On a new compactification of moduli of vector bundles on a surface, IV: Nonreduced moduli

The construction for nonreduced projective moduli scheme of semistable admissible pairs is performed. We establish the relation of this moduli scheme with reduced moduli scheme built up in the previous article and prove that nonreduced moduli scheme contains an open subscheme which is isomorphic to moduli scheme of semistable vector bundles.Comment: 20 pages, additions and removal

Changes in properties of the transport network graph when using simplification algorithms

In the course of solving problems of managing and planning the development of large transport networks, a big amount of heterogeneous data from various sources is accumulated. The methods of graph theory are used to systematize information, process it, and calculate network characteristics. However, the problem arises of the enormous complexity and duration of computations over graphs of large networks. One of the approaches to solve this problem is the simplification of the original graph. In our report we study the influence of processing and basic graph simplification on the initial properties of the network. © 2019 Author(s).Russian Foundation for Basic Research, RFBR: number17-08-01123-aThe investigation was funded by RFBR, project number17-08-01123-a

Branching dendrites with resonant membrane: a “sum-over-trips” approach

Dendrites form the major components of neurons. They are complex branching structures that receive and process thousands of synaptic inputs from other neurons. It is well known that dendritic morphology plays an important role in the function of dendrites. Another important contribution to the response characteristics of a single neuron comes from the intrinsic resonant properties of dendritic membrane. In this paper we combine the effects of dendritic branching and resonant membrane dynamics by generalising the “sum-over-trips” approach (Abbott et al. in Biol Cybernetics 66, 49–60 1991). To illustrate how this formalism can shed light on the role of architecture and resonances in determining neuronal output we consider dual recording and reconstruction data from a rat CA1 hippocampal pyramidal cell. Specifically we explore the way in which an Ih current contributes to a voltage overshoot at the soma

Typology of Semantic Relations Extracted by the Instrument RusVectōrēs

The question about the types of semantic relations extractable by the Web-service RusVectōrēs is considered. The research urgency is caused by insufficient state of knowledge about linguistic potential of this instrument and distributive semantics in whole. The novelty of the research is seen in the fact that the problem concerning typology of semantic relations extractable on the base of distributional semantics - that is the method that uses automatic processing of big textual data without taking into account linguistic information - is posed for the first time. Classification of semantic relations including eight types of paradigmatic and three types of syntagmatic relations is proposed. It is shown that application of the method under consideration provides the set of semantic associates that consists predominantly of the words that stand in paradigmatic relations with the entry word; and among them hyponyms or co-hyponyms are the most frequent. The question about an effect that the semantic group of the entry word may have on the types of extractable semantic relations is studied. It is shown that the effect can be traced, although it needs additional investigations on more representative data for further specification. The comparative analysis of five semantic groups of the words gave evidence for the abovementioned general trend (about predominance of hyponyms and co-hyponyms) and allowed to produce several specific hypothesis about correlations between the semantic type of an entry word and the types of semantic relations extracted for the word

Possibility of Extracting Semantic Associates of Russian Verbs by the Instrument RusVectōrēs

The paper presents the results of investigating distributional semantics’ potential in its realization in the form Web-service RusVectōrēs. The question about applying the service for studying semantics of Russian verbs is considered. The research urgency is caused by insufficient level of information about linguistic possibilities of distributional semantics in whole. The novelty of the research consist in the fact that the question about applying the instrument RusVectōrēs for investigating verb semantics is posed for the first time. Classification of semantic relations extracted by RusVectōrēs for Russian verbs is proposed. The analyzed data include two lists of entry verbs and the set of semantic associates for each verb; the integral set of considered semantic associates consists of 468 verbs. Special attention is paid to semantic relations that can be treated as lexical functions because this sort of relations appeared to be the most frequent for Russian verbs; the whole number of extracted lexical functions is equal to 28. It is shown that lexical functions that correspond to aspectual variants of verbs, to synonymic relations and conversion are the most frequent; hyponyms and co-hyponyms are the most frequent among semantic relations that differ from lexical functions; situational relations and actant relations are comparatively rare. Special attention is paid to the details that are important for applying the instruments of lexical functions to semantic relations extracted for verbs by the service RusVectōrēs

Democratization in a passive dendritic tree : an analytical investigation

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as “dendritic democracy”. Although well studied experimentally, to date this phenomenon has not been thoroughly explored from a mathematical perspective. In this paper we adopt a passive model of a dendritic tree with distributed excitatory synaptic conductances and analyze a number of key measures of democracy. In particular, via moment methods we derive laws for the transport, from synapse to soma, of strength, characteristic time, and dispersion. These laws lead immediately to synaptic scalings that overcome attenuation with distance. We follow this with a Neumann approximation of Green’s representation that readily produces the synaptic scaling that democratizes the peak somatic voltage response. Results are obtained for both idealized geometries and for the more realistic geometry of a rat CA1 pyramidal cell. For each measure of democratization we produce and contrast the synaptic scaling associated with treating the synapse as either a conductance change or a current injection. We find that our respective scalings agree up to a critical distance from the soma and we reveal how this critical distance decreases with decreasing branch radius

Quantitative prediction of selectivity in iridium-catalysed hydrogen isotope exchange reactions

A pallette of commonly used directing groups, including various pharmaceutically relevant nitrogen-containing heterocycles, are quantitatively ranked based on the results of intermolecular hydrogen isotope exchange competition reactions using two iridium complexes: [Ir(COD)(IMes)(PPh3)][BArF24] and [IrCl(COD)(IMes)]. The directing group power scales that have been constructred from these data reveal a wide range of reactivity covering four orders of magnitude. Intramolecular competition experiments have demonstrated that the obtained reactivity scale provides accurate predictions of regioselectivity within molecules with multiple competing directing groups. This work contributes to our understanding and control of regioselectivity in metal-catalysed C-H activation reactions

A quantitative empirical directing group scale for selectivity in iridium-catalysed hydrogen isotope exchange reactions

A palette of commonly used directing groups, including various pharmaceutically relevant nitrogen-containing heterocycles, are quantitatively ranked based on the results of intermolecular hydrogen isotope exchange competition reactions using two iridium complexes: [Ir(COD)(IMes)(PPh3)][BArF24] and [IrCl(COD)(IMes)]. The directing group power scales that have been constructed from these data reveal a wide range of reactivity covering four orders of magnitude. Intramolecular competition experiments have demonstrated that the obtained reactivity scale provides accurate predictions of regioselectivity within molecules with multiple competing directing groups. This work contributes to our understanding and control of regioselectivity in metal-catalysed C-H activation reactions