Shift invariant preduals of ℓ₁(ℤ)

The Banach space ℓ<sub>1</sub>(ℤ) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ℓ<sub>1</sub>(ℤ) weak<sup>*</sup>-continuous. This is equivalent to making the natural convolution multiplication on ℓ<sub>1</sub>(ℤ) separately weak*-continuous and so turning ℓ<sub>1</sub>(ℤ) into a dual Banach algebra. We call such preduals <i>shift-invariant</i>. It is known that the only shift-invariant predual arising from the standard duality between C<sub>0</sub>(K) (for countable locally compact K) and ℓ<sub>1</sub>(ℤ) is c<sub>0</sub>(ℤ). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak<sup>*</sup>-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c<sub>0</sub>. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ℤ. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c<sub>0</sub>

Completely positive multipliers of quantum groups

We show that any completely positive multiplier of the convolution algebra of the dual of an operator algebraic quantum group \G (either a locally compact quantum group, or a quantum group coming from a modular or manageable multiplicative unitary) is induced in a canonical fashion by a unitary corepresentation of \G. It follows that there is an order bijection between the completely positive multipliers of L^1(\G) and the positive functionals on the universal quantum group C_0^u(\G). We provide a direct link between the Junge, Neufang, Ruan representation result and the representing element of a multiplier, and use this to show that their representation map is always weak$^*$-weak$^*$-continuous.Comment: 18 pages; major rewrit

Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers

We introduce a noncommutative analogue of the Fig\'a-Talamanca-Herz algebra $A_p(G)$ on the natural predual of the operator space $\frak{M}_{p,cb}$ of completely bounded Schur multipliers on Schatten space $S_p$. We determine the isometric Schur multipliers and prove that the space $\frak{M}_{p}$ of bounded Schur multipliers on Schatten space $S_p$ is the closure in the weak operator topology of the span of isometric multipliers.Comment: 24 pages; corrected typo

Fast algorithms for handling diagonal constraints in timed automata

A popular method for solving reachability in timed automata proceeds by enumerating reachable sets of valuations represented as zones. A na\"ive enumeration of zones does not terminate. Various termination mechanisms have been studied over the years. Coming up with efficient termination mechanisms has been remarkably more challenging when the automaton has diagonal constraints in guards. In this paper, we propose a new termination mechanism for timed automata with diagonal constraints based on a new simulation relation between zones. Experiments with an implementation of this simulation show significant gains over existing methods.Comment: Shorter version of this article to appear in CAV 201

Predicting clinical diagnosis in Huntington's disease: An imaging polymarker.

OBJECTIVE: Huntington's disease (HD) gene carriers can be identified before clinical diagnosis; however, statistical models for predicting when overt motor symptoms will manifest are too imprecise to be useful at the level of the individual. Perfecting this prediction is integral to the search for disease modifying therapies. This study aimed to identify an imaging marker capable of reliably predicting real-life clinical diagnosis in HD. METHOD: A multivariate machine learning approach was applied to resting-state and structural magnetic resonance imaging scans from 19 premanifest HD gene carriers (preHD, 8 of whom developed clinical disease in the 5 years postscanning) and 21 healthy controls. A classification model was developed using cross-group comparisons between preHD and controls, and within the preHD group in relation to "estimated" and "actual" proximity to disease onset. Imaging measures were modeled individually, and combined, and permutation modeling robustly tested classification accuracy. RESULTS: Classification performance for preHDs versus controls was greatest when all measures were combined. The resulting polymarker predicted converters with high accuracy, including those who were not expected to manifest in that time scale based on the currently adopted statistical models. INTERPRETATION: We propose that a holistic multivariate machine learning treatment of brain abnormalities in the premanifest phase can be used to accurately identify those patients within 5 years of developing motor features of HD, with implications for prognostication and preclinical trials. Ann Neurol 2018;83:532-543.SLM is funded by a National Institute for Health Research (NIHR) Translational Research Collaboration for Rare Diseases fellowship. This research has been funded/supported by the National Institute for Health Research Rare Diseases Translational Research Collaboration (NIHR RD-TRC). The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Health. RAB is funded by the NIHR Cambridge Biomedical Research Centre and the Cambridge University NHS Foundation Trust. RED is employed on an EC Marie-Curie CIG, awarded to AH, SJT, EJ and RS receive funding from a Wellcome Collaborative Award (200181/Z/15/Z

Parameter-Independent Strategies for pMDPs via POMDPs

Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition probabilities to account for stochastic uncertainties of the environment such as noise or input disturbances. We study pMDPs with reachability objectives where the parameter values are unknown and impossible to measure directly during execution, but there is a probability distribution known over the parameter values. We study for the first time computing parameter-independent strategies that are expectation optimal, i.e., optimize the expected reachability probability under the probability distribution over the parameters. We present an encoding of our problem to partially observable MDPs (POMDPs), i.e., a reduction of our problem to computing optimal strategies in POMDPs. We evaluate our method experimentally on several benchmarks: a motivating (repeated) learner model; a series of benchmarks of varying configurations of a robot moving on a grid; and a consensus protocol.Comment: Extended version of a QEST 2018 pape

The determinants of election to the United Nations Security Council

This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s11127-013-0096-4.The United Nations Security Council (UNSC) is the foremost international body responsible for the maintenance of international peace and security. Members vote on issues of global importance and consequently receive perks—election to the UNSC predicts, for instance, World Bank and IMF loans. But who gets elected to the UNSC? Addressing this question empirically is not straightforward as it requires a model that allows for discrete choices at the regional and international levels; the former nominates candidates while the latter ratifies them. Using an original multiple discrete choice model to analyze a dataset of 180 elections from 1970 to 2005, we find that UNSC election appears to derive from a compromise between the demands of populous countries to win election more frequently and a norm of giving each country its turn. We also find evidence that richer countries from the developing world win election more often, while involvement in warfare lowers election probability. By contrast, development aid does not predict election

Corticosterone Potentiation of Cocaine-Induced Reinstatement of Conditioned Place Preference in Mice is Mediated by Blockade of the Organic Cation Transporter 3

The mechanisms by which stressful life events increase the risk of relapse in recovering cocaine addicts are not well understood. We previously reported that stress, via elevated corticosterone, potentiates cocaine-primed reinstatement of cocaine seeking following self-administration in rats and that this potentiation appears to involve corticosterone-induced blockade of dopamine clearance via the organic cation transporter 3 (OCT3). In the present study, we use a conditioned place preference/reinstatement paradigm in mice to directly test the hypothesis that corticosterone potentiates cocaine-primed reinstatement by blockade of OCT3. Consistent with our findings following self-administration in rats, pretreatment of male C57/BL6 mice with corticosterone (using a dose that reproduced stress-level plasma concentrations) potentiated cocaine-primed reinstatement of extinguished cocaine-induced conditioned place preference. Corticosterone failed to re-establish extinguished preference alone but produced a leftward shift in the dose–response curve for cocaine-primed reinstatement. A similar potentiating effect was observed upon pretreatment of mice with the non-glucocorticoid OCT3 blocker, normetanephrine. To determine the role of OCT3 blockade in these effects, we examined the abilities of corticosterone and normetanephrine to potentiate cocaine-primed reinstatement in OCT3-deficient and wild-type mice. Conditioned place preference, extinction and reinstatement of extinguished preference in response to low-dose cocaine administration did not differ between genotypes. However, corticosterone and normetanephrine failed to potentiate cocaine-primed reinstatement in OCT3-deficient mice. Together, these data provide the first direct evidence that the interaction of corticosterone with OCT3 mediates corticosterone effects on drug-seeking behavior and establish OCT3 function as an important determinant of susceptibility to cocaine use