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How to Improve Performance in Bayesian Inference Tasks: A Comparison of Five Visualizations
(2019-02-20)
Bayes’ formula is a fundamental statistical method for inference judgments in uncertain situations used by both laymen and professionals. However, since people often fail in situations where Bayes’ formula can be applied, how to improve their performance in Bayesian situations is a crucial question. We based our research on a widely accepted beneficial strategy in Bayesian situations, representing the statistical information in the form of natural frequencies. In addition to this numerical format, we used five ...
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Control of Jump Markov Uncertain Linear Systems With General Probability Distributions
(2022-02-25)
This paper introduces a method to control a class of jump Markov linear systems with uncertain initialization of the continuous state and affected by disturbances. Both types of uncertainties are modeled as stochastic processes with arbitrarily chosen probability distributions, for which however, the expected values and (co-)variances are known. The paper elaborates on the control task of steering the uncertain system into a target set by use of continuous controls, while chance constraints have to be satisfied for ...
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A New Identity for Generalized Hypergeometric Functions and Applications
(2019-01-18)
We establish a new identity for generalized hypergeometric functions and apply it for first- and second-kind Gauss summation formulas to obtain some new summation formulas. The presented identity indeed extends some results of the recent published paper (Some summation theorems for generalized hypergeometric functions, Axioms, 7 (2018), Article 38).
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A Hybrid Optimization Method Combining Network Expansion Planning and Switching State Optimization
(2020-07-01)
Combining switching state optimization (SSO) and network expansion planning (NEP) in AC systems results in a mixed-integer non-linear optimization problem. Two methodically different solution approaches are mathematical programming and heuristic methods. In this paper, we develop a hybrid optimization method combining both methods to solve the combined optimization of SSO and NEP. The presented hybrid method applies a DC programming model as an initialization strategy to reduce the search space of the heuristic. A ...
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Using heuristic worked examples to promote solving of reality-based tasks in mathematics in lower secondary school
(2022-04-19)
This study examined whether learning with heuristic worked examples can improve students’ competency in solving reality-based tasks in mathematics (mathematical modeling competency). We randomly assigned 134 students in Grade 5 and 180 students in Grade 7 to one of three conditions: control condition (students worked on reality-based tasks), worked example condition (students studied worked examples representing a realistic process of problem-solving by fictitious students negotiating solutions to the tasks), and ...
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An 8-bit precision cipher for fast image encryption
(2022-04-21)
Implementing chaos based ciphers usually involves 32-bit floating-point arithmetics that is hardware resources costly. The limitation of the computational precision is hardware imposed and transforms chaotic orbits into limit cycles with short periods, hence alters their randomness. In cryptographic applications, short period dynamics and weak randomness result in security issues. In order to address this concern, we propose an 8-bit precision cipher that can be implemented with low-end microprocessors running 8-bit ...
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30 Years with Vladimir Gerdt
(2022-11-12)
My first meeting with Vladimir was in March 1990. I had started two months before as a Ph.D. student of Jacques Calmet in the computer science department of Karlsruhe University and Vladimir was visiting our computer algebra group for a seminar talk on his research. For him, it was one of his first travels into the west, as under Soviet rule he was not considered as sufficiently politically reliable for travels outside of the eastern block. It turned out that after his visit we were both riding on the same train to ...
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Complementary decompositions of monomial ideals and involutive bases
(2022-06-25)
Complementary decompositions of monomial ideals - also known as Stanley decompositions - play an important role in many places in commutative algebra. In this article, we discuss and compare several algorithms for their computation. This includes a classical recursive one, an algorithm already proposed by Janet and a construction proposed by Hironaka in his work on idealistic exponents. We relate Janet’s algorithm to the Janet tree of the Janet basis and extend this idea to Janet-like bases to obtain an optimised ...
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On Non-linear Characterizations of Classical Orthogonal Polynomials
(2022-12-03)
Classical orthogonal polynomials are known to satisfy seven equivalent properties, namely the Pearson equation for the linear functional, the second-order differential/difference/q-differential/ divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations, and the Riccati equation for the formal Stieltjes function. In this work, following previous work by Kil et al., we state and prove a non-linear characterization result for classical orthogonal polynomials ...
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On the Finite Orthogonality of q-Pseudo-Jacobi Polynomials
(2020-08-08)
Using the Sturm–Liouville theory in q-difference spaces, we prove the finite orthogonality of q-Pseudo Jacobi polynomials. Their norm square values are then explicitly computed by means of the Favard theorem.