72 research outputs found
Applying quantitative semantics to higher-order quantum computing
Finding a denotational semantics for higher order quantum computation is a
long-standing problem in the semantics of quantum programming languages. Most
past approaches to this problem fell short in one way or another, either
limiting the language to an unusably small finitary fragment, or giving up
important features of quantum physics such as entanglement. In this paper, we
propose a denotational semantics for a quantum lambda calculus with recursion
and an infinite data type, using constructions from quantitative semantics of
linear logic
Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals
High-order derivatives of analytic functions are expressible as Cauchy
integrals over circular contours, which can very effectively be approximated,
e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius
of convergence is equal, numerical stability strongly depends on r. We give a
comprehensive study of this effect; in particular we show that there is a
unique radius that minimizes the loss of accuracy caused by round-off errors.
For large classes of functions, though not for all, this radius actually gives
about full accuracy; a remarkable fact that we explain by the theory of Hardy
spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and
by the saddle-point method of asymptotic analysis. Many examples and
non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature
rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat
Cap-Gly Proteins at Microtubule Plus Ends: Is EB1 Detyrosination Involved?
Localization of CAP-Gly proteins such as CLIP170 at microtubule+ends results from their dual interaction with α-tubulin and EB1 through their C-terminal amino acids âEEY. Detyrosination (cleavage of the terminal tyrosine) of α-tubulin by tubulin-carboxypeptidase abolishes CLIP170 binding. Can detyrosination affect EB1 and thus regulate the presence of CLIP170 at microtubule+ends as well? We developed specific antibodies to discriminate tyrosinated vs detyrosinated forms of EB1 and detected only tyrosinated EB1 in fibroblasts, astrocytes, and total brain tissue. Over-expressed EB1 was not detyrosinated in cells and chimeric EB1 with the eight C-terminal amino acids of α-tubulin was only barely detyrosinated. Our results indicate that detyrosination regulates CLIPs interaction with α-tubulin, but not with EB1. They highlight the specificity of carboxypeptidase toward tubulin
Modeling oscillatory Microtubule--Polymerization
Polymerization of microtubules is ubiquitous in biological cells and under
certain conditions it becomes oscillatory in time. Here simple reaction models
are analyzed that capture such oscillations as well as the length distribution
of microtubules. We assume reaction conditions that are stationary over many
oscillation periods, and it is a Hopf bifurcation that leads to a persistent
oscillatory microtubule polymerization in these models. Analytical expressions
are derived for the threshold of the bifurcation and the oscillation frequency
in terms of reaction rates as well as typical trends of their parameter
dependence are presented. Both, a catastrophe rate that depends on the density
of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay
reaction, such as the depolymerization of shrinking microtubules or the decay
of oligomers, support oscillations. For a tubulin dimer concentration below the
threshold oscillatory microtubule polymerization occurs transiently on the
route to a stationary state, as shown by numerical solutions of the model
equations. Close to threshold a so--called amplitude equation is derived and it
is shown that the bifurcation to microtubule oscillations is supercritical.Comment: 21 pages and 12 figure
Laplace Operators on Fractals and Related Functional Equations
We give an overview over the application of functional equations, namely the
classical Poincar\'e and renewal equations, to the study of the spectrum of
Laplace operators on self-similar fractals. We compare the techniques used to
those used in the euclidean situation. Furthermore, we use the obtained
information on the spectral zeta function to define the Casimir energy of
fractals. We give numerical values for this energy for the Sierpi\'nski gasket
The junctions that donât fit the scheme: special symmetrical cell-cell junctions of their own kind
A reassessment of the factors affecting microtubule assembly and disassembly in vitro.
Current models of microtubule assembly from pure tubulin involve a nucleation phase followed by microtubule elongation at a constant polymer number. Both the rate of microtubule nucleation and elongation are thought to be tightly influenced by the free GTP-tubulin concentration, in a law of mass action-dependent manner. However, these basic hypotheses have remained largely untested due to a lack of data reporting actual measurements of the microtubule length and number concentration during microtubule assembly.Here, we performed simultaneous measurements of the polymeric tubulin concentration, of the free GTP-tubulin concentration, and of the microtubule length and number concentration in both polymerizing and depolymerizing conditions. In agreement with previous work we find that the microtubule nucleation rate is strongly dependent on the initial GTP-tubulin concentration. But we find that microtubule nucleation persists during microtubule elongation. At any given initial tubulin-GTP concentration, the microtubule nucleation rate remains constant during polymer assembly, despite the wide variation in free GTP-tubulin concentration. We also find a remarkable constancy of the rate of microtubule elongation during assembly. Apparently, the rate of microtubule elongation is intrinsic to the polymers, insensitive to large variations of the free GTP-tubulin concentration. Finally we observe that when, following assembly, microtubules depolymerize below the free GTP-tubulin critical concentration, the rate-limiting factor for disassembly is the frequency of microtubule catastrophe. At all time-points during disassembly, the microtubule catastrophe frequency is independent of the free GTP-tubulin concentration but, as the microtubule nucleation rate, is strongly dependent on the initial free GTP-tubulin concentration. We conclude that the dynamics of both microtubule assembly and disassembly depend largely on factors other than the free GTP-tubulin concentration. We propose that intrinsic structural factors and endogenous regulators, whose concentration varies with the initial conditions, are also major determinants of these dynamics
THE TYCHO SYSTEM : COMPUTER ANALYSIS OF TWO DIMENSIONAL GEL ELECTROPHORESIS
En collaboration avec Argonne National Laboratory, le LETI a implémenté le systÚme TYCHO d'aide au dépouillement de gels d'électrophorÚse bi-dimensionnelle sur son équipement informatique. Ce systÚme contient des outils généraux de traitement d'images présentant des performances intéressantes, et, en outre, la majeure partie de ce logiciel n'est pas spécifique à l'application d'électrophorÚse. Le LETI développe également une instrumentation spécifique à partir des principes utilisés dans TYCHO. Cet article donne une vue générale des deux systÚmes et décrit plus précisément les techniques utilisées par le traitement d'image et les performances des systÚmes.In collaboration with Argonne National Laboratory, the TYCHO system, developed at Argonne by the group of Professor Anderson to assist two-dimensional electrophoresis gel analysis, has been implemented on the LETI computer equipment. This system contains high performance general images processing programs with interesting performances and furthermore much of this software is not restricted to electrophoresis application. The LETI has also been developing specific instrumentation based on the same principles. This paper gives a general overview of the two systems, with their hardware and software components, and then describes in greater detail the techniques used in image processing and the performances of the systems
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