Continuous Case Research Articles

Convergent scheme for a non-local transport system modeling dislocations dynamics

In this paper, we consider a diagonal hyperbolic, not necessarily strictly hyperbolic, nonlinear and non-local system of transport equations that arises in the theory of dislocations densities dynamics. Under certain monotony assumptions on the initial data, global existence and uniqueness results of Hloc1 solutions for this system was proved in Hajj (2007). We propose a natural implicit scheme verifying a gradient L2 estimate at the discrete level compatible with that obtained in the continuous case in Hajj (2007). Which leads us to prove the convergence of the numerical solution to the continuous one. To our knowledge, this is the first convergent scheme proposed for this model.

Optimizing Allocation Rules in Discrete and Continuous Discriminant Analysis

This paper presents an approach for the study of probabilistic outcomes in experiments with multiple possible results. An approach to obtain confidence ellipsoids for the vector of probabilities, which represents the likelihood of specific results, for both discrete and continuous discriminant analysis, is presented. The obtention of optimal allocation rules, in order to reduce the allocation costs is investigated. In the context of discrete discriminant analysis, the approach focuses on assigning elements to specific groups in an optimal way. Whereas in the continuous case, the approach involves determining the regions where each action is the optimal choice. The effectiveness of the proposed approach is examined with two numerical applications. One of them uses real data, while the other one uses simulated data.

Sensitivity analysis for matched observational studies with continuous exposures and binary outcomes

Summary Matching is one of the most widely used study designs for adjusting for measured confounders in observational studies. However, unmeasured confounding may exist and cannot be removed by matching. Therefore, a sensitivity analysis is typically needed to assess a causal conclusion’s sensitivity to unmeasured confounding. Sensitivity analysis frameworks for binary exposures have been well-established for various matching designs and are commonly used in various studies. However, unlike the binary exposure case, there still lacks valid and general sensitivity analysis methods for continuous exposures, except in some special cases such as pair matching. To fill this gap in the binary outcome case, we develop a sensitivity analysis framework for general matching designs with continuous exposures and binary outcomes. First, we use probabilistic lattice theory to show our sensitivity analysis approach is finite-population- exact under Fisher’s sharp null. Second, we prove a novel design sensitivity formula as a powerful tool for asymptotically evaluating the performance of our sensitivity analysis approach. Third, to allow effect heterogeneity with binary outcomes, we introduce a framework for conducting asymptotically exact inference and sensitivity analysis on generalized attributable effects with binary outcomes via mixed- integer programming. Fourth, for the continuous outcomes case, we show that conducting an asymptotically exact sensitivity analysis in matched observational studies when both the exposures and outcomes are continuous is generally NP-hard, except in some special cases such as pair matching. As a real data application, we apply our new methods to study the effect of early-life lead exposure on juvenile delinquency. An implementation of the methods in this work is available in the R package doseSens.

Evaluating the effectiveness of size-limited execution trace with near-omniscient debugging

Debugging is an important task to identify the defects in the software. Especially, logging is an important feature of a software system to record runtime information. Detailed logging allows developers to collect run-time information when they cannot use an interactive debugger, such as continuous integration and web application server cases. However, extensive logging leads to larger execution traces because few instructions can be repeated many times. In our previous work, to record detailed program behavior within limited storage space constraints, we proposed near-omniscient debugging, which is a methodology that records and visualizes an execution trace using fixed size buffers for each observed instruction. In this paper, we evaluate the effectiveness of near-omniscient debugging in recording infected states while reducing the size of execution traces. We conduct experiments on the Defects4J dataset and evaluate the effectiveness based on the completeness, trace size and runtime overhead. The result shows that near-omniscient debugging can completely record infected states for nearly 80 percent of bugs (with a buffer size of 1024 events). The size of execution traces can be reduced by a factor of one thousand for large repetitive executions.

Stability robust for fractional generalized multi-dimensional state–space models

In this work, we consider a new class of generalized fractional linear multidimensional state–space systems described by the Roesser model. We discuss a novel technique for analysing robust stability, focusing specifically on the stability of the closed-loop system in terms of the H 2 and H ∞ norms. Both discrete-time and continuous-time cases are addressed across various regions of the complex plane. An extension of the bounded real lemma is proposed, dealing with both continuous and discrete cases. This lemma is used to provide sufficient conditions, in the form of linear matrix inequalities, to ensure stability margin for the perturbed system. Motivating examples are presented to demonstrate the effectiveness of our main results.

The Philosophy of Probability Value Behavior: Fractions and Composite Probability Functions in the Continuous Case

This paper focuses on probability value behavior in the case of continuous sample space by employing fractions intervals and composite functions. The study evaluates value behavior rather than finding values directly, which involves utilization of some concepts from continuity, geometric probability, and measure theory. This paper primarily uses an experiment that contains two major events, head H and tail T, in all their occurrence phases. This spread in infinite and uncountable fractions by a continuous motion within intervals and in the predominant circumstances where events are probabilistic values. As a result, every circumstance reflects many important characteristics of probability theory. Among the main results, this paper provides proven propositions that help design experiments upon understanding the case nature, with some explanations to the existing relation between probability value and the case nature. Also, this paper provides a proven corollary that allows visualizing negative probability values as a particular trial. This in turn proposes necessary uses for the composite probability function P_j 〖(p〗_i). Moreover, this paper provides numerical explanations of limits, which can demonstrate the nature of P_j 〖(p〗_i), alongside some techniques. Also, this paper considered conditional probability through some corollaries and the possibility of using the non-negative function of the interval i, alongside many important results in form of discussions.

Generally Applicable Q-Table Compression Method and Its Application for Constrained Stochastic Graph Traversal Optimization Problems

We analyzed a special class of graph traversal problems, where the distances are stochastic, and the agent is restricted to take a limited range in one go. We showed that both constrained shortest Hamiltonian pathfinding problems and disassembly line balancing problems belong to the class of constrained shortest pathfinding problems, which can be represented as mixed-integer optimization problems. Reinforcement learning (RL) methods have proven their efficiency in multiple complex problems. However, researchers concluded that the learning time increases radically by growing the state- and action spaces. In continuous cases, approximation techniques are used, but these methods have several limitations in mixed-integer searching spaces. We present the Q-table compression method as a multistep method with dimension reduction, state fusion, and space compression techniques that project a mixed-integer optimization problem into a discrete one. The RL agent is then trained using an extended Q-value-based method to deliver a human-interpretable model for optimal action selection. Our approach was tested in selected constrained stochastic graph traversal use cases, and comparative results are shown to the simple grid-based discretization method.

Duals of convolution thinned relationships

In a recent article, J. Peyhardi gives a number of novel results related to quasi Pólya thinning which encompass a number of important mixture relationships between univariate discrete distributions. In this note, I explore the duals of the general results on convolution thinning given in Peyhardi's Theorem 1 in order to obtain new relationships and to gain new insights into old relationships. Some consequences—for integer‐valued autoregressive processes—and analogues—in the continuous case—are noted.

An Updated Review on the Alarming Epidemic of the Monkeypox Virus

Abstract: After the COVID-19 pandemic, the world has been vulnerable due to another virus called monkeypox. Monkeypox is a very uncommon zoonotic infectious condition that occurs in both human and non-human primates with similar clinical characteristics as smallpox along with remarkable epidemic potential because of the increasing existence of human outbursts in recent scenarios. The increasing number of cases of this virus is developing curiosity among the people, hence scientists are aiming to become aware of various pathological characteristics and management of this virus before it becomes an epidemic. Currently, the monkeypox outbreak is a trending headline and has increased as an alarming tone after continuous upcoming cases. Previous studies revealed that the first human suspected case was found on September 1, 1970, when a 9-month-old baby was admitted to the Basankusu Hospital in the Democratic Republic of Congo. It is hard to distinguish monkeypox from the smallpox virus therefore, laboratory testing is the technique of disease identification and monitoring. Various new approaches and vaccines are being positioned for the prevention and clinical management of monkeypox through the entanglement of metallic and organic nanocarriers. However, more researchers suggested that virology and ecology of the virus in endemic areas is essential to recognize and avoid further worldwide occurrence of this virus. On behalf of an exhaustive literature survey, We are providing a rationalizing overview of monkeypox in the context of its present global outbreak, as well as its symptoms, prevention, treatment, assessment, and clinical studies.

Energy-minimizing configurations for an elastic rod with self-contact energy close to the inextensible–unshearable and hard-contact limits

We study self-contact configurations of elastic rods by adding a repulsive energy to the bend, twist, shear, and stretch energies of a classical elastic rod. We use a discretized approach, with the parameters of the discrete rod calibrated to approach the continuous case as the number N of rod segments goes to infinity, and use a quasi-Newton approach to minimize the discretized energy. We explore convergence of the results as N→∞, and also as we vary shear, stretch, and contact parameters to approach the inextensible–unshearable and hard-contact limits. For a straight and isotropic rod, we present results for three sets of boundary conditions – loop, buckled strut, and hairpin, in each case as an imposed twist angle is increased – and compare energies and configurations for the non-contact and contact problems. Finally, we show how our results change when isotropy is broken in two ways: by the rod being bent in its undeformed state, or by the rod having unequal bending stiffnesses.

The Philosophy of Probability Values Behaviour, through Fractions and Composite Probability Function in the Continuous Case

This paper deals with probability theory, and it is an extension to a published paper that has the same title, but for the discrete case. This present paper is aiming to study probability values behavior, in the case of continuous sample space, through fractions intervals and composite function. This aim tends to study the value behavior rather than finding the value itself. Also, this aim requires usage of some concepts of continuity, geometric probability, and measure theory, which also need a brief treatment. This paper is mainly using an experiment with a design that helps to study the probability fractions values in the form of intervals in the case of one direction movement and in the case of different directions. As a result, every case reflects some aspects of probability values behavior and can clarify many important characteristics of the probability theory. In addition to applying the composite function by some important theorems of conditional probability. These are besides a proven proposition that helps to design experiment, upon the understanding of the case nature. In addition to a corollary that allows to visualize negative probability values, as a particular case (trial), that upon the validity of the explanation of negativity which should be consistent with the probability axioms.

Trends and Extremes in Time Series Based on Fuzzy Logic

The authors develop the theory of discrete differentiation and, on its basis, solve the problem of detecting trends in records, using the idea of the connection between trends and derivatives in classical analysis but implementing it using fuzzy logic methods. The solution to this problem is carried out by constructing fuzzy measures of the trend and extremum for a recording. The theoretical justification of the regression approach to classical differentiation in the continuous case given in this work provides an answer to the question of what discrete differentiation is, which is used in constructing fuzzy measures of the trend and extremum. The detection of trends using trend and extremum measures is more stable and of higher quality than using traditional data analysis methods, which consist in studying the intervals of constant sign of the derivative for a piecewise smooth approximation of the original record. The approach proposed by the authors, due to its implementation within the framework of fuzzy logic, is largely focused on the researcher analyzing the record and at the same time uses the idea of multiscale. The latter circumstance provides a more complete and in-depth understanding of the process behind the recording.

Memories of a Glorious or Difficult Past? Portugal, Padrão dos Descobrimentos and the (Lack of a) 21st Century Reckoning

AbstractThe purpose of this paper is to analyse a particularly influential case of memory continuity in Portugal, that of Padrão dos Descobrimentos. Spaces of collective memory (such as public monuments) raise questions about what we celebrate, remember or rescue from oblivion, providing an opportunity to rethink the trauma. As such, care for public spaces is associated with ethical and cultural values. One of the difficulties with certain monuments has to do with the fact that they recall actions that today we see as traumatic acts. Thus, it is important to reflect on a critical use of memory. On August 8, 2021, Padrão dos Descobrimentos was the subject of a graffiti. One of the sides of the monument could read: “Blindly sailing for money, humanity is drowning in a scarlet sea”. A great controversy immediately arose around the meaning of this gesture, as well as the role played by a monument that, after being temporarily built in 1940 for the Portuguese World Exhibition, was, in its current version, inaugurated in 1960, on the occasion of the fifth centenary of the death of Infante D. Henrique. This episode reignited a deeper cleavage around the uses of history and memory, the Portuguese colonial past, and the role of the Padrão dos Descobrimentos as an instrument for the reproduction of nationalism. In this sense, and with the authors proposing a new theoretical frame of reference based on the thought of Arendt and Ricoeur, its critical reading becomes relevant.

Exploring Reasons for Non-Engagement From a Peer-Led Diversionary Intervention for Veterans in Police Custody.

UK veterans with complex needs arrested in police custody can access support through pre-charge diversion into treatment and ancillary services. We consider why veterans in police custody disengaged from a peer-led criminal justice diversionary support service in one UK region that adopted a continuous case management approach. Seven hundred and fifty-seven veterans were assessed to have high levels of comorbid health needs and socio-economic harms, with one-quarter (26.7%, n = 202) subsequently disengaging from the service. A logistic regression model using Multivariate Imputation by Chained Equations identified that veterans of a younger age, no-fixed-abode, a history of incarceration, and those from a Royal Navy background were likelier to disengage from the intervention. We conclude that this peer-based diversionary model has some efficacy in maintaining the engagement of a highly complex, comorbid segment of criminally-justice-exposed UK military veterans. The perceived benefits of an integrated peer-based model predicated on continuous case-management techniques are discussed.

Uncertainty quantification based on residual Tsallis entropy of order statistics

<abstract><p>In this study, we focused on investigating the properties of residual Tsallis entropy for order statistics. The reliability of engineering systems is highly influenced by order statistics, for example, when modeling the lifetime of a series system and the lifetime of a parallel system. The residual Tsallis entropy of the ith order statistic from a continuous distribution function and its deviation from the residual Tsallis entropy of the ith order statistics from a uniform distribution were investigated. In the mathematical framework, a method was provided to represent the residual Tsallis entropy of the ith order statistic in the continuous case with respect to the case where the distribution was uniform. This approach can provide insight into the behavior and properties of the residual Tsallis entropy for order statistics. We also investigated the monotonicity of the new uncertainty measure under different conditions. An investigation of these properties leads to a deeper understanding of the relationship between the position of the order statistics and the resulting Tsallis entropy. Finally, we presented the computational results and proposed estimators for estimating the residual Tsallis entropy of an exponential distribution. For this purpose, we derived a maximum likelihood estimator.</p></abstract>

On Skin Model Describability using Laplace-Beltrami Operator for Geometrical Product Specification and Verification

The skin model serves as a foundational concept defined in ISO standards on Geometrical Product Specifications and verification (ISO GPS), facilitating the consideration of geometric variations on the surfaces of mechanical products. However, the lack of a solid scientific foundation and practical operational applications has become a barrier for skin model concept to keep up with the development of standardized feature operations. A previous investigation was devoted to a scientific approach to defining and interpreting the skin model for ISO GPS, grounded in the structure of solids and set theory. In this paper, the use of the Laplace-Beltrami Operator (LBO) is explored as a mathematical operation to enhance the computational representations of the skin model. The describability of skin model is achieved by applying LBO in both continuous and discrete cases. Geometric filter banks, established through LBO, are employed for skin model to identify defects at various scales of observation. An application of LBO is demonstrated through a case study to highlight the use of established geometric filter banks for skin model. Further discussions show that the spectral analysis of a surface using LBO enables the characterization of skin model, contributing to the current and future standardization of geometrical product specification and verification. Finally, conclusion and future works are highlighted.

Performance study on turbulent heat transfer using rectangular air duct integrated with continuous and intermittent ribs turbulators

To continue the scientific path specialized in enhancing the thermal performance of thermal systems, several tests are carried out to improve the overall performance of a rectangular duct as air flows through it. This study reports experimentally and numerically the heat transfer enhancement and overall performance of a rectangular air duct with various arrangement of continuous and intermittent ribs turbulators. The ribs are inserting in several array arrangements at a 90o relative to the direction of flow. Three ribs lengths s= 30, 60 and 150 mm employed with the several arrangements that?s tested in the current study, with the pitch ratios (p/e)= 5.0 and height ratios (e/H) = 0.330. These cases include: continuous ribs case (CR), intermittent-continuous-intermittent ribs case (ICIR) and intermittent-ribs (IR). Reynolds number (Re) is ranging from 10,000 to 35,000. The experimental work was performed by designed and fabricated test rig while the numerical work was performed in commercially ANSYS Fluent 17.2. the outcomes show that (IR) case offers the best overall performance for all tested velocities, its 1.54 for experimental study and 1.57 for numerical study at Re=10000. Also, the highest friction factor values are found in (IR) case, it is found to be 0.082 in Re=10000.

Modulating functions based state estimator for Caputo fractional systems

This paper aims to design a non-asymptotic and robust state estimator applicable both for Caputo fractional linear and nonlinear systems with noisy outputs. For this purpose, a fractional observable canonical form is considered to show the idea of the proposed method. First, the considered form is transformed by taking a fractional derivative operator. Second, based on the new form, the modulating functions method with the additive index law of fractional derivatives is used to get exact formulas for the sought variables in continuous noise-free case, which only contain the integrals involving the output and the fractional derivative of the input, without producing any source of errors. Moreover, the integral forms can reduce noisy effect as low-pass filters. Hence, fast convergent and robust estimation can be obtained using discrete noisy outputs. After constructing the required modulating functions, two numerical examples are given to demonstrate the advantages of the proposed estimator by comparing with the fractional order Luenberger-like observer.

유·초 연계교육의 국내 실천 동향 분석

This study was conducted to examine the domestic practicing trends of continuity between preschool and elementary education, and to confirm what future tasks will be for leum education in the future. The subjects of this study are 56 cases of continuity between preschool and elementary education practices for young children, and supporting teachers and parents on continuity between preschool and elementary education. In this study, the text presented in the analysis data was examined using the content analysis method, and then the frequency by category was calculated and cases were analyzed. As a result of the study, first, “continuity between preschool and elementary education practices through curriculum implementation” was the most common with 66 times, and relatively the least with 0 training for childcare teachers, 0 conference for childcare teachers, and 1 conference for parents. Second, in terms of curriculum implementation, continuity between preschool and elementary education provides an opportunity for young children to explore elementary schools on their own, but most of them are one-time experience activities, and literacy and learning were also emphasized from the perspective of learning readiness. In terms of strengthening teachers and parents' capabilities, continuity between preschool and elementary education focuses on understanding the curriculum, and the conference was primarily centered on kindergarten teachers or was conducted as a one-time meeting between parents before and after school. In terms of creating an educational environment, continuity between preschool and elementary education formed a common space and a play space in the classroom of the first grade of elementary school and opened a new integrated school, but there were few attempts to link it with existing private kindergartens and daycare centers. Through the results, the study suggests the implementation of continuity between preschool and elementary education that reflects the subjectivity of young children, and the discovery of cases of continuity between preschool and elementary education that utilize community resources and support various young children's characteristics.

An incentive compatible ZD strategy-based data sharing model for federated learning: A perspective of iterated prisoner's dilemma

Federated learning has been increasingly adopted as an effective means to cope with the significant increase in the volume of training data needed for machine learning and address the privacy concerns in using these data. However, moral hazard may occur when individual data providers (IDPs) use smaller amounts or low-quality data to train their local models and submit these low-quality results (gradients) to free-ride on the benefits of the federated learning. Therefore, federated learning operators often face the dilemma of encouraging more IDPs to participate in data sharing and ensuring truthful contributions from IDPs to obtain high-quality global training results. This article proposes a spontaneous cooperative data-sharing model to address this dilemma. Through an iterated prisoner's dilemma model solved by the zero-determinant (ZD) strategy, we show that the optimal ZD strategies of all IDPs are to maximize their training efforts when participating in federated learning. According to the comparisons with other approaches through simulations, we demonstrate that either the two-IDP with binary strategies case or the multi-IDP with continuous strategies case could result in the optimal individual utility and social welfare. Therefore, the proposed spontaneous cooperative model effectively avoids the existing moral hazard problem in federated learning and provides a viable instrument for the federated learning operator to maximize the performance of the global model without the need to evaluate the quality of local gradients.