Black holes admitting a Freudenthal dual

The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm Delta(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the requirement that \tilde{x} be integer restricts us to the subset of black holes for which Delta(x) is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete U-duality invariants are Freudenthal invariant. Similarly, the quantised charges A of five dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest order entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a perfect cube, for which A**=A and which leaves N(A) invariant. The two dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde

Body Mass Index's influence on arterial hypertension in Type 1 diabetes - A brief report from IMI-SOPHIA study

Information on BMI and risk of developing hypertension in type 1 diabetes (T1D) is scarce, and it comes mostly from cross-sectional analyses. This study underscores a risk of developing hypertension in T1D individuals with high BMI, and this risk appears to be higher than in those with type 2 diabetes.</p

Body Mass Index's influence on arterial hypertension in Type 1 diabetes - A brief report from IMI-SOPHIA study

Information on BMI and risk of developing hypertension in type 1 diabetes (T1D) is scarce, and it comes mostly from cross-sectional analyses. This study underscores a risk of developing hypertension in T1D individuals with high BMI, and this risk appears to be higher than in those with type 2 diabetes.</p

High intensity exercise as a dishabituating stimulus restores counterregulatory responses in recurrently hypoglycemic rodents

Hypoglycemia is a major adverse effect of insulin therapy for people with type 1 diabetes (T1D). Profound defects in the normal counterregulatory response to hypoglycemia explain the frequency of hypoglycemia occurrence in T1D. Defective counterregulation results to a large extent from prior exposure to hypoglycemia per se, leading to a condition called impaired awareness of hypoglycemia (IAH), the cause of which is unknown. In the current study, we investigate the hypothesis that IAH develops through a special type of adaptive memory referred to as habituation. To test this hypothesis, we used a novel intense stimulus (high-intensity exercise) to demonstrate two classic features of a habituated response, namely dishabituation and response recovery. We demonstrate that after recurrent hypoglycemia the introduction of a novel dishabituating stimulus (a single burst of high-intensity exercise) in male Sprague-Dawley rats restores the defective hypoglycemia counterregulatory response. In addition, the rats showed an enhanced response to the novel stimulus (response recovery). We make the further observation using proteomic analysis of hypothalamic extracts that high-intensity exercise in recurrently hypoglycemic rats increases levels of a number of proteins linked with brain-derived neurotrophic factor signaling. These findings may lead to novel therapeutic approaches for individuals with T1D and IAH.</jats:p

Nrf2-mediated neuroprotection response to recurrent hypoglycemia is insufficient to prevent cognitive impairment in a rodent model of type 1 diabetes

It remains uncertain whether recurrent nonsevere hypoglycemia (Hypo) results in long-term cognitive impairment in type 1 diabetes (T1D). This study tested the hypothesis that specifically in the T1D state, Hypo leads to cognitive impairment via a pathological response to oxidative stress. Wild-type (Control) and nuclear factor–erythroid 2 p45–related factor 2 (Nrf2) null mice were studied. Eight groups of mice (Control and Nrf2−/− ± T1D and ± Hypo) were subject to recurrent, twice-weekly, insulin or saline injections over 4 weeks, after which cognitive function was assessed and brain tissue analyzed. Recurrent moderate hypoglycemia in T1D, but not Control, mice significantly impaired cognitive performance, and this was associated with hippocampal oxidative damage and inflammation despite an enhanced expression of Nrf2 and its target genes Hmox1 and Nqo1. In Nrf2−/− mice, both T1D and Hypo independently resulted in impaired cognitive performance, and this was associated with oxidative cell damage and marked inflammation. Together, these data suggest that Hypo induces an Nrf2-dependent antioxidant response in the hippocampus, which counteracts oxidative damage. However, in T1D, this neuroprotective mechanism is insufficient to prevent neuronal oxidative damage, resulting in chronic deficits in working and long-term memory.</jats:p

Three fermions with six single particle states can be entangled in two inequivalent ways

Using a generalization of Cayley's hyperdeterminant as a new measure of tripartite fermionic entanglement we obtain the SLOCC classification of three-fermion systems with six single particle states. A special subclass of such three-fermion systems is shown to have the same properties as the well-known three-qubit ones. Our results can be presented in a unified way using Freudenthal triple systems based on cubic Jordan algebras. For systems with an arbitrary number of fermions and single particle states we propose the Pl\"ucker relations as a sufficient and necessary condition of separability.Comment: 23 pages LATE

Observations on Integral and Continuous U-duality Orbits in N=8 Supergravity

One would often like to know when two a priori distinct extremal black p-brane solutions are in fact U-duality related. In the classical supergravity limit the answer for a large class of theories has been known for some time. However, in the full quantum theory the U-duality group is broken to a discrete subgroup and the question of U-duality orbits in this case is a nuanced matter. In the present work we address this issue in the context of N=8 supergravity in four, five and six dimensions. The purpose of this note is to present and clarify what is currently known about these discrete orbits while at the same time filling in some of the details not yet appearing in the literature. To this end we exploit the mathematical framework of integral Jordan algebras and Freudenthal triple systems. The charge vector of the dyonic black string in D=6 is SO(5,5;Z) related to a two-charge reduced canonical form uniquely specified by a set of two arithmetic U-duality invariants. Similarly, the black hole (string) charge vectors in D=5 are E_{6(6)}(Z) equivalent to a three-charge canonical form, again uniquely fixed by a set of three arithmetic U-duality invariants. The situation in four dimensions is less clear: while black holes preserving more than 1/8 of the supersymmetries may be fully classified by known arithmetic E_{7(7)}(Z) invariants, 1/8-BPS and non-BPS black holes yield increasingly subtle orbit structures, which remain to be properly understood. However, for the very special subclass of projective black holes a complete classification is known. All projective black holes are E_{7(7)}(Z) related to a four or five charge canonical form determined uniquely by the set of known arithmetic U-duality invariants. Moreover, E_{7(7)}(Z) acts transitively on the charge vectors of black holes with a given leading-order entropy.Comment: 43 pages, 8 tables; minor corrections, references added; version to appear in Class. Quantum Gra