prove asymptotically optimal estimates on the spectral norm and the cut-norm of random submatrices of A. The result for the cut-norm yields a slight improvement on the best-known sample complexity for an approximation algorithm for MAX-2CSP problems. We use methods of Probability in Banach spaces, in particular the law of large numbers for operator-valued random variables. [ABSTRACT FROM AUTHOR]

We propose SoftCorner, which is a novel approach to estimate the worst delay (3σ delay) of a VLSI system. SoftCorner is a modification of deterministic static timing analysis to overcome its tendency to give pessimistic estimates of the system delays when it uses 3σ corner delays for logic gates. The basic idea of SoftCorner is to use corner delays that are relaxed to th, 95th and 85th percentiles with an average error 4 times faster than the MC simulation on average.

Goodness-of-fit tests are constructed for the two-parameter Birnbaum-Saunders distribution in the case where the parameters are unknown and therefore are estimated from the data. In each test, the procedure starts by computing efficient estimators of the parameters. Then the data are transformed by a normal transformation and normality tests are applied on the transformed data, thereby avoiding reliance on parametric asymptotic critical values or the need for bootstrap computations. Three classes of tests are considered, the first class being the classical tests based on the empirical distribution function, while the other class utilizes the empirical characteristic function and the final class utilizes the Kullback-Leibler information function. All methods are extended to cover the case of generalized three-parameter Birnbaum-Saunders distributions. [ABSTRACT FROM AUTHOR]

Recent machine learning algorithms dedicated to solving semi-linear PDEs are improved by using different neural network architectures and different parameterizations. These algorithms are compared to a new one that solves a fixed point problem by using deep learning techniques. This new algorithm appears to be competitive in terms of accuracy with the best existing algorithms. [ABSTRACT FROM AUTHOR]

We demonstrate that a temperature schedule for single-spin flip transition matrix calculations can be simply and rapidly generated by monitoring the average size of the Wolff clusters at a set of discrete temperatures. Optimizing this schedule yields a potentially interesting quantity related to the fractal structure of Ising clusters. We also introduce a technique in which the transition matrix is constructed at a sequence of discrete temperatures at which Wolff cluster reversals are alternated with certain series of single-spin flip steps. The single spin-flip transitions are then employed to construct a single transition matrix. [ABSTRACT FROM AUTHOR]

Separation in microfluidic devices is a crucial enabling step for many industrial, biomedical, clinical or chemical applications. Acoustic methods offer contactless, biocompatible, scalable sorting with high degree of reconfigurability and are therefore favored techniques. The literature reports on various techniques to achieve particle separation, but these do not investigate the sensitivity of these methods or are difficult to compare due to the lack of figures of merit. In this paper, we present analytical and numerical sensitivity analysis of the time-of-flight and a phase-modulated sorting scheme against various extrinsic and intrinsic properties. The results reveal great robustness of the phase-modulated sorting method against variations of the flow rate or acoustic energy density, while the time-offlight method shows lower efficiency drop against size and density variations. The results presented in this paper provide a better understanding of the two sorting methods and offer advice on the selection of the right technique for a given sorting application. [ABSTRACT FROM AUTHOR]

This study proposes a strategy to make the lookback option cheaper and more practical, and suggests the use of its properties to reduce risk exposure in cryptocurrency markets through blockchain enforced smart contracts and correct for informational inefficiencies surrounding prices and volatility. This paper generalizes partial, discretely-monitored lookback options that dilute premiums by selecting a subset of specified periods to determine payoff, which we call amnesiac lookback options. Prior literature on discretely-monitored lookback options considers the number of periods and assumes equidistant lookback periods in pricing partial lookback options. This study by contrast considers random sampling of lookback periods and compares resulting payoff of the call, put and spread options under floating and fixed strikes. Amnesiac lookbacks are priced with Monte Carlo simulations of Gaussian random walks under equidistant and random periods. Results are compared to analytic and binomial pricing models for the same derivatives. Simulations show diminishing marginal increases to the fair price as the number of selected periods is increased. The returns correspond to a Hill curve whose parameters are set by interest rate and volatility. We demonstrate over-pricing under equidistant monitoring assumptions with error increasing as the lookback periods decrease. An example of a direct implication for event trading is when shock is forecasted but its timing uncertain, equidistant sampling produces a lower error on the true maximum than random choice. We conclude that the instrument provides an ideal space for investors to balance their risk, and as a prime candidate to hedge extreme volatility. We discuss the application of the amnesiac lookback option and path-dependent options to cryptocurrencies and blockchain commodities in the context of smart contracts.

We demonstrate that a series of procedures for increasing the efficiency of transition matrix calculations can be realized by integrating the standard single-spin flip transition matrix method with global cluster flipping techniques. Our calculations employ a simple and accurate method based on detailed balance for computing the density of states from the Ising model transition matrix. [ABSTRACT FROM AUTHOR]

We present an information-theoretic approach to stochastic optimal control problems that can be used to derive general sampling-based optimization schemes. This new mathematical method is used to develop a sampling-based model predictive control algorithm. We apply this information-theoretic model predictive control scheme to the task of aggressive autonomous driving around a dirt test track, and compare its performance with a model predictive control version of the cross-entropy method. [ABSTRACT FROM AUTHOR]

This paper studies the optimal investment strategies under the dynamic elasticity of variance (DEV) model which maximize the expected utility of terminal wealth. The DEV model is an extension of the constant elasticity of variance model, in which the volatility term is a power function of stock prices with the power being a nonparametric time function. It is not possible to find the explicit solution to the utility maximization problem under the DEV model. In this paper, a dual-control Monte-Carlo method is developed to compute the optimal investment strategies for a variety of utility functions, including power, non-hyperbolic absolute risk aversion and symmetric asymptotic hyperbolic absolute risk aversion utilities. Numerical examples show that this dual-control Monte-Carlo method is quite efficient. [ABSTRACT FROM AUTHOR]

A new solution for the three-dimensional transient heat conduction from a homogeneous medium to a non-homogeneous multi-layered composite material with temperature dependent thermal properties using a mesh-free Monte-Carlo method is proposed. The novel contributions include a new algorithm to account for the impact of thermal diffusivities from source to sink in the calculation of the particles’ step length (particles are represented as bundles of energy emitted from each source), and a derivation of the three-dimensional peripheral integration to account for the influence of material properties around the sink on its temperature. Simulations developed using the proposed method are compared against both experimental measurements and results from a finite element simulation. [ABSTRACT FROM AUTHOR]

This work introduces a method to generate implicit models from data. The algorithm is based on Bayesian networks, discrete codification and genetic algorithms. The concept of bit-wise Pseudo-Bayes networks is introduced in this work. It refers to Bayesian networks generated from discretized data. The network describes the model in function of the correlations between bits. The model is consider implicit in the sense the meaning of the original variables is lost during discretization, but it can provide random samples with a distribution that is similar to the one of the original data. These samples can be the input of other algorithms that rely on samples of data in a transparent fashion. Moreover, this approach alleviates the problem of storing and handling of larges volumes of data, a common occurrence in modern data science, and circumvent the problems of identification process. The algorithm to generate bit-wise Pseudo-Bayes models is described in detail, and introduces innovations to representation of Bayesian networks based on extended chain structures. Also, it introduces new discretization methods and compares them to others reported in the literature, which have been mainly used to evolutionary continuous optimization. The performance of the proposed algorithm is studied using two data sets: prices data from the stock of the Dow Jones industrial average, and prices data from the stocks of the Mexican Índice de precios y cotizaciones. The proposed method is compared against other discrete modeling techniques reported in the literature, attaining a higher performance. The results indicate direct discretization methods were effective when they are coupled with Bayesian networks, but further research is needed to guarantee scalability. The study indicated the Dow Jones data set was more difficult than the Mexican index data set, but this was attributed to 2008 American crisis. [ABSTRACT FROM AUTHOR]

We describe and justify a full-angle scattering (FAS) method to faithfully reproduce the accumulated differential angular Rutherford scattering probability distribution function (pdf) of particles in a plasma. The FAS method splits the scattering events into two regions. At small angles it is described by cumulative scattering events resulting, via the central limit theorem, in a Gaussian-like pdf; at larger angles it is described by single-event scatters and retains a pdf that follows the form of the Rutherford differential cross-section. The FAS method is verified using discrete Monte-Carlo scattering simulations run at small timesteps to include each individual scattering event. We identify the FAS regime of interest as where the ratio of temporal/spatial scale-of-interest to slowing-down time/length is from 10 − 3 to 0.3–0.7; the upper limit corresponds to Coulomb logarithm of 20–2, respectively. Two test problems, high-velocity interpenetrating plasma flows and keV-temperature ion equilibration, are used to highlight systems where including FAS is important to capture relevant physics. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new information measure, related to cumulative extropy, called weighted negative cumulative extropy measure. Various properties of the proposed measure are obtained and it is shown that weighted negative cumulative extropy measure has relationship with both weighted mean residual and mean past lifetimes of the associated random variable. Non-parametric estimator of the proposed measure is provided and, using this estimator, a goodness-of-fit test for uniform distribution is developed. The proposed test performs reasonably well. • A new weighted information measure is proposed. • Various properties of the proposed measure are studied. • A Non-parametric estimator of the said measure is provided. • Application in testing uniformity is considered. [ABSTRACT FROM AUTHOR]

Diffuse in vivo flow cytometry (DiFC) is an emerging fluorescence sensing method to non-invasively detect labeled circulating cells in vivo. However, due to signal-to-noise ratio (SNR) constraints largely attributed to background tissue autofluorescence (AF), DiFC's measurement depth is limited. The dual ratio (DR)/dual slope is an optical measurement method that aims to suppress noise and enhance SNR to deep tissue regions. We aim to investigate the combination of DR and near-infrared (NIR) DiFC to improve circulating cells' maximum detectable depth and SNR. Phantom experiments were used to estimate the key parameters in a diffuse fluorescence excitation and emission model. This model and parameters were implemented in Monte Carlo to simulate DR DiFC while varying noise and AF parameters to identify the advantages and limitations of the proposed technique. Two key factors must be true to give DR DiFC an advantage over traditional DiFC: first, the fraction of noise that DR methods cannot cancel cannot be above the order of 10% for acceptable SNR. Second, DR DiFC has an advantage, in terms of SNR, if the distribution of tissue AF contributors is surface-weighted. DR cancelable noise may be designed (e.g., through the use of source multiplexing), and indications point to the AF contributors' distribution being truly surface-weighted in vivo. Successful and worthwhile implementation of DR DiFC depends on these considerations, but results point to DR DiFC having possible advantages over traditional DiFC. [ABSTRACT FROM AUTHOR]

In this paper, a recently introduced accelerated sampling technique [D. Yevick, Int. J. Mod. Phys. C 27, 1650041 (2016)] for constructing transition matrices is further developed and applied to a two-dimensional Ising spin system. By permitting backward displacements up to a certain limit for each forward step while evolving the system to first higher and then lower energies within a restricted interval that is steadily displaced toward zero temperature as the computation proceeds, accuracy can be greatly enhanced. Simultaneously, the elements obtained from numerous independent calculations are collected in a single transition matrix. The relative accuracy of this novel method is established through a comparison to a transition matrix procedure based on the Metropolis algorithm in which the temperature is appropriately varied during the calculation and the results interpreted in terms of the distribution of realizations over both energy and magnetization. [ABSTRACT FROM AUTHOR]