Preduals of semigroup algebras

For a locally compact group G, the measure convolution algebra M(G) carries a natural coproduct. In previous work, we showed that the canonical predual C 0(G) of M(G) is the unique predual which makes both the product and the coproduct on M(G) weak*-continuous. Given a discrete semigroup S, the convolution algebra ℓ 1(S) also carries a coproduct. In this paper we examine preduals for ℓ 1(S) making both the product and the coproduct weak*-continuous. Under certain conditions on S, we show that ℓ 1(S) has a unique such predual. Such S include the free semigroup on finitely many generators. In general, however, this need not be the case even for quite simple semigroups and we construct uncountably many such preduals on ℓ 1(S) when S is either ℤ+×ℤ or (ℕ,⋅)

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>

White matter tract integrity in treatment-resistant gambling disorder

Background Gambling disorder is a relatively common psychiatric disorder recently re-classified within the DSM-5 under the category of ‘substance-related and addictive disorders’. Aims To compare white matter integrity in patients with gambling disorder with healthy controls; to explore relationships between white matter integrity and disease severity in gambling disorder. Method In total, 16 participants with treatment-resistant gambling disorder and 15 healthy controls underwent magnetic resonance imaging (MRI). White matter integrity was analysed using tract-based spatial statistics. Results Gambling disorder was associated with reduced fractional anisotropy in the corpus callosum and superior longitudinal fasciculus. Fractional anisotropy in distributed white matter tracts elsewhere correlated positively with disease severity. Conclusions Reduced corpus callosum fractional anisotropy is suggestive of disorganised/damaged tracts in patients with gambling disorder, and this may represent a trait/vulnerability marker for the disorder. Future research should explore these measures in a larger sample, ideally incorporating a range of imaging markers (for example functional MRI) and enrolling unaffected first-degree relatives of patients.This research was supported by a grant from the National Center for Responsible Gaming to Dr. Grant, and by a grant from the Academy of Medical Sciences to Dr. Chamberlain (UK). Dr. Grant has received research grants from NIMH, National Center for Responsible Gaming, and Forest and Roche Pharmaceuticals Dr. Grant receives yearly compensation from Springer Publishing for acting as Editor-in-Chief of the Journal of Gambling Studies and has received royalties from Oxford University Press, American Psychiatric Publishing, Inc., Norton Press, and McGraw Hill. Dr. Chamberlain consults for Cambridge Cognition. Mr. Odlaug has received a research grant from the Trichotillomania Learning Center, consults for H. Lundbeck A/S, and has received royalties from Oxford University Press. Mr. Leppink and Ms. Derbyshire report no conflicts of interest.This is the author accepted manuscript. The final version is available from the Royal College of Psychiatrists via http://dx.doi.org/10.1192/bjp.bp.115.16550

White matter tract integrity in treatment-resistant gambling disorder.

BACKGROUND: Gambling disorder is a relatively common psychiatric disorder recently re-classified within the DSM-5 under the category of 'substance-related and addictive disorders'. AIMS: To compare white matter integrity in patients with gambling disorder with healthy controls; to explore relationships between white matter integrity and disease severity in gambling disorder. METHOD: In total, 16 participants with treatment-resistant gambling disorder and 15 healthy controls underwent magnetic resonance imaging (MRI). White matter integrity was analysed using tract-based spatial statistics. RESULTS: Gambling disorder was associated with reduced fractional anisotropy in the corpus callosum and superior longitudinal fasciculus. Fractional anisotropy in distributed white matter tracts elsewhere correlated positively with disease severity. CONCLUSIONS: Reduced corpus callosum fractional anisotropy is suggestive of disorganised/damaged tracts in patients with gambling disorder, and this may represent a trait/vulnerability marker for the disorder. Future research should explore these measures in a larger sample, ideally incorporating a range of imaging markers (for example functional MRI) and enrolling unaffected first-degree relatives of patients.This research was supported by a grant from the National Center for Responsible Gaming to Dr. Grant, and by a grant from the Academy of Medical Sciences to Dr. Chamberlain (UK). Dr. Grant has received research grants from NIMH, National Center for Responsible Gaming, and Forest and Roche Pharmaceuticals Dr. Grant receives yearly compensation from Springer Publishing for acting as Editor-in-Chief of the Journal of Gambling Studies and has received royalties from Oxford University Press, American Psychiatric Publishing, Inc., Norton Press, and McGraw Hill. Dr. Chamberlain consults for Cambridge Cognition. Mr. Odlaug has received a research grant from the Trichotillomania Learning Center, consults for H. Lundbeck A/S, and has received royalties from Oxford University Press. Mr. Leppink and Ms. Derbyshire report no conflicts of interest.This is the author accepted manuscript. The final version is available from the Royal College of Psychiatrists via http://dx.doi.org/10.1192/bjp.bp.115.16550

LTL Parameter Synthesis of Parametric Timed Automata

The parameter synthesis problem for parametric timed automata is undecidable in general even for very simple reachability properties. In this paper we introduce restrictions on parameter valuations under which the parameter synthesis problem is decidable for LTL properties. The investigated bounded integer parameter synthesis problem could be solved using an explicit enumeration of all possible parameter valuations. We propose an alternative symbolic zone-based method for this problem which results in a faster computation. Our technique extends the ideas of the automata-based approach to LTL model checking of timed automata. To justify the usefulness of our approach, we provide experimental evaluation and compare our method with explicit enumeration technique.Comment: 23 pages, extended versio

Antidepressant-like drug effects in juvenile and adolescent mice in the tail suspension test: relationship with hippocampal serotonin and norepinephrine transporter expression and function

Nathan C. Mitchell, Georgianna G. Gould, Corey M. Smolik, Wouter Koek and Lynette C. Daw

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

Spontaneous alloying in binary metal microclusters - A molecular dynamics study -

Microcanonical molecular dynamics study of the spontaneous alloying(SA), which is a manifestation of fast atomic diffusion in a nano-sized metal cluster, is done in terms of a simple two dimensional binary Morse model. Important features observed by Yasuda and Mori are well reproduced in our simulation. The temperature dependence and size dependence of the SA phenomena are extensively explored by examining long time dynamics. The dominant role of negative heat of solution in completing the SA is also discussed. We point out that a presence of melting surface induces the diffusion of core atoms even if they are solid-like. In other words, the {\it surface melting} at substantially low temperature plays a key role in attaining the SA.Comment: 15 pages, 12 fgures, Submitted to Phys.Rev.