1,903 research outputs found
Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps
In this Letter we propose a systematic approach for detecting and calculating
preserved measures and integrals of a rational map. The approach is based on
the use of cofactors and Discrete Darboux Polynomials and relies on the use of
symbolic algebra tools. Given sufficient computing power, all rational
preserved integrals can be found.
We show, in two examples, how to use this method to detect and determine
preserved measures and integrals of the considered rational maps.Comment: 8 pages, 1 Figur
The Importance of DNA Repair in Tumor Suppression
The transition from a normal to cancerous cell requires a number of highly
specific mutations that affect cell cycle regulation, apoptosis,
differentiation, and many other cell functions. One hallmark of cancerous
genomes is genomic instability, with mutation rates far greater than those of
normal cells. In microsatellite instability (MIN tumors), these are often
caused by damage to mismatch repair genes, allowing further mutation of the
genome and tumor progression. These mutation rates may lie near the error
catastrophe found in the quasispecies model of adaptive RNA genomes, suggesting
that further increasing mutation rates will destroy cancerous genomes. However,
recent results have demonstrated that DNA genomes exhibit an error threshold at
mutation rates far lower than their conservative counterparts. Furthermore,
while the maximum viable mutation rate in conservative systems increases
indefinitely with increasing master sequence fitness, the semiconservative
threshold plateaus at a relatively low value. This implies a paradox, wherein
inaccessible mutation rates are found in viable tumor cells. In this paper, we
address this paradox, demonstrating an isomorphism between the conservatively
replicating (RNA) quasispecies model and the semiconservative (DNA) model with
post-methylation DNA repair mechanisms impaired. Thus, as DNA repair becomes
inactivated, the maximum viable mutation rate increases smoothly to that of a
conservatively replicating system on a transformed landscape, with an upper
bound that is dependent on replication rates. We postulate that inactivation of
post-methylation repair mechanisms are fundamental to the progression of a
tumor cell and hence these mechanisms act as a method for prevention and
destruction of cancerous genomes.Comment: 7 pages, 5 figures; Approximation replaced with exact calculation;
Minor error corrected; Minor changes to model syste
Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm
The discrete-time Toda equation arises as a universal equation for the
relevant Hankel determinants associated with one-variable orthogonal
polynomials through the mechanism of adjacency, which amounts to the inclusion
of shifted weight functions in the orthogonality condition. In this paper we
extend this mechanism to a new class of two-variable orthogonal polynomials
where the variables are related via an elliptic curve. This leads to a `Higher
order Analogue of the Discrete-time Toda' (HADT) equation for the associated
Hankel determinants, together with its Lax pair, which is derived from the
relevant recurrence relations for the orthogonal polynomials. In a similar way
as the quotient-difference (QD) algorithm is related to the discrete-time Toda
equation, a novel quotient-quotient-difference (QQD) scheme is presented for
the HADT equation. We show that for both the HADT equation and the QQD scheme,
there exists well-posed -periodic initial value problems, for almost all
\s\in\Z^2. From the Lax-pairs we furthermore derive invariants for
corresponding reductions to dynamical mappings for some explicit examples.Comment: 38 page
Electronic tuneability of a structurally rigid surface intermetallic and Kondo lattice: CePt / Pt(111)
We present an extensive study of structure, composition, electronic and
magnetic properties of Ce--Pt surface intermetallic phases on Pt(111) as a
function of their thickness. The sequence of structural phases appearing in low
energy electron diffraction (LEED) may invariably be attributed to a single
underlying intermetallic atomic lattice. Findings from both microscopic and
spectroscopic methods, respectively, prove compatible with CePt formation
when their characteristic probing depth is adequately taken into account. The
intermetallic film thickness serves as an effective tuning parameter which
brings about characteristic variations of the Cerium valence and related
properties. Soft x-ray absorption (XAS) and magnetic circular dichroism (XMCD)
prove well suited to trace the changing Ce valence and to assess relevant
aspects of Kondo physics in the CePt surface intermetallic. We find
characteristic Kondo scales of the order of 10 K and evidence for
considerable magnetic Kondo screening of the local Ce moments.
CePt/Pt(111) and related systems therefore appear to be promising
candidates for further studies of low-dimensional Kondo lattices at surfaces.Comment: 14 pages, 11 figure
Relating imperatives to action
The aim of this chapter is to provide an analysis of the use of logically complex imperatives, in particular, imperatives of the form Do A1 or A2 and Do A, if B. We argue for an analysis of imperatives in terms of classical logic which takes into account the influence of background information on imperatives. We show that by doing so one can avoid some counter-intuitive results which have been associated with analyses of imperatives in terms of classical logic. In particular, I address Hamblin's observations concerning rule-like imperatives and Ross' Paradox. The analysis is carried out within an agent-based logical framework. This analysis explicates what it means for an agent to have a successful policy for action with respect to satisfying his or her commitments, where some of these commitments have been introduced as a result of imperative language use
Generating multimedia presentations: from plain text to screenplay
In many Natural Language Generation (NLG) applications, the output is limited to plain text – i.e., a string of words with punctuation and paragraph breaks, but no indications for layout, or pictures, or dialogue. In several projects, we have begun to explore NLG applications in which these extra media are brought into play. This paper gives an informal account of what we have learned. For coherence, we focus on the domain of patient information leaflets, and follow an example in which the same content is expressed first in plain text, then in formatted text, then in text with pictures, and finally in a dialogue script that can be performed by two animated agents. We show how the same meaning can be mapped to realisation patterns in different media, and how the expanded options for expressing meaning are related to the perceived style and tone of the presentation. Throughout, we stress that the extra media are not simple added to plain text, but integrated with it: thus the use of formatting, or pictures, or dialogue, may require radical rewording of the text itself
Linear Darboux polynomials for Lotka-Volterra systems, trees and superintegrable families
We present a method to construct superintegrable -component Lotka-Volterra
systems with parameters. We apply the method to Lotka-Volterra systems
with components for , and present several -dimensional
superintegrable families. The Lotka-Volterra systems are in one-to-one
correspondence with trees on vertices.Comment: 14 pages, 4 figure
Uncovering dispersion properties in semiconductor waveguides to study photon-pair generation
This work was supported by the FWF through project no. I-2065-N27, the DFG Project no. SCHN1376/2-1, the ERC project EnSeNa (257531) and the State of Bavaria.We investigate the dispersion properties of ridge Bragg-reflection waveguides to deduce their phasematching characteristics. These are crucial for exploiting them as sources of parametric down-conversion (PDC). In order to estimate the phasematching bandwidth we first determine the group refractive indices of the interacting modes via Fabry–Perot experiments in two distant wavelength regions. Second, by measuring the spectra of the emitted PDC photons, we gain access to their group index dispersion. Our results offer a simple approach for determining the PDC process parameters in the spectral domain, and provide important feedback for designing such sources, especially in the broadband case.Publisher PDFPeer reviewe
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