WDVV Equations, Darboux-Egoroff Metric and the Dressing Method

Dressing technique is used to construct commuting Lax operators which provide an integrable (canonical) structure behind Witten--Dijkgraaf--Verlinde--Verlinde equations. The commuting flows are related to the isomonodromic flows. Examples of the canonical integrable structure are given in two- and three-dimensional cases. The three-dimensional example is associated with the rational Landau-Ginzburg potentials.Comment: Contribution to the conference "Workshop on Integrable Theories, Solitons and Duality", Unesp2002, LaTeX file w. JHEP style fil

Enumeration of hypermaps and Hirota equations for extended rationally constrained KP

We consider the Hurwitz Dubrovin--Frobenius manifold structure on the space of meromorphic functions on the Riemann sphere with exactly two poles, one simple and one of arbitrary order. We prove that the all genera partition function (also known as the total descendant potential) associated with this Dubrovin--Frobenius manifold is a tau function of a rational reduction of the Kadomtsev--Petviashvili hierarchy. This statement was conjectured by Liu, Zhang, and Zhou. We also provide a partial enumerative meaning for this partition function associating one particular set of times with enumeration of rooted hypermaps.Comment: 39 page

Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows

We use a Grassmannian framework to define multi-component tau functions as expectation values of certain multi-component Fermi operators satisfying simple bilinear commutation relations on Clifford algebra. The tau functions contain both positive and negative flows and are shown to satisfy the 2n-component KP hierarchy. The hierarchy equations can be formulated in terms of pseudo-differential equations for n × n matrix wave functions derived in terms of tau functions. These equations are cast in form of Sato-Wilson relations. A reduction process leads to the AKNS, two-component Camassa-Holm and Cecotti-Vafa models and the formalism provides simple formulas for their solutions

Darboux-Egoroff Metrics, Rational Landau-Ginzburg Potentials and the Painleve VI Equation

We present a class of three-dimensional integrable structures associated with the Darboux-Egoroff metric and classical Euler equations of free rotations of a rigid body. They are obtained as canonical structures of rational Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.Comment: 20 page

Discomfort and factual recollection in intensive care unit patients

INTRODUCTION: A stay in the intensive care unit (ICU), although potentially life-saving, may cause considerable discomfort to patients. However, retrospective assessment of discomfort is difficult because recollection of stressful events may be impaired by sedation and severe illness during the ICU stay. This study addresses the following questions. What is the incidence of discomfort reported by patients recently discharged from an ICU? What were the sources of discomfort reported? What was the degree of factual recollection during patients' stay in the ICU? Finally, was discomfort reported more often in patients with good factual recollection? METHODS: All ICU patients older than 18 years who had needed prolonged (>24 hour) admission with tracheal intubation and mechanical ventilation were consecutively included. Within three days after discharge from the ICU, a structured, in-person interview was conducted with each individual patient. All patients were asked to complete a questionnaire consisting of 14 questions specifically concerning the environment of the ICU they had stayed in. Furthermore, they were asked whether they remembered any discomfort during their stay; if they did then they were asked to specify which sources of discomfort they could recall. A reference group of surgical ward patients, matched by sex and age to the ICU group, was studied to validate the questionnaire. RESULTS: A total of 125 patients discharged from the ICU were included in this study. Data for 123 ICU patients and 48 surgical ward patients were analyzed. The prevalence of recollection of any type of discomfort in the ICU patients was 54% (n = 66). These 66 patients were asked to identify the sources of discomfort, and presence of an endotracheal tube, hallucinations and medical activities were identified as such sources. The median (min–max) score for factual recollection in the ICU patients was 15 (0–28). The median (min–max) score for factual recollection in the reference group was 25 (19–28). Analysis revealed that discomfort was positively related to factual recollection (odds ratio 1.1; P < 0.001), especially discomfort caused by the presence of an endotracheal tube, medical activities and noise. Hallucinations were reported more often with increasing age. Pain as a source of discomfort was predominantly reported by younger patients. CONCLUSION: Among postdischarge ICU patients, 54% recalled discomfort. However, memory was often impaired: the median factual recollection score of ICU patients was significantly lower than that of matched control patients. The presence of an endotracheal tube, hallucinations and medical activities were most frequently reported as sources of discomfort. Patients with a higher factual recollection score were at greater risk for remembering the stressful presence of an endotracheal tube, medical activities and noise. Younger patients were more likely to report pain as a source of discomfort

Reliability of Reagent Strips for Semi-quantitative Measurement of Glucosuria in a Neonatal Intensive Care Setting

Background: Glucosuria in preterm infants is often measured using a visually readable reagent strip, e.g., when monitoring total parenteral nutrition or during sepsis or when treating with corticosteroids. However, the specific circumstances in a neonatal intensive care unit (NICU), such as the use of diapers and the high temperature in incubators, could affect its reliability. Objectives: To evaluate the reliability of the semi-quantitative measurement of glucosuria under the specific circumstances of a NICU setting. Methods: Nine hundred assessments of artificially supplemented (contrived) urine samples, intended to simulate pathological specimens, were performed under the following varying conditions: environmental temperature (21 degrees C and 34 degrees C); different times of contact of the urine with the diaper; and using two different methods of collecting urine from the diaper. Each reagent strip was read independently by three observers. The test strips scores were categorized as 0, 1+, 2+, 3+, or 4+ in ascending degree of glucosuria. Results: Agreement was excellent under all the different conditions (temperature, weighted kappa (kappa(w)) = 0.92; method of urine collection, kappa(w) = 0.88; time, p = 0.266). Inter-observer reliability was very good (multi-rater kappa = 0.81). The deviation between the different conditions was seldom larger than one category (2.94 The reagent strip readings were concordant with the true urinary glucose concentrations in 79.0% of assessments. The discordance was never larger than one category. Conclusion: The reliability of the semi-quantitative measurement of glucosuria in newborn infants using reagent strips is good, even under the conditions of a NICU. Changes in the rating of reagent strips of more than one category are most likely to be beyond measurement error

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

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