Logical Inference Inevitably Appears: Fuzzy-Based Explanation,
2023
The University of Texas at El Paso
Logical Inference Inevitably Appears: Fuzzy-Based Explanation, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich, Orsolya Csiszar
Departmental Technical Reports (CS)
Many thousands years ago, our primitive ancestors did not have the ability to reason logically and to perform logical inference. This ability appeared later. A natural question is: was this appearance inevitable -- or was this a lucky incident that could have been missed? In this paper, we use fuzzy techniques to provide a possible answer to this question. Our answer is: yes, the appearance of logical inference in inevitable.
Is Fully Explainable Ai Even Possible: Fuzzy-Based Analysis,
2023
Czech Technical University in Prague
Is Fully Explainable Ai Even Possible: Fuzzy-Based Analysis, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the main limitations of many current AI-based decision-making systems is that they do not provide any understandable explanations of how they came up with the produced decision. Taking into account that these systems are not perfect, that their decisions are sometimes far from good, the absence of an explanation makes it difficult to separate good decisions from suspicious ones. Because of this, many researchers are working on making AI explainable. In some applications areas -- e.g., in chess -- practitioners get an impression that there is a limit to understandability, that some decisions remain inhuman -- not explainable. …
Why Fuzzy Control Is Often More Robust (And Smoother): A Theoretical Explanation,
2023
Aalen University of Applied Sciences
Why Fuzzy Control Is Often More Robust (And Smoother): A Theoretical Explanation, Orsolya Csiszar, Gábor Csiszar, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, practitioners use easier-to-compute fuzzy control to approximate the more-difficult-co-compute optimal control. As expected, for many characteristics, this approximate control is slightly worse than the optimal control it approximates, However, with respect to robustness or smoothness, the approximating fuzzy control is often better than the original one. In this paper, we provide a theoretical explanation for this somewhat mysterious empirical phenomenon.
(R1977) On Geometry Of Equiform Smarandache Ruled Surfaces Via Equiform Frame In Minkowski 3-Space,
2023
Imam Mohammad Ibn Saud Islamic University (IMSIU); Beni-Suef University
(R1977) On Geometry Of Equiform Smarandache Ruled Surfaces Via Equiform Frame In Minkowski 3-Space, Emad Solouma
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, some geometric properties of equiform Smarandache ruled surfaces in Minkowski space E13 using an equiform frame are investigated. Also, we give the sufficient conditions that make these surfaces are equiform developable and equiform minimal related to the equiform curvatures and when the equiform base curve contained in a plane or general helix. Finally, we provide an example, such as these surfaces.
Exploring The Genotypic And Phenotypic Differences Distinguishing Lactobacillus Jensenii And Lactobacillus Mulieris,
2023
Loyola University Chicago
Exploring The Genotypic And Phenotypic Differences Distinguishing Lactobacillus Jensenii And Lactobacillus Mulieris, Adriana Ene, Swarnali Banerjee, Alan J. Wolfe, Catherine Putonti
Mathematics and Statistics: Faculty Publications and Other Works
Lactobacillus crispatus, Lactobacillus gasseri, Lactobacillus iners, and Lactobacillus jensenii are dominant species of the urogenital microbiota. Prior studies suggest that these Lactobacillus species play a significant role in the urobiome of healthy females. In our prior genomic analysis of all publicly available L. jensenii and Lactobacillus mulieris genomes at the time (n = 43), we identified genes unique to these two closely related species. This motivated our further exploration here into their genotypic differences as well as into their phenotypic differences. First, we expanded genome sequence representatives of both species to 61 strains, including publicly available …
On Colorings And Orientations Of Signed Graphs,
2023
Wright State University - Main Campus
On Colorings And Orientations Of Signed Graphs, Daniel Slilaty
Mathematics and Statistics Faculty Publications
A classical theorem independently due to Gallai and Roy states that a graph G has a proper k-coloring if and only if G has an orientation without coherent paths of length k. An analogue of this result for signed graphs is proved in this article.
Why Softmax? Because It Is The Only Consistent Approach To Probability-Based Classification,
2023
Alpine Relay
Why Softmax? Because It Is The Only Consistent Approach To Probability-Based Classification, Anatole Lokshin, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical problems, the most effective classification techniques are based on deep learning. In this approach, once the neural network generates values corresponding to different classes, these values are transformed into probabilities by using the softmax formula. Researchers tried other transformation, but they did not work as well as softmax. A natural question is: why is softmax so effective? In this paper, we provide a possible explanation for this effectiveness: namely, we prove that softmax is the only consistent approach to probability-based classification. In precise terms, it is the only approach for which two reasonable probability-based ideas -- Least …
Selecting The Most Adequate Fuzzy Operation For Explainable Ai: Empirical Fact And Its Possible Theoretical Explanation,
2023
Aalen University of Applied Sciences
Selecting The Most Adequate Fuzzy Operation For Explainable Ai: Empirical Fact And Its Possible Theoretical Explanation, Orsolya Csiszar, Gábor Csiszar, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
A reasonable way to make AI results explainable is to approximate the corresponding deep-learning-generated function by a simple expression formed by fuzzy operations. Experiments on real data show that out of all easy-to-compute fuzzy operations, the best approximation is attained if we use an operation a + b − 0.5 ( limited to the interval [0,1]$. In this paper, we provide a possible theoretical explanation for this empirical result.
Discrete Polylogarithm Functions,
2023
Marshall University
Discrete Polylogarithm Functions, Tom Cuchta, Dallas Freeman
Mathematics Faculty Research
We investigate a discrete analogue of the polylogarithm function. Difference and summation relations are obtained, as well as its connection to the discrete hypergeometric series.
Representations From Group Actions On Words And Matrices,
2023
California Polytechnic State University, San Luis Obispo
Representations From Group Actions On Words And Matrices, Joel T. Anderson
Master's Theses
We provide a combinatorial interpretation of the frequency of any irreducible representation of Sn in representations of Sn arising from group actions on words. Recognizing that representations arising from group actions naturally split across orbits yields combinatorial interpretations of the irreducible decompositions of representations from similar group actions. The generalization from group actions on words to group actions on matrices gives rise to representations that prove to be much less transparent. We share the progress made thus far on the open problem of determining the irreducible decomposition of certain representations of Sm × Sn arising from group actions on matrices.
Analyzing Tortuosity In Patterns Formed By Colonies Of Embryonic Stem Cells Using Topological Data Analysis,
2023
California Polytechnic State University, San Luis Obispo
Analyzing Tortuosity In Patterns Formed By Colonies Of Embryonic Stem Cells Using Topological Data Analysis, Jackie Driscoll
Master's Theses
Pluripotent stem cells have been observed to segregate into Turing-like patterns during the early stages of Dox-inducible hiPSC differentiation. In this thesis, we de- velop a tool to quantify the tortuosity in the patterns formed by colonies of pluripo- tent stem cells using methods from topological data analysis. We use clustering techniques and the mapper algorithm to create simplicial complexes representing samples of cells and detail a method of evaluating the tortuosity of these complexes. We use the resulting persistence landscapes and their associated norms to evaluate experimental data and simulated data from an agent based model. This thesis finds …
Engaging Students With High-Stakes Problems,
2023
Coastal Carolina University
Engaging Students With High-Stakes Problems, Deepak Basyal
Mathematics and Statistics
Engaging students in meaningful mathematics problem-solving is the intention of many education stakeholders around the world. Research suggests that the implementation of high-stakes problems in mathematics teaching is one way to strengthen students’ conceptual understanding. Many carefully crafted open-ended problems constitute high-stakes problems, and proper use of such problems in teaching and learning not only encourages learners’ flexible thinking but also helps detect their misconceptions. However, what is less practiced and understood is: how exactly one should aim to implement such problems in a classroom setting. Teaching pre-service middle school teachers for a few years using high-stakes (mostly open-ended problems) …
Apex Calculus: Und Edition (June 2023),
2023
Virginia Military Institute
Apex Calculus: Und Edition (June 2023), Gregory Hartman, Department Of Mathematics, University Of North Dakota
Open Educational Resources
This text comprises a three–volume series on Calculus. The first part covers material taught in many “Calculus 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6. The second text covers material often taught in “Calculus 2”: integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 7 through 10. The third text covers topics common in “Calculus 3” or “Multivariable Calculus”: parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 11 through 15. All three are available separately for free. …
Jones Polynomial Obstructions For Positivity Of Knots,
2023
Dartmouth College
Jones Polynomial Obstructions For Positivity Of Knots, Lizzie Buchanan
Dartmouth College Ph.D Dissertations
The fundamental problem in knot theory is distinguishing one knot from another. We accomplish this by looking at knot invariants. One such invariant is positivity. A knot is positive if it has a diagram in which all crossings are positive. A knot is almost-positive if it does not have a diagram where all crossings are positive, but it does have a diagram in which all but one crossings are positive. Given a knot with an almost-positive diagram, it is in general very hard to determine whether it might also have a positive diagram. This work provides positivity obstructions for three …
Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods,
2023
The University of Southern Mississippi
Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods, Nirmohi Charbe
Master's Theses
In this thesis we shall perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal cable. Assume a non-uniform cross section area along the longitudinal axis. At the present time, the effects of torsion, curvature and material capacitance are ignored. There is particular interest to generalize the application of the PDEs including and …
Strongly Invertible Knots, Equivariant Slice Genera, And An Equivariant Algebraic Concordance Group,
2023
Swarthmore College
Strongly Invertible Knots, Equivariant Slice Genera, And An Equivariant Algebraic Concordance Group, Allison N. Miller, M. Powell
Mathematics & Statistics Faculty Works
We use the Blanchfield form to obtain a lower bound on the equivariant slice genus of a strongly invertible knot. For our main application, let K be a strongly invertible genus one slice knot with nontrivial Alexander polynomial. We show that the equivariant slice genus of an equivariant connected sum #n K is at least n/4. We also formulate an equivariant algebraic concordance group, and show that the kernel of the forgetful map to the classical algebraic concordance group is infinite rank.
(R1965) Some More Properties On Generalized Double Fuzzy Z Alpha Open Sets,
2023
J. J. College of Arts and Science (Autonomous), Affiliated to Bharathidasan University
(R1965) Some More Properties On Generalized Double Fuzzy Z Alpha Open Sets, K. Jayapandian, A. Saivarajan, O. Uma Maheswari, J. Sathiyaraj
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a new class of sets termed as double fuzzy generalized Z alpha closed sets and double fuzzy generalized Z alpha open sets are introduced with the help of double fuzzy Z alpha open and double fuzzy Z alpha closed sets, respectively. Using these sets double fuzzy generalized Z alpha border, double fuzzy generalized Z alpha exterior and double fuzzy generalized Z alpha frontier of a fuzzy set in double fuzzy topological spaces are introduced. Also, the topological properties and characterizations of these sets and operators are studied. Furthermore, suitable examples have been provided to illustrate the theory.
(R2050) Dual Quaternion Matrices And Matlab Applications,
2023
Beykent University
(R2050) Dual Quaternion Matrices And Matlab Applications, Kemal Gökhan Nalbant, Salim Yüce
Applications and Applied Mathematics: An International Journal (AAM)
There are many studies in the literature on real quaternions and real quaternion matrices. There are few studies in the literature on dual quaternions. Definitions of the matrices of dual quaternions used in this study will be given. The originality of our research, the set of dual quaternion matrix we studied, will be defined for the first time in this study, and its properties will be given. Moreover, this study is critical because it is an applied study related to dual quaternion matrices. It will be easier to solve examples with large matrix sizes with MATLAB. People who use different …
(R2051) Analysis Of Map/Ph1, Ph2/2 Queueing Model With Working Breakdown, Repairs, Optional Service, And Balking,
2023
Puducherry Technological University
(R2051) Analysis Of Map/Ph1, Ph2/2 Queueing Model With Working Breakdown, Repairs, Optional Service, And Balking, G. Ayyappan, G. Archana
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a classical queueing system with two types of heterogeneous servers has been considered. The Markovian Arrival Process (MAP) is used for the customer arrival, while phase type distribution (PH) is applicable for the offering of service to customers as well as the repair time of servers. Optional service are provided by the servers to the unsatisfied customers. The server-2 may get breakdown during the busy period of any type of service. Though the server- 2 got breakdown, server-2 has a capacity to provide the service at a slower rate to the current customer who is receiving service …
(R2028) A Brief Note On Space Time Fractional Order Thermoelastic Response In A Layer,
2023
Shri Lemdeo Patil Mahavidyalaya,Mandhal
(R2028) A Brief Note On Space Time Fractional Order Thermoelastic Response In A Layer, Navneet Lamba, Jyoti Verma, Kishor Deshmukh
Applications and Applied Mathematics: An International Journal (AAM)
In this study, a one-dimensional layer of a solid is used to investigate the exact analytical solution of the heat conduction equation with space-time fractional order derivatives and to analyze its associated thermoelastic response using a quasi-static approach. The assumed thermoelastic problem was subjected to certain initial and boundary conditions at the initial and final ends of the layer. The memory effects and long-range interaction were discussed with the help of the Caputo-type fractional-order derivative and finite Riesz fractional derivative. Laplace transform and Fourier transform techniques for spatial coordinates were used to investigate the solution of the temperature distribution and …
