449 research outputs found
A categorical framework for the quantum harmonic oscillator
This paper describes how the structure of the state space of the quantum
harmonic oscillator can be described by an adjunction of categories, that
encodes the raising and lowering operators into a commutative comonoid. The
formulation is an entirely general one in which Hilbert spaces play no special
role. Generalised coherent states arise through the hom-set isomorphisms
defining the adjunction, and we prove that they are eigenstates of the lowering
operators. Surprisingly, generalised exponentials also emerge naturally in this
setting, and we demonstrate that coherent states are produced by the
exponential of a raising morphism acting on the zero-particle state. Finally,
we examine all of these constructions in a suitable category of Hilbert spaces,
and find that they reproduce the conventional mathematical structures.Comment: 44 pages, many figure
Predicate Transformers and Linear Logic, yet another denotational model
International audienceIn the refinement calculus, monotonic predicate transformers are used to model specifications for (imperative) programs. Together with a natural notion of simulation, they form a category enjoying many algebraic properties. We build on this structure to make predicate transformers into a de notational model of full linear logic: all the logical constructions have a natural interpretation in terms of predicate transformers (i.e. in terms of specifications). We then interpret proofs of a formula by a safety property for the corresponding specification
Estimation of the length of interactions in arena game semantics
We estimate the maximal length of interactions between strategies in HO/N
game semantics, in the spirit of the work by Schwichtenberg and Beckmann for
the length of reduction in simply typed lambdacalculus. Because of the
operational content of game semantics, the bounds presented here also apply to
head linear reduction on lambda-terms and to the execution of programs by
abstract machines (PAM/KAM), including in presence of computational effects
such as non-determinism or ground type references. The proof proceeds by
extracting from the games model a combinatorial rewriting rule on trees of
natural numbers, which can then be analyzed independently of game semantics or
lambda-calculus.Comment: Foundations of Software Science and Computational Structures 14th
International Conference, FOSSACS 2011, Saarbr\"ucken : Germany (2011
Generating reversible circuits from higher-order functional programs
Boolean reversible circuits are boolean circuits made of reversible
elementary gates. Despite their constrained form, they can simulate any boolean
function. The synthesis and validation of a reversible circuit simulating a
given function is a difficult problem. In 1973, Bennett proposed to generate
reversible circuits from traces of execution of Turing machines. In this paper,
we propose a novel presentation of this approach, adapted to higher-order
programs. Starting with a PCF-like language, we use a monadic representation of
the trace of execution to turn a regular boolean program into a
circuit-generating code. We show that a circuit traced out of a program
computes the same boolean function as the original program. This technique has
been successfully applied to generate large oracles with the quantum
programming language Quipper.Comment: 21 pages. A shorter preprint has been accepted for publication in the
Proceedings of Reversible Computation 2016. The final publication is
available at http://link.springer.co
Subsystems of a finite quantum system and Bell-like inequalities
YesThe set of subsystems Sigma(m) of a finite quantum system Sigma(n) with variables in Z(n) together with logical connectives, is a Heyting algebra. The probabilities tau(m vertical bar rho(n)) Tr vertical bar B(m)rho(n)] (where B(m) is the projector to Sigma(m)) are compatible with associativity of the join in the Heyting algebra, only if the variables belong to the same chain. Consequently, contextuality in the present formalism, has the chains as contexts. Various Bell-like inequalities are discussed. They are violated, and this proves that quantum mechanics is a contextual theory
Findings from the SASA! Study: a cluster randomized controlled trial to assess the impact of a community mobilization intervention to prevent violence against women and reduce HIV risk in Kampala, Uganda
Background
Intimate partner violence (IPV) and HIV are important and interconnected public health concerns. While it is recognized that they share common social drivers, there is limited evidence surrounding the potential of community interventions to reduce violence and HIV risk at the community level. The SASA! study assessed the community-level impact of SASA!, a community mobilization intervention to prevent violence and reduce HIV-risk behaviors.
Methods
From 2007 to 2012 a pair-matched cluster randomized controlled trial (CRT) was conducted in eight communities (four intervention and four control) in Kampala, Uganda. Cross-sectional surveys of a random sample of community members, 18- to 49-years old, were undertaken at baseline (nâ=â1,583) and four years post intervention implementation (nâ=â2,532). Six violence and HIV-related primary outcomes were defined a priori. An adjusted cluster-level intention-to-treat analysis compared outcomes in intervention and control communities at follow-up.
Results
The intervention was associated with significantly lower social acceptance of IPV among women (adjusted risk ratio 0.54, 95% confidence interval (CI) 0.38 to 0.79) and lower acceptance among men (0.13, 95% CI 0.01 to 1.15); significantly greater acceptance that a woman can refuse sex among women (1.28, 95% CI 1.07 to 1.52) and men (1.31, 95% CI 1.00 to 1.70); 52% lower past year experience of physical IPV among women (0.48, 95% CI 0.16 to 1.39); and lower levels of past year experience of sexual IPV (0.76, 95% CI 0.33 to 1.72). Women experiencing violence in intervention communities were more likely to receive supportive community responses. Reported past year sexual concurrency by men was significantly lower in intervention compared to control communities (0.57, 95% CI 0.36 to 0.91).
Conclusions
This is the first CRT in sub-Saharan Africa to assess the community impact of a mobilization program on the social acceptability of IPV, the past year prevalence of IPV and levels of sexual concurrency. SASA! achieved important community impacts, and is now being delivered in control communities and replicated in 15 countries
Migration Planning Among Female Prospective Labour Migrants from Nepal: A Comparison of First-Time and Repeat-Migrants
As international female labour migration has increased, so too have efforts to prevent the exploitation of labour migrants. However, evidence to underpin prevention efforts remains limited, with little known about labour migrantsâ migration planning processes. Using data from a survey of female prospective labour migrants from Nepal, this article compares socioâdemographics and migrationâplanning processes between firstâtime and repeat-migrants. We identified several factors which might increase repeatâmigrantsâ vulnerability to exploitation during the migration process, or obstruct their engagement in preâmigration interventions: more rapid migration planning than firstâtime migrants; lower involvement in community groups; and a perception that they already have the knowledge they need. Only oneâthird of repeatâmigrants planned to go to the same destination and 42 per cent to work in the same sector as previously. With repeatâmigration a common livelihoods strategy, it is crucial that interventions are guided by evidence on the needs of both firstâtimeâ and repeatâmigrants
On Linear Information Systems
Scott's information systems provide a categorically equivalent, intensional
description of Scott domains and continuous functions. Following a well
established pattern in denotational semantics, we define a linear version of
information systems, providing a model of intuitionistic linear logic (a
new-Seely category), with a "set-theoretic" interpretation of exponentials that
recovers Scott continuous functions via the co-Kleisli construction. From a
domain theoretic point of view, linear information systems are equivalent to
prime algebraic Scott domains, which in turn generalize prime algebraic
lattices, already known to provide a model of classical linear logic
Observed communication semantics for classical processes
Classical Linear Logic (CLL) has long inspired readings of its proofs as communicating processes. Wadler's CP calculus is one of these readings. Wadler gave CP an operational semantics by selecting a subset of the cut-elimination rules of CLL to use as reduction rules. This semantics has an appealing close connection to the logic, but does not resolve the status of the other cut-elimination rules, and does not admit an obvious notion of observational equivalence. We propose a new operational semantics for CP based on the idea of observing communication, and use this semantics to define an intuitively reasonable notion of observational equivalence. To reason about observational equivalence, we use the standard relational denotational semantics of CLL. We show that this denotational semantics is adequate for our operational semantics. This allows us to deduce that, for instance, all the cut-elimination rules of CLL are observational equivalences
Report on the Standardization Project ``Formal Methods in Conformance Testing''
This paper presents the latest developments in the âFormal Methods in Conformance
Testingâ (FMCT) project of ISO and ITUâT. The project has been initiated to study
the role of formal description techniques in the conformance testing process. The goal
is to develop a standard that defines the meaning of conformance in the context of formal
description techniques. We give an account of the current status of FMCT in the
standardization process as well as an overview of the technical status of the proposed
standard. Moreover, we indicate some of its strong and weak points, and we give some
directions for future work on FMCT
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