The Orbifold-String Theories of Permutation-Type: I. One Twisted BRST per Cycle per Sector

We resume our discussion of the new orbifold-string theories of permutation-type, focusing in the present series on the algebraic formulation of the general bosonic prototype and especially the target space-times of the theories. In this first paper of the series, we construct one twisted BRST system for each cycle $j$ in each twisted sector $\sigma$ of the general case, verifying in particular the previously-conjectured algebra $[Q_{i}(\sigma),Q_{j}(\sigma)]_{+} =0$ of the BRST charges. The BRST systems then imply a set of extended physical-state conditions for the matter of each cycle at cycle central charge $\hat{c}_{j}(\sigma)=26f_{j}(\sigma)$ where $f_{j}(\sigma)$ is the length of cycle $j$.Comment: 31 page

Well-posedness of one-way wave equations and absorbing boundary conditions

A one-way wave equation is a partial differential which, in some approximate sense, behaves like the wave equation in one direction but permits no propagation in the opposite one. The construction of such equations can be reduced to the approximation of the square root of (1-s sup 2) on -1, 1 by a rational function r(s) = p sub m (s)/q sub n(s). Those rational functions r for which the corresponding one-way wave equation is well-posed are characterized both as a partial differential equation and as an absorbing boundary condition for the wave equation. We find that if r(s) interpolates the square root of (1-s sup 2) at sufficiently many points in (-1,1), then well-posedness is assured. It follows that absorbing boundary conditions based on Pade approximation are well-posed if and only if (m, n) lies in one of two distinct diagonals in the Pade table, the two proposed by Engquist and Majda. Analogous results also hold for one-way wave equations derived from Chebyshev or least-squares approximation

The connection between non-exponential relaxation and fragility in supercooled liquids

Among the outstanding problems in the theory of supercooled liquids are the reasons for the rapid increase in their viscosity and relaxation times as the temperature is lowered towards the glass transition temperature, the non-exponential time dependence of the relaxation, and the possible connection between these two properties. The ferromagnetic Potts model on a square latice is a simple system that is found to exhibit these properties. Our calculations show that in this system the connection between them is associated with the dependence on temperature and time of the average environment of the sites. Some of the consequences of this for understanding the behavior of supercooled liquids are discussed.Comment: 12 pages, 8 figure

Probabilistic Algorithmic Knowledge

The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the information provided by a randomized knowledge algorithm when its answers have some probability of being incorrect. We formalize this information in terms of evidence; a randomized knowledge algorithm returning ``Yes'' to a query about a fact \phi provides evidence for \phi being true. Finally, we discuss the extent to which this evidence can be used as a basis for decisions.Comment: 26 pages. A preliminary version appeared in Proc. 9th Conference on Theoretical Aspects of Rationality and Knowledge (TARK'03

A glance at imaging bladder cancer.

Purpose: Early and accurate diagnosis of Bladder cancer (BCa) will contribute extensively to the management of the disease. The purpose of this review was to briefly describe the conventional imaging methods and other novel imaging modalities used for early detection of BCa and outline their pros and cons. Methods: Literature search was performed on Pubmed, PMC, and Google scholar for the period of January 2014 to February 2018 and using such words as bladder cancer, bladder tumor, bladder cancer detection, diagnosis and imaging . Results: A total of 81 published papers were retrieved and are included in the review. For patients with hematuria and suspected of BCa, cystoscopy and CT are most commonly recommended. Ultrasonography, MRI, PET/CT using 18F-FDG or 11C-choline and recently PET/MRI using 18F-FDG also play a prominent role in detection of BCa. Conclusion: For initial diagnosis of BCa, cystoscopy is generally performed. However, cystoscopy can not accurately detect carcinoma insitu (CIS) and can not distinguish benign masses from malignant lesions. CT is used in two modes, CT and computed tomographic urography (CTU), both for dignosis and staging of BCa. However, they cannot differentiate T1 and T2 BCa. MRI is performed to diagnose invasive BCa and can differentiate muscle invasive bladder carcinoma (MIBC) from non-muscle invasive bladder carcinoma (NMIBC). However, CT and MRI have low sensitivity for nodal staging. For nodal staging PET/CT is preferred. PET/MRI provides better differentiation of normal and pathologic structures as compared with PET/CT. Nonetheless none of the approaches can address all issues related for the management of BCa. Novel imaging methods that target specific biomarkers, image BCa early and accurately, and stage the disease are warranted

Controllability and observabiliy of an artificial advection-diffusion problem

In this paper we study the controllability of an artificial advection-diffusion system through the boundary. Suitable Carleman estimates give us the observability on the adjoint system in the one dimensional case. We also study some basic properties of our problem such as backward uniqueness and we get an intuitive result on the control cost for vanishing viscosity.Comment: 20 pages, accepted for publication in MCSS. DOI: 10.1007/s00498-012-0076-

Non-Abelian Wilson Surfaces

A definition of non-abelian genus zero open Wilson surfaces is proposed. The ambiguity in surface-ordering is compensated by the gauge transformations.Comment: JHEP Latex, 10 pages, 6 figures; v2, refs and comments added in sec.