1,408 research outputs found
Gap junctions, dendrites and resonances : a recipe for tuning network dynamics
No full textGap junctions, also referred to as electrical synapses, are expressed along the entire central nervous system and are important in mediating various brain rhythms in both normal and pathological states. These connections can form between the dendritic trees of individual cells. Many dendrites express membrane channels that confer on them a form of sub-threshold resonant dynamics. To obtain insight into the modulatory role of gap junctions in tuning networks of resonant dendritic trees, we generalise the “sum-over-trips” formalism for calculating the response function of a single branching dendrite to a gap junctionally coupled network. Each cell in the network is modelled by a soma connected to an arbitrary structure of dendrites with resonant membrane. The network is treated as a single extended tree structure with dendro-dendritic gap junction coupling. We present the generalised “sum-over-trips” rules for constructing the network response function in terms of a set of coefficients defined at special branching, somatic and gap-junctional nodes. Applying this framework to a two-cell network, we construct compact closed form solutions for the network response function in the Laplace (frequency) domain and study how a preferred frequency in each soma depends on the location and strength of the gap junction
Computational convergence of the path integral for real dendritic morphologies
No full textNeurons are characterised by a morphological structure unique amongst biological cells, the core of which is the dendritic tree. The vast number of dendritic geometries, combined with heterogeneous properties of the cell membrane, continue to challenge scientists in predicting neuronal input-output relationships, even in the case of sub-threshold dendritic currents. The Green’s function obtained for a given dendritic geometry provides this functional relationship for passive or quasi-active dendrites and can be constructed by a sum-over-trips approach based on a path integral formalism. In this paper, we introduce a number of efficient algorithms for realisation of the sum-over-trips framework and investigate the convergence of these algorithms on different dendritic geometries. We demonstrate that the convergence of the trip sampling methods strongly depends on dendritic morphology as well as the biophysical properties of the cell membrane. For real morphologies, the number of trips to guarantee a small convergence error might become very large and strongly affect computational efficiency. As an alternative, we introduce a highly-efficient matrix method which can be applied to arbitrary branching structures
Editorial for special issue on neurodynamics
No full text“Neurodynamics” is an interdisciplinary area of mathematics where dynamical systems theory (deterministic and stochastic) is the primary tool for elucidating the fundamental mechanisms responsible for the behaviour of neural systems (whether biological or synthetic). A meeting on this topic was held at the International Centre for Mathematical Sciences in Edinburgh from March 5–7 in 2012. In this special issue, we have invited seven of the main contributors to this event to expand on their presentations and highlight the use of mathematics in understanding the dynamics of neural systems
Structures of the conformational isomers and polymorph modifications of N-substituted 2,6-(E,E)-bis(ferrocenylidene)piperid-4-ones: photo- and electrochemically induced E/Z isomerization
No full textFour N-substituted 2,6-(E,E)-bis(ferrocenylidene)piperid-4-ones (NH 1, NMe 2, NEt 3, NCH2Ph 4) were prepared by aldol condensation between ferrocenecarbaldehyde and two equivalents of N-substituted piperid-4-ones with high yields. The N-protonated compounds were obtained by reaction with HBF4·Et2O acid. The molecular structures of compounds 2, 3, 2·HBF4 and 4·HBF4 were confirmed by X-ray diffraction analysis and three types of conformational isomers were elucidated. Two polymorph modifications were found for compound 2·HBF4. The electron transfer properties of the complexes were examined by electrochemical and spectroelectrochemical techniques. Complexes 1-4 undergo a reversible process of two-electron oxidation and partially reversible one-electron reduction. The photo- and electrochemically induced E/Z isomerisation of the complexes was monitored by UV-vis and 1H NMR spectroscopy
Экономный алгоритм нахождения средних минимальных расстояний
No full textLet £o,..., £n be strings drawn from some finite alphabet. In this paper we describe an algorithm for finding mean minimum distances between strings io,..., £s for all s ^ n. The complexity of the algorithm is O(nm), where m is the length of strings.Пусть заданы n + 1 строк £0 ... , £n с символами из некоторого конечного алфавита. В работе предлагается алгоритм нахождения величин среднего значения fc-го минимального расстояния между строками £о,... , £s для всех значений
A multiplex real-time PCR method for detection of GSTM1 and GSTT1 copy numbers.
No full textObjectives: Deletion polymorphisms of Glutathione-S-transferase (GST) M I and T I are considered risk factors for various diseases. However, most previous studies only distinguished "null" and "non-null" genotypes. Our aim was to develop a reliable. high-throughput GSTM1/T1 genotyping method able to determine allele copy numbers. Design and methods: We developed a multiplex real time PCR method to distinguish between heterozygous (1/0) and homozygous (1/1) GSTM1 and GSTT1 genotypes. The principle of relative quantification was applied and an expectation-maximisation (EM) algorithm was developed to assign one of 3 possible genotypes: 1/1, 1/0 or 0/0 for each of the two genes. Results: 1320 Caucasians were genotyped using the newly developed method. The observed genotype distributions did not deviate from the expected and were in Hardly-Weinberg equilibrium. GSTM1 duplication was detected in one sample. Conclusion: This new semiquantitative genotyping method is a sensitive and promising tool for large-scale molecular epidemiological and clinical studies
Fast algorithm for finding mean minimum distances
No full textLet £o,..., £n be strings drawn from some finite alphabet. In this paper we describe an algorithm for finding mean minimum distances between strings io,..., £s for all s ^ n. The complexity of the algorithm is O(nm), where m is the length of strings
Смещение оценки энтропии для симметричных мер Бернулли и слабой метрики
No full textWe consider symmetric Bernoulli measures and new weak metrics and obtain a closed-form expression of the entropy estimator bias.Для симметричной меры Бернулли и новой слабой метрики найдено смещение оценки энтропии
Изоморфизм компактификаций модулей векторных расслоений: неприведенные схемы модулей
No full textWe continue the study of the compactification of the moduli scheme for Gieseker-semistable vector bundles on a nonsingular irreducible projective algebraic surface S with polarization L, by locally free sheaves. The relation of main components of the moduli functor or admissible semistable pairs and main components of the Gieseker – Maruyama moduli functor (for semistable torsion-free coherent sheaves) with the same Hilbert polynomial on the surface S is investigated. The compactification of interest arises when families of Gieseker-semistable vector bundles E on the nonsingular polarized projective surface (S, L) are completed by vector bundles E on projective polarized schemes (S, L) of special form. The form of the scheme S, of its polarization L and of the vector bundle E is described in the text. The collection ((S, L), E) is called a semistable admissible pair. Vector bundles E on the surface (S, L) and E on schemes (S, L) are supposed to have equal ranks and Hilbert polynomials which are compute with respect to polarizations L and L, respectively. Pairs of the form ((S, L), E) named as S-pairs are also included into the class under the scope. Since the purpose is to study the compactification of moduli space for vector bundles, only families which contain S-pairs are considered. We build up the natural transformation of the moduli functor for admissible semistable pairs to the Gieseker – Maruyama moduli functor for semistable torsion-free coherent sheaves on the surface (S, L), with same rank and Hilbert polynomial. It is demonstrated that this natural transformation is inverse to the natural transformation built in the preceding paper and defined by the standard resolution of a family of torsion-free coherent sheaves with a possibly nonreduced base scheme. The functorial isomorphism constructed determines the scheme isomorphism of compactifications of moduli space for semistable vector bundles on the surface (S, L).В работе продолжено изучение компактификации схемы модулей полустабильных по Гизекеру векторных расслоений на неособой неприводимой проективной алгебраической поверхности S с поляризацией L, локально свободными пучками. Исследуется связь основных компонент функтора модулей допустимых полустабильных пар и основных компонент функтора модулей Гизекера –Маруямы (полустабильных когерентных пучков без кручения) с тем же полиномом Гильберта на поверхности S. Рассматриваемая компактификация получается, если семейства полустабильных по Гизекеру векторных расслоений E на поляризованной неособой проективной поверхности (S,L) пополняются векторными расслоениями E на проективных поляризованных схемах (S,L) специального вида. Вид схемы S, поляризации L и расслоения E описан в тексте работы. Набор ((S,L),E) назван полустабильной допустимой парой. Векторные расслоения E на поверхности (S,L) и E на схемах (S,L) предполагаются имеющими равные ранги и полиномы Гильберта, вычисляемые относительно поляризаций L и L соответственно. Пары вида ((S,L),E), называемые S-парами, также входят в рассматриваемый класс. Поскольку целью исследования является изучение компактификации пространства модулей векторных расслоений, рассматриваются только семейства, содержащие S-пары. Построено естественное преобразование функтора модулей допустимых полустабильных пар в функтор модулей Гизекера – Маруямы полустабильных когерентных пучков без кручения на поверхности (S,L), имеющих те же ранг и полином Гильберта. Показано, что это естественное преобразование является двусторонним обратным к естественному преобразованию, построенному в предшествующей работе и определяемому стандартным разрешением семейства когерентных пучков без кручения, имеющего возможно неприведенную базисную схему. Построенный изоморфизм функторов модулей определяет изоморфизм компактификаций пространства модулей полустабильных векторных расслоений на поверхности (S,L) как алгебраических схем
Построение оценки энтропии для специальной метрики и произвольной функции
No full textThe paper proposes a generalization of entropy as in [1]. At first, to constract the estimator, we select the metrics on the space of sequances. This metrics is based on a matrix that can be interpreted as an edge coloring of a complete graph with loops. A generalization consists in that instead of using the logarithm in the estimation of the entropy, we apply a similar function which may be arbitrary at the given range. The proposed function is not monotone, so the task of optimizing the average deviation which is a quadratic optimization problem, is solved in the whole space and not on the simplex. The main properties of the estimator, such as asymptotic unbiasedness and power decrease dispersion, are proved in a similar way.В статье предлагается обобщение оценки энтропии, предложенной в работе [1]. Для построения оценки сначала выбирается метрика на пространстве последовательностей. Эта метрика строится по матрице, которую можно интерпретировать как реберную раскраску полного графа с петлями. Обобщение состоит в том, что вместо логарифма в оценке энтропии применяется похожая функция, которая может быть произвольной на заданном интервале. Предлагаемая функция не является монотонной, поэтому задача оптимизации среднего отклонения, которая является задачей квадратичной оптимизации, решается на всем пространстве, а не на симплексе. Основные свойства оценки, такие как, асимптотическая несмещенность и степенное убывание дисперсии, доказываются аналогичным образом
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