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54
Analysis of Functional MRI TimeSeries
 HUMAN BRAIN MAPPING
, 1994
"... A method for detecting significant and regionally specific correlations between sensory input and the brain's physiological response, as measured with functional magnetic resonance imaging (MRI), is presented in this paper. The method involves testing for correlations between sensory input and ..."
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Cited by 274 (10 self)
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A method for detecting significant and regionally specific correlations between sensory input and the brain's physiological response, as measured with functional magnetic resonance imaging (MRI), is presented in this paper. The method involves testing for correlations between sensory input and the hemodynamic response after convolving the sensory input with an estimate of the hernodynamic response function. This estimate is obtained without reference to any assumed input. To lend the approach statistical validity, it is brought into the framework of statistical parametric mapping by using a measure of crosscorrelations between sensory input and hemodynamic response that is valid in the presence of intrinsic autocorrelations. These autocorrelations are necessarily present, due to the hemodynamic response function or temporal point spread function.
PROBABILISTIC PREDICATE TRANSFORMERS
, 1995
"... Predicate transformers facilitate reasoning about imperative programs, including those exhibiting demonic nondeterministic choice. Probabilistic predicate transformers extend that facility to programs containing probabilistic choice, so that one can in principle determine not only whether a program ..."
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Cited by 136 (41 self)
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Predicate transformers facilitate reasoning about imperative programs, including those exhibiting demonic nondeterministic choice. Probabilistic predicate transformers extend that facility to programs containing probabilistic choice, so that one can in principle determine not only whether a program is guaranteed to establish a certain result, but also its probability of doing so. We bring together independent work of Claire Jones and Jifeng He, showing how their constructions can be made to correspond � from that link between a predicatebased and a relationbased view of probabilistic execution we are able to propose `probabilistic healthiness conditions', generalising those of Dijkstra for ordinary predicate transformers. The associated calculus seems suitable for exploring further the rigorous derivation of imperative probabilistic programs.
Proof Rules for Probabilistic Loops
 Proceedings of the BCSFACS 7th Refinement Workshop, Workshops in Computing
, 1996
"... Probabilistic predicate transformers provide a semantics for imperative programs containing both demonic and probabilistic nondeterminism. Like the (standard) predicate transformers popularised by Dijkstra, they model programs as functions from final results to the initial conditions sufficient to a ..."
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Cited by 41 (19 self)
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Probabilistic predicate transformers provide a semantics for imperative programs containing both demonic and probabilistic nondeterminism. Like the (standard) predicate transformers popularised by Dijkstra, they model programs as functions from final results to the initial conditions sufficient to achieve them. This paper presents practical proof rules, using the probabilistic transformers, for reasoning about iterations when probability is present. They are thoroughly illustrated by example: probabilistic binary chop, faulty factorial, the martingale gambling strategy and Herman's probabilistic selfstabilisation. Just as for traditional programs, weakestprecondition based proof rules for program derivation are an important step on the way to designing more general refinement techniques, or even a refinement calculus, for imperative probabilistic programming. 1 Introduction The standard predicate transformers described by Dijkstra [3] provide a model in which a program is a funct...
Demonic, Angelic and Unbounded Probabilistic Choices in Sequential Programs
 ACTA INFORMATICA
, 1998
"... Probabilistic predicate transformers extend standard predicate transformers by adding probabilistic choice to (transformers for) sequential programs. Demonic nondeterminism is retained. For finite state spaces, the basic theory is set out elsewhere [15], together with a statement of the probabilisti ..."
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Cited by 18 (8 self)
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Probabilistic predicate transformers extend standard predicate transformers by adding probabilistic choice to (transformers for) sequential programs. Demonic nondeterminism is retained. For finite state spaces, the basic theory is set out elsewhere [15], together with a statement of the probabilistic `healthiness conditions' that generalise the `positive conjunctivity' of ordinary predicate transformers. Here we extend the earlier results to infinite state spaces, and investigate the structure of the transformer space generally: as Back and von Wright [1] did for `standard' (nonprobabilistic) transformers, we nest deterministic, demonic and demonic/angelic transformers, showing how each can be constructed from the one before. In the end we thus find healthiness conditions for a system in which deterministic, demonic, probabilistic and angelic choices all coexist.
Statistical adjustment of signal censoring in gene expression experiments. Bioinformatics 19: 1055–1060
, 2003
"... Motivation: Numerical output of spotted microarrays displays censoring of pixel intensities at some software dependent threshold. This reduces the quality of gene expression data, because it seriously violates the linearity of expression with respect to signal intensity. Statistical methods based on ..."
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Cited by 18 (5 self)
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Motivation: Numerical output of spotted microarrays displays censoring of pixel intensities at some software dependent threshold. This reduces the quality of gene expression data, because it seriously violates the linearity of expression with respect to signal intensity. Statistical methods based on typically available spot summaries together with some parametric assumptions can suggest ways to correct for this defect. Results: Amaximum likelihood approach is suggested together with a sensible approximation to the joint density of the mean, median and variance—which are typically available to the biological enduser. The method ‘corrects ’ the gene expression values for pixel censoring. A byproduct of our approach is a comparison between several twoparameter models for pixel intensity values. It suggests that pixels separated by one or two other pixels can be considered independent draws from a Lognormal or a Gamma distribution. Availability: The R/SPlus code is available at
Results on the quantitative µcalculus qMµ
 ACM Transactions on Computational Logic
"... Abstract. The µcalculus is a powerful tool for specifying and verifying transition systems, including those with both demonic (universal) and angelic (existential) choice; its quantitative generalisation qMµ [17,29,9] extends that to probabilistic choice. We show here that for a finitestate system ..."
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Cited by 17 (4 self)
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Abstract. The µcalculus is a powerful tool for specifying and verifying transition systems, including those with both demonic (universal) and angelic (existential) choice; its quantitative generalisation qMµ [17,29,9] extends that to probabilistic choice. We show here that for a finitestate system the logical interpretation of qMµ, via fixedpoints in a domain of realvalued functions into [0,1], is equivalent to an operational interpretation given as a turnbased gambling game between two players. The equivalence sets qMµ on a par with the standard µcalculus, in that it too can benefit from a solid interface linking the logical and operational frameworks. The logical interpretation provides direct access to axioms, laws and metatheorems. The operational, game based interpretation aids the intuition and continues in the more general context to provide a surprisingly practical specification tool — meeting for example Vardi’s challenge to “figure out the meaning of AF AX p ” as a branchingtime formula. A corollary of our proofs is an extension of Everett’s singlynested games result in the finite turnbased case: we prove welldefinedness of the minimax value, and existence of fixed memoriless strategies, for all qMµ games/formulae, of arbitrary (including alternating) nesting structure. 1
An expectationbased model for probabilistic temporal logic
 Logic Journal of the IGPL
, 1999
"... We interpret the modal µcalculus over a new model [10], to give a temporal logic suitable for systems exhibiting both probabilistic and demonic nondeterminism. The logical formulae are realvalued, and the statements are not limited to properties that hold with probability 1. In achieving that conc ..."
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Cited by 16 (11 self)
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We interpret the modal µcalculus over a new model [10], to give a temporal logic suitable for systems exhibiting both probabilistic and demonic nondeterminism. The logical formulae are realvalued, and the statements are not limited to properties that hold with probability 1. In achieving that conceptual step, our technical contribution is to determine the correct quantitative generalisation of the Boolean operators: one that allows many of the standard Booleanbased temporal laws to carry over the reals with little or no structural alteration, even for properties that hold with probability strictly between 0 and 1. The generalisation is not obvious, but is dictated by our discovery elsewhere of the algebraic property that characterises the nexttime operator over the new model: it is arithmetic ‘sublinearity ’ [20, Fig.4 p.342], which replaces the Boolean conjunctivity that characterises nexttime in a modal algebra. We confirm by example that the new modal laws can be used for quantitative reasoning about probabilistic/demonic behaviour. The random walk is treated using only those laws and realnumber arithmetic: arguing from precise numeric premises, more specific than simply ‘with some nonzero probability’, we reach numeric conclusions that are not simply ‘with probability 1’.
Random quantum circuits are approximate 2designs
, 2008
"... Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haardistributed unitary. However, this requires exponential time. We show that random circuits of only polynomial length will approxima ..."
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Cited by 14 (3 self)
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Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haardistributed unitary. However, this requires exponential time. We show that random circuits of only polynomial length will approximate the first and second moments of the Haar distribution, thus forming approximate 1 and 2designs. Previous constructions required longer circuits and worked only for specific gate sets. As a corollary of our main result, we also improve previous bounds on the convergence rate of random walks on the Clifford group. 1
Ants and Agents: a Process Algebra Approach to Modelling Ant Colony Behaviour
 Bulletin of Mathematical Biology
, 2001
"... this paper we show how process algebras can be usefully applied to understanding social insect biology, in particular to studying the relationship between algorithmic behaviour of individual insects and the dynamical behaviour of their colony. We argue that process algebras provide a useful formalis ..."
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Cited by 13 (2 self)
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this paper we show how process algebras can be usefully applied to understanding social insect biology, in particular to studying the relationship between algorithmic behaviour of individual insects and the dynamical behaviour of their colony. We argue that process algebras provide a useful formalism for understanding this relationship, since they combine computer simulation, Markov chain analysis and meanfield methods of analysis. Indeed, process algebras can provide a framework for relating these three methods of analysis to each other and to experiments. We illustrate our approach with a series of graded examples of modelling activity in ant colonies. c # 2001 Society for Mathematical Biology # Author to whom correspondence should be addressed. Email: sumpter@maths.ox.ac.uk 00928240/01/050951 + 30 $35.00/0 c # 2001 Society for Mathematical Biology 952 D. J. T. Sumpter et al
Partial Correctness for Probabilistic Demonic Programs
 THEORETICAL COMPUTER SCIENCE
, 1997
"... Recent work in sequential program semantics has produced both an operational [4] and an axiomatic [13, 17] treatment of total correctness for probabilistic demonic programs, extending Kozen's original work [9, 10] that did not include demonic nondeterminism. For practical applications however ( ..."
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Cited by 12 (2 self)
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Recent work in sequential program semantics has produced both an operational [4] and an axiomatic [13, 17] treatment of total correctness for probabilistic demonic programs, extending Kozen's original work [9, 10] that did not include demonic nondeterminism. For practical applications however (eg. combining loop invariants with termination constraints) it is important to retain the traditional distinction between partial and total correctness. Jones [6] defines probabilistic partial correctness for probabilistic, but again not demonic programs. In this paper we combine all the above, giving an operational and axiomatic framework for both partial and total correctness of probabilistic and demonic sequential programs; among other things that provides the theory to support practical reasoning about probabilistic demonic loops [11].