2025-06-24
13:59 |
How Sir Harold Jeffreys would create a belief function based on data
Daniel, Milan ; Jiroušek, Radim ; Kratochvíl, Václav
Not all normalized nonnegative monotone set functions are belief functions. This paper investigates ways to modify them to obtain a belief function that preserves some of their properties. The problem is motivated by an approach to data-based learning of belief function models. The approach is based on the idea that classical methods of mathematical statistics can provide estimates of lower bounds for unknown probabilities. Thus, methods of mathematical statistics can be used to obtain a reasonable rough estimate, which is further elaborated to obtain a desired belief function model.
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2025-06-24
13:59 |
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2025-05-31
00:01 |
A note on the OD-QSSA and Bohl-Marek methods applied to a class of mathematical models
Papáček, Štěpán ; Matonoha, Ctirad
The complex (bio)chemical reaction systems, frequently possess fast/slow phenomena, represent both diffculties and challenges for numerical simulation. We develop and test an enhancement of the classical QSSA (quasisteady-state approximation) model reduction method applied to a system of chemical reactions. The novel model reduction method, the so-called delayed quasi-steady-state approximation method, proposed by Vejchodsky (2014) and further developed by Papacek (2021) and Matonoha (2022), is extensively presented on a case study based on Michaelis-Menten enzymatic reaction completed with the substrate transport. Eventually, an innovative approach called the Bohl-Marek method is shown on the same numerical example.
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2025-01-12
00:00 |
On underactuated bipedal systems walking: Gait pattern modeling and analysis of a stepladder with decorator
Polach, P. ; Prokýšek, R. ; Papáček, Štěpán
This paper presents how to model one specific, well-known underactuated mechanical system, a stepladder with an operator inducing the motion, and how to analyze the stability of its corresponding gait pattern. Conversely to Compass gait and other common bipedal robotic systems, the leg order is preserved during walking, i.e., the swing leg never overcomes the stance leg. Let us underline three key features of this planar or 2D system, enabling the overall ordered cyclic displacement, e.g., from left to right, i.e., in the positive direction of x-axis in an inertial (Cartesian) system of coordinates.
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2024-12-14
00:13 |
Calculating Electric Vehicle Range Using Dynamic Programming with Battery Current and Velocity Setpoints
Sedláček, O. ; Uglickich, Evženie
This work was made during an internship at Institute of Information Theory and Automation organized by Otevřená věda. The effort put into this internship resulted in a program simulating and predicting the range of a BMW i3 60 Ah electric car using Bayesian estimation of regression model and optimal control with dynamic programming. After a dataset is entered, the program trains models to be used for the simulation and then allows you to set setpoints to a vehicle speed or battery current. Once the simulation with the setpoints is completed, it will return the speed at which the car was traveling, how much current was drawn from the battery, and the range of the electric vehicle traveling at that speed. In addition, the graph of the ride of the simulated car is shown after the computation. We have used the driving data of the BMW i3 60 Ah electric car from publicly available datasets.
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2024-12-14
00:13 |
DISTRIBUTION STRATEGY PLANNING FOR LAST-MILE DELIVERY AMID POTENTIAL URBAN POLICY TRAFFIC CHANGES: A DECISION MAKING MODEL APPROACH
Plajner, Martin ; Petřík, T.
In our prior research, we formulated a technique for planning distribution strategy amid future uncertainties. Conventional planning methods, which involve designing potential scenarios and defining probabilities, frequently face difficulties because of unforeseeable future events. Suboptimal strategies can emerge if the probabilities were assigned incorrectly at the beginning. The contribution of this article is a new method that avoids making rigid assumptions about the exact probability of each future scenario. Instead, it explores the entire allowable probability space and selects an optimal strategy in most situations. In the case study, the method’s usability is shown on a real-world company operating in Prague. We use it to model the impact of a city policy on the company’s operations within the city limits. Due to the frequent traffic restrictions in other major European cities and the overall trend of following more environmentally friendly policies, Prague is also expected to take this path. Accordingly, the company's operations could be significantly affected. By utilizing historical delivery data from the company and specialized simulation software, we model diverse distribution network scenarios under potential traffic restrictions, already in effect in other European cities, and probabilistically assess the future the company is facing.
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2024-11-26
10:48 |
A tribute to Klir’s research on entropy for belief functions
Jiroušek, Radim ; Kratochvíl, Václav
This is a short paper to remind us that although Prof. George Klir passed away eight years ago, his ideas are still alive. He was one of the first to have the idea to extend information theory beyond probability theory and to see the potential of fuzzy sets and belief functions. Some of the problems he raised have not yet been satisfactorily solved. In this paper, we take a fresh look at the problem of what properties entropy should have if it is to be considered a measure of information. Based on these requirements, we consider 24 definitions of entropy for belief functions and study how well they satisfy the proposed conditions.
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2024-11-26
10:48 |
On cardinalities of different degrees of Belief functions conjunctive conflictness
Daniel, Milan ; Kratochvíl, Václav
This paper examines mutual conflict behavior between belief function structures across different discernment frame sizes (\(\Omega\)). Through experiments on \(\Omega_2\) to \(\Omega_6\), we observe that as frame size increases, non-conflicting pairs and higher-order hidden conflicts become exceedingly relatively rare despite the exponential growth of cardinalities of their classes. The super-exponential growth of possible belief structures complicates exhaustive analysis, leading us to employ random sampling. Our findings reveal that the cardinality of a class of first-degree hidden conflicts (HC\(_1\)) grows faster than non-conflicts as frame size increases, highlighting the challenges and implications of applying belief function theory in complex decision-making scenarios.
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2024-11-26
10:48 |
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2024-11-10
00:01 |
On combinatorial descriptions of faces of the cone of supermodular functions
Studený, Milan
This paper is to relate five different ways of combinatorial description of non-empty faces of the cone of supermodular functions on the power set of a finite basic set N. Instead of this cone we consider its subcone of supermodular games; it is also a polyhedral cone and has the same (= isomorphic) lattice of faces. This step allows one to associate supermodular games with certain polytopes in N-dimensional real Euclidean space, known as cores (of these games) in context of cooperative game theory, or generalized permutohedra in context of polyhedral geometry. Non-empty faces of the supermodular cone then correspond to normal fans of those polytopes. This (basically) geometric way of description of faces of the cone then leads to the combinatorial ways of their description.\n\nThe first combinatorial way is to identify the faces with certain partitions of the set of enumerations of N, known as rank tests in context of algebraic statistics. The second combinatorial way is to identify faces with certain collections of posets on N, known as (complete) fans of posets in context of polyhedral geometry. The third combinatorial way is to identify the faces with certain coverings of the power set of N, introduced relatively recently in context of cooperative game theory under name core structures. The fourth combinatorial way is to identify the faces with certain formal conditional independence structures, introduced formerly in context of multivariate statistics under name structural semi-graphoids.\nThe fifth way is to identify the faces with certain subgraphs of the permutohedral graph, whose nodes are enumerations of N. We prove the equivalence of those six ways of description of non-empty faces of the supermodular cone. This result also allows one to describe the faces of the polyhedral cone of (rank functions of) polymatroids over N and the faces of the submodular cone over N: this is because these cones have the same face lattice as the supermodular cone over N. The respective polytopes are known as base polytopes in context of optimization and (poly)matroid theory.
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