28,927 research outputs found
Healthiness from Duality
Healthiness is a good old question in program logics that dates back to
Dijkstra. It asks for an intrinsic characterization of those predicate
transformers which arise as the (backward) interpretation of a certain class of
programs. There are several results known for healthiness conditions: for
deterministic programs, nondeterministic ones, probabilistic ones, etc.
Building upon our previous works on so-called state-and-effect triangles, we
contribute a unified categorical framework for investigating healthiness
conditions. We find the framework to be centered around a dual adjunction
induced by a dualizing object, together with our notion of relative
Eilenberg-Moore algebra playing fundamental roles too. The latter notion seems
interesting in its own right in the context of monads, Lawvere theories and
enriched categories.Comment: 13 pages, Extended version with appendices of a paper accepted to
LICS 201
Experimental Demonstration of a Quantum Circuit using Linear Optics Gates
One of the main advantages of an optical approach to quantum computing is the
fact that optical fibers can be used to connect the logic and memory devices to
form useful circuits, in analogy with the wires of a conventional computer.
Here we describe an experimental demonstration of a simple quantum circuit of
that kind in which two probabilistic exclusive-OR (XOR) logic gates were
combined to calculate the parity of three input qubits.Comment: v2 is final PRA versio
A New GrĂĽnwald-Letnikov Derivative Derived from a Second-Order Scheme
A novel derivation of a second-order accurate GrĂĽnwald-Letnikov-type approximation to the fractional derivative of a function is presented. This scheme is shown to be second-order accurate under certain modifications to account for poor accuracy in approximating the asymptotic behavior near the lower limit of differentiation. Some example functions are chosen and numerical results are presented to illustrate the efficacy of this new method over some other popular choices for discretizing fractional derivatives
Finite element analysis of gradient coil deformation and vibration in NMR microscopy
Resolution degradation due to gradient coil deformation and vibration in NMR microscopy is investigated using finite element analysis. From the analysis, deformations due to the Lorentz force can be as large as 1-10 ÎĽm depending on the gradient strength and coil frame material. Thus, these deformations can be one of the major resolution limiting factors in NMR microscopy. Coil vibration, which depends on the input current waveform and resolution degradation due to time-variant deformation and time-invariant deformation are investigated by numerical simulations
Variation of proton flux profiles with the observer's latitude in simulated gradual SEP events
We study the variation of the shape of the proton intensity-time profiles in
simulated gradual Solar Energetic Particle (SEP) events with the relative
observer's position in space with respect to the main direction of propagation
of an interplanetary (IP) shock. Using a three-dimensional (3D)
magnetohydrodynamic (MHD) code to simulate such a shock, we determine the
evolution of the downstream-to-upstream ratios of the plasma variables at its
front. Under the assumption of an existing relation between the normalized
ratio in speed across the shock front and the injection rate of
shock-accelerated particles, we model the transport of the particles and we
obtain the proton flux profiles to be measured by a grid of 18 virtual
observers located at 0.4 and 1.0 AU, with different latitudes and longitudes
with respect to the shock nose. The differences among flux profiles are the
result of the way each observer establishes a magnetic connection with the
shock front, and we find that changes in the observer's latitude may result in
intensity changes of up to one order of magnitude at both radial distances
considered here. The peak intensity variation with the radial distance for the
pair of observers located at the same angular position is also derived. This is
the first time that the latitudinal dependence of the peak intensity with the
observer's heliocentric radial distance has been quantified within the
framework of gradual SEP event simulations.Comment: 20 pages, 6 Figures, 2 Table
Combinatorial models of rigidity and renormalization
We first introduce the percolation problems associated with the graph
theoretical concepts of -sparsity, and make contact with the physical
concepts of ordinary and rigidity percolation. We then devise a renormalization
transformation for -percolation problems, and investigate its domain of
validity. In particular, we show that it allows an exact solution of
-percolation problems on hierarchical graphs, for . We
introduce and solve by renormalization such a model, which has the interesting
feature of showing both ordinary percolation and rigidity percolation phase
transitions, depending on the values of the parameters.Comment: 22 pages, 6 figure
Involutive Categories and Monoids, with a GNS-correspondence
This paper develops the basics of the theory of involutive categories and
shows that such categories provide the natural setting in which to describe
involutive monoids. It is shown how categories of Eilenberg-Moore algebras of
involutive monads are involutive, with conjugation for modules and vector
spaces as special case. The core of the so-called Gelfand-Naimark-Segal (GNS)
construction is identified as a bijective correspondence between states on
involutive monoids and inner products. This correspondence exists in arbritrary
involutive categories
Centrality Measures in Spatial Networks of Urban Streets
We study centrality in urban street patterns of different world cities
represented as networks in geographical space. The results indicate that a
spatial analysis based on a set of four centrality indices allows an extended
visualization and characterization of the city structure. Planned and
self-organized cities clearly belong to two different universality classes. In
particular, self-organized cities exhibit scale-free properties similar to
those found in the degree distributions of non-spatial networks.Comment: 4 pages, 3 figure
On coalgebras with internal moves
In the first part of the paper we recall the coalgebraic approach to handling
the so-called invisible transitions that appear in different state-based
systems semantics. We claim that these transitions are always part of the unit
of a certain monad. Hence, coalgebras with internal moves are exactly
coalgebras over a monadic type. The rest of the paper is devoted to supporting
our claim by studying two important behavioural equivalences for state-based
systems with internal moves, namely: weak bisimulation and trace semantics.
We continue our research on weak bisimulations for coalgebras over order
enriched monads. The key notions used in this paper and proposed by us in our
previous work are the notions of an order saturation monad and a saturator. A
saturator operator can be intuitively understood as a reflexive, transitive
closure operator. There are two approaches towards defining saturators for
coalgebras with internal moves. Here, we give necessary conditions for them to
yield the same notion of weak bisimulation.
Finally, we propose a definition of trace semantics for coalgebras with
silent moves via a uniform fixed point operator. We compare strong and weak
bisimilation together with trace semantics for coalgebras with internal steps.Comment: Article: 23 pages, Appendix: 3 page
- …