Discrete Space Research Articles

On the Nuisance Parameter Elimination Principle in Hypothesis Testing.

The Non-Informative Nuisance Parameter Principle concerns the problem of how inferences about a parameter of interest should be made in the presence of nuisance parameters. The principle is examined in the context of the hypothesis testing problem. We prove that the mixed test obeys the principle for discrete sample spaces. We also show how adherence of the mixed test to the principle can make performance of the test much easier. These findings are illustrated with new solutions to well-known problems of testing hypotheses for count data.

Construction And Performance Evaluation of Big Data Prediction Model Based on Fuzzy Clustering Algorithm in Cloud Computing Environment

In the evolving landscape of biomedical biometrics, where multimodal approaches are increasingly crucial for reliable user authentication, this research presents a comprehensive study. The primary focus is on the construction and performance evaluation of a robust big data prediction model within a cloud computing environment. The advent of big data and cloud computing has revolutionized the field of biomedical biometrics, offering immense potential for advanced data analysis and prediction. This research presents the development and evaluation of a robust prediction model for multimodal biometric data in biomedical applications. The proposed model incorporation of Reliable Discrete Variable Topology (RDVT) into the prediction model. RDVT introduces a topological data structure that enhances data reliability and ensures the integrity of multimodal biometric information. The construction and training of the prediction model are meticulously detailed, encompassing data preprocessing, feature extraction, clustering, classification, and model evaluation. Additionally, the integration of a fuzzy clustering algorithm enhances the model's ability to handle uncertainty and imprecision in biometric data. The advancement of multimodal biometrics in the biomedical field by introducing the Reliable Discrete Variable Topology (RDVT) and a big data prediction model based on a fuzzy clustering algorithm in a cloud computing environment. The model's performance is rigorously assessed through extensive experimentation, including accuracy, precision, recall, and F1-score measurements.

Social workers’ assessment of a child’s need for services as ‘craftwork’ practice

ABSTRACT This study examines assessment practices when social workers determine whether a child needs child welfare or child protection services. It describes the elements employed when constructing assessment practice. The data consist of 28 group interviews among assessment teams from child and family services. The analytical framework, based on the theory of decision-making ecology and thematic mapping, allowed for a theory-driven reflective analysis . Our results highlight the distinctive nature of the assessment process, which contains the following elements: 1) individual and holistic assessments, 2) changing structures, 3) conflicting or shared understandings, and 4) unclear legal guidance. The assessment process is case-related and situational, such that tailoring also contains elements that combine decision-maker, organisational, and external factors, leaving significant space for professional discretion. Such an assessment practice represents a contextually crafted practice.

A collision-based hybrid method for the BGK equation

We apply the collision-based hybrid method introduced by Hauck and McClarren [1] to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator. Although it helps the numerical scheme become stable with a large time step size, it is still not obvious to achieve the desired order of accuracy due to the relationship between the size of the spatial cell and the mean free path. Without asymptotic preserving property, a very restricted grid size is required to resolve the mean free path, which is not practical. Our approaches are based on the noncollision-collision decomposition of the BGK equation. We introduce the arbitrary order of nodal discontinuous Galerkin (DG) discretization in space with a semi-implicit time-stepping method; we employ the backward Euler time integration for the uncollided equation and the 2nd order predictor-corrector scheme for the collided equation, i.e., both source terms in uncollided and collided equations are treated implicitly and only streaming term in the collided equation is solved explicitly. This improves the computational efficiency without the complexity of the numerical implementation. Numerical results are presented for various Knudsen numbers to present the effectiveness and accuracy of our hybrid method. Also, we compare the solutions of the hybrid and non-hybrid schemes.

Tomographic Universality of the Discrete Wigner Function

We observe that the discrete Wigner functions (DWFs) of n-partite systems with odd local dimensions are tomographically universal, as reflected in the delta function form of the DWF for any stabilizer. However, in the n-qubit case, this property does not hold due to the non-factorization of the mapping kernel, the explicit form of which depends on a particular partition of the discrete phase space. Nonetheless, it turns out that the DWF for some specific stabilizers, not included in the set used for the construction of the Wigner map, takes on the form of a delta function. This implies that the possibility of classical simulations of Pauli measurements in a given stabilizer state for qubit systems is closely tied to the experimental setup.

Influence of the discrete lattice spacing on the formation of intrinsic localized structures in the Salerno model

We report in this paper the influence of the discrete lattice spacing on the formation of intrinsic localized structures in the Salerno model. Through the linear stability analysis, appearance criterions of the modulation instability (MI) are derived. We show via the growth rate that, the discrete lattice spacing and the nonlinearity term can affect significantly the formation of instability zones. We find that for large values of the discrete lattice spacing, the MI is developed to increase the number instability zones whereas for very low values of this parameter, the MI growth rate is arisen up to enlarge the bandwidth. The theoretical findings have been numerically tested via the discrete spatial Fourier transform method and the direct simulations, and have been found to be in full agreement with the analytical prediction. Moreover, it has been revealed that a higher modulation index can dramatically modify the shape and the amplitude of the modulated waves.

Superdeterminism without Conspiracy

Superdeterminism—where the Measurement Independence assumption in Bell’s Theorem is violated—is frequently assumed to imply implausibly conspiratorial correlations between properties λ of particles being measured and measurement settings x and y. But it does not have to be so: a superdeterministic but non-conspiratorial locally causal model is developed where each pair of entangled particles has unique λ. The model is based on a specific but arbitrarily fine discretisation of complex Hilbert space, where λ defines the information, over and above the freely chosen nominal settings x and y, which fixes the exact measurement settings X and Y of a run of a Bell experiment. Pearlean interventions, needed to assess whether x and y are Bell-type free variables, are shown to be inconsistent with rational-number constraints on the discretised Hilbert states. These constraints limit the post-hoc freedom to vary x keeping λ and y fixed but disappear with any coarse-graining of λ, X, and Y, rendering so-called drug-trial conspiracies irrelevant. Points in the discretised space can be realised as ensembles of symbolically labelled deterministic trajectories on an ‘all-at-once’ fractal attractor. It is shown how quantum mechanics might be ‘gloriously explained and derived’ as the singular continuum limit of the discretisation of Hilbert space. It is argued that the real message behind Bell’s Theorem has less to do with locality, realism, or freedom to choose, and more to do with the need to develop more explicitly holistic theories when attempting to synthesise quantum and gravitational physics.

Convergence with rates for a Riccati-based discretization of SLQ problems with SPDEs

Abstract We consider a new discretization in space (parameter $h>0$) and time (parameter $\tau>0$) of a stochastic optimal control problem, where a quadratic functional is minimized subject to a linear stochastic heat equation with linear noise. Its construction is based on the perturbation of a generalized difference Riccati equation to approximate the related feedback law. We prove a convergence rate of almost ${\mathcal O}(h^{2}+\tau )$ for its solution, and conclude from it a rate of almost ${\mathcal O}(h^{2}+\tau )$ resp. ${\mathcal O}(h^{2}+\tau ^{1/2})$ for computable approximations of the optimal state and control with additive resp. multiplicative noise.

Geotechnical reliability‐based design optimization updating under changing design scenarios

AbstractIn the context of geotechnical uncertainty characterization, the reliability‐based design optimization (RBDO) provides an effective means to achieve the most balanced design outcome between the targeted safety and the risk‐based cost planning. As a common practice, the geotechnical RBDO is conducted on the premise of prescribed statistical information of those uncertain parameters. Nevertheless, the uncertain geotechnical parameters are usually subject to amendment resulting from further site investigation. In other words, changing design scenarios must be properly handled in advanced geotechnical RBDO. Thus, in this study, a novel reliability updating method using a sample reweighting technique that requires only a single simulation run is developed for RBDO. Simultaneously, the RBDO is readily extendable to RBDO updating under changing design scenarios while avoiding any further re‐evaluation of the performance functions. The proposed RBDO updating method allows for the consideration of a continuous design space encompassing an infinite number of feasible designs, whereas the existing simulation‐based method can only consider a finite number of feasible designs in a discrete design space. Moreover, the efficiency and flexibility of the proposed RBDO updating method are illustrated through a standard RBDO test problem and a practical rock slope design example, where the changing design scenarios of different means, standard deviations, correlation coefficient, and distributions are respectively studied.

An Innovative Multi-Objective Rescheduling System for Mitigating Pandemic Spread in Aviation Networks

The novel coronavirus outbreak has significantly heightened environmental costs and operational challenges for civil aviation airlines, prompting emergency airport closures in affected regions and a substantial decline in ridership. The consequential need to reassess, delay, or cancel flight itineraries has led to disruptions at airports, amplifying the risk of disease transmission. In response, this paper proposes a spatial approach to efficiently address pandemic spread in the civil aviation network. The methodology prioritizes the use of a static gravity model for calculating route-specific infection pressures, enabling strategic flight rescheduling to control infection levels at airports (nodes) and among airlines (edges). Temporally, this study considers intervals between takeoffs and landings to minimize crowd gatherings, mitigating the novel coronavirus transmission rate. By constructing a discrete space–time network for irregular flights, this research generates a viable set of routes for aircraft operating in special circumstances, minimizing both route-specific infection pressures and operational costs for airlines. Remarkably, the introduced method demonstrates substantial savings, reaching almost 53.4%, compared to traditional plans. This showcases its efficacy in optimizing responses to pandemic-induced disruptions within the civil aviation network, offering a comprehensive solution that balances operational efficiency and public health considerations in the face of unprecedented challenges.

THE NEWTON-RAPHSON METHOD OF REAL-VALUED FUNCTIONS IN DISCRETE METRIC SPACE

This paper studies the Newton-Raphson method to approximate a root of a real-valued function in one-dimensional real discrete metric space. The method involves a derivative and is considered to be convergent very fast. However, the derivative is derived from the limit definition with respect to the Euclidean distance, different from that of the discrete metric space. This research investigates the Newton-Raphson method with respect to derivatives defined in discrete metric spaces by deriving the derivative first. The results show that the constructed Newton-Raphson method can be an alternative root-finding method exemplified by some examples.
 Keywords: Newton-Raphson method, discrete metric space, metric space derivative

Model order reduction with novel discrete empirical interpolation methods in space–time

This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin projection onto a linear low-dimensional subspace. In unsteady applications, space–time reduced basis (ST-RB) methods have been developed to achieve a dimension reduction both in space and time, eliminating the computational burden of time marching schemes. However, nonaffine parameterizations dilute any computational speedup achievable by traditional ROMs. Computational efficiency can be recovered by linearizing the nonaffine operators via hyper-reduction, such as the empirical interpolation method in matrix form. In this work, we implement new hyper-reduction techniques explicitly tailored to deal with unsteady problems and embed them in a ST-RB framework. For each of the proposed methods, we develop a posteriori error bounds. We run numerical tests to compare the performance of the proposed ROMs against high-fidelity simulations, in which we combine the finite element method for space discretization on 3D geometries and the Backward Euler time integrator. In particular, we consider a heat equation and an unsteady Stokes equation. The numerical experiments demonstrate the accuracy and computational efficiency our methods retain with respect to the high-fidelity simulations.

On the complex version of the Cahn–Hilliard–Oono type equation for long interactions phase separation

Abstract This paper focuses on the complex version of the Cahn-Hilliard-Oono equation with Neumann boundary conditions, which is used to capture long-range nonlocal interactions in the phase separation process. The first part of the paper establishes the well-posedness of the corresponding stationary problem associated with the equation. Subsequently, a numerical model is constructed using a finite element discretization in space and a backward Euler scheme in time. We demonstrate the existence of a unique solution to the stationary problem and obtain error estimates for the numerical solution. This, in turn, serves as proof of the convergence of the semi-discrete scheme to the continuous problem. Finally, we establish the convergence of the fully discrete problem to the semi-discrete formulation.

Reduced-Order Modeling for Heston Stochastic Volatility Model

In this paper, we compare the intrusive proper orthogonal decomposition (POD) with Galerkin projection and the data-driven dynamic mode decomposition (DMD), for Heston's option pricing model. The full order model is obtained by discontinuous Galerkin discretization in space and backward Euler in time. Numerical results for butterfly spread, European and digital call options reveal that in general DMD requires more modes than the POD modes for the same level of accuracy. However, the speed-up factors are much higher for DMD than POD due to the non-intrusive nature of the DMD.

Real-time estimation of barycenter position for fuel cell distributed drive electric tractor based on derived UKF

ABSTRACT The FCDET is considered as a promising and advanced agricultural machinery due to its convenience and controllability. To enhance the control performance of the FCDET unit dynamic system, understanding the accurate position of the center of gravity (CoG) of the tractor unit in longitudinal motion and the operating environment is essential. In this paper, we proposed a real-time estimation method of CoG position of longitudinal motion for FCDET plowing and transportation conditions. CoG height and longitudinal axis distance distribution coefficients are used as state estimation variables, and the data obtained from displacement and velocity sensors are used as state observation variables, establishing a discrete system state space model and proving the observability. The proposed Derived UKF algorithm introduces the Sage-Husa adaptive noise equation within the Square-Root UKF framework to address the non-positive definite matrix problem. The research shows that the precise CoG longitudinal position effectively reflects changes in operational pavement load. The Derived UKF algorithm exhibits high state estimation accuracy in plowing and transportation conditions, with mean absolute errors of 14.2% and 5.0% of the state amplitude, respectively. This study supports the practical application of real-time state parameter estimation algorithms in controlling advanced agricultural machinery distributed drive systems.

Improved Feedback Quantizer with Discrete Space Vector.

The use of advanced modulation and control schemes for power converters, such as a Feedback Quantizer and Predictive Control, is widely studied in the literature. This work focuses on improving the closed-loop modulation scheme called Feedback Quantizer, which is applied to a three-phase voltage source inverter. This scheme has the natural behavior of mitigating harmonics at low frequencies, which are detrimental to electrical equipment such as transformers. This modulation scheme also provides good tracking for the voltage reference at the fundamental frequency. On the other hand, the disadvantage of this scheme is that it has a variable switching frequency, creating a harmonic spectrum in frequency dispersion, and it also needs a small sampling time to obtain good results. The proposed scheme to improve the modulation scheme is based on a Discrete Space Vector with virtual vectors to obtain a better approximation of the optimal vectors for use in the algorithm. The proposal improves the conventional scheme at a high sampling time (200 μs), obtaining a THD less than 2% in the load current, decreases the noise created by the conventional scheme, and provides a fixed switching frequency. Experimental tests demonstrate the correct operation of the proposed scheme.

PTCAS: Prompt tuning with continuous answer search for relation extraction

Tremendous progress has been made in the development of fine-tuned pretrained language models (PLMs) that achieve outstanding results on almost all natural language processing (NLP) tasks. Further stimulation of rich knowledge distribution within PLMs can be achieved through additional prompts for fine-tuning, namely, prompt tuning. Generally, prompt engineering involves prompt template engineering, which is the process of searching for an appropriate template for a specific task, and answer engineering, whose objective is to seek an answer space and map it to the original task label set. Existing prompt-based methods are primarily designed manually and search for appropriate verbalization in a discrete answer space, which is insufficient and always results in suboptimal performance for complex NLP tasks such as relation extraction (RE). Therefore, we propose a novel prompt-tuning method with a continuous answer search for RE, which enables the model to find optimal answer word representations in a continuous space through gradient descent and thus fully exploit the relation semantics. To further exploit entity-type information and integrate structured knowledge into our approach, we designed and added an additional TransH-based structured knowledge constraint to the optimization procedure. We conducted comprehensive experiments on four RE benchmarks to evaluate the effectiveness of the proposed approach. The experimental results show that our approach achieves competitive or superior performance without manual answer engineering compared to existing baselines under both fully supervised and low-resource scenarios.

Structure-preserving spatial discretization of a coupled Heat-Wave system formulated as an irreversible port-Hamiltonian system.

The port-Hamiltonian (pH) framework allows one to properly model, interconnect, simulate and control various types of systems. Yet, properly modeling irreversibility remains a challenge as one has to include a nonlinear relation between flows and efforts, leading to a nonlinear Dirac structure. In this work, we will focus on the modelling of a distributed coupling of the heat and wave equations as pH systems. In particular, the representation of the coupled dynamics as an irreversible pH system is presented and its properties discussed. A discretization in space which preserves both the second and first principles of thermodynamics is detailed. Finally some numerical results are presented.

Геометрическая модель прогнозирования свойств систем с интервальными параметрами

We consider interval geometric modeling of complex multi parametric systems having a set of parameters of different character. Some of the parameters may have interval indefiniteness. System information basis is incomplete one. The processed information depends on continuous, discrete and conventional data. Geometric model has a form of matrix and each element of it corresponds to some state of the system. Each state is described by interval function of continuous input and output parameters. The set of interval functions generates some discrete set of multidimensional surfaces in discrete space. We use this approach and our modeling algorithm to find predictive model of drape coefficient. The algorithm is based on linear approximation of numerical factors in factor spaces. Interval functions make it possible for us to vary some numerical factors within the given intervals. As an example, the interval model of fabric drape coefficient is found. Fabric thickness and closeness of texture are considered as input parameters.

HWI inequalities in discrete spaces via couplings

HWI inequalities in discrete spaces via couplings