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Generalization of Deuring Reduction Theorem [article]

Alexey Zaytsev
2012 arXiv   pre-print
In this paper we generalize the Deuring theorem on a reduction of elliptic curve with complex multiplication. More precisely, for an Abelian variety A, arising after reduction of an Abelian variety with complex multiplication by a CM field K over a number field at a pace of good reduction. We establish a connection between a decomposition of the first truncated Barsotti-Tate group scheme A[p] and a decomposition of p_K into prime ideals. In particular, we produce these explicit relationships for Abelian varieties of dimensions 1, 2 and 3.
arXiv:1209.5207v1 fatcat:mgprn442uvbntn7i4oxipr5gmu

Solvability of equations in elementary functions [article]

Alexey Kanel-Belov, Alexey Malistov, Rodion Zaytsev
2020 arXiv   pre-print
We prove that the equation tan(x) - x = a is unsolvable in elementary functions
arXiv:1911.10409v2 fatcat:24v5b4kpyfbfxeak7opwx4twbq

The Galois closure of the Garcia-Stichtenoth tower [article]

Alexey Zaytsev
2005 arXiv   pre-print
We describe the Galois closure of the Garcia-Stichtenoth tower and prove that it is optimal.
arXiv:math/0504431v1 fatcat:kxtkecyad5arplixv36b3z4fmu

Multifidelity Bayesian Optimization for Binomial Output [article]

Leonid Matyushin, Alexey Zaytsev, Oleg Alenkin, Andrey Ustuzhanin
2019 arXiv   pre-print
The key idea of Bayesian optimization is replacing an expensive target function with a cheap surrogate model. By selection of an acquisition function for Bayesian optimization, we trade off between exploration and exploitation. The acquisition function typically depends on the mean and the variance of the surrogate model at a given point. The most common Gaussian process-based surrogate model assumes that the target with fixed parameters is a realization of a Gaussian process. However, often
more » ... target function doesn't satisfy this approximation. Here we consider target functions that come from the binomial distribution with the parameter that depends on inputs. Typically we can vary how many Bernoulli samples we obtain during each evaluation. We propose a general Gaussian process model that takes into account Bernoulli outputs. To make things work we consider a simple acquisition function based on Expected Improvement and a heuristic strategy to choose the number of samples at each point thus taking into account precision of the obtained output.
arXiv:1902.06937v1 fatcat:xokhac7rtffjjhvzdnvrdy45s4

Characteristic Polynomial of Supersingular Abelian Varieties over Finite Fields [article]

Vijaykumar Singh, Gary McGuire, Alexey Zaytsev
2011 arXiv   pre-print
In this article, we give a complete description of the characteristic polynomials of supersingular abelian varieties over finite fields. We list them for the dimensions upto 7.
arXiv:1110.1116v1 fatcat:qnpkulwalndahidk6syc3bag3e

Unsupervised anomaly detection for discrete sequence healthcare data [article]

Victoria Snorovikhina, Alexey Zaytsev
2020 arXiv   pre-print
Fraud in healthcare is widespread, as doctors could prescribe unnecessary treatments to increase bills. Insurance companies want to detect these anomalous fraudulent bills and reduce their losses. Traditional fraud detection methods use expert rules and manual data processing. Recently, machine learning techniques automate this process, but hand-labeled data is extremely costly and usually out of date. We propose a machine learning model that automates fraud detection in an unsupervised way.
more » ... deep learning approaches include LSTM neural network for prediction next patient visit and a seq2seq model. For normalization of produced anomaly scores, we propose Empirical Distribution Function (EDF) approach. So, the algorithm works with high class imbalance problems. We use real data on sequences of patients' visits data from Allianz company for the validation. The models provide state-of-the-art results for unsupervised anomaly detection for fraud detection in healthcare. Our EDF approach further improves the quality of LSTM model.
arXiv:2007.10098v2 fatcat:zfstsmb5yjdjlhqwdcmasowaoq

Animal model of assessing cerebrovascular functional reserve by imaging photoplethysmography

Oleg V. Mamontov, Alexey Y. Sokolov, Maxim A. Volynsky, Anastasija V. Osipchuk, Valery V. Zaytsev, Roman V. Romashko, Alexei A. Kamshilin
2020 Scientific Reports  
Assessment of the cerebral blood-flow-reserve in patients with cerebrovascular diseases is extremely important in terms of making prognosis, determining treatment tactics, and controlling the revascularization outcome in the case of reconstructive interventions on the brain vessels. However, there is no easy-to-use, contactless method for either assessing the functional reserve of the cortical vascular network or intraoperative monitoring of surgical intervention. Our study aims to demonstrate
more » ... easibility of green-light imaging photoplethysmography (iPPG) to estimate cerebrovascular functional reserve in animal model of craniosurgical intervention. Custom-made iPPG system was exploited to visualize intracranial vessels in anesthetized Wistar rats (n = 15). Video frames of rat's cortex were recorded concurrently with systemic blood pressure, end-tidal CO2, and electrocardiogram. We found that injection of dorzolamide (carbonic-anhydrase inhibitor) significantly increased the blood-pulsations amplitude in all animals by 35 ± 19% (p < 0.001). Such an increase negatively correlated with significant decrease in end-tidal CO2 by 32 ± 7% (p < 0.001). It is noteworthy that the dorzolamide injection did not lead to significant changes in systemic blood pressure. Concluding, pulsations amplitude is a marker of the vascular tone that can be used to evaluate the functional cerebrovascular reserve. Imaging PPG is a simple and convenient method to assess cerebral blood flow, including during various neurosurgical interventions.
doi:10.1038/s41598-020-75824-w pmid:33149189 fatcat:4dzh5v6myndtnh2wvzxc2kzj4e

The Galois closure of the Garcia–Stichtenoth tower

Alexey Zaytsev
2007 Finite Fields and Their Applications  
We describe the Galois closure of the Garcia-Stichtenoth tower and prove that it is optimal.
doi:10.1016/j.ffa.2007.02.001 fatcat:bxnuv2gjjrgitlicdb22kmk74e

Computing algorithm for reduction type of CM abelian varieties [article]

Artyom Smirnov, Alexey Zaytsev
2018 arXiv   pre-print
Let A be an abelian variety over a number field, with a good reduction at a prime ideal containing a prime number p. Denote by A an abelian variety over a finite field of characteristic p, obtained by the reduction of A at the prime ideal. In this paper we derive an algorithm which allows to decompose the group scheme A[p] into indecomposable quasi-polarized BT_1-group schemes. This can be done for the unramified p on the basis of its decomposition into prime ideals in the endomorphism algebra
more » ... f A. We also compute all types of such correspondence for abelian varieties of dimension up to 5. As a consequence we establish the relation between the decompositions of prime p and the corresponding pairs of p-rank and a-number of an abelian variety A.
arXiv:1809.10368v2 fatcat:bzubrg5egvhtnb4xs5ctxkmtne

A Differentiable Language Model Adversarial Attack on Text Classifiers [article]

Ivan Fursov, Alexey Zaytsev, Pavel Burnyshev, Ekaterina Dmitrieva, Nikita Klyuchnikov, Andrey Kravchenko, Ekaterina Artemova, Evgeny Burnaev
2021 arXiv   pre-print
Robustness of huge Transformer-based models for natural language processing is an important issue due to their capabilities and wide adoption. One way to understand and improve robustness of these models is an exploration of an adversarial attack scenario: check if a small perturbation of an input can fool a model. Due to the discrete nature of textual data, gradient-based adversarial methods, widely used in computer vision, are not applicable per~se. The standard strategy to overcome this
more » ... is to develop token-level transformations, which do not take the whole sentence into account. In this paper, we propose a new black-box sentence-level attack. Our method fine-tunes a pre-trained language model to generate adversarial examples. A proposed differentiable loss function depends on a substitute classifier score and an approximate edit distance computed via a deep learning model. We show that the proposed attack outperforms competitors on a diverse set of NLP problems for both computed metrics and human evaluation. Moreover, due to the usage of the fine-tuned language model, the generated adversarial examples are hard to detect, thus current models are not robust. Hence, it is difficult to defend from the proposed attack, which is not the case for other attacks.
arXiv:2107.11275v1 fatcat:ava6j4azlzagfm2ibbcks32n7q

COHORTNEY: Non-Parametric Clustering of Event Sequences [article]

Vladislav Zhuzhel, Rodrigo Rivera-Castro, Nina Kaploukhaya, Liliya Mironova, Alexey Zaytsev, Evgeny Burnaev
2021 arXiv   pre-print
., Zaytsev, A., Kluchnikov, N., Kravchenko, A., Burnaev, E.: Gradientbased adversarial attacks on categorical sequence models via traversing an embedded world. arXiv preprint arXiv:2003.04173 (2020) 12  ... 
arXiv:2104.01440v2 fatcat:lfz2pdqohfgr7chwm6gtbon73a

Optimal curves of low genus over finite fields [article]

Alexey Zaytsev
2011 arXiv   pre-print
The Hasse-Weil-Serre bound is improved for curves of low genera over finite fields with discriminant in -3,-4,-7,-8,-11,-19 by studying optimal curves.
arXiv:0706.4203v3 fatcat:sro5wwy7snhgrgdx6zoi3uoj4e

Adversarial Attacks on Deep Models for Financial Transaction Records [article]

Ivan Fursov, Matvey Morozov, Nina Kaploukhaya, Elizaveta Kovtun, Rodrigo Rivera-Castro, Gleb Gusev, Dmitry Babaev, Ivan Kireev, Alexey Zaytsev, Evgeny Burnaev
2021 arXiv   pre-print
Machine learning models using transaction records as inputs are popular among financial institutions. The most efficient models use deep-learning architectures similar to those in the NLP community, posing a challenge due to their tremendous number of parameters and limited robustness. In particular, deep-learning models are vulnerable to adversarial attacks: a little change in the input harms the model's output. In this work, we examine adversarial attacks on transaction records data and
more » ... es from these attacks. The transaction records data have a different structure than the canonical NLP or time series data, as neighbouring records are less connected than words in sentences, and each record consists of both discrete merchant code and continuous transaction amount. We consider a black-box attack scenario, where the attack doesn't know the true decision model, and pay special attention to adding transaction tokens to the end of a sequence. These limitations provide more realistic scenario, previously unexplored in NLP world. The proposed adversarial attacks and the respective defences demonstrate remarkable performance using relevant datasets from the financial industry. Our results show that a couple of generated transactions are sufficient to fool a deep-learning model. Further, we improve model robustness via adversarial training or separate adversarial examples detection. This work shows that embedding protection from adversarial attacks improves model robustness, allowing a wider adoption of deep models for transaction records in banking and finance.
arXiv:2106.08361v1 fatcat:l4s5xldrafgater7fv73nl5rme

Nanometer to Millimeter Scale Peptide-Porphyrin Materials

Daniil V. Zaytsev, Fei Xie, Madhumita Mukherjee, Alexey Bludin, Borries Demeler, Robert M. Breece, David L. Tierney, Michael Y. Ogawa
2010 Biomacromolecules  
Biomacromolecules, Vol. 11, No. 10, 2010 Zaytsev et al.  ...  porphyrin) Co-N (pyridine) R f b R u b 1 4 N (porphyrin) 1.95 (1.6) 96 393 2 4 N (porphyrin) + 2 N (pyridine) 1.95 (2.0) 2.27 (3.6) 41 315 Biomacromolecules, Vol. 11, No. 10, 2010 Zaytsev  ... 
doi:10.1021/bm100540t pmid:20804210 pmcid:PMC2952671 fatcat:jeptfdc3ojgmbgel3htsymotsa

Wavelet-domain de-noising of optical coherent tomography data for biomedical applications

Kirill I Zaytsev, Konstantin G Kudrin, Nikita V Chernomyrdin, Alexey M Khorokhorov, Alexander B Prytov, Irina N Dolganova, Alexey V Perchik, Igor V Reshetov, Stanislav O Yurchenko
2015 Journal of Physics, Conference Series  
doi:10.1088/1742-6596/584/1/012013 fatcat:evm2w22jtje5dl6gi6pgtnhhcu
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