9,233 research outputs found
Probabilistic Methodology and Techniques for Artefact Conception and Development
The purpose of this paper is to make a state of the art on probabilistic methodology and techniques for artefact conception and development. It is the 8th deliverable of the BIBA (Bayesian Inspired Brain and Artefacts) project. We first present the incompletness problem as the central difficulty that both living creatures and artefacts have to face: how can they perceive, infer, decide and act efficiently with incomplete and uncertain knowledge?. We then introduce a generic probabilistic formalism called Bayesian Programming. This formalism is then used to review the main probabilistic methodology
and techniques. This review is organized in 3 parts: first the probabilistic models from Bayesian networks to Kalman filters and from sensor fusion to CAD systems, second the inference techniques and finally the learning and model acquisition and comparison methodologies. We conclude with the perspectives of the BIBA project as they rise from this state of the art
Bayesian robot Programming
We propose a new method to program robots based on Bayesian inference and learning. The capacities of this programming method are demonstrated through a succession of increasingly complex experiments. Starting from the learning of simple reactive behaviors, we present instances of behavior combinations, sensor fusion, hierarchical behavior composition, situation recognition and temporal sequencing. This series of experiments comprises the steps in the incremental development of a complex robot program. The advantages and drawbacks of this approach are discussed along with these different experiments and summed up as a conclusion. These different robotics programs may be seen as an illustration of probabilistic programming applicable whenever one must deal with problems based on uncertain or incomplete knowledge. The scope of possible applications is obviously much broader than robotics
An Explicit Framework for Interaction Nets
Interaction nets are a graphical formalism inspired by Linear Logic
proof-nets often used for studying higher order rewriting e.g. \Beta-reduction.
Traditional presentations of interaction nets are based on graph theory and
rely on elementary properties of graph theory. We give here a more explicit
presentation based on notions borrowed from Girard's Geometry of Interaction:
interaction nets are presented as partial permutations and a composition of
nets, the gluing, is derived from the execution formula. We then define
contexts and reduction as the context closure of rules. We prove strong
confluence of the reduction within our framework and show how interaction nets
can be viewed as the quotient of some generalized proof-nets
Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
We use hexagonalization to compute four-point correlation functions of long
BPS operators with special R-charge polarizations. We perform the computation
at weak coupling and show that at any loop order our correlators can be
expressed in terms of single-valued polylogarithms with uniform maximal
transcendentality. As a check of our results we extract nine-loop OPE data and
compare it against sum rules of (squared) structures constants of non-protected
exchanged operators described by hundreds of Bethe solutions.Comment: 39 pages + appendices, 19 figure
Causal flow preserving optimisation of quantum circuits in the ZX-calculus
Optimising quantum circuits to minimise resource usage is crucial, especially
with near-term hardware limited by quantum volume. This paper introduces an
optimisation algorithm aiming to minimise non-Clifford gate count and two-qubit
gate count by building on ZX-calculus-based strategies. By translating a
circuit into a ZX-diagram it can be simplified before being extracted back into
a circuit. We assert that simplifications preserve a graph-theoretic property
called causal flow. This has the advantage that qubit lines are well defined
throughout, permitting a trivial extraction procedure and in turn enabling the
calculation of an individual transformation's impact on the resulting circuit.
A general procedure for a decision strategy is introduced, inspired by an
existing heuristic based method. Both phase teleportation and the neighbour
unfusion rule are generalised. In particular, allowing unfusion of multiple
neighbours is shown to lead to significant improvements in optimisation. When
run on a set of benchmark circuits, the algorithm developed reduces the
two-qubit gate count by an average of 19.8%, beating both the previous best
ZX-based strategy (14.6%) and non-ZX strategy (18.5%) at the time of
publication. This lays a foundation for multiple avenues of improvement. A
particularly effective strategy for optimising QFT circuits is also noted,
resulting in exactly one two-qubit gate per non-Clifford gate.Comment: 20 pages, 7 figure
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