On a secondary construction of quadratic APN functions

Almost perfect nonlinear functions possess the optimal resistance to the differential cryptanalysis and are widely studied. Most known constructions of APN functions are obtained as functions over finite fields F27 and very little is known about combinatorial constructions in F2n. We consider how to obtain a quadratic APN function in n + 1 variables from a given quadratic APN function in n variables using special restrictions on new terms

The Seventh International Olympiad in Cryptography: problems and solutions

The International Olympiad in Cryptography NSUCRYPTO is the unique Olympiad containing scientific mathematical problems for professionals, school and university students from any country. Its aim is to involve young researchers in solving curious and tough scientific problems of modern cryptography. In 2020, it was held for the seventh time. Prizes and diplomas were awarded to 84 participants in the first round and 49 teams in the second round from 32 countries. In this paper, problems and their solutions of NSUCRYPTO'2020 are presented. We consider problems related to attacks on ciphers and hash functions, protocols, permutations, primality tests, etc. We discuss several open problems on JPEG encoding, Miller -- Rabin primality test, special bases in the vector space, AES-GCM. The problem of a modified Miller -- Rabin primality test was solved during the Olympiad. The problem for finding special bases was partially solved

Конструкция, место и клиническая эффективность технологии интерактивной терапии (стимуляции) мозга при цереброваскулярной патологии

Highlights. Interactive brain stimulation is the next step in neurofeedback technology, it implies the possibility of volitional regulation of the hemodynamic response of specific brain region in order to transform entire brain network and obtain the desired clinical and behavioral dynamics in patients (subjects). One of the indications for using the technology is post-stroke movements disorders when the volitional influence is focused on the motor area of the brain.Background. Neurofeedback and closely related concepts of neural interface system and “interactive brain” are considered as the foundation for developing algorithms for controlling neuroplasticity. Interactive brain therapy (stimulation) is a recently developed type of neurofeedback therapy, which implies dependence of feedback on a hemodynamic response signal recorded by functional magnetic resonance imaging (fMRI). The technology focuses on the region of interest with good accuracy and enables teaching the subject to control the activity of both individual cerebral structures and the functional connectivity between them, causing behavioral metamorphoses.Aim. To demonstrate the study design involving interactive stimulation of secondary motor areas of the brain using a bimodal fMRI-electroencephalography platform, and to describe the dynamics of the motor networks during treatment in patients with hemiparesis in the early period of recovery from stroke.Methods. The study involved 11 patients who were trained to regulate the activity of the secondary motor area and premotor cortex of the affected hemisphere, receiving feedback on the fMRI signal and the activity of the mu- (8–13 Hz) and beta2 (18–26 Hz) EEG ranges of the areas of interest. The block-designed training consisted of 6 sessions (imagination of movement – rest) with an interval of 2–3 days. During treatment the dynamics of the hemodynamic response of the areas of interest was analyzed. In test sessions (before treatment, immediately after the end, and six months later) functional connections within the motor network were reconstructed and hand function was assessed (grip strength, Fugle-Meyer Assessment, Box and Blocks test).Results. Upon completion of treatment, an increase in grip strength and dexterity was achieved; there was an increase in the fMRI signal of the premotor cortex of the ipsilateral hemisphere, and a strengthening of the interhemispheric functional connectivity of the secondary motor areas.Conclusion. fMRI and the interactive brain therapy technology built on its basis, on the one hand, provide the technological foundation for the “interactive brain” and the transformation of spontaneous neuroplasticity into a controlled one, and on the other hand, serve as an important tool for monitoring the process of restructuring of cerebral networks after a stroke, providing the ability to record the emergence (or disappearance) of connectivity between brain regions, and to measure its strength in dynamics, that is, to give a numerical description of neuroplasticity.Основные положения. Интерактивная стимуляция мозга – развитие технологии нейробиоуправления, подразумевающее возможность волевого регулирования гемодинамического отклика конкретных структур мозга с целью изменения параметров активности церебральных сетей и достижения желаемой клинической и поведенческой динамики у пациентов (испытуемых). Одним из показаний к применению технологии являются двигательные нарушения вследствие инсульта; в этом случае фокус волевого воздействия направлен на моторные области мозга.Актуальность. Нейробиоуправление и тесно связанные с ним интерфейсы «мозг – компьютер» рассматривают как базу для создания алгоритмов управляемой нейропластичности. Интерактивная терапия (стимуляция) мозга – недавно сформировавшаяся модальность нейробиоуправления, подразумевающая зависимость обратной связи от сигнала гемодинамического отклика, регистрируемого средствами функциональной магнитно-резонансной томографии (фМРТ). Технология позволяет с высокой точностью фокусироваться на регионе интереса и обучить субъекта контролю как активности отдельных церебральных структур, так и функциональной связности между ними с инициированием поведенческих изменений.Цель. Продемонстрировать дизайн эксперимента с интерактивной стимуляцией вторичных моторных зон мозга на бимодальной фМРТ-электроэнцефалографии платформе и описать динамику моторной сети в ходе лечения на репрезентативном примере больного с гемипарезом в раннем восстановительном периоде инсульта.Материалы и методы. 11 пациентов обучались регулировать активность дополнительной моторной области и премоторной коры пораженного полушария, получая обратную связь по сигналу фМРТ и активности мю-ритма (8–13 Гц) и бета-2-ритма (18–26 Гц) электроэнцефалографии в центральных отведениях. Курс состоял из 6 сессий в блочном дизайне (воображение движения чередовалось с отдыхом) с интервалом в 2–3 дня. В ходе лечения изучена динамика активации зон интереса. В тестовых сессиях (до лечения, сразу по его окончании и через полгода после завершения курса) проведена реконструкция функциональных связей внутри моторной церебральной сети и оценена функция руки (динамометрия хвата, шкала Фугл-Майера, тест Box and Block).Результаты. По завершении лечения достигнуто увеличение силы и ловкости руки; отмечены усиление фМРТ-сигнала премоторной коры ипсилатерального полушария и укрепление межполушарной функциональной связности вторичных моторных зон.Заключение. Таким образом, фМРТ и построенная на ее основе технология интерактивной стимуляции мозга, с одной стороны, обеспечивают технологическую основу для перевода спонтанной нейропластичности в управляемую в интересах более полной реабилитации постинсультного дефекта. С другой – фМРТ-мониторинг служит важным инструментом наблюдения за процессом перестройки церебральных сетей после инсульта, обеспечивая возможность измерять функциональную связность в динамике, то есть давать численную характеристику нейропластичности

New Insights into the Folding of a β-Sheet Miniprotein in a Reduced Space of Collective Hydrogen Bond Variables: Application to a Hydrodynamic Analysis of the Folding Flow

A new analysis of the 20 μs equilibrium folding/unfolding molecular dynamics simulations of the three-stranded antiparallel β-sheet miniprotein (beta3s) in implicit solvent is presented. The conformation space is reduced in dimensionality by introduction of linear combinations of hydrogen bond distances as the collective variables making use of a specially adapted principal component analysis (PCA); i.e., to make structured conformations more pronounced, only the formed bonds are included in determining the principal components. It is shown that a three-dimensional (3D) subspace gives a meaningful representation of the folding behavior. The first component, to which eight native hydrogen bonds make the major contribution (four in each beta hairpin), is found to play the role of the reaction coordinate for the overall folding process, while the second and third components distinguish the structured conformations. The representative points of the trajectory in the 3D space are grouped into conformational clusters that correspond to locally stable conformations of beta3s identified in earlier work. A simplified kinetic network based on the three components is constructed, and it is complemented by a hydrodynamic analysis. The latter, making use of "passive tracers" in 3D space, indicates that the folding flow is much more complex than suggested by the kinetic network. A 2D representation of streamlines shows there are vortices which correspond to repeated local rearrangement, not only around minima of the free energy surface but also in flat regions between minima. The vortices revealed by the hydrodynamic analysis are apparently not evident in folding pathways generated by transition-path sampling. Making use of the fact that the values of the collective hydrogen bond variables are linearly related to the Cartesian coordinate space, the RMSD between clusters is determined. Interestingly, the transition rates show an approximate exponential correlation with distance in the hydrogen bond subspace. Comparison with the many published studies shows good agreement with the present analysis for the parts that can be compared, supporting the robust character of our understanding of this "hydrogen atom" of protein folding