Two-matrix model and c=1 string theory

We show that the most general two--matrix model with bilinear coupling underlies $c=1$ string theory. More precisely we prove that $W_{1+\infty}$ constraints, a subset of the correlation functions and the integrable hierarchy characterizing such two--matrix model, correspond exactly to the $W_{1+\infty}$ constraints, to the discrete tachyon correlation functions and to the integrable hierarchy of the $c=1$ string.Comment: 12 pages, LaTeX, SISSA 54/94/EP (misprints corrected

Topological Field Theory Interpretations and LG Representation of c=1 String Theory

We analyze the topological nature of $c=1$ string theory at the self--dual radius. We find that it admits two distinct topological field theory structures characterized by two different puncture operators. We show it first in the unperturbed theory in which the only parameter is the cosmological constant, then in the presence of any infinitesimal tachyonic perturbation. We also discuss in detail a Landau--Ginzburg representation of one of the two topological field theory structures.Comment: 25 pages, LaTeX, report number adde

Extended Toda lattice hierarchy, extended two-matrix model and c=1 string theory

We show how the two--matrix model and Toda lattice hierarchy presented in a previous paper can be solved exactly: we obtain compact formulas for correlators of pure tachyonic states at every genus. We then extend the model to incorporate a set of discrete states organized in finite dimensional $sl_2$ representations. We solve also this extended model and find the correlators of the discrete states by means of the $W$ constraints and the flow equations. Our results coincide with the ones existing in the literature in those cases in which particular correlators have been explicitly calculated. We conclude that the extented two--matrix model is a realization of the discrete states of $c=1$ string theory.Comment: 34 pages, LaTeX, SISSA 84/94/EP, BONN-HE-08/9

Multi-View 3D Transesophageal Echocardiography Registration and Volume Compounding for Mitral Valve Procedure Planning

Three-dimensional ultrasound mosaicing can increase image quality and expand the field of view. However, limited work has been done applying these compounded approaches for cardiac procedures focused on the mitral valve. For procedures targeting the mitral valve, transesophageal echocardiography (TEE) is the primary imaging modality used as it provides clear 3D images of the valve and surrounding tissues. However, TEE suffers from image artefacts and signal dropout, particularly for structures lying below the valve, including chordae tendineae, making it necessary to acquire alternative echo views to visualize these structures. Due to the limited field of view obtainable, the entire ventricle cannot be directly visualized in sufficient detail from a single image acquisition in 3D. We propose applying an image compounding technique to TEE volumes acquired from a mid-esophageal position and several transgastric positions in order to reconstruct a high-detail volume of the mitral valve and sub-valvular structures. This compounding technique utilizes both fully and semi-simultaneous group-wise registration to align the multiple 3D volumes, followed by a weighted intensity compounding step based on the monogenic signal. This compounding technique is validated using images acquired from two excised porcine mitral valve units and three patient data sets. We demonstrate that this compounding technique accurately captures the physical structures present, including the mitral valve, chordae tendineae and papillary muscles. The chordae length measurement error between the compounded ultrasound and ground-truth CT for two porcine valves is reported as 0.7 ± 0.6 mm and 0.6 ± 0.6 mm

A characterization of the squares in a Fibonacci string

A (finite) Fibonacci stringFn is defined as follows: F0 = b, F1 = a; for every integer n ⩾ 2, Fn = Fn − 1Fn − 2. For n ⩾ 1, the length of Fn is denoted by . The infinite Fibonacci stringF is the string which contains every Fn, n ⩾ 1, as a prefix. Apart from their general theoretical importance, Fibonacci strings are often cited as worst-case examples for algorithms which compute all the repetitions or all the “Abelian squares” in a given string. In this paper we provide a characterization of all the squares in F, hence in every prefix Fn; this characterization naturally gives rise to a algorithm which specifies all the squares of Fn in an appropriate encoding. This encoding is made possible by the fact that the squares of Fn occur consecutively, in “runs”, the number of which is . By contrast, the known general algorithms for the computation of the repetitions in an arbitrary string require time (and produce outputs) when applied to a Fibonacci string Fn

The covers of a circular Fibonacci string

Fibonacci strings turn out to constitute worst cases for a number of computer algorithms which find generic patterns in strings. Examples of such patterns are repetitions, Abelian squares, and "covers". In particular, we characterize in this paper the covers of a circular Fibonacci string C(F k ) and show that they are \Theta(jF k j 2 ) in number. We show also that, by making use of an appropriate encoding, these covers can be reported in \Theta(jF k j) time. By contrast, the fastest known algorithm for computing the covers of an arbitrary circular string of length n requires time O(n log n)

A linear algorithm for computing all the squares of a Fibonacci string

A (finite) Fibonacci string $F_n$ is defined as follows: $F_0 = b$, $F_1 = a$; for every integer $n \ge 2$, $F_n = F_{n-1}F_{n- 2}$. For $n \ge 1$, the length of $F_n$ is denoted by $f_n = |F_n|$, while it is convenient to define $f_0 \equiv 0$. The infinite Fibonacci string $F$ is the string which contains every $F_n$, $n \ge 1$, as a prefix. Apart from their general theoretical importance, Fibonacci strings are often cited as worst case examples for algorithms which compute all the repetitions or all the ``Abelian squares'' in a given string. In this paper we provide a characterization of all the squares in $F$, hence in every prefix $F_n$; this characterization naturally gives rise to a $\Theta(f_n)$ algorithm which specifies all the squares of $F_n$ in an appropriate encoding. This encoding is made possible by the fact that the squares of $F_n$ occur consecutively, in ``runs'', the number of which is $\Theta(f_n)$. By contrast, the known general algorithms for the computation of the repetitions in an arbitrary string require $\Theta(f_n\log f_n)$ time (and produce $\Theta(f_n\log f_n)$ outputs) when applied to a Fibonacci string $F_n$

Can a Lattice String Have a Vanishing Cosmological Constant?

We prove that a class of one-loop partition functions found by Dienes, giving rise to a vanishing cosmological constant to one-loop, cannot be realized by a consistent lattice string. The construction of non-supersymmetric string with a vanishing cosmological constant therefore remains as elusive as ever. We also discuss a new test that any one-loop partition function for a lattice string must satisfy.Comment: 14 page

A Precious Bequest: Contemporary Research with the WPA-CCC Collections from Moundville, Alabama *

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72459/1/j.1749-6632.1981.tb28184.x.pd

Stevin numbers and reality

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420