One-and-a-half quantum de Finetti theorems

We prove a new kind of quantum de Finetti theorem for representations of the unitary group U(d). Consider a pure state that lies in the irreducible representation U_{mu+nu} for Young diagrams mu and nu. U_{mu+nu} is contained in the tensor product of U_mu and U_nu; let xi be the state obtained by tracing out U_nu. We show that xi is close to a convex combination of states Uv, where U is in U(d) and v is the highest weight vector in U_mu. When U_{mu+nu} is the symmetric representation, this yields the conventional quantum de Finetti theorem for symmetric states, and our method of proof gives near-optimal bounds for the approximation of xi by a convex combination of product states. For the class of symmetric Werner states, we give a second de Finetti-style theorem (our 'half' theorem); the de Finetti-approximation in this case takes a particularly simple form, involving only product states with a fixed spectrum. Our proof uses purely group theoretic methods, and makes a link with the shifted Schur functions. It also provides some useful examples, and gives some insight into the structure of the set of convex combinations of product states.Comment: 14 pages, 3 figures, v4: minor additions (including figures), published versio

ENIGMA and global neuroscience: A decade of large-scale studies of the brain in health and disease across more than 40 countries

This review summarizes the last decade of work by the ENIGMA (Enhancing NeuroImaging Genetics through Meta Analysis) Consortium, a global alliance of over 1400 scientists across 43 countries, studying the human brain in health and disease. Building on large-scale genetic studies that discovered the first robustly replicated genetic loci associated with brain metrics, ENIGMA has diversified into over 50 working groups (WGs), pooling worldwide data and expertise to answer fundamental questions in neuroscience, psychiatry, neurology, and genetics. Most ENIGMA WGs focus on specific psychiatric and neurological conditions, other WGs study normal variation due to sex and gender differences, or development and aging; still other WGs develop methodological pipelines and tools to facilitate harmonized analyses of "big data" (i.e., genetic and epigenetic data, multimodal MRI, and electroencephalography data). These international efforts have yielded the largest neuroimaging studies to date in schizophrenia, bipolar disorder, major depressive disorder, post-traumatic stress disorder, substance use disorders, obsessive-compulsive disorder, attention-deficit/hyperactivity disorder, autism spectrum disorders, epilepsy, and 22q11.2 deletion syndrome. More recent ENIGMA WGs have formed to study anxiety disorders, suicidal thoughts and behavior, sleep and insomnia, eating disorders, irritability, brain injury, antisocial personality and conduct disorder, and dissociative identity disorder. Here, we summarize the first decade of ENIGMA's activities and ongoing projects, and describe the successes and challenges encountered along the way. We highlight the advantages of collaborative large-scale coordinated data analyses for testing reproducibility and robustness of findings, offering the opportunity to identify brain systems involved in clinical syndromes across diverse samples and associated genetic, environmental, demographic, cognitive, and psychosocial factors

Antiretroviral therapy with or without protease inhibitors impairs postprandial TAG hydrolysis in HIV-infected men

Mechanisms underlying the lipodystrophy syndrome associated with antiretroviral therapy (ART) for HIV infection are not completely understood. We investigated the effect of ART on blood lipid concentrations in the fasting state and after consumption of a meal containing [1-13C]palmitic acid in HIV-positive men receiving nucleoside reverse transcriptase inhibitors (NRTI, n 7), NRTI combined with protease inhibitors (PI; NRTIPI, n 6), in HIV-positive but therapy-naïve men (noART, n 5) and in HIV-seronegative men (controls, n 6). HIV-positive subjects had higher fasting TAG concentrations and resting energy expenditure than controls. Subjects receiving NRTIPI therapy had higher fasting NEFA concentrations than the other groups. There were no significant differences in postprandial lipid metabolism between noART subjects and controls. NRTI therapy impaired hydrolysis of meal-derived TAG, most evidently when combined with PI (the NRTIPI group). Accumulation of 13C-label in the NEFA fraction was not different between groups. In the NRTIPI group, fasting and postprandial NEFA concentrations were significantly higher than other groups. Postprandial glucose and insulin responses in HIV-positive subjects did not differ from controls. These findings suggest that ART dyslipidaemia is associated with impaired postprandial TAG clearance, which is exacerbated by NRTIPI therapy. If dyslipidaemia is to be minimised in ART, the specific adverse effects of particular combinations during the fed state should be considered

'She possessed her own fortune': Women investors from the late nineteenth century to the early twentieth century

There is a growing literature on the history of investment in Britain. However, the role played by women as investors has been almost wholly ignored. This paper argues that women were an important class of stock market investors and produces empirical evidence, most notably share registers, to show that women engaged in a number of different types of investment, and were important in both public and private companies as long-term holders of securities in the nineteenth and early twentieth centuries. The article concludes by suggesting the impact of these findings on our understanding of women's financial position and of their role in corporate governance