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June 4, 2026
Machine Learning Models Can Help Reduce Volatility and Boost Stock Market Returns
The use of machine learning models makes it possible to achieve greater accuracy in predicting risks in the Russian stock market compared to classical econometric approaches. The predictive power of these models increases by 23%, while the average investor’s return can reach up to 13% per annum. These conclusions were drawn by Nikita Lysenok from the Department of Financial Market Infrastructure at the HSE Faculty of Economic Sciences. The paper has been published in Fundamental and Applied Mathematics.
June 3, 2026
Pocket Money, Personal Interest, and Family Practices: What Shapes Students Economic Literacy?
University students' economic literacy depends not only on their field of study but also on their interest in economics, the learning environment, and family financial practices. For example, students who received pocket money irregularly tend to perform better on economic literacy tests than their peers who received financial support on a regular basis. These findings come from a study conducted by HSE University involving more than 1,100 students from five Russian universities. The findings have been published in Cakrawala Pendidikan.
June 3, 2026
Creative Work as a Remedy for Burnout
The creative, supportive atmosphere and innovative methods at the Centre for Sociocultural Research make it appealing to early-career scholars. Over years of working at HSE University, they grow into researchers and lecturers recognised both in Russia and abroad. Chief Research Fellow Zarina Lepshokova and Leading Research Fellow Ekaterina Bushina spoke about their journey at the centre and at HSE, their research, and the role of mentors in their academic success.

 

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О замкнутых классах функций трехзначной логики, порожденных периодическими симметрическими функциями

С. 319–322.
Mikhailovich A.
Language: Russian
Full text
Keywords: функции многозначной логикизамкнутые классыпорождающие системыбазис

In book

Проблемы теоретической кибернетики. Материалы XVI Международной конференции (Нижний Новгород, 20–25 июня 2011 г.)
Н. Новгород: Нижегородского госуниверситета, 2011.
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Числа, удаленные от простых, образуют базис порядка 2
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Для натурального $n$ обозначим через $F(n)$ расстояние от $n$ до ближайшего простого числа. Используя метод из недавней работы К. Форда, С. Конягина, Дж. Мейнарда, К. Померанса и Т. Тао ``Long gaps in sieved sets'' (J. Eur. Math. Soc., 23:2 (2021), 667--700), мы доказываем, что всякое достаточно большое натуральное $N$ может быть представлено в виде $N=n_1+n_2$, ...
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Improvement of Nonmonotone Complexity Estimates of k-Valued Logic Functions
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The problem of determining the nonmonotone complexity of the implementation ofk-valued logic functions by logic circuits in bases consisting of all monotone (with respect to thestandard order) functions and finitely many nonmonotone functions is investigated. In calculatingthe complexity measure under examination only those elements of the circuit which are assignednonmonotone basis functions are taken into ...
Added: November 19, 2023
Нижняя оценка немонотонной сложности функций многозначной логики
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The problem of the complexity of multi-valued logic functions realization by circuits in a special basis is investigated. This kind of basis consists of elements of two types. The first type of elements are monotone functions with zero weight. The second type of elements are non-monotone elements with unit weight. The non-empty set of elements of this type is ...
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Альтюссеровский поворот в марксизме и его значение для теории социального
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Rehabilitation of Marxist thought present in Althusser’s compilation of the articles titled by catching appeal “For Marx” is carried out in two directions: general – when theoretical line of understanding of the society and history is derived out of Marxism as political ideology; specific – when revealing the “ rational kernel” of Marxist philosophy of ...
Added: January 11, 2021
Circuit complexity of k-valued logic functions in one infinite basis
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We investigate the realization complexity of k-valued logic functions k ≥ 2 by combinational circuits in an infinite basis that includes the negation of the Lukasiewicz function, i.e., the function k−1−x, and all monotone functions. Complexity is understood as the total number of circuit elements. For an arbitrary function f, we establish lower and upper ...
Added: April 22, 2019
The minimum number of negations in circuits for systems of multi-valued functions
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The paper is concerned with the complexity of realization of 𝑘-valued logic functions by logic circuits over an infinite complete bases containing all monotone functions; the weight of monotone functions (the cost of use) is assumed to be 0. The complexity problem of realizations of Boolean functions over a basis having negation as the only ...
Added: March 14, 2018
On complexity of multi-valued logic functions over one infinite basis
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The complexity of realization of k-valued logic functions by circuits in a special infinite basis is under study. This basis consists of Post negation (i.e. function x+1(mod k)) and all monotone functions. The complexity of the circuit is the total number of elements of this circuit. For an arbitrary function f, we find the lower and upper bounds ...
Added: March 11, 2018
Asymptotics of growth for non-monotone complexity of multi-valued logic function systems
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The problem of the complexity of multi-valued logic functions realization by circuits in a special basis is investigated. This kind of basis consists of elements of two types. The 􏰌first type of elements are monotone functions with zero weight. The second type of elements are non-monotone elements with unit weight. The non-empty set of elements ...
Added: September 28, 2017
О сложности функций многозначной логики в одном бесконечном базисе
Kochergin V., Mikhailovich A., Дискретный анализ и исследование операций 2018 Т. 25 № 1 С. 42–74
The complexity of realization of k-valued logic functions by circuits in a special infinite basis  is invesigated. This basis consists of Post negation (i.e. function x+1(mod k)) and all monotone functions. The complexity of the circuit is the total number of elements of this circuit. The upper and the lower bounds of the complexity were ...
Added: September 28, 2017
Оценки немонотонной сложности логических схем
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Problem of multi-valued function realization by logic circuits in special bases is investigated. These bases consist of all monotone functions with zero weight and finite number of non-monotone functions with unit weight. ...
Added: September 22, 2017
Об одном фрагменте решётки замкнутых классов функций многозначной логики
Mikhailovich A., В кн.: Материалы 5-й Российской школы-семинара "Синтаксис и семантика логических систем".: Улан-Удэ: Издательство Бурятского госуниверситета, 2017. С. 91–95.
Lattice of all closed classes from closure of all functions from Janov and Muchnik examples has been described. ...
Added: September 22, 2017
Материалы 5-й Российской школы-семинара "Синтаксис и семантика логических систем"
Улан-Удэ: Издательство Бурятского госуниверситета, 2017.
The collection represents proceedings of the 5th school-seminar "Syntax and Semantics of Logic Systems" (Ulan-Ude, 08.08.2017 - 12.08.2017). The conference subject area includes: theory of models and universal algebra; theory of boolean and finite-valued functions; formal languages and logic calculus; mathematical logic in education. ...
Added: September 22, 2017
О строении одного замкнутого класса функций трехзначной логики
Mikhailovich A., В кн.: Материалы XVIII международной конференции "Проблемы теоретической кибернетики" (Пенза, 19-23 июня 2017 г.).: М.: МАКС Пресс, 2017. С. 166–168.
All closed classes from Muchnik's example of closed class with infinite bases are described. ...
Added: September 21, 2017
Поведение функции Шеннона сложности функций в одном бесконечном базисе
Михайлович А. В., Кочергин В. В., В кн.: Материалы XVIII международной конференции "Проблемы теоретической кибернетики" (Пенза, 19-23 июня 2017 г.).: М.: МАКС Пресс, 2017. С. 142–144.
The problem of multi-valued functions realization by circuits over special basis is inverstigated. The basis consis of Post negation and all monotone functions. ...
Added: September 21, 2017
О минимальном числе отрицаний при реализации систем функций многозначной логики
Mikhailovich A., Kochergin V., Дискретная математика 2016 Т. 28 № 4 С. 80–90
In this paper we consider the complexity of realization of k-valued logic functions by logic circuits over an infinite complete basis of special type. This basis contain all monotone functions with zero weight and non-monotone functions with non-zero weight. The problem of the complexity of a Boolean functions realization over basis containing all monotone functions ...
Added: February 25, 2017
О базируемости классов функций трехзначной логики, порожденных периодическими симметрическими функциями
Mikhailovich A., В кн.: Материалы XII Международного семинара "Дискретная математика и её приложения" имени академика О.Б. Лупанова (Москва, МГУ, 20-25 июня 2016г.).: М.: Изд-во механико-математического факультета МГУ, 2016. С. 209–212.
Closed classes of three-valued logic, generated by periodical functions taking values from the set {0,1} are considered. Criteria of basis exitstence and finite basis existence for classes generated by periodical functions with period of the form p^k (p is fixed prime number, k is arbitrary natural number) are obtained. ...
Added: September 1, 2016
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