164 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
Quantum computations without definite causal structure
We show that quantum theory allows for transformations of black boxes that
cannot be realized by inserting the input black boxes within a circuit in a
pre-defined causal order. The simplest example of such a transformation is the
classical switch of black boxes, where two input black boxes are arranged in
two different orders conditionally on the value of a classical bit. The quantum
version of this transformation-the quantum switch-produces an output circuit
where the order of the connections is controlled by a quantum bit, which
becomes entangled with the circuit structure. Simulating these transformations
in a circuit with fixed causal structure requires either postselection, or an
extra query to the input black boxes.Comment: Updated version with expanded presentatio
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
Semantics of a Typed Algebraic Lambda-Calculus
Algebraic lambda-calculi have been studied in various ways, but their
semantics remain mostly untouched. In this paper we propose a semantic analysis
of a general simply-typed lambda-calculus endowed with a structure of vector
space. We sketch the relation with two established vectorial lambda-calculi.
Then we study the problems arising from the addition of a fixed point
combinator and how to modify the equational theory to solve them. We sketch an
algebraic vectorial PCF and its possible denotational interpretations
Quasi-classical rate coefficient calculations for the rotational (de)excitation of H2O by H2
The interpretation of water line emission from existing observations and
future HIFI/Herschel data requires a detailed knowledge of collisional rate
coefficients. Among all relevant collisional mechanisms, the rotational
(de)excitation of H2O by H2 molecules is the process of most interest in
interstellar space. To determine rate coefficients for rotational de-excitation
among the lowest 45 para and 45 ortho rotational levels of H2O colliding with
both para and ortho-H2 in the temperature range 20-2000 K. Rate coefficients
are calculated on a recent high-accuracy H2O-H2 potential energy surface using
quasi-classical trajectory calculations. Trajectories are sampled by a
canonical Monte-Carlo procedure. H2 molecules are assumed to be rotationally
thermalized at the kinetic temperature. By comparison with quantum calculations
available for low lying levels, classical rates are found to be accurate within
a factor of 1-3 for the dominant transitions, that is those with rates larger
than a few 10^{-12}cm^{3}s^{-1}. Large velocity gradient modelling shows that
the new rates have a significant impact on emission line fluxes and that they
should be adopted in any detailed population model of water in warm and hot
environments.Comment: 8 pages, 2 figures, 1 table (the online material (4 tables) can be
obtained upon request to [email protected]
Rotational Excitation of HC_3N by H_2 and He at low temperatures
Rates for rotational excitation of HC3N by collisions with He atoms and H2
molecules are computed for kinetic temperatures in the range 5-20K and 5-100K,
respectively. These rates are obtained from extensive quantum and
quasi-classical calculations using new accurate potential energy surfaces
(PES)
Abstract basins of attraction
Abstract basins appear naturally in different areas of several complex
variables. In this survey we want to describe three different topics in which
they play an important role, leading to interesting open problems
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
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
Molecular excitation in the Interstellar Medium: recent advances in collisional, radiative and chemical processes
We review the different excitation processes in the interstellar mediumComment: Accepted in Chem. Re
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