Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Mathematics (465)
- Engineering (59)
- Artificial Intelligence and Robotics (46)
- Applied Mathematics (37)
- Social and Behavioral Sciences (33)
-
- Education (23)
- Electrical and Computer Engineering (23)
- Computer Engineering (19)
- Physics (19)
- Electrical and Electronics (18)
- Life Sciences (17)
- Databases and Information Systems (16)
- Environmental Sciences (15)
- Software Engineering (15)
- Earth Sciences (14)
- Statistics and Probability (14)
- Economics (11)
- Programming Languages and Compilers (10)
- Arts and Humanities (8)
- Mechanical Engineering (8)
- Medicine and Health Sciences (8)
- Civil and Environmental Engineering (7)
- Geography (7)
- Geophysics and Seismology (7)
- Bioinformatics (6)
- Civil Engineering (6)
- Geology (6)
- Biomedical (5)
- Keyword
-
- Technical Reports (390)
- UTEP Computer Science Department (389)
- Machine Learning (30)
- Interval uncertainty (24)
- Fuzzy logic (15)
-
- Optimization (14)
- Deep Learning (13)
- Machine learning (13)
- Interval computations (12)
- Android (8)
- Classification (8)
- Deep learning (8)
- Uncertainty (8)
- Decision making (7)
- Documentation (7)
- Usability (7)
- Data processing (6)
- Game Theory (6)
- Java (6)
- Prosody (6)
- Artificial Intelligence (5)
- Constraints (5)
- Control (5)
- Dialog (5)
- F-transform (5)
- Feasible algorithms (5)
- Functional program verification (5)
- Fuzzy uncertainty (5)
- GPU (5)
- NP-hard (5)
- Publication Year
- Publication
- Publication Type
Articles 61 - 90 of 1174
Full-Text Articles in Computer Sciences
Training Neural Networks On Interval Data: Unexpected Results And Their Explanation, Edwin Tomy George, Vladik Kreinovich, Christoph Lauter, Martine Ceberio, Luc Jaulin
Training Neural Networks On Interval Data: Unexpected Results And Their Explanation, Edwin Tomy George, Vladik Kreinovich, Christoph Lauter, Martine Ceberio, Luc Jaulin
Departmental Technical Reports (CS)
In many practically useful numerical computations, training-and-then-using a neural network turned out to be a much faster alternative than running the original computations. When we applied a similar idea to take into account interval uncertainty, we encountered two unexpected results: (1) that while for numerical computations, it is usually better to represent an interval by its midpoint and half-width, for neural networks, it is more efficient to represent an interval by its endpoints, and (2) that while usually, it is better to train a neural network on the whole data processing algorithm, in our problems, it turned out to be …
What If The Resulting Interval Is Too Wide: From A Heuristic Fuzzy-Technique Idea To A Mathematically Justified Approach, Marc Fina, Vladik Kreinovich
What If The Resulting Interval Is Too Wide: From A Heuristic Fuzzy-Technique Idea To A Mathematically Justified Approach, Marc Fina, Vladik Kreinovich
Departmental Technical Reports (CS)
In engineering designs, we usually need to make sure that the values of some characteristics y do not exceed a certain threshold y0 – e.g., that the stress at each location does not exceed a certain critical value. Usually, we know how each of these characteristics y depends on the design parameters x1, . . . ,xn, i.e., we know the function y= f (x1, . . . ,xn). However, it is not enough to use the nominal values of the design parameters in our analysis, since the actual values are, in general, somewhat different from the nominal values. Often, …
Shapley Value Under Interval Uncertainty And Partial Information, Kittawit Autchariyapanikul, Olga Kosheleva, Vladik Kreinovich
Shapley Value Under Interval Uncertainty And Partial Information, Kittawit Autchariyapanikul, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the 1950s, the future Nobelist Lloyd Shapley solved the problem of how to fairly divide the common gain. Namely, he showed that some reasonable requirements determine a unique division -- which is now known as the Shapley value. The main limitation of Shapley's solution is that it assumes that for each subgroup of the original group of participants, we know exactly how much this group could gain if it acted by itself, without involving others. In practice, we rarely know these exact values. At best, we know the bounds on each such value -- i.e., in other words, an …
Random Forest For High-Dimensional Data, George Ekow Quaye
Random Forest For High-Dimensional Data, George Ekow Quaye
Open Access Theses & Dissertations
The exponential growth of data has led to a rapid increase in high-dimensional datasets across various domains, presenting significant challenges in data analysis, particularly in predictive modeling tasks. Traditional Random Forest (RF), while robust, often struggles with datasets filled with numerous noisy or non-informative features, compromising both performance and accuracy. This study introduces an advanced algorithm, High-Dimensional Random Forests (HDRF), designed to address these challenges by integrating robust multivariate feature selection techniques directly into the decision tree construction process. Unlike standard RF, HDRF incorporates ridge regression-based variable screening at each decision split, enhancing its ability to identify and utilize the …
Semantic Linguistic User Profiles For Automatic Computational Narrative Creation For Scientific Models, Angel Uriel Ortega Castillo
Semantic Linguistic User Profiles For Automatic Computational Narrative Creation For Scientific Models, Angel Uriel Ortega Castillo
Open Access Theses & Dissertations
The outcomes of scientific models can be hard to understand given the need for context, domain knowledge, and many variables and data being used. This research aims to provide users of scientific models with understandable information that can be automatically generated. For the context of this research, understandable is defined as being correctly interpreted (i.e., with respect to the original intent of the data). Scientific information can be conveyed to users in the form of a narrative or visualizations, and these are not necessarily separate from each other, but rather complimentary. One of the objectives of this research is to …
Improving Cyber Defense Using Detailed Bayesian Models Of Attacker Reconnaissance., Nazia Sharmin
Improving Cyber Defense Using Detailed Bayesian Models Of Attacker Reconnaissance., Nazia Sharmin
Open Access Theses & Dissertations
The continued success of cyber-attacks motivates the need for continued innovation in cyber defense. In particular, there is a need for novel methods to mitigate attacker reconnaissance, usually the first stage in planning an attack. One of the few general approaches in this stage is using deception and information manipulation to affect what the attacker can learn about a system or network. Existing work in moving target defense, game-theoretic models of cyber deception/camouflage, and adversarial learning has provided a framework for optimizing deception strategies. However, most of the current literature is based on limited models of how attackers actually perform …
Neural Networks For Decisions Under Uncertainty, Edwin Tomy George
Neural Networks For Decisions Under Uncertainty, Edwin Tomy George
Open Access Theses & Dissertations
Neural networks are used in many real-world applications, ranging from classification tasks to medical diagnostics. For each task, a neural network is typically able to make predictions due to its ability to extract meaningful patterns from processing large amounts of data. Thus, given the increases in available data in recent decades, the performance of neural networks in making accurate predictions has greatly increased. However, this data often comes with ingrained uncertainties due to measurement errors or the inherent variability of individual data points. Neural networks can learn despite the errors in the overall data, but what if we want them …
If Subsequent Results Are Too Easy To Obtain, The Proof Most Probably Has Errors: Explanation Of The Empirical Observation, Olga Kosheleva, Vladik Kreinovich
If Subsequent Results Are Too Easy To Obtain, The Proof Most Probably Has Errors: Explanation Of The Empirical Observation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Many modern mathematical proofs are very complex, checking them is difficult; as a result, errors sneak into published proofs, even into proofs published in highly reputable journals. Sometimes, the errors are repairable, but sometimes, it turns out that the supposedly proven result is actually wrong. When the error is not noticed for some time, the published result is used to prove many other results -- and when the error is eventually found, all these new results are invalidated. This happened several times. Since it is not realistic to more thoroughly check all the proofs, and we want to minimize the …
Why Angles Between Galactic Center Filaments And Galactic Plane Follow A Bimodal Distribution: A Symmetry-Based Explanation, Julio C. Urenda, Vladik Kreinovich
Why Angles Between Galactic Center Filaments And Galactic Plane Follow A Bimodal Distribution: A Symmetry-Based Explanation, Julio C. Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
Recent observations have shown that the angles between the Galaxy Center filaments and the Galactic plane follow a bimodal distribution: a large number of filaments are approximately orthogonal to the Galactic plane, a large number of filaments are approximately parallel to the Galactic plane, and much fewer filaments have other orientations. In this paper, we show this bimodal distribution can be explained by natural geometric symmetries.
Why Seismicity In Ireland Is Low: A Possible Geometric Explanation, Julio C. Urenda, Aaron Velasco, Vladik Kreinovich
Why Seismicity In Ireland Is Low: A Possible Geometric Explanation, Julio C. Urenda, Aaron Velasco, Vladik Kreinovich
Departmental Technical Reports (CS)
For each geographic location, its seismicity level is usually determined by how close this location is to the boundaries of tectonic plates. However, there is one notable exception: while Ireland and Britain are at approximately the same distance from such boundaries, the seismicity level in Ireland is much lower than in Britain. A recent paper provided a partial explanation for this phenomenon: namely, it turns out that the lithosphere under Ireland is unusually thick, and this can potentially lead to lower seismicity. However, the current explanation of the relation between the lithosphere thickness and seismicity level strongly depends on the …
Is Alaska Negative-Tax Arrangement Fair? Almost: Mathematical Analysis, Chon Van Le, Vladik Kreinovich
Is Alaska Negative-Tax Arrangement Fair? Almost: Mathematical Analysis, Chon Van Le, Vladik Kreinovich
Departmental Technical Reports (CS)
In the State of Alaska there is no state income tax. Instead, there is a negative tex: every year every resident gets some money from the state. At present, every resident -- from the poorest to the richest -- gets the exact same amount of money: in 2024, it is expected to be around $1500. A natural question is: Is this fair? Maybe poor people should get more since their needs are greater? Maybe the rich people should get proportionally more, since fairness means equal added happiness for all, and for rich people, extra $1500 is barely noticeable? There have …
For 2 X N Cases, Proportional Fitting Problem Reduces To A Single Equation, Olga Kosheleva, Vladik Kreinovich
For 2 X N Cases, Proportional Fitting Problem Reduces To A Single Equation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, for each of two classifications, we know the probabilities that a randomly selected object belong to different categories. For example, we know what proportion of people are below 20 years old, what proportion is between 20 and 30, etc., and we also know what proportion of people earns less than 10K, between 10K and 20K, etc. In such situations, we are often interested in proportion of people who are classified by two classifications into two given categories. For example, we are interested in the proportion of people whose age is between 20 and 30 and whose …
Stochastic Dominance: Cases Of Interval And P-Box Uncertainty, Kittawit Autchariyapanikul, Olga Kosheleva, Vladik Kreinovich
Stochastic Dominance: Cases Of Interval And P-Box Uncertainty, Kittawit Autchariyapanikul, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Traditional decision theory recommendation about making a decision assume that we know both the probabilities of different outcomes of each possible decision, and we know the utility function -- that describes the decision maker's preferences. Sometimes, we can make a recommendation even when we only have partial information about utility. Such cases are known as cases of stochastic dominance. In other cases, in addition to not knowing the utility function, we also only have partial information about the probabilities of different outcomes. For example, we may only known bounds on the outcomes (case of interval uncertainty) or bounds on the …
How To Propagate Uncertainty Via Ai Algorithms, Olga Kosheleva, Vladik Kreinovich
How To Propagate Uncertainty Via Ai Algorithms, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Any data processing starts with measurement results. Measurement results are never absolutely accurate. Because of this measurement uncertainty, the results of processing measurement results are, in general, somewhat different from what we would have obtained if we knew the exact values of the measured quantities. To make a decision based on the result of data processing, we need to know how accurate is this result, i.e., we need to propagate the measurement uncertainty through the data processing algorithm. There are many techniques for uncertainty propagation. Usually, they involve applying the same data processing algorithm several times to appropriately modified data. …
For Discrete-Time Linear Dynamical Systems Under Interval Uncertainty, Predicting Two Moments Ahead Is Np-Hard, Luc Jaulin, Olga Kosheleva, Vladik Kreinovich
For Discrete-Time Linear Dynamical Systems Under Interval Uncertainty, Predicting Two Moments Ahead Is Np-Hard, Luc Jaulin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In the first approximation, when changes are small, most real-world systems are described by linear dynamical equations. If we know the initial state of the system, and we know its dynamics, then we can, in principle, predict the system's state many moments ahead. In practice, however, we usually know both the initial state and the coefficients of the system's dynamics with some uncertainty. Frequently, we encounter interval uncertainty, when for each parameter, we only know its range, but we have no information about the probability of different values from this range. In such situations, we want to know the range …
How To Make Ai More Reliable, Olga Kosheleva, Vladik Kreinovich
How To Make Ai More Reliable, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the reasons why the results of the current AI methods (especially deep-learning-based methods) are not absolutely reliable is that, in contrast to more traditional data processing techniques which are based on solid mathematical and statistical foundations, modern AI techniques use a lot of semi-heuristic methods. These methods have been, in many cases, empirically successful, but the absence of solid justification makes us less certain that these methods will work in other cases as well. To make AI more reliable, it is therefore necessary to provide mathematical foundations for the current semi-heuristic techniques. In this paper, we show that …
What To Do If An Inflexible Tolerance Problem Has No Solutions: Probabilistic Justification Of Piegat's Semi-Heuristic Idea, Olga Kosheleva, Vladik Kreinovich
What To Do If An Inflexible Tolerance Problem Has No Solutions: Probabilistic Justification Of Piegat's Semi-Heuristic Idea, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, it is desirable to select the control parameters x1, ..., xn in such a way that the resulting quantities y1, ..., ym of the system lie within desired ranges. In such situations, we usually know the general formulas describing the dependence of yi on xj, but the coefficients of these formulas are usually only known with interval uncertainty. In such a situation, we want to find the tuples for which all yi's are in the desired intervals for all possible tuples of coefficients. But what if no such parameters are possible? Since we cannot guarantee the …
Why Magenta Is Not A Real Color, And How It Is Related To Fuzzy Control And Quantum Computing, Victor L. Timchenko, Yuriy P. Kondratenko, Olga Kosheleva, Vladik Kreinovich
Why Magenta Is Not A Real Color, And How It Is Related To Fuzzy Control And Quantum Computing, Victor L. Timchenko, Yuriy P. Kondratenko, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
It is well known that every color can be represented as a combination of three basic colors: red, green, and blue. In particular, we can get several colors by combining two of the basic colors. Interestingly, while a combination of two neighboring colors leads to a color that corresponds to a certain frequency, the combination of two non-neighboring colors -- red and blue -- leads to magenta, a color that does not correspond to any frequency. In this paper, we provide a simple explanation for this phenomenon, and we also show that a similar phenomenon happens in two other areas …
Why Fully Consistent Quantum Field Theories Require That The Space-Time Be At Least 10-Dimensional: A Commonsense Field-Based Explanation, Olga Kosheleva, Vladik Kreinovich
Why Fully Consistent Quantum Field Theories Require That The Space-Time Be At Least 10-Dimensional: A Commonsense Field-Based Explanation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that quantum field theories that describe fields in our usual 4-dimensional space-times are not fully consistent: they predict meaningless infinite values for some physical quantities. There are some known tricks to avoid such infinities, but it is definitely desirable to have a fully consistent theory, a theory that would produce correct results without having to use additional tricks. It turns out that the only way to have such a theory is to consider space-times of higher dimensions, the smallest of which is 10. There are complex mathematical reasons for why 10 is the smallest such dimension. However, …
Towards A More Subtle (And Hopefully More Adequate) Fuzzy "And"-Operation: Normalization-Invariant Multi-Input Aggregation Operators, Yusuf Güven, Vladik Kreinovich
Towards A More Subtle (And Hopefully More Adequate) Fuzzy "And"-Operation: Normalization-Invariant Multi-Input Aggregation Operators, Yusuf Güven, Vladik Kreinovich
Departmental Technical Reports (CS)
Many reasonable conditions have been formulated for a fuzzy "and"-operation: idempotency, commutativity, associativity, etc. It is known that the only "and"-operation that satisfies all these conditions is minimum, but minimum is not the most adequate description of expert's "and", and it often does not lead to the best control or the best decision. Many other more adequate "and"-operations (t-norms) have been proposed and effectively used, but they do not satisfy the natural idempotency condition. In this paper, we show that a small relaxation of the usual description of "and"-operations leads to the possibility of non-minimum idempotent operations. We also show …
Why Empirical Membership Functions Are Well-Approximated By Piecewise Quadratic Functions: Theoretical Explanation For Empirical Formulas Of Novak's Fuzzy Natural Logic, Olga Kosheleva, Vladik Kreinovich
Why Empirical Membership Functions Are Well-Approximated By Piecewise Quadratic Functions: Theoretical Explanation For Empirical Formulas Of Novak's Fuzzy Natural Logic, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Empirical analysis shows that membership functions describing expert opinions have a shape that is well described by a smooth combination of two quadratic segments. In this paper, we provide a theoretical explanation for this empirical phenomenon.
Why Is Grade Distribution Often Bimodal? Why Individualized Teaching Adds Two Sigmas To The Average Grade? And How Are These Facts Related?, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Why Is Grade Distribution Often Bimodal? Why Individualized Teaching Adds Two Sigmas To The Average Grade? And How Are These Facts Related?, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
To make education more effective, to better use emerging technologies in education, we need to better understand the education process, to gain insights on this process. How can we check whether a new idea is indeed a useful insight? A natural criterion is that the new idea should explain some previously-difficult-to-explain empirical phenomenon. Since one of the main advantages of emerging educational technologies -- such as AI -- is the possibility of individualized education, a natural phenomenon to explain is the fact -- discovered by Benjamin Bloom -- that individualization adds two sigmas to the average grade. In this paper, …
Topics In The Study Of The Pragmatic Functions Of Phonetic Reduction In Dialog, Nigel G. Ward, Carlos A. Ortega
Topics In The Study Of The Pragmatic Functions Of Phonetic Reduction In Dialog, Nigel G. Ward, Carlos A. Ortega
Departmental Technical Reports (CS)
Reduced articulatory precision is common in speech, but for dialog its acoustic properties and pragmatic functions have been little studied. We here try to remedy this gap. This technical report contains content that was omitted from the journal article (Ward et. al, submitted). Specifically, we here report 1) lessons learned about annotating for perceived reduction, 2) the finding that, unlike in read speech, the correlates of reduction in dialog include high pitch, wide pitch range, and intensity, and 3) a baseline model for predicting reduction in dialog, using simple acoustic/prosodic features, that achieves correlations with human perceptions of 0.24 for …
How To Make A Neural Network Learn From A Small Number Of Examples -- And Learn Fast: An Idea, Chitta Baral, Vladik Kreinovich
How To Make A Neural Network Learn From A Small Number Of Examples -- And Learn Fast: An Idea, Chitta Baral, Vladik Kreinovich
Departmental Technical Reports (CS)
Current deep learning techniques have led to spectacular results, but they still have limitations. One of them is that, in contrast to humans who can learn from a few examples and learn fast, modern deep learning techniques require a large amount of data to learn, and they take a long time to train. In this paper, we show that neural networks do have a potential to learn from a small number of examples -- and learn fast. We speculate that the corresponding idea may already be implicitly implemented in Large Language Models -- which may partially explain their (somewhat mysterious) …
How Can We Explain Empirical Formulas For Shrinkage Cracking Of Cement-Stabilized Pavement Layers, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich
How Can We Explain Empirical Formulas For Shrinkage Cracking Of Cement-Stabilized Pavement Layers, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich
Departmental Technical Reports (CS)
In pavement construction, one of the frequent defects is shrinkage cracking of the cement-stabilized pavement layer. To minimize this defect, it is important to be able to predict how this cracking depends on the quantities describing the pavement layer and the corresponding environment. Cracking is usually described by two parameters: the average width of the crack and the crack spacing. Empirical analysis shows that the dependence of the width on all related quantities is described by a power law. Power laws are ubiquitous in physics, they describe a frequent case when the dependence is scale-invariant -- i.e., does not change …
In-Between Frame Generation For 2d Animation Using Generative Adversarial Networks, Francisco Arriaga Pazos
In-Between Frame Generation For 2d Animation Using Generative Adversarial Networks, Francisco Arriaga Pazos
Open Access Theses & Dissertations
Traditional 2D animation remains a largely manual process where each frame in a video is hand-drawn, as no robust algorithmic solutions exist to assist in this process. This project introduces a system that generates intermediate frames in an uncolored 2D animated video sequence using Generative Adversarial Networks (GAN), a deep learning approach widely used for tasks within the creative realm. We treat the task as a frame interpolation problem, and show that adding a GAN dynamic to a system significantly improves the perceptual fidelity of the generated images, as measured by perceptual oriented metrics that aim to capture human judgment …
Dynamic Storytelling Algorithms Using Contextual Aspects Of A Large Language Model, Alireza Pasha Nouri
Dynamic Storytelling Algorithms Using Contextual Aspects Of A Large Language Model, Alireza Pasha Nouri
Open Access Theses & Dissertations
Storytelling is a set of algorithms used to create narratives by connecting documents in a sequencethat accurately reflects the evolution of events and entities within a particular topic or theme. Early storytelling algorithms face challenges in encoding the progression and interconnections of information between consecutive texts, given that the conventional approaches rely primarily on connecting document pairs based on content overlap. They often neglect critical linguistic features, such as word contexts, semantics, the roles words play across different documents, and attention to the historical contexts of the underlying documents. Many existing storytelling models frequently produce story chains that, while connected …
Modeling The Spatiotemporal Variations Of The Magnetic Field In Active Regions On The Sun Using Deep Neural Networks, Godwill Asare Mensah Mensah
Modeling The Spatiotemporal Variations Of The Magnetic Field In Active Regions On The Sun Using Deep Neural Networks, Godwill Asare Mensah Mensah
Open Access Theses & Dissertations
Solar active regions are areas on the Sun's surface that have especially strong magnetic fields. Active regions are usually linked to a number of phenomena that can have serious detrimental consequences on technology and, in turn, human life. Examples of these phenomena include solar flares and coronal mass ejections, or CMEs. The precise predictionof solar flares and coronal mass ejections is still an open problem since the fundamental processes underpinning the formation and development of active regions are still not well understood. One key area of research at the intersection of solar physics and artificial intelligence is deriving insights from …
Automated Composition Of Multivariable Scientific Workflows Considering Scientific Assumptions, Raul Alejandro Vargas Acosta
Automated Composition Of Multivariable Scientific Workflows Considering Scientific Assumptions, Raul Alejandro Vargas Acosta
Open Access Theses & Dissertations
Many ground-breaking scientific experiments require the execution of multiple complex scientific computations. Thus, scientific workflows (i.e., a sequence of scientific computations) have received significant attention, more specifically, the automated composition of scientific workflows. Scientific workflows that repurpose data may have unique scientific assumptions that need to be considered when composing a workflow. Workflow composition tools have enabled a wider range of stakeholders (e.g., policymakers, the general public, and researchers) to create and execute workflows; however, domain expertise is still required for these tasks. The overarching goal of this work is to further improve the automatic composition of scientific workflows by …
Update From Aristotle To Newton, From Sets To Fuzzy Sets, And From Sigmoid To Relu: What Do All These Transitions Have In Common?, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Update From Aristotle To Newton, From Sets To Fuzzy Sets, And From Sigmoid To Relu: What Do All These Transitions Have In Common?, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we show that there is a -- somewhat unexpected -- common trend behind several seemingly unrelated historic transitions: from Aristotelian physics to modern (Newton's) approach, from crisp sets (such as intervals) to fuzzy sets, and from traditional neural networks, with close-to-step-function sigmoid activation functions to modern successful deep neural networks that use a completely different ReLU activation function. In all these cases, the main idea of the corresponding transition can be explained, in mathematical terms, as going from the first order to second order differential equations.