Multiple sums and integrals as neutral BKP tau functions

We consider multiple sums and multi-integrals as tau functions of the BKP hierarchy using neutral fermions as the simplest tool for deriving these. The sums are over projective Schur functions $Q_\alpha$ for strict partitions $\alpha$. We consider two types of such sums: weighted sums of $Q_\alpha$ over strict partitions $\alpha$ and sums over products $Q_\alpha Q_\gamma$. In this way we obtain discrete analogues of the beta-ensembles ($\beta=1,2,4$). Continuous versions are represented as multiple integrals. Such sums and integrals are of interest in a number of problems in mathematics and physics.Comment: 16 page

fMRI network correlates of predisposing risk factors for delirium: a cross-sectional study

Delirium, the clinical expression of acute encephalopathy, is a common neuropsychiatric syndrome that is related to poor outcomes, such as long-term cognitive impairment. Disturbances of functional brain networks are hypothesized to predispose for delirium. The aim of this study in non-delirious elderly individuals was to investigate whether predisposing risk factors for delirium are associated with fMRI network characteristics that have been observed during delirium. As predisposing risk factors, we studied age, alcohol misuse, cognitive impairment, depression, functional impairment, history of transient ischemic attack or stroke, and physical status. In this multicenter study, we included 554 subjects and analyzed resting-state fMRI data from 222 elderly subjects (63% male, age range: 65-85 year) after rigorous motion correction. Functional network characteristics were analyzed and based on the minimum spanning tree (MST). Global functional connectivity strength, network efficiency (MST diameter) and network integration (MST leaf fraction) were analyzed, as these measures were altered during delirium in previous studies. Linear regression analyses were used to investigate the relation between predisposing delirium risk factors and delirium-related fMRI characteristics, adjusted for confounding and multiple testing. Predisposing risk factors for delirium were not associated with delirium-related fMRI network characteristics. Older age within our elderly cohort was related to global functional connectivity strength (beta = 0.182, p < 0.05), but in the opposite direction than hypothesized. Delirium-related functional network impairments can therefore not be considered as the common mechanism for predisposition for delirium.Neuro Imaging Researc

Virasoro Symmetry of Constrained KP Hierarchies

Additional non-isospectral symmetries are formulated for the constrained Kadomtsev-Petviashvili (\cKP) integrable hierarchies. The problem of compatibility of additional symmetries with the underlying constraints is solved explicitly for the Virasoro part of the additional symmetry through appropriate modification of the standard additional-symmetry flows for the general (unconstrained) KP hierarchy. We also discuss the special case of \cKP --truncated KP hierarchies, obtained as Darboux-B\"{a}cklund orbits of initial purely differential Lax operators. The latter give rise to Toda-lattice-like structures relevant for discrete (multi-)matrix models. Our construction establishes the condition for commutativity of the additional-symmetry flows with the discrete Darboux-B\"{a}cklund transformations of \cKP hierarchies leading to a new derivation of the string-equation constraint in matrix models.Comment: LaTeX, 11 pg

Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies

We propose a method for computing any Gelfand-Dickey tau function living in Segal-Wilson Grassmannian as the asymptotics of block Toeplitz determinant associated to a certain class of symbols. Also truncated block Toeplitz determinants associated to the same symbols are shown to be tau function for rational reductions of KP. Connection with Riemann-Hilbert problems is investigated both from the point of view of integrable systems and block Toeplitz operator theory. Examples of applications to algebro-geometric solutions are given.Comment: 35 pages. Typos corrected, some changes in the introductio

Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets

We show that the quantum field theoretical formulation of the $\tau$-function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that i) the partial charge transformations preserving the neutral sector are Laplace transformations, ii) the basic vertex operators are Levy and adjoint Levy transformations and iii) the diagonal soliton vertex operators generate fundamental transformations. We also show that the bilinear identity for the multicomponent Kadomtsev-Petviashvili hierarchy becomes, through a generalized Miwa map, a bilinear identity for the multidimensional quadrilateral lattice equations.Comment: 28 pages, 3 Postscript figure

Проблемы научно-технического прогресса в бурении скважин: сборник докладов Всероссийской научно-технической конференции с международным участием , посвященной 60-летию кафедры бурения скважин, Томск, 2014 г.

В материалах сборника представлены результаты исследований научных работников по важным вопросам бурения геологоразведочных, технических, нефтяных и газовых скважин, проведения горно-разведочных выработок: разрушение горных пород, упрочнение породоразрушающего инструмента, скважинная гидродобыча руды, подземное выщелачивание урана, новые подходы по изучению буровых растворов, цементирование обсадных колонн, поиск новых путей получения информации с забоя в процессе бурения; даны решения ряда актуальных вопросов при проведении горноразведочных выработок

A new extended q-deformed KP hierarchy

A method is proposed in this paper to construct a new extended q-deformed KP ($q$-KP) hiearchy and its Lax representation. This new extended $q$-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy with self-consistent sources and the constrained q-deformed KP hierarchy, which include two types of q-deformed KdV equation with sources and two types of q-deformed Boussinesq equation with sources. All of these results reduce to the classical ones when $q$ goes to 1. This provides a general way to construct (2+1)- and (1+1)-dimensional q-deformed soliton equations with sources and their Lax representations.Comment: 17 pages, no figur