Geometrical Construction of Heterogeneous Loop Amplitudes in 2D Gravity

We study a disk amplitude which has a complicated heterogeneous matter configuration on the boundary in a system of the (3,4) conformal matter coupled to two-dimensional gravity. It is analyzed using the two-matrix chain model in the large N limit. We show that the disk amplitude calculated by Schwinger-Dyson equations can completely be reproduced through purely geometrical consideration. From this result, we speculate that all heterogeneous loop amplitudes can be derived from the geometrical consideration and the consistency among relevant amplitudes.Comment: 13 pages, 11 figure

Macroscopic nn-Loop Amplitude for Minimal Models Coupled to Two-Dimensional Gravity: Fusion Rules and Interactions

We investigate the structure of the macroscopic $n$-loop amplitude obtained from the two-matrix model at the unitary minimal critical point $(m+1,m)$. We derive a general formula for the $n$-resolvent correlator at the continuum planar limit whose inverse Laplace transform provides the amplitude in terms of the boundary lengths $\ell_{i}$ and the renormalized cosmological constant $t$. The amplitude is found to contain a term consisting of $\left( \frac{\partial} {\partial t} \right)^{n-3}$ multiplied by the product of modified Bessel functions summed over their degrees which conform to the fusion rules and the crossing symmetry. This is found to be supplemented by an increasing number of other terms with $n$ which represent residual interactions of loops. We reveal the nature of these interactions by explicitly determining them as the convolution of modified Bessel functions and their derivatives for the case $n=4$ and the case $n=5$. We derive a set of recursion relations which relate the terms in the $n$-resolvents to those in the $(n-1)$-resolvents.Comment: 30 pages, Latex, figures: figures have been introduced to represent our results on the resolvents. A better formula for the resolvents has been put and the section on residual interactions has been expanded to a large exten

Macroscopoic Three-Loop Amplitudes and the Fusion Rules from the Two-Matrix Model

From the computation of three-point singlet correlators in the two-matrix model, we obtain an explicit expression for the macroscopic three-loop amplitudes having boundary lengths $\ell_{i}$ $(i = 1\sim 3)$ in the case of the unitary series $(p,q)= (m+1,m)$ coupled to two-dimensional gravity. The sum appearing in this expression is found to conform to the structure of the CFT fusion rules while the summand factorizes through a product of three modified Bessel functions. We briefly discuss a possible generalization of these features to macroscopic $n$-loop amplitudes.Comment: 9 pages, no figure, late

Continuum Annulus Amplitude from the Two-Matrix Model

An explicit expression for continuum annulus amplitudes having boundary lengths $\ell_{1}$ and $\ell_{2}$ is obtained from the two-matrix model for the case of the unitary series; $(p,q) = (m + 1, m)$. In the limit of vanishing cosmological constant, we find an integral representation of these amplitudes which is reproduced, for the cases of the $m = 2~(c=0)$ and the $m \rightarrow \infty~(c=1)$, by a continuum approach consisting of quantum mechanics of loops and a matter system integrated over the modular parameter of the annulus. We comment on a possible relation to the unconventional branch of the Liouville gravity.Comment: 9 pages, OU-HET 190, revised version. A part of the conclusions has been corrected. A new result on integral representation of the annulus amplitudes has been adde

Boundary operators in minimal Liouville gravity and matrix models

We interpret the matrix boundaries of the one matrix model (1MM) recently constructed by two of the authors as an outcome of a relation among FZZT branes. In the double scaling limit, the 1MM is described by the (2,2p+1) minimal Liouville gravity. These matrix operators are shown to create a boundary with matter boundary conditions given by the Cardy states. We also demonstrate a recursion relation among the matrix disc correlator with two different boundaries. This construction is then extended to the two matrix model and the disc correlator with two boundaries is compared with the Liouville boundary two point functions. In addition, the realization within the matrix model of several symmetries among FZZT branes is discussed.Comment: 26 page

Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.Comment: 21 pages, LaTex file, no figure

Evaluation of the aquatic macroinvertebrate community as a tool for monitoring a reservoir in the Pitangui river basin, Paraná, Brazil

Os macroinvertebrados bentônicos e nectônicos representam elementos importantes na estrutura e funcionamento dos ecossistemas aquáticos e sua distribuição é influenciada pela natureza química do substrato, composição da vegetação e profundidade da lâmina d'água. O conhecimento desta fauna contribui para a avaliação da qualidade da água e a elaboração de ações visando à conservação da biodiversidade. No presente estudo foram avaliadas diferentes medidas bióticas da comunidade de invertebrados da represa de Alagados, importante manancial da cidade de Ponta Grossa, no Paraná. Em cinco diferentes pontos de amostragem, foram coletados 18.473 exemplares de macroinvertebrados aquáticos ou semi-aquáticos, pertencentes a 46 táxons dos filos Annelida (Hirudinea e Oligochaeta), Mollusca (Gastropoda), Platyhelminthes (Turbellaria), Nematoda e Arthropoda (Arachnida, Crustacea e Insecta). Esta comunidade foi constituída predominantemente por organismos predadores (45,7% dos táxons amostrados), seguidos de coletores e/ou filtradores (23,9%); raspadores (15,2%), fragmentadores (13%) e detritívoros (2,2%). De modo geral, os índices de diversidade (H') e equitabilidade (J) foram significativamente baixos para os cinco locais investigados, com H' variando de 0,3301 a 1,0396. Quanto à tolerância dos organismos à poluição orgânica, alguns táxons mais sensíveis foram muito raros (Plecoptera) ou em baixa frequência (Trichoptera e Ephemeroptera). Entre os grupos mais resistentes a ambientes poluídos estão os Chironomidae e os Hirudinea, ambos bastante comuns nas amostras de Alagados. Este estudo reforça a importância da análise de bioindicadores na avaliação da qualidade de água para consumo humano e também para a conservação de ecossistemas, considerando que um programa de monitoramento ambiental deve integrar medidas físicas, químicas e biológicas.Benthic and nektonic macroinvertebrates play an important role in the structure and function of aquatic ecosystems and their distribution is influenced by chemical features of the substrate, vegetation composition, and water depth. Knowledge on the fauna contributes to the assessment of water quality and development of biodiversity conservation activities. Different biotic factors affecting the invertebrate community were evaluated in the Alagados reservoir, the main water source of the city of Ponta Grossa, Paraná. In five different sampling points, 18,473 specimens of aquatic or semiaquatic macroinvertebrates were collected, belonging to 46 taxa of the phylla Annelida (Hirudinea and Oligochaeta), Mollusca (Gastropoda), Platyhelminthes (Turbellaria), Nematoda and Arthropoda (Arachnida, Crustacea and Insecta). This community was composed mainly of predators (45.7% of the taxa sampled), collectors and/or filterers (23.9%), scrapers (15.2%), shredders (13.0%) and detritivores (2.2%). Diversity (H') and evenness (J) indices were significantly low for the sites examined, and H' ranged between 0.3301 and 1.0396. Regarding tolerance of organisms to organic pollution, more sensitive taxa were very rare (Plecoptera) or unusual (Trichoptera and Ephemeroptera). Among the more resistant groups are Chironomidae and Hirudinea, both fairly common in the samples. This study corroborates the importance of bioindicators as a tool to assess water quality for human consumption and for the conservation of aquatic environments, integrating physical, chemical and biological factors in monitoring programs

Instabilities and Oscillations in Isotropic Active Gels

We present a generic formulation of the continuum elasticity of an isotropic crosslinked active gel. The gel is described by a two-component model consisting of an elastic network coupled frictionally to a permeating fluid. Activity is induced by active crosslinkers that undergo an ATP-activated cycle and transmit forces to the network. The on/off dynamics of the active crosslinkers is described via rate equations for unbound and bound motors. For large activity motors yield a contractile instability of the network. At smaller values of activity, the on/off motor dynamics provides an effective inertial drag on the network that opposes elastic restoring forces, resulting in spontaneous oscillations. Our work provides a continuum formulation that unifies earlier microscopic models of oscillations in muscle sarcomeres and a generic framework for the description of the large scale properties of isotropic active solids.Comment: 13 pages, 5 figure

Robot-assisted pancreatoduodenectomy with preservation of the vascular supply for autologous islet cell isolation and transplantation: a case report

<p>Abstract</p> <p>Introduction</p> <p>For patients with chronic pancreatitis presenting with medically intractable abdominal pain, surgical intervention may be the only treatment option. However, extensive pancreatic resections are typically performed open and are associated with a substantial amount of postoperative pain, wound complications and long recovery time. Minimally invasive surgery offers an avenue to improve results; however, current limitations of laparoscopic surgery render its application in the setting of chronic pancreatitis technically demanding. Additionally, pancreatic resections are associated with a high incidence of diabetes. Transplantation of islets isolated from the resected pancreas portion offers a way to prevent post-surgical diabetes; however, preservation of the vascular supply during pancreatic resection, which determines islet cell viability, is technically difficult using current laparoscopic approaches. With recent advances in the surgical field, robotic surgery now provides a means to overcome these obstacles to achieve the end goals of pain relief and preserved endocrine function. We present the first report of a novel, minimally invasive robotic approach for resection of the pancreatic head that preserves vascular supply and enables the isolation of a high yield of viable islets for transplantation.</p> <p>Case presentation</p> <p>A 35-year old Caucasian woman presented with intractable chronic abdominal pain secondary to chronic pancreatitis, with a stricture of her main pancreatic duct at the level of the ampulla of Vater and distal dilatation. She was offered a robotic-assisted pylorus-preserving pancreatoduodenectomy and subsequent islet transplantation, to both provide pain relief and preserve insulin-secretory reserves.</p> <p>Conclusion</p> <p>We present a novel, minimally invasive robotic approach for resection of the pancreatic head with complete preservation of the vascular supply, minimal warm ischemia time (less than three minutes) and excellent islet recovery (134,727 islet equivalent). Our patient is currently pain-free with normal glycemic control. Robot-assisted pylorus-preserving pancreatoduodenectomy and autologous islet transplantation can be safely performed and has the potential to minimize operative traumas as well as to partially preserve endocrine function. Results from this case report suggest that this dual procedure should be considered as a treatment option for patients with chronic pancreatitis at earlier stages of the disease, before irreversible islet loss occurs.</p