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Articles 511 - 540 of 2396
Full-Text Articles in Mathematics
Spiral Arms Around A Star: Geometric Explanation, Juan L. Puebla, Vladik Kreinovich
Spiral Arms Around A Star: Geometric Explanation, Juan L. Puebla, Vladik Kreinovich
Departmental Technical Reports (CS)
Recently, astronomers discovered spiral arms around a star. While their shape is similar to the shape of the spiral arms in the galaxies, however, because of the different scale, galaxy-related physical explanations of galactic spirals cannot be directly applied to explaining star-size spiral arms. In this paper, we show that, in contrast to more specific physical explanation, more general symmetry-based geometric explanations of galactic spiral can explain spiral arms around a star.
Why Self-Esteem Helps To Solve Problems: An Algorithmic Explanation, Oscar Ortiz, Henry Salgado, Olga Kosheleva, Vladik Kreinovich
Why Self-Esteem Helps To Solve Problems: An Algorithmic Explanation, Oscar Ortiz, Henry Salgado, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that self-esteem helps solve problems. From the algorithmic viewpoint, this seems like a mystery: a boost in self-esteem does not provide us with new algorithms, does not provide us with ability to compute faster -- but somehow, with the same algorithmic tools and the same ability to perform the corresponding computations, students become better problem solvers. In this paper, we provide an algorithmic explanation for this surprising empirical phenomenon.
How To Describe Hypothetic Truly Rare Events (With Probability 0), Luc Longpre, Vladik Kreinovich
How To Describe Hypothetic Truly Rare Events (With Probability 0), Luc Longpre, Vladik Kreinovich
Departmental Technical Reports (CS)
In probability theory, rare events are usually described as events with low probability p, i.e., events for which in N observations, the event happens n(N) ~ p*N times. Physicists and philosophers suggested that there may be events which are even rarer, in which n(N) grows slower than N. However, this idea has not been developed, since it was not clear how to describe it in precise terms. In this paper, we propose a possible precise description of this idea, and we use this description to answer a natural question: when two different functions n(N) lead to the same class of …
One More Physics-Based Explanation For Rectified Linear Neurons, Jonatan Contreras, Martine Ceberio, Vladik Kreinovich
One More Physics-Based Explanation For Rectified Linear Neurons, Jonatan Contreras, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
The main idea behind artificial neural networks is to simulate how data is processed in the data processing devoice that has been optimized by million-years natural selection -- our brain. Such networks are indeed very successful, but interestingly, the most recent successes came when researchers replaces the original biology-motivated sigmoid activation function with a completely different one -- known as rectified linear function. In this paper, we explain that this somewhat unexpected function actually naturally appears in physics-based data processing.
How To Make Quantum Ideas Less Counter-Intuitive: A Simple Analysis Of Measurement Uncertainty Can Help, Olga Kosheleva, Vladik Kreinovich, Louis Ray Lopez
How To Make Quantum Ideas Less Counter-Intuitive: A Simple Analysis Of Measurement Uncertainty Can Help, Olga Kosheleva, Vladik Kreinovich, Louis Ray Lopez
Departmental Technical Reports (CS)
Our intuition about physics is based on macro-scale phenomena, phenomena which are well described by non-quantum physics. As a result, many quantum ideas sound counter-intuitive -- and this slows down students' learning of quantum physics. In this paper, we show that a simple analysis of measurement uncertainty can make many of the quantum ideas much less counter-intuitive and thus, much easier to accept and understand.
Physical Meaning Often Leads To Natural Derivations In Elementary Mathematics: On The Examples Of Solving Quadratic And Cubic Equations, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Physical Meaning Often Leads To Natural Derivations In Elementary Mathematics: On The Examples Of Solving Quadratic And Cubic Equations, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Usual derivation of many formulas of elementary mathematics -- such as the formulas for solving quadratic equation -- often leave un unfortunate impression that mathematics is a collection of unrelated unnatural trick. In this paper, on the example of formulas for solving quadratic and cubic equations, we show that these derivations can be made much more natural if we take physical meaning into account.
Why Immunodepressive Drugs Often Make People Happier, Joshua Ramos, Dario Vasquez, Ruth Trejo, Vladik Kreinovich
Why Immunodepressive Drugs Often Make People Happier, Joshua Ramos, Dario Vasquez, Ruth Trejo, Vladik Kreinovich
Departmental Technical Reports (CS)
Many immunodepressive drugs have an unusual side effect on the patient's mood: they often make the patient happier. This side hae been observed for many different immunodepressive drugs, with different chemical composition. Thus, it is natural to conclude that there must be some general reason for this empirical phenomenon, a reason not related to the chemical composition of any specific drug -- but rather with their general functionality. In this paper, we provide such an explanation.
Explaining An Empirical Formula For Bioreaction To Similar Stimuli (Covid-19 And Beyond), Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Explaining An Empirical Formula For Bioreaction To Similar Stimuli (Covid-19 And Beyond), Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong
Departmental Technical Reports (CS)
A recent comparative analysis of biological reaction to unchanging vs. rapidly changing stimuli -- such as Covid-19 or flu viruses -- uses an empirical formula describing how the reaction to a similar stimulus depends on the distance between the new and original stimuli. In this paper, we provide a from-first-principles explanation for this empirical formula.
Session 5: Equipment Finance Credit Risk Modeling - A Case Study In Creative Model Development & Nimble Data Engineering, Edward Krueger, Landon Thompson, Josh Moore
Session 5: Equipment Finance Credit Risk Modeling - A Case Study In Creative Model Development & Nimble Data Engineering, Edward Krueger, Landon Thompson, Josh Moore
SDSU Data Science Symposium
This presentation will focus first on providing an overview of Channel and the Risk Analytics team that performed this case study. Given that context, we’ll then dive into our approach for building the modeling development data set, techniques and tools used to develop and implement the model into a production environment, and some of the challenges faced upon launch. Then, the presentation will pivot to the data engineering pipeline. During this portion, we will explore the application process and what happens to the data we collect. This will include how we extract & store the data along with how it …
Ordered Weighted Averaging (Owa), Decision Making Under Uncertainty, And Deep Learning: How Is This All Related?, Vladik Kreinovich
Ordered Weighted Averaging (Owa), Decision Making Under Uncertainty, And Deep Learning: How Is This All Related?, Vladik Kreinovich
Departmental Technical Reports (CS)
Among many research areas to which Ron Yager contributed are decision making under uncertainty (in particular, under interval and fuzzy uncertainty) and aggregation -- where he proposed, analyzed, and utilized ordered weighted averaging (OWA). The OWA algorithm itself provides only a specific type of data aggregation. However, it turns out that if we allow several OWA stages, one after another, we obtain a scheme with a universal approximation property -- moreover, a scheme which is perfectly equivalent to modern ReLU-based deep neural networks. In this sense, Ron Yager can be viewed as a (grand)father of ReLU-based deep learning. We also …
Unexpected Economic Consequence Of Cloud Computing: A Boost To Algorithmic Creativity, Francisco Zapata, Eric Smith, Vladik Kreinovich
Unexpected Economic Consequence Of Cloud Computing: A Boost To Algorithmic Creativity, Francisco Zapata, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
While theoreticians have been designing more and more efficient algorithms, in the past, practitioners were not very interested in this activity: if a company already owns computers that provide computations in required time, there is nothing to gain by using faster algorithms. We show the situation has drastically changed with the transition to cloud computing: many companies have not yet realized this, but with the transition to cloud computing, any algorithmic speed up leads to immediate financial gain. This also has serious consequences for the whole computing profession: there is a need for professionals better trained in subtle aspects of …
Unreachable Statements Are Inevitable In Software Testing: Theoretical Explanation, Francisco Zapata, Eric Smith, Vladik Kreinovich
Unreachable Statements Are Inevitable In Software Testing: Theoretical Explanation, Francisco Zapata, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
Business gurus recommend that an organization should have, in addition to clearly described realistic goals, also additional aspirational goals -- goals for which we may not have resources and which most probably will not be reached at all. At first glance, adding such a vague goal cannot lead to a drastic change in how the company operates, but surprisingly, for many companies, the mere presence of such aspirational goals boosts the company's performance. In this paper, we show that a simple geometric model of this situation can explain the unexpected success of aspirational goals.
A Natural Causality-Motivated Description Of Learning, Olga Kosheleva, Vladik Kreinovich
A Natural Causality-Motivated Description Of Learning, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Teaching is not easy. One of the main reasons why it is not easy is that the existing descriptions of the teaching process are not very precise -- and thus, we cannot use the usual optimization techniques, techniques which require a precise model of the corresponding phenomenon. It is therefore desirable to come up with a precise description of the learning process. To come up with such a description, we notice that on the set of all possible states of learning, there is a natural order s ≤ s' meaning that we can bring the student from the state s …
Why Gaussian Copulas Are Ubiquitous In Economics: Fuzzy-Related Explanation, Chon Van Le, Olga Kosheleva, Vladik Kreinovich
Why Gaussian Copulas Are Ubiquitous In Economics: Fuzzy-Related Explanation, Chon Van Le, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many real-life situations, deviations are caused by a large number of independent factors. It is known that in such situations, the distribution of the resulting deviations is close to Gaussian, and thus, that the copulas -- that describe the multi-D distributions as a function of 1-D (marginal) ones -- are also Gaussian. In the past, these conclusions were also applied to economic phenomena, until the 2008 crisis showed that in economics, Gaussian models can lead to disastrous consequences. At present, all economists agree that the economic distributions are not Gaussian -- however, surprisingly, Gaussian copulas still often provide an …
Video Or Text? Bullets Or No Bullets? Why Not Both?, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Video Or Text? Bullets Or No Bullets? Why Not Both?, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Departmental Technical Reports (CS)
Some students – which are, in terms of pop-psychology – more left-brain – prefer linear exposition, others – more right-brain ones – prefer 2-D images and texts with visual emphasis (e.g., with bullets). At present, instructors try to find a middle grounds between these two audiences, but why not prepare each material in two ways, aimed at both audiences?
Computing The Range Of A Function-Of-Few-Linear-Combinations Under Linear Constraints: A Feasible Algorithm, Salvador Robles, Martine Ceberio, Vladik Kreinovich
Computing The Range Of A Function-Of-Few-Linear-Combinations Under Linear Constraints: A Feasible Algorithm, Salvador Robles, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we need to find the range of a given function under interval uncertainty. For nonlinear functions -- even for quadratic ones -- this problem is, in general, NP-hard; however, feasible algorithms exist for many specific cases. In particular, recently a feasible algorithm was developed for computing the range of the absolute value of a Fourier coefficient under uncertainty. In this paper, we generalize this algorithm to the case when we have a function of a few linear combinations of inputs. The resulting algorithm also handles the case when, in addition to intervals containing each input, we …
Commonsense-Continuous Dynamical Systems -- Stationary States, Prediction, And Reconstruction Of The Past: Fuzzy-Based Analysis, Olga Kosheleva, Vladik Kreinovich
Commonsense-Continuous Dynamical Systems -- Stationary States, Prediction, And Reconstruction Of The Past: Fuzzy-Based Analysis, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Traditional analysis of dynamical systems usually assumes that the mapping is continuous -- in precise mathematical sense. However, as many formal definitions, the mathematical definition of continuity does not always adequately capture the commonsense notion of continuity: that small changes in the input should lead to small changes in the output. In this paper, we provide a natural fuzzy-based formalization of this intuitive notion, and analyze how the requirement of commonsense continuity affects the properties of dynamical systems. Specifically, we show that for such systems, the set of fixed points is closed and convex, and that the only such systems …
Need For Techniques Intermediate Between Interval And Probabilistic Ones, Olga Kosheleva, Vladik Kreinovich
Need For Techniques Intermediate Between Interval And Probabilistic Ones, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In high performance computing, when we process a large amount of data, we do not have much information about the dependence between measurement errors corresponding to different inputs. To gauge the uncertainty of the result of data processing, the two usual approaches are: the interval approach, when we consider the worst-case scenario in which all measurement errors are strongly correlated, and the probabilistic approach, when we assume that all these errors are independent. The problem is that usually, the interval approach leads to too pessimistic, too large uncertainty estimates, while the probabilistic approach often underestimates the resulting uncertainty. To get …
Fuzzy Or Neural, Type-1 Or Type-2 -- When Each Is Better: First-Approximation Analysis, Vladik Kreinovich, Olga Kosheleva
Fuzzy Or Neural, Type-1 Or Type-2 -- When Each Is Better: First-Approximation Analysis, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
In many practical situations, we need to determine the dependence between different quantities based on the empirical data. Several methods exist for solving this problem, including neural techniques and different versions of fuzzy techniques: type-1, type-2, etc. In some cases, some of these techniques work better, in other cases, other methods work better. Usually, practitioners try several techniques and select the one that works best for their problem. This trying often requires a lot of efforts. It would be more efficient if we could have a priori recommendations about which technique is better. In this paper, we use the first-approximation …
Why Ideas First Appear In Informal Form? Why It Is Very Difficult To Know Yourself? Fuzzy-Based Explanation, Miroslav Svitek, Vladik Kreinovich
Why Ideas First Appear In Informal Form? Why It Is Very Difficult To Know Yourself? Fuzzy-Based Explanation, Miroslav Svitek, Vladik Kreinovich
Departmental Technical Reports (CS)
To a lay person reading about history of physics, it may sound as if the progress of physics comes from geniuses whose inspiration leads them to precise equations that -- almost magically -- explain all the data: this is what Newton did with mechanics, this is what Schroedinger did with quantum physics, this is what Einstein did with gravitation. However, a deeper study of history of physics shows that in all these cases, these geniuses did not start from scratch -- they formalized ideas that first appeared in imprecise ("fuzzy") form. In this paper, we explain -- on the qualitative …
Why Aspirational Goals: Geometric Explanation, Olga Kosheleva, Vladik Kreinovich
Why Aspirational Goals: Geometric Explanation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Business gurus recommend that an organization should have, in addition to clearly described realistic goals, also additional aspirational goals -- goals for which we may not have resources and which most probably will not be reached at all. At first glance, adding such a vague goal cannot lead to a drastic change in how the company operates, but surprisingly, for many companies, the mere presence of such aspirational goals boosts the company's performance. In this paper, we show that a simple geometric model of this situation can explain the unexpected success of aspirational goals.
Why Pre-Teaching: A Geometric Explanation, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Why Pre-Teaching: A Geometric Explanation, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Departmental Technical Reports (CS)
Traditionally, subjects are taught in sequential order: e.g., first, students study algebra, then they use the knowledge of algebra to study the basis ideas of calculus. In this traditional scheme, teachers usually do not explain any calculus ideas before students are ready – since they believe that this would only confuse students. However, lately, empirical evidence has shows that, contrary to this common belief, pre-teaching – when students get a brief introduction to the forthcoming new topic before this topic starts – helps students learn. In this paper, we provide a geometric explanation for this unexpected empirical phenomenon.
Why Core Curriculum? Why Art And Nature Enhance Creativity? A Mathematical Explanation, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Why Core Curriculum? Why Art And Nature Enhance Creativity? A Mathematical Explanation, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Departmental Technical Reports (CS)
Teaching is not easy. One of the main reasons why it is not easy is that the existing descriptions of the teaching process are not very precise -- and thus, we cannot use the usual optimization techniques, techniques which require a precise model of the corresponding phenomenon. It is therefore desirable to come up with a precise description of the learning process. To come up with such a description, we notice that on the set of all possible states of learning, there is a natural order s ≤ s' meaning that we can bring the student from the state s …
Data Processing Under Fuzzy Uncertainty: Towards More Efficient Algorithm, Hung T. Nguyen, Olga Kosheleva, Vladik Kreinovich
Data Processing Under Fuzzy Uncertainty: Towards More Efficient Algorithm, Hung T. Nguyen, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we need to process data under fuzzy uncertainty: we have fuzzy information about the algorithm's input, and we want to find the resulting information about the algorithm's output. It is known that this problem can be reduced to computing the range of the algorithm over alpha-cuts of the input. Since the fuzzy degrees are usually known with accuracy at best 0.1, it is sufficient to repeat this range-computing procedure for 11 values alpha = 0, 0.1, ..., 1.0. However, a straightforward application of this idea requires 11 times longer computation time than each range estimation -- …
How To Describe Relative Approximation Error? A New Justification For Gustafson's Logarithmic Expression, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
How To Describe Relative Approximation Error? A New Justification For Gustafson's Logarithmic Expression, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
How can we describe relative approximation error? When the value b approximate a value a, the usual description of this error is the ratio |b − a|/|a|. The problem with this approach is that, contrary to our intuition, we get different numbers gauging how well a approximates b and how well b approximates a. To avoid this problem, John Gustafson proposed to use the logarithmic measure |ln(b/a)|. In this paper, we show that this is, in effect, the only regular scale-invariant way to describe the relative approximation error.
How To React To Student Evaluations, Olga Kosheleva, Vladik Kreinovich, Christian Servin
How To React To Student Evaluations, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Departmental Technical Reports (CS)
If most students comment that the course was too fast, a natural idea is to slow it down. If most students comment that the course was too slow, a natural idea is to speed it up. But what if half the students think the speed was too fast and half that the speed was too slow? A frequent reaction to such a situation is to conclude that the speed was just right and not change the speed the next time, but this may not be the right reaction: under the same speed, half of the students will struggle and may …
Provably Weak Instances Of Plwe Revisited, Again, Katherine Mendel
Provably Weak Instances Of Plwe Revisited, Again, Katherine Mendel
CSB and SJU Distinguished Thesis
Learning with Errors has emerged as a promising possibility for postquantum cryptography. Variants known as RLWE and PLWE have been shown to be more efficient, but the increased structure can leave them vulnerable to attacks for certain instantiations. This work aims to identify specific cases where proposed cryptographic schemes based on PLWE work particularly poorly under a specific attack.
The Nature Of Numbers: Real Computing, Bradley J. Lucier
The Nature Of Numbers: Real Computing, Bradley J. Lucier
Journal of Humanistic Mathematics
While studying the computable real numbers as a professional mathematician, I came to see the computable reals, and not the real numbers as usually presented in undergraduate real analysis classes, as the natural culmination of my evolving understanding of numbers as a schoolchild. This paper attempts to trace and explain that evolution. The first part recounts the nature of numbers as they were presented to us grade-school children. In particular, the introduction of square roots induced a step change in my understanding of numbers. Another incident gave me insight into the brilliance of Alan Turing in his paper introducing both …
Optimal Eavesdropping In Quantum Cryptography, Atanu Acharyya Dr.
Optimal Eavesdropping In Quantum Cryptography, Atanu Acharyya Dr.
Doctoral Theses
Quantum key distribution (QKD) has raised some promise for more secured communication than its classical counterpart. It allows the legitimate parties to detect eavesdropping which introduces error in the channel. If disturbed, there are ways to distill a secure key within some threshold error-rate. The amount of information gained by an attacker is generally quantified by (Shannon) mutual information. Knowing the maximum amount of information that an intruder can gain is important for post-processing purposes, and we mainly focus on that side in the thesis. Renyi information is also useful especially when post-processing is considered. The scope of this thesis …
Why Sine Membership Functions, Sofia Holguin, Javier Viaña, Kelly Cohen, Anca Ralescu, Vladik Kreinovich
Why Sine Membership Functions, Sofia Holguin, Javier Viaña, Kelly Cohen, Anca Ralescu, Vladik Kreinovich
Departmental Technical Reports (CS)
In applications of fuzzy techniques to several practical problems -- in particular, to the problem of predicting passenger flows in the airports -- the most efficient membership function is a sine function; to be precise, a portion of a sine function between the two zeros. In this paper, we provide a theoretical explanation for this empirical success.