Andrey Akinshin

@Article{akinshin2024qrdehd,
  title = {Quantile-respectful density estimation based on the Harrell-Davis quantile estimator},
  author = {Akinshin, Andrey},
  year = {2024},
  month = {4},
  day = {8},
  arxiv = {2404.03835},
  abstract = {Traditional density and quantile estimators are often inconsistent with each other. Their simultaneous usage may lead to inconsistent results. To address this issue, we propose a novel smooth density estimator that is naturally consistent with the Harrell-Davis quantile estimator. We also provide a jittering implementation to support discrete-continuous mixture distributions.}
}

@Article{akinshin2023wqe,
  title = {Weighted quantile estimators},
  author = {Akinshin, Andrey},
  year = {2023},
  month = {4},
  arxiv = {2304.07265},
  abstract = {In this paper, we consider a generic scheme that allows building weighted versions of various quantile estimators, such as traditional quantile estimators based on linear interpolation of two order statistics, the Harrell-Davis quantile estimator and its trimmed modification. The obtained weighted quantile estimators are especially useful in the problem of estimating a distribution at the tail of a time series using quantile exponential smoothing. The presented approach can also be applied to other problems, such as quantile estimation of weighted mixture distributions.}
}

@Article{akinshin2023strat,
  year = {2023},
  month = {jan},
  publisher = {Institute of Cytology and Genetics, SB RAS},
  volume = {26},
  number = {8},
  pages = {758--764},
  url = {https://pubmed.ncbi.nlm.nih.gov/36694713/},
  author = {A. A. Akinshin and V. P. Golubyatnikov and N. B. Ayupova and L. S. Minushkina},
  title = {Stratifications and foliations in phase portraits of gene network models},
  journal = {Vavilov Journal of Genetics and Breeding}
}

@Inproceedings{akinshin2022bgrs,
  title = {Mathematical and numerical modelling of the circadian oscillator},
  author = {Golubyatnikov, V and Akinshin, A and Ayupova, N and Kirillova, N and Podkolodnyy, N and Podkolodnaya, O},
  booktitle = {Bioinformatics of Genome Regulation and Structure/Systems Biology (BGRS/SB-2022)},
  pages = {1096--1096},
  year = {2022},
  doi = {10.18699/SBB-2022-657}
}

@Article{akinshin2022circadian,
  author = {Akinshin, A. A. and Ayupova, N. B. and Golubyatnikov, V. P. and Kirillova, N. E. and Podkolodnaya, O. A. and Podkolodnyy, N. L.},
  title = {On a Numerical Model of a Circadian Oscillator},
  journal = {Numerical Analysis and Applications},
  year = {2022},
  month = {Sep},
  day = {01},
  volume = {15},
  number = {3},
  pages = {187-196},
  abstract = {For a model of a circadian oscillator presented in the form of a 6-dimensional nonlinear dynamical system, conditions of uniqueness of an equilibrium point and conditions of existence of a periodic trajectory (cycle) are established. A client-server application is developed to perform numerical experiments with this model on a cloud server and to visualize the results of these experiments.},
  issn = {1995-4247},
  doi = {10.1134/S1995423922030016},
  url = {https://rdcu.be/cUri9}
}

@Article{akinshin2022frc,
  title = {Finite-sample Rousseeuw-Croux scale estimators},
  author = {Akinshin, Andrey},
  year = {2022},
  month = {9},
  arxiv = {2209.12268},
  abstract = {The Rousseeuw-Croux $S_n$, $Q_n$ scale estimators and the median absolute deviation MAD_n can be used as consistent estimators for the standard deviation under normality. All of them are highly robust: the breakdown point of all three estimators is $50\%$. However, $S_n$ and $Q_n$ are much more efficient than MAD_n: their asymptotic Gaussian efficiency values are $58\%$ and $82\%$ respectively compared to $37\%$ for MAD_n. Although these values look impressive, they are only asymptotic values. The actual Gaussian efficiency of $S_n$ and $Q_n$ for small sample sizes is noticeably lower than in the asymptotic case. The original work by Rousseeuw and Croux (1993) provides only rough approximations of the finite-sample bias-correction factors for $S_n,\, Q_n$ and brief notes on their finite-sample efficiency values. In this paper, we perform extensive Monte-Carlo simulations in order to obtain refined values of the finite-sample properties of the Rousseeuw-Croux scale estimators. We present accurate values of the bias-correction factors and Gaussian efficiency for small samples ($n \leq 100$) and prediction equations for samples of larger sizes.}
}

@Article{akinshin2022madfactors,
  title = {Finite-sample bias-correction factors for the median absolute deviation based on the Harrell-Davis quantile estimator and its trimmed modification},
  author = {Akinshin, Andrey},
  year = {2022},
  month = {7},
  arxiv = {2207.12005},
  abstract = {The median absolute deviation is a widely used robust measure of statistical dispersion. Using a scale constant, we can use it as an asymptotically consistent estimator for the standard deviation under normality. For finite samples, the scale constant should be corrected in order to obtain an unbiased estimator. The bias-correction factor depends on the sample size and the median estimator. When we use the traditional sample median, the factor values are well known, but this approach does not provide optimal statistical efficiency. In this paper, we present the bias-correction factors for the median absolute deviation based on the Harrell-Davis quantile estimator and its trimmed modification which allow us to achieve better statistical efficiency of the standard deviation estimations. The obtained estimators are especially useful for samples with a small number of elements.}
}

@Article{akinshin2022qad,
  title = {Quantile absolute deviation},
  author = {Akinshin, Andrey},
  year = {2022},
  month = {8},
  arxiv = {2208.13459}
}

@Article{akinshin2022thdqe,
  author = {Akinshin, Andrey},
  title = {Trimmed Harrell-Davis quantile estimator based on the highest density interval of the given width},
  journal = {Communications in Statistics - Simulation and Computation},
  pages = {1-11},
  year = {2022},
  month = {3},
  publisher = {Taylor & Francis},
  doi = {10.1080/03610918.2022.2050396},
  arxiv = {2111.11776},
  abstract = {Traditional quantile estimators that are based on one or two order statistics are a common way to estimate distribution quantiles based on the given samples. These estimators are robust, but their statistical efficiency is not always good enough. A more efficient alternative is the Harrell-Davis quantile estimator which uses a weighted sum of all order statistics. Whereas this approach provides more accurate estimations for the light-tailed distributions, it’s not robust. To be able to customize the tradeoff between statistical efficiency and robustness, we could consider a trimmed modification of the Harrell-Davis quantile estimator. In this approach, we discard order statistics with low weights according to the highest density interval of the beta distribution.}
}

@Article{akinshin2021mathcomp,
  abstract = {We consider a reconstruction problem for "spike-train" signals $F$ of an a priori known form $F(x)=\sum_j=1^da_j\delta\left(x-x_j\right),$ from their moments $m_k(F)=\int x^kF(x)dx.$ We assume that the moments $m_k(F)$, $k=0,1,\ldots,2d-1$, are known with an absolute error not exceeding $e > 0$. This problem is essentially equivalent to solving the Prony system $\sum_j=1^d a_jx_j^k=m_k(F), \ k=0,1,\ldots,2d-1.$ We study the "geometry of error amplification" in reconstruction of $F$ from $m_k(F),$ in situations where the nodes $x_1,\ldots,x_d$ near-collide, i.e. form a cluster of size $h \ll 1$. We show that in this case, error amplification is governed by certain algebraic varieties in the parameter space of signals $F$, which we call the "Prony varieties". Based on this we produce lower and upper bounds, of the same order, on the worst case reconstruction error. In addition we derive separate lower and upper bounds on the reconstruction of the amplitudes and the nodes. Finally we discuss how to use the geometry of the Prony varieties to improve the reconstruction accuracy given additional a priori information.},
  author = {Akinshin, Andrey and Goldman, Gil and Yomdin, Yosef},
  journal = {Mathematics of Computation},
  volume = {90},
  number = {327},
  pages = {267--302},
  year = {2021},
  language = {english},
  title = {Geometry of error amplification in solving the Prony system with near-colliding nodes},
  url = {https://www.webofscience.com/wos/woscc/full-record/WOS:000586628500012?SID=EUW1ED0DD1KNHsN5oZEzd1M2NoL7u},
  doi = {10.1090/mcom/3571},
  arxiv = {1701.04058}
}

@Inproceedings{akinshin2020bgrs,
  author = {Bukharina, T.A. and Akinshin, A.A. and Golubyatnikov, V.P. and Furman, D.P.},
  booktitle = {The Twelfth International Multiconference "Bioinformatics of genome regulation and structure/systems biology (BGRS/SB-2020)"},
  language = {english},
  pages = {143--144},
  title = {A Model of one central regulatory circuit},
  publisher = {Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University},
  url = {https://publ.icgbio.ru/wp-content/uploads/2020/07/BGRS2020_15.07-144-145.pdf},
  doi = {10.18699/BGRS/SB-2020-090},
  year = {2020},
  month = {7}
}

@Article{akinshin2020sjim,
  author = {Akinshin, A. A. and Bukharina, T. A. and Golubyatnikov, V. P. and Furman, D. P.},
  title = {Mathematical and Numerical Models of the Central Regulatory Circuit of the Morphogenesis System of Drosophila},
  journal = {Journal of Applied and Industrial Mathematics},
  year = {2020},
  month = {May},
  day = {01},
  volume = {14},
  number = {2},
  pages = {249-255},
  abstract = {The results are presented of mathematical and computer simulation of the functioning of the central regulatory circuit (CRC) which is the system integrator of the gene networks ofmorphogenesis of Drosophila mechanoreceptors. The main element of the CRC is represented bythe complex of Achaete-Scute (AS-C) genes, the main genes of the mechanoreceptor morphogenesis.The content level of the proteins encoded by the AS-Cgenes is a determining factor for initiating the development of a mechanoreceptor. We carried outa comparative study of the CRC behavior under normal conditions and in the presence ofmutational changes in the Achaete-Scute complex. Theresults of simulation are in good accord with the available biological data.},
  issn = {1990-4797},
  doi = {10.1134/S1990478920020040},
  url = {https://rdcu.be/b5yyl https://link.springer.com/article/10.1134/S1990478920020040}
}

@Book{akinshin2019pdnb,
  author = {Akinshin, Andrey},
  doi = {10.1007/978-1-4842-4941-3},
  edition = {1},
  isbn = {978-1-4842-4940-6},
  pages = {662},
  publisher = {Apress},
  title = {Pro .NET Benchmarking},
  url = {https://link.springer.com/book/10.1007/978-1-4842-4941-3},
  year = {2019}
}

@Article{akinshin2017logeek,
  author = {Akinshin, Andrey},
  journal = {Logeek Magazine},
  language = {english},
  pages = {10--15},
  title = {The hard world of microbenchmarking},
  url = {https://career.luxoft.com/files/logeek-magazine/pdf/2283-b2e-logeek-magazine-3-a4-2017-02-27-net.pdf},
  volume = {3},
  year = {2017}
}

@Inproceedings{akinshin2017spiketrains,
  abstract = {We consider a signal reconstruction problem for signals \$F\$ of the form \$ F(x)=\backslashsum\_\j=1\\^\d\a\_\j\\backslashdelta\backslashleft(x-x\_\j\\backslashright),\$ from their moments \$m\_k(F)=\backslashint x\^kF(x)dx.\$ We assume \$m\_k(F)\$ to be known for \$k=0,1,\backslashldots,N,\$ with an absolute error not exceeding \$\backslashepsilon \textgreater 0\$. We study the "geometry of error amplification" in reconstruction of \$F\$ from \$m\_k(F),\$ in situations where two neighboring nodes \$x\_i\$ and \$x\_\i+1\\$ near-collide, i.e \$x\_\i+1\-x\_i=h \backslashll 1\$. We show that the error amplification is governed by certain algebraic curves \$S\_\F,i\,\$ in the parameter space of signals \$F\$, along which the first three moments \$m\_0,m\_1,m\_2\$ remain constant.},
  archiveprefix = {arXiv},
  arxivid = {1701.01482},
  author = {Akinshin, Andrey and Goldman, Gil and Golubyatnikov, Vladimir and Yomdin, Yosef},
  language = {english},
  pages = {1--17},
  booktitle = {7th International Conference on Complex Analysis and Dynamical Systems (CA&DS VII)},
  series = {Contemporary Mathematics},
  volume = {699},
  doi = {10.1090/conm/699/14078},
  title = {Accuracy of reconstruction of spike-trains with two near-colliding nodes},
  url = {https://publons.com/publon/34688522/},
  year = {2017},
  arxiv = {1701.01482}
}

@Inproceedings{akinshin2016semr,
  author = {Akinshin, A.A. and Golubyatnikov, V P and Kazantsev, M.V.},
  doi = {10.17377/semi.2016.13.020},
  issn = {1813-3304},
  journal = {Siberian Electronic Mathematical Reports},
  language = {english},
  pages = {A.23--A.24},
  title = {On discrete structures in phase portraits of some non-linear dynamical systems},
  url = {http://semr.math.nsc.ru/v13/a1-41.pdf},
  volume = {13},
  year = {2016}
}

@Book{akinshin2015knockout,
  abstract = {This book is intended for.NET developers who want to use the MVVM design pattern to create powerful client-side JavaScript linked to server-side C\# logic. Basic experience with ASP.NET, Razor, and creating web applications is needed. Since this book is not a C\# or JavaScript tutorial, you should have basic knowledge of these programming languages.},
  author = {Akinshin, Andrey},
  isbn = {978-1783984008},
  language = {english},
  pages = {188},
  publisher = {PacktPub},
  title = {Getting Started with Knockout.js for .NET Developers},
  url = {https://www.packtpub.com/application-development/getting-started-knockoutjs-net-developers},
  year = {2015}
}

@Inproceedings{akinshin2015sbb,
  abstract = {Existence and location of periodical trajectories are important properties of multi-dimensional dynamical systems. In particular, this relates to systems that model gene networks. We can reduce the areas where cyclic trajectories may be located due to analysis of some discrete structures describing the dynamical system, such as state transition diagrams},
  address = {Novosibirsk},
  author = {Akinshin, A.A. and Kazantsev, M.V.},
  booktitle = {5th International Young Scientists School “System Biology and Bioinformatics”},
  pages = {1},
  title = {State transition diagrams in hypothetical models of cyclic gene networks functioning},
  url = {http://conf.nsc.ru/SBB2015/en},
  year = {2015}
}

@Inproceedings{akinshin2015sampta,
  abstract = {We consider Fourier reconstruction problem for signals F, which are linear combinations of shifted delta-functions. We assume the Fourier transform of F to be known on the frequency interval [-N,N], with an absolute error not exceeding e \textgreater 0. We give an absolute lower bound (which is valid with any reconstruction method) for the "worst case" reconstruction error of F in situations where the nodes (i.e. the positions of the shifted delta-functions in F) are known to form an l elements cluster of a size h \textless\textless 1. Using "decimation" reconstruction algorithm we provide an upper bound for the reconstruction error, essentially of the same form as the lower one. Roughly, our main result states that for N*h of order of (2l-1)-st root of e the worst case reconstruction error of the cluster nodes is of the same order as h, and hence the inside configuration of the cluster nodes (in the worst case scenario) cannot be reconstructed at all. On the other hand, decimation algorithm reconstructs F with the accuracy of order of 2l-st root of e.},
  address = {Washington, DC},
  author = {Akinshin, A and Batenkov, D and Yomdin, Y},
  booktitle = {Sampling Theory and Applications (SampTA), 2015 International Conference on},
  doi = {10.1109/SAMPTA.2015.7148965},
  isbn = {978-1-4673-7353-1},
  number = {264},
  pages = {617--621},
  publisher = {IEEE},
  title = {Accuracy of spike-train Fourier reconstruction for colliding nodes},
  url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7148965 https://publons.com/publon/14766954/},
  year = {2015},
  arxiv = {1502.06932}
}

@Inproceedings{akinshin2014brew,
  abstract = {Gene networks are sets of genes functioning in a coordinated manner. Their major components are the biopolymers DNA, RNA, and proteins. In this paper, we consider a small network with several genes (they can be considered standalone) and observe the concentration of the corresponding proteins. Researching the dynamic behavior of gene networks is a complicated problem. Therefore, we research the principles of their functioning on special hypothetical model objects. These models can be described by a nonlinear differential system. Symmetry is a very important property of living systems. The phenomenon of symmetry can be observed in completely different biological models. The analysis of gene networks model symmetry allows us to construct special methods to solve such standard problems as the problem of existence and stability of attractors, to build the graphical representation of the gene network phase portraits, to determine equilibrium points, to simulate trajectory, etc. Also we performed computer modeling and conducted simulation experiments with our models in R language to verify obtained results.},
  address = {Bielefeld, Germany},
  author = {Akinshin, A A and Golubyatnikov, V P and Likhoshvai, V A},
  booktitle = {The 12th Bioinformatics Research and Education Workshop},
  language = {english},
  organization = {Center for Biotechnology — CeBiTec},
  pages = {1--5},
  title = {Symmetry in gene network models},
  url = {http://wiki.techfak.uni-bielefeld.de/didy/brew},
  year = {2014}
}

@Inproceedings{akinshin2014dayofgeometry,
  address = {Novosibirsk},
  author = {Akinshin, A A and Bukharina, T A and Furman, D P and Golubyatnikov, V P},
  booktitle = {Geometry days in Novosibirsk - 2014: Abstracts of the International Conference},
  isbn = {978-5-86134-145-5},
  language = {english},
  pages = {85--86},
  title = {A model of one biological 2-cells complex},
  year = {2014}
}

@Inproceedings{akinshin2014mmhpcbbb_a,
  author = {Akinshin, A A and Bukharina, T A and Furman, D P and Golubyatnikov, V P},
  booktitle = {International Conference «Mathematical Modeling and High Performance Computing in Bioinformatics, Biomedicine and Biotechnology»},
  language = {english},
  pages = {10},
  title = {An Extended Model of D. Melanogaster Machrochaete Morphogenesis Gene Network},
  url = {http://conf.nsc.ru/mmhpc2014/},
  year = {2014}
}

@Inproceedings{akinshin2014mmhpcbbb_b,
  author = {Akinshin, A A and Bukharina, T A and Furman, D P and Golubyatnikov, V P},
  booktitle = {International Conference «Mathematical Modeling and High Performance Computing in Bioinformatics, Biomedicine and Biotechnology»},
  language = {english},
  pages = {11},
  title = {Modeling of Two-Cells Complex in Morphogenesis of D. Melanogaster Mechanoreceptors},
  year = {2014}
}

@Article{akinshin2014nsu,
  abstract = {We consider the phase portrait of a 6-dimensional nonlinear dynamical system considered as a model of an early stage of morphogenesis of D. melanogaster, i.e., appearance of its parental cell in the proneural cluster. Sufficient conditions of existence of two stable equilibrium points of this system are described, and biological interpretation is given.},
  address = {Novosibirsk},
  author = {Akinshin, A A and Bukharina, T A and Furman, D P and Golubyatnikov, V P},
  journal = {Vestnik NSU [NSU Herald]},
  custom-tags = {Vak},
  language = {russian},
  number = {4},
  pages = {3-10},
  title = {Mathematical modeling of interaction of two cells in proneural cluster of D.mealnogaster},
  url = {http://www.mathnet.ru/php/archive.phtml?wshow=paper\&jrnid=vngu\&paperid=350\&option\_lang=eng},
  volume = {14},
  year = {2014}
}

@Inproceedings{akinshin2013brew,
  address = {Berlin, Germany},
  author = {Akinshin, A A and Golubyatnikov, V P and Likhoshvai, V A},
  booktitle = {The 11th Bioinformatics Research and Education Workshop},
  language = {english},
  organization = {Computational Molecular Biology Department, Max Planck Institute for Molecular Genetics and IMPRS-CBSC},
  title = {Mathematical and computational models of gene networks functioning},
  url = {http://cmb.molgen.mpg.de/brew2013/},
  year = {2013}
}

@Inproceedings{akinshin2013febs,
  abstract = {Gene networks are sets of genes functioning in a coordinated manner, their major components are the biopolymers DNA, RNA, and proteins. In this work, we consider a small network with several genes (they can be considered standalone) and observe the concentration of the corresponding proteins. Studying the dynamic behavior of gene networks is a complicated problem. Therefore, we research the principles of their functioning on special hypothetical model. These models can be describe by nonlinear system of differential equations. We are very interested in the questions on existence and stability of attractors in such models. Particular attention is paid to some multidimensional symmetric systems with negative and positive feedbacks. These systems are studied with a specially developed algorithm, which reduces them to a single equation with delayed argument. Cycles in this equation searched by Andronov-Hopf theorem and stability analyzes using the first Lyapunov coefficient. Computer modelling and numerical experiments with our models has been implemented in our special computer program called PhasePortraitAnalyzer. The mathematical core is developed in R, and the interface part is created using C\# + WPF. Its software can build the graphical representation of the gene networks phase portraits, search equilibrium points, simulate the trajectory and perform other calculations for analyzing the target system. We can prove the correctness of the numerical solutions using some theorems on topology of the models.},
  annote = {SW06.W29-32},
  author = {Akinshin, A A},
  booktitle = {8th FEBS Congress, Saint Petersburg, Russia, July 6-11, 2013},
  doi = {10.1111/febs.12396},
  language = {english},
  pages = {547},
  title = {Numerical analysis of gene networks models},
  url = {https://apps.webofknowledge.com/full\_record.do?product=UA\&search\_mode=GeneralSearch\&qid=1\&SID=U1kYDgZoTuCyURIaqPx\&page=1\&doc=4 https://publons.com/publon/34688524/},
  volume = {280},
  year = {2013}
}

@Inproceedings{akinshin2013sbb,
  author = {Akinshin, A A},
  booktitle = {5th International Young Scientists School “System Biology and Bioinformatics”},
  language = {english},
  pages = {27},
  title = {Analysis of phase portraits in some gene networks models},
  year = {2013}
}

@Article{akinshin2013sjim_b,
  author = {Akinshin, A A and Golubyatnikov, V P and Golubyatnikov, I V},
  doi = {10.1134/S1990478913030022},
  issn = {1990-4797},
  journal = {Journal of Applied and Industrial Mathematics},
  language = {english},
  number = {3},
  pages = {296--301},
  publisher = {Springer US},
  title = {On some multidimensional models of gene network functioning},
  url = {http://elibrary.ru/item.asp?id=20455452 http://link.springer.com/article/10.1134/S1990478913030022},
  volume = {7},
  year = {2013}
}

@Inproceedings{akinshin2013sobolev,
  address = {Novosibirsk},
  author = {Akinshin, A A and Golubyatnikov, V P},
  booktitle = {International Conference «Differential Equations. Function Spaces. Approximation Theory»},
  language = {english},
  organization = {IM SB RAS},
  pages = {311},
  title = {Oscillating trajectories in some nonlinear dynamical systems},
  year = {2013}
}

@Article{akinshin2013sjim_a,
  abstract = {We study the occurrence of Andronov-Hopf bifurcation cycles in a neighborhood of stationary points of nonlinear delay equations: we formulate conditions for the existence of a bifurcation, find the bifurcation values, and analyze the stability of the bifurcation cycles.},
  address = {Novosibirsk},
  author = {Akinshin, A A},
  journal = {Sibirskii Zhurnal Industrial'noi Matematiki [Siberian Journal of Industrial Mathematics]},
  custom-tags = {Vak},
  language = {russian},
  number = {55},
  pages = {3--15},
  title = {Andronov-Hopf bifurcation for some nonlinear delay equations},
  url = {http://elibrary.ru/item.asp?id=20379316 http://www.mathnet.ru/php/archive.phtml?wshow=paper\&jrnid=sjim\&paperid=788\&option\_lang=eng},
  volume = {XVI},
  year = {2013}
}

@Article{akinshin2012astu,
  address = {Barnaul},
  author = {Akinshin, A A},
  institution = {AltSTU},
  journal = {Polzunovskiy Vestnik [Polzunov Herald]},
  custom-tags = {Vak},
  language = {russian},
  pages = {214--218},
  title = {Research of discrete structures in some cyclic dynamical systems (In Russian)},
  url = {http://elib.altstu.ru/elib/books/Files/pv2012\_04/pdf/214akinshin.pdf http://elibrary.ru/item.asp?id=18947027},
  volume = {4},
  year = {2012}
}

@Inproceedings{akinshin2012bgrs.a,
  author = {Akinshin, A A and Golubyatnikov, V P},
  booktitle = {The eighth international conference on bioinformatics of genome regulation and structure / systems biology},
  isbn = {978-5-91291-011},
  language = {english},
  pages = {28},
  title = {Non-uniqueness of cycles in gene networks models},
  url = {http://www.bionet.nsc.ru/meeting/bgrs2012/BGRS2012\_Proceedings.pdf},
  year = {2012}
}

@Inproceedings{akinshin2012bgrs.b,
  author = {Akinshin, A A and Golubyatnikov, V P and Gaidov, Yu A and Golubyatnikov, I V},
  booktitle = {The eighth international conference on bioinformatics of genome regulation and structure / systems biology},
  isbn = {978-5-91291-011},
  language = {english},
  pages = {29},
  title = {Unstable cycles in gene networks models},
  url = {http://www.bionet.nsc.ru/meeting/bgrs2012/BGRS2012\_Proceedings.pdf},
  year = {2012}
}

@Article{akinshin2012nsu,
  abstract = {We show non-uniqueness of cycles in phase portraits of some odd-dimensional nonlinear dynamical systems considered as models of gene networks regulated by negative feedbacks. We find geometric and analytic characteristics of these cycles and construct a graph, which describes qualitative behavior of trajectories of these dynamical systems.},
  address = {Novosibirsk},
  author = {Akinshin, A A and Golubyatnikov, V P},
  institution = {NSU},
  issn = {1818-7897},
  journal = {Vestnik NSU [NSU Herald]. Series “Mathematics, mechanics, and informatics'”},
  custom-tags = {Vak},
  language = {russian},
  number = {2},
  pages = {3--12},
  title = {Geometric characteristics of cycles in some symmetric dynamical systems (In Russian)},
  url = {http://elibrary.ru/item.asp?id=18756520 http://www.mathnet.ru/php/archive.phtml?wshow=paper\&jrnid=vngu\&paperid=114\&option\_lang=eng},
  volume = {12},
  year = {2012}
}

@Inproceedings{akinshin2012sbb,
  author = {Akinshin, A A},
  booktitle = {Abstracts of Young scientist's school “Bioinformatics ans systems biology”},
  language = {english},
  pages = {13},
  title = {Computer analysis of phase portraits in gene networks models},
  year = {2012}
}

@Inproceedings{akinshin2012sct,
  author = {Akinshin, A A and Golubyatnikov, V P},
  booktitle = {VI-th international conference Solitons, Collapses and Turbulence: Achievements, Developments and Perspectives.},
  language = {english},
  pages = {71--72},
  title = {On Nonuniqueness of Cycles in Dissipative Dynamical Systems of Chemical Kinetics},
  url = {http://conf.nsc.ru/files/conferences/sct2012/abstracts/114645/128115/Golubyatnikov.pdf},
  year = {2012}
}

@Inproceedings{akinshin2011lyapunov,
  abstract = {We find conditions of existence of stable cycles in some models of gene networks regulated by negative feedbacks and by simple combinations of negative and positive feedbacks. Special algorithms and programs for numerical simulations of these results are elaborated as well.},
  address = {Novosibirsk},
  author = {Akinshin, A A and Golubyatnikov, V P and Golubyatnikov, I V},
  booktitle = {International Conference “Modern Problems of Mathematics, Informatics and Bioinformatics”, devoted to the 100th anniversary of professor Alexei A. Lyapunov},
  isbn = {978-5-905569-03-6},
  language = {english},
  pages = {81},
  title = {Mathematical and numerical modeling of gene network functioning},
  url = {http://conf.nsc.ru/Lyap-100/ru/reportview/48237 http://conf.nsc.ru/files/conferences/Lyap-100/89299/Program-Thezises.pdf},
  year = {2011}
}