Bogdan Grechuk

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All published works

Action	Title	Year	Authors
+ PDF Chat	Generalised Fermat equation: a survey of solved cases	2024	Ashleigh G. Wilcox Bogdan Grechuk
+ PDF Chat	FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI	2024	Elliot Glazer Ege Erdil Tamay Besiroglu Diego Chicharro Evan Chen Amy C. Gunning Caroline Olsson Jean-Stanislas Denain Anson Ho Emily de Oliveira Santos
+ PDF Chat	On the solution uniqueness in portfolio optimization and risk analysis	2024	Bogdan Grechuk Andrzej Palczewski Jan Palczewski
+ PDF Chat	A systematic approach to Diophantine equations: open problems	2024	Bogdan Grechuk
+	Alternative Orderings of Diophantine Equations	2024	Bogdan Grechuk
+	Existence of Non-Trivial Solutions to Homogeneous Equations	2024	Bogdan Grechuk
+	Polynomial Diophantine Equations	2024	Bogdan Grechuk
+	Explicit Descriptions of the Solution Sets	2024	Bogdan Grechuk
+	Explicit Solutions to Small Equations	2024	Bogdan Grechuk
+	Existence of Polynomial Parametrizations	2024	Bogdan Grechuk
+	Equations in Two Variables	2024	Bogdan Grechuk
+	Existence of Integer Solutions	2024	Bogdan Grechuk
+ PDF Chat	Buffered and Reduced Multidimensional Distribution Functions and Their Application in Optimization	2023	Bogdan Grechuk Michael Zabarankin Alexander Mafusalov Stan Uryasev
+	Diophantine equations with three monomials	2023	Bogdan Grechuk Tetiana Grechuk Ashleigh G. Wilcox
+	Diophantine equations with three monomials	2023	Bogdan Grechuk Tetiana Grechuk Ashleigh G. Wilcox
+ PDF Chat	High-Dimensional Separability for One- and Few-Shot Learning	2021	Alexander N. Gorban Bogdan Grechuk Evgeny M. Mirkes Sergey V. Stasenko Ivan Tyukin
+	Diophantine equations: a systematic approach	2021	Bogdan Grechuk
+	High-Dimensional Separability for One- And Few-Shot Learning	2021	Alexander N. Gorban Bogdan Grechuk Evgeny M. Mirkes Sergey V. Stasenko Ivan Tyukin
+	General stochastic separation theorems with optimal bounds	2021	Bogdan Grechuk Alexander N. Gorban Ivan Tyukin
+	Probability and Statistics	2021	Bogdan Grechuk
+	Logic and Set Theory	2021	Bogdan Grechuk
+	Geometry and Topology	2021	Bogdan Grechuk
+	Algebra	2021	Bogdan Grechuk
+	Number Theory	2021	Bogdan Grechuk
+	Combinatorics	2021	Bogdan Grechuk
+	Analysis	2021	Bogdan Grechuk
+	Diophantine equations: a systematic approach	2021	Bogdan Grechuk
+	A convex cover for closed unit curves has area at least 0.1	2020	Bogdan Grechuk Sittichoke Som-am
+ PDF Chat	A Convex Cover for Closed Unit Curves has Area at Least 0.0975	2020	Bogdan Grechuk Sittichoke Som-am
+	A convex cover for closed unit curves has area at least 0.1	2020	Bogdan Grechuk Sittichoke Som-am
+	Matrix Difference Equations in Applied Mathematics	2020	Michael Zabarankin Bogdan Grechuk
+	A convex cover for closed unit curves has area at least 0.1	2020	Bogdan Grechuk Sittichoke Som-am
+	Practical stochastic separation theorems for product distributions	2019	Bogdan Grechuk
+	Theorems of the 21st Century	2019	Bogdan Grechuk
+	A convex cover for closed unit curves has area at least 0.0975	2019	Bogdan Grechuk Sittichoke Som-Am
+ PDF Chat	Correction of AI systems by linear discriminants: Probabilistic foundations	2018	Alexander N. Gorban A. Golubkov Bogdan Grechuk Evgeny M. Mirkes Ivan Tyukin
+ PDF Chat	Regression analysis: likelihood, error and entropy	2018	Bogdan Grechuk Michael Zabarankin
+	Augmented Artificial Intelligence: a Conceptual Framework	2018	Alexander N. Gorban Bogdan Grechuk Ivan Tyukin
+	On the solution uniqueness in portfolio optimization and risk analysis	2018	Bogdan Grechuk Andrzej Palczewski Jan Palczewski
+	Lower Semicontinuous Functions.	2011	Bogdan Grechuk
+	CHEBYSHEV INEQUALITIES WITH LAW-INVARIANT DEVIATION MEASURES	2009	Bogdan Grechuk Anton Molyboha Michael Zabarankin

Common Coauthors

Coauthor	Papers Together
Alexander N. Gorban	5
Ivan Tyukin	5
Sittichoke Som-am	4
Michael Zabarankin	4
Ashleigh G. Wilcox	3
Evgeny M. Mirkes	3
Sergey V. Stasenko	2
Jan Palczewski	2
Tetiana Grechuk	2
Andrzej Palczewski	2
Evan Chen	1
Shreepranav Varma Enugandla	1
Jean-Stanislas Denain	1
Natalie Stewart	1
Sittichoke Som-Am	1
Elizabeth Pratt	1
Ege Erdil	1
Lionel Levine	1
Tamay Besiroglu	1
Qiuyu Ren	1
Caroline Olsson	1
Alexander Mafusalov	1
Anton Molyboha	1
Olli Järviniemi	1
Jaime Sevilla	1
Robert D Sandler	1
Diego Chicharro	1
Tetiana Grechuk	1
Anson Ho	1
Emily de Oliveira Santos	1
Matthew Barnett	1
Elliot Glazer	1
Grant Barkley	1
A. Golubkov	1
Amy C. Gunning	1
Stan Uryasev	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Stochastic separation theorems	2017	Alexander N. Gorban Ivan Tyukin	6
+ PDF Chat	Blessing of dimensionality: mathematical foundations of the statistical physics of data	2018	Alexander N. Gorban Ivan Tyukin	6
+ PDF Chat	Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups	2010	L. N. Vaserstein	5
+ PDF Chat	The Concentration of Measure Phenomenon	2005	Michel Ledoux	5
+ PDF Chat	Approximation with random bases: Pro et Contra	2015	Alexander N. Gorban Ivan Tyukin Danil Prokhorov Konstantin Sofeikov	5
+ PDF Chat	Correction of AI systems by linear discriminants: Probabilistic foundations	2018	Alexander N. Gorban A. Golubkov Bogdan Grechuk Evgeny M. Mirkes Ivan Tyukin	5
+ PDF Chat	On the equation $y^m = P(x)$	1976	Andrzej Schinzel R. Tijdeman	5
+	Mathematical problems	1902	David Hilbert	5
+	Solving Genus Zero Diophantine Equations with at Most Two Infinite Valuations	2002	Dimitrios Poulakis Evaggelos Voskos	4
+	Generalized deviations in risk analysis	2005	R. T. Rockafellar Stan Uryasev Michael Zabarankin	4
+ PDF Chat	High-Dimensional Brain: A Tool for Encoding and Rapid Learning of Memories by Single Neurons	2018	Ivan Tyukin Alexander N. Gorban Carlos Calvo Julia Makarova Valeri A. Makarov	4
+	Concentration Property on Probability Spaces	2000	Apostolos Giannopoulos Vitali Milman	4
+ PDF Chat	Interpolating Thin-Shell and Sharp Large-Deviation Estimates for Lsotropic Log-Concave Measures	2011	Olivier Guédon Emanuel Milman	4
+	Augmented Artificial Intelligence: a Conceptual Framework	2018	Alexander N. Gorban Bogdan Grechuk Ivan Tyukin	4
+	Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing	2009	David L. Donoho Jared Tanner	4
+	The Blessing of Dimensionality: Separation Theorems in the Thermodynamic Limit**The work is partially supported by Innovate UK, Technology Strategy Board, Knowledge Transfer Partnership grant KTP009890	2016	Alexander N. Gorban Ivan Tyukin Ilya Romanenko	4
+ PDF Chat	Points entiers sur les courbes de genre 0	1993	Dimitrios Poulakis	4
+	Solving Diophantine Problems Modulo Every Prime	1967	James Ax	4
+	Integer points on curves of genus 1	1970	A. Baker J. Coates	4
+	Prototypical Networks for Few-shot Learning	2017	Jake Snell Kevin Swersky Richard S. Zemel	3
+	Packing smooth curves in<i>R</i><sup>q</sup>	1979	J. M. Marstrand	3
+	Covers for closed curves of length two	2011	Zoltán Füredi John E. Wetzel	3
+ PDF Chat	Fractional Norms and Quasinorms Do Not Help to Overcome the Curse of Dimensionality	2020	Evgeny M. Mirkes Jeza Allohibi Alexander N. Gorban	3
+ PDF Chat	Computing all integer solutions of a genus 1 equation	2003	Roel Stroeker Nikos Tzanakis	3
+	The Decision Problem for Exponential Diophantine Equations	1961	Martin Davis Hilary Putnam Julia Robinson	3
+ PDF Chat	One-trial correction of legacy AI systems and stochastic separation theorems	2019	Alexander N. Gorban Richard R. Burton Ilya Romanenko Ivan Tyukin	3
+	The unreasonable effectiveness of small neural ensembles in high-dimensional brain	2018	Alexander N. Gorban Valeri A. Makarov Ivan Tyukin	3
+ PDF Chat	Knowledge Transfer Between Artificial Intelligence Systems	2018	Ivan Tyukin Alexander N. Gorban Konstantin I. Sofeykov Ilya Romanenko	3
+	High-Dimensional Probability: An Introduction with Applications in Data Science	2018	Roman Vershynin	3
+	A continuous, constructive solution to Hilbert's 17th problem	1984	Charles N. Delzell	3
+	Der zentralsymmetrische Kern und die zentralsymmetrische Hülle von konvexen Körpern	1950	István Fáry L. Rédei	3
+ PDF Chat	A quantitative version of Runge's theorem on diophantine equations	1992	Peter Walsh	3
+	General stochastic separation theorems with optimal bounds	2021	Bogdan Grechuk Alexander N. Gorban Ivan Tyukin	3
+ PDF Chat	On the Equations <i>z<sup>m</sup> </i> = <i>F</i> (<i>x, y</i> ) and <i>Ax<sup>p</sup> </i> + <i>By<sup>q</sup> </i> = <i>Cz<sup>r</sup> </i>	1995	Henri Darmon Andrew Granville	3
+	Modular Elliptic Curves and Fermat's Last Theorem	1995	Andrew Wiles	3
+ PDF Chat	LOWER BOUND FOR CONVEX HULL AREA AND UNIVERSAL COVER PROBLEMS	2013	Tirasan Khandhawit D. Pagonakis Sira Sriswasdi	3
+	A LOWER BOUND FOR LEBESGUE'S UNIVERSAL COVER PROBLEM	2005	Peter Braß Mehrbod Sharifi	3
+	The More, the Merrier: the Blessing of Dimensionality for Learning Large Gaussian Mixtures	2013	Joseph Anderson Mikhail Belkin Navin Goyal Luis Rademacher James Voss	3
+	A Polynomial Time Algorithm for Diophantine Equations in One Variable	1999	Felipe Cucker Pascal Koiran S. Smale	3
+ PDF Chat	The primes contain arbitrarily long arithmetic progressions	2008	Benjamin Green Terence Tao	2
+ PDF Chat	Isoperimetric and Analytic Inequalities for Log-Concave Probability Measures	1999	Sergey G. Bobkov	2
+ PDF Chat	On the Erdős distinct distances problem in the plane	2014	Larry Guth Nets Hawk Katz	2
+	Small ball probability estimates for log-concave measures	2011	Grigoris Paouris	2
+ PDF Chat	On sets of integers containing k elements in arithmetic progression	1975	Endre Szemerédi	2
+ PDF Chat	Interlacing families I: Bipartite Ramanujan graphs of all degrees	2015	Adam W. Marcus Daniel A. Spielman Nikhil Srivastava	2
+	On Certain Sets of Integers	1953	K. F. Roth	2
+	Über die Zerlegung definiter Funktionen in Quadrate	1927	Emil Artin	2
+	Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation	1967	Harry Furstenberg	2
+	Absolute Irreducibility of Polynomials via Newton Polytopes	2001	Shuhong Gao	2
+	CHEBYSHEV INEQUALITIES WITH LAW-INVARIANT DEVIATION MEASURES	2009	Bogdan Grechuk Anton Molyboha Michael Zabarankin	2