Search Results - "Grigoriev, Dima"

Evolution of biological cooperation: an algorithmic approach by Sudakow, Ivan, Reinitz, John, Vakulenko, Sergey A., Grigoriev, Dima

“…This manuscript presents an algorithmic approach to cooperation in biological systems, drawing on fundamental ideas from statistical mechanics and probability…”
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Tropical Combinatorial Nullstellensatz and Sparse Polynomials by Grigoriev, Dima, Podolskii, Vladimir V.

“…Tropical algebra emerges in many fields of mathematics such as algebraic geometry, mathematical physics and combinatorial optimization. In part, its importance…”
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Complexity of deciding whether a tropical linear prevariety is a tropical variety by Grigoriev, Dima, Vorobjov, Nicolai

“…We give an algorithm, with a singly exponential complexity, deciding whether a tropical linear prevariety is a tropical linear variety . The algorithm relies…”
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Tropical cryptography III: Digital signatures by Chen, Jiale, Grigoriev, Dima, Shpilrain, Vladimir

“…We use tropical algebras as platforms for a very efficient digital signature protocol. Security relies on computational hardness of factoring one-variable…”
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Efficiently and Effectively Recognizing Toricity of Steady State Varieties by Grigoriev, Dima, Iosif, Alexandru, Rahkooy, Hamid, Sturm, Thomas, Weber, Andreas

“…We consider the problem of testing whether the points in a complex or real variety with non-zero coordinates form a multiplicative group or, more generally, a…”
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On a tropical dual Nullstellensatz by Grigoriev, Dima

“…Since a tropical Nullstellensatz fails even for tropical univariate polynomials we study a conjecture on a tropical dual Nullstellensatz for tropical…”
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Nash resolution for binomial varieties as Euclidean division. A priori termination bound, polynomial complexity in essential dimension 2 by Grigoriev, Dima, Milman, Pierre D.

“…We establish a (novel for desingularization algorithms) a priori bound on the length of resolution of singularities by means of the compositions of the…”
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A Simple 3-Parameter Model for Cancer Incidences by Zhang, Xiaoxiao, Fröhlich, Holger, Grigoriev, Dima, Vakulenko, Sergey, Zimmermann, Jörg, Weber, Andreas Günter

“…We propose a simple 3-parameter model that provides very good fits for incidence curves of 18 common solid cancers even when variations due to different…”
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The entropy of the radical ideal of a tropical curve by Grigoriev, Dima

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Tropical Newton-Puiseux polynomials II by Grigoriev, Dima

“…Tropical Newton-Puiseux polynomials, defined as piece-wise linear functions with rational coefficients of the variables, play a role as tropical algebraic…”
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Entropy of tropical holonomic sequences by Grigoriev, Dima

“…We introduce tropical holonomic sequences of a given order and calculate their entropy in case of the second order…”
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Tropical differential equations by Grigoriev, Dima

“…Tropical differential equations are introduced and an algorithm is designed which tests solvability of a system of tropical linear differential equations…”
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Tropical cryptography II: Extensions by homomorphisms by Grigoriev, Dima, Shpilrain, Vladimir

“…We use extensions of tropical algebras as platforms for very efficient public key exchange protocols…”
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On a tropical version of the Jacobian conjecture by Grigoriev, Dima, Radchenko, Danylo

“…We prove that, for a tropical rational map if for any point the convex hull of Jacobian matrices at smooth points in a neighborhood of the point does not…”
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Hybrid models of the cell cycle molecular machinery by Noel, Vincent, Grigoriev, Dima, Vakulenko, Sergei, Radulescu, Ovidiu

“…Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the…”
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A tropical version of Hilbert polynomial (in dimension one) by Elizarov, Nikita, Grigoriev, Dima

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Tropical Cryptography by Grigoriev, Dima, Shpilrain, Vladimir

“…We employ tropical algebras as platforms for several cryptographic schemes that would be vulnerable to linear algebra attacks were they based on "usual"…”
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Complexity of Solving Tropical Linear Systems by Grigoriev, Dima

“…An algorithm is designed for solving a tropical linear system with complexity polynomial in the size of the system…”
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Tropical Combinatorial Nullstellensatz and Sparse Polynomials by Grigoriev, Dima, Podolskii, Vladimir

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Complexity of deciding whether a tropical linear prevariety is a tropical variety by Grigoriev, Dima, Vorobjov, Nicolai

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