A tribute to Anatole Beck (1930-2014)

A little over a year since his passing, Adam Ostaszewki, Professor of Mathematics at LSE, remembers Anatole Beck, our friend and colleague, with input from Steve Alpern and Kenneth Binmore. They have also put together a bibliography of Anatole’s work

Bifurcation analysis of the Topp model

In this paper, we study the 3-dimensional Topp model for the dynamicsof diabetes. We show that for suitable parameter values an equilibrium of this modelbifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests thatnear this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arisethrough period doubling cascades of limit cycles.Keywords Dynamics of diabetes · Topp model · Reduced planar quartic Toppsystem · Singular point · Limit cycle · Hopf-saddle-node bifurcation · Perioddoubling bifurcation · Shilnikov homoclinic orbit · Chao

INTEGRATION OF INTERDISCIPLINARY SCIENTIFIC KNOWLEDGE IN TEACHING INVERSE PROBLEMS FOR DIFFERENTIAL EQUATIONS

Problem and goal. In the process of teaching students inverse problems for differential equations, one of the important goals is to form students ‘ fundamental knowledge in the field of inverse problems, in the field of applied and computational mathematics; to develop mathematical creativity that allows students after graduation, working in research institutions, to successfully solve a variety of complex mathematical problems in the implementation of practical applied research. Methodology. In the process of teaching students inverse problems for differential equations, the system of humanitarian-oriented training sessions is designed, the methods of rational reasoning are used, an individual approach to learning is implemented. Results. Humanitarian-oriented training sessions on inverse problems for differential equations are aimed at creating situations that require students, according to the results of solving the inverse problem, to make logical conclusions of applied and humanitarian character, to overcome moral contradictions, to make a reasonable choice of the right position in society. The skills and experience gained in the course of training in the application of rational reasoning in the study of inverse problems for differential equations allow students not only to effectively investigate applied problems, but also to form fundamental knowledge in the field of applied mathematics. Individual approach in teaching inverse problems for differential equations acts as a didactic principle of training, education and development of students, taking into account the personal characteristics of students, the level of intellectual development, cognitive interests and other factors that affect the success of learning. Conclusion. Humanitarian-oriented training sessions on inverse problems for differential equations, methods of rational reasoning, individual approach to learning allows the students to form a system of fundamental knowledge in inverse problems for partial differential equations, integrating multidisciplinary scientific knowledge, to identify humanitarian and scientific-educational potential of such learning, to justify the positive contribution of teaching inverse problems for differential equations in humanization and fundamentalization of mathematical education

The differential geometric structure in supervised learning of classifiers

In this thesis, we study the overfitting problem in supervised learning of classifiers from a geometric perspective. As with many inverse problems, learning a classification function from a given set of example-label pairs is an ill-posed problem, i.e., there exist infinitely many classification functions that can correctly predict the class labels for all training examples. Among them, according to Occam's razor, simpler functions are favored since they are less overfitted to training examples and are therefore expected to perform better on unseen examples. The standard technique to enforce Occam's razor is to introduce a regularization scheme, which penalizes some type of complexity of the learned classification function. Some widely used regularization techniques are functional norm-based (Tikhonov) techniques, ensemble-based techniques, early stopping techniques, etc. However, there is important geometric information in the learned classification function that is closely related to overfitting, and has been overlooked by previous methods. In this thesis, we study the complexity of a classification function from a new geometric perspective. In particular, we investigate the differential geometric structure in the submanifold corresponding to the estimator of the class probability P(y|x), based on the observation that overfitting produces rapid local oscillations and hence large mean curvature of this submanifold. We also show that our geometric perspective of supervised learning is naturally related to an elastic model in physics, where our complexity measure is a high dimensional extension of the surface energy in physics. This study leads to a new geometric regularization approach for supervised learning of classifiers. In our approach, the learning process can be viewed as a submanifold fitting problem that is solved by a mean curvature flow method. In particular, our approach finds the submanifold by iteratively fitting the training examples in a curvature or volume decreasing manner. Our technique is unified for both binary and multiclass classification, and can be applied to regularize any classification function that satisfies two requirements: firstly, an estimator of the class probability can be obtained; secondly, first and second derivatives of the class probability estimator can be calculated. For applications, where we apply our regularization technique to standard loss functions for classification, our RBF-based implementation compares favorably to widely used regularization methods for both binary and multiclass classification. We also design a specific algorithm to incorporate our regularization technique into the standard forward-backward training of deep neural networks. For theoretical analysis, we establish Bayes consistency for a specific loss function under some mild initialization assumptions. We also discuss the extension of our approach to situations where the input space is a submanifold, rather than a Euclidean space.2018-11-30T00:00:00

Graduate School of Engineering and Management Catalog 2018-2019

The Graduate Catalog represents the offerings, programs, and requirements in effect at the time of publication

Моделювання, керування та інформаційні технології

Aniksuhyn A., Zhyvolovych O. Generalized solvability and optimal control for an integro-differential equation of a hyperbolic type 8 Babudzhan R., Isaienkov K., Krasii D., Melkonian R., Vodka O., Zadorozhniy I. Collection and processing of bearing vibration data for their technical condition classification by machine learning methods 10 Bardan A., Bihun Y. Computer modeling of differential games . 16 Beridze Z., Shavadze Ju., Imnaishvili G., Geladze M. Concept and functions of building a private network (VPN) 19 Bomba A., Klymiuk Y. Computer prediction of technological modes of rapid cone shaped adsorption filters with automated discharge of part of heat from separation surfaces in filtering model 21 Boyko N., Dypko O. Analysis of machine learning methods using spam filtering 25 Boyko N., Kulchytska O. Analysis of tumor classification algorithms for breast cancer prediction by machine learning methods 29 Denysov S., Semenov V., Vedel Ya. A novel adaptive method for operator inclusions 33 Didmanidze M., Chachanidze G., Didmanidze T. Modern trends in unemployment . 36 Bagrationi I., Zaslavski V., Didmanidze I., Yamkova O. Ethics of information technology in the context of a global worldview . 38 Didmanidze D., Zoidze K., Akhvlediani N., Tsitskishvili G., Samnidze N., Diasamidze M. Use of computer teaching systems in the learning process . 42 Dobrydnyk Yu., Khrystyuk A. Analysis of the elevator as an object of automation 44 Gamzayev R., Shkoda B. Development and investigation of adaptive micro-service architecture for messaging software systems . 46 Gayev Ye. Student' own discoveries in information theory curriculum 50 Didmanidze I., Geladze D., Motskobili Ia, Akhvlediani D., Koridze L. Follow digitally by using a blog . 52 Kirpichnikov A., Khrystyuk A. Automatic apiary care system 54 Kunytskyi S., Ivanchuk N. Mathematical modeling of water purification in a bioplato filter 56 Kyrylych V., Milchenko O. Optimal control of a hyperbolic system that describes Slutsky demand . 58 6 Makaradze N., Nakashidze-Makharadze T., Zaslavski V., Gurgenidze M., Samnidze N., Diasamidze M. Challenges of using computer-based educational technologies in higher education 60 Mamenko P., Zinchenko S., Nosov P., Kyrychenko K., Popovych I., Nahrybelnyi Ya., Kobets V. Research of divergence trajectory with a given risk of ships collisions . 64 Mateichuk V., Zinchenko S., Tovstokoryi O., Nosov P., Nahrybelnyi Ya., Popovych I., Kobets V. Automatic vessel control in stormy conditions 68 Petrivskyi Ya., Petrivskyi V., Bychkov O., Pyzh O. Some features of creating a computer vision system 72 Poliakov V. Calculation of organic substrate decomposition in biofilm and bioreactor-filter taking into account its limitation and inhibition 75 Poliakov V. Mathematical modeling of suspension filtration on a rapid filter at an unregulated rate 78 Prokip V. On the semi-scalar equivalence of polynomial matrices 80 Pysarchuk O., Mironov Y. A proposal of algorithm for automated chromosomal abnormality detection . 83 Rybak O., Tarasenko S. Sperner’s Theorem . 87 Sandrakov G., Hulianytskyi A., Semenov V. Modeling of filtration processes in periodic porous media 90 Stepanets O., Mariiash Yu. Optimal control of the blowing mode parameters during basic oxygen furnace steelmaking process . 94 Stepanchenko O., Shostak L., Kozhushko O., Moshynskyi V., Martyniuk P. Modelling soil organic carbon turnover with assimilation of satellite soil moisture data 97 Vinnychenko D., Nazarova N., Vinnychenko I. The dependence of the deviation of the output stabilized current of the resonant power supply during frequency control in the systems of materials pulse processing 100 Voloshchuk V., Nekrashevych O., Gikalo P. Exergy analysis of a reversible chiller 105 Шарко О., Петрушенко Н., Мосін М., Шарко М., Василенко Н., Белоусов А. Інформаційно-керуючі системи та технології оцінки ступеня підготовленості підприємств до інноваційної діяльності за допомогою ланцюгів Маркова . 107 Барановський С., Бомба А., Прищепа О. Модифікація моделі інфекційного захворювання для урахування дифузійних збурень в умовах логістичної динаміки 110 Бомба А., Бойчура М., Мічута О. Ідентифікація параметрів структури ґрунтових криволінійних масивів числовими методами квазіконформних відображень . 112 Василець К. Метод оцінювання невизначеності вимірювання електроенергії вузлом комерційного обліку 114 Волощук В., Некрашевич О., Гікало П. Доцільність застосування критеріїв ексергетичного аналізу для оцінювання ефективності об'єктів теплоенергетики . 117 Гудь В. Математичне моделювання енергетичної ефективності постійних магнітів в циліндричних магнітних системах . 120 Демидюк М. Параметрична оптимізація циклічних транспортних операцій маніпуляторів з активними і пасивними приводами 122 Клепач М., Клепач М. Вейвлет аналіз температурних трендів днища скловарної печі 125 Козирєв С. Керування високовольтним імпульсним розрядом в екзотермічному середовищі . 127 Очко О., Аврука І. Безпечне збереження конфіденційної інформації на серверах . 131 Реут Д., Древецький В., Матус С. Застосування комп’ютерного зору для автоматичного вимірювання швидкості рідин з тонкодисперсними домішками 133 Сафоник А., Грицюк І. Розроблення інформаційної системи для спектрофотометричного аналізу . 135 Ткачук В. Квантовий генетичний алгоритм та його реалізація на квантовому компютері 137 Цвєткова Т. Комп’ютерна візуалізація гідродинамічного поля в області зкриволінійними межами 140 Шпортько О., Бомба А., Шпортько Л. Пристосування словникових методів компресії до прогресуючого ієрархічного стиснення зображень без втрат . 142 Сафоник А., Таргоній І. Розробка системи керування напруженістю магнітного поля для процесу знезалізнення технологічних вод . 14

Clemson Graduate School Catalog, 1967-1968

https://tigerprints.clemson.edu/grad_anncmnt/1034/thumbnail.jp

Collaborative Management of Complex Major Construction Projects: AnyLogic-Based Simulation Modelling

Complex supply chain system collaborative management of major construction projects effectively integrates the different participants in the construction project. This paper establishes a simulation model based on AnyLogic to reveal the collaborative elements in the complex supply chain management system and the modes of action as well as the transmission problems of the intent information. Thus it is promoting the participants to become an organism with coordinated development and coevolution. This study can help improve the efficiency and management of the complex system of major construction projects