On the instabilities of the static, spherically symmetric SU(2) Einstein-Yang-Mills-Dilaton solitons and black holes

We prove that the number of odd parity instabilities of the n-th SU(2) Einstein-Yang-Mills-Dilaton soliton and black hole equals n.Comment: Added reference

Hudson's Theorem for finite-dimensional quantum systems

We show that, on a Hilbert space of odd dimension, the only pure states to possess a non-negative Wigner function are stabilizer states. The Clifford group is identified as the set of unitary operations which preserve positivity. The result can be seen as a discrete version of Hudson's Theorem. Hudson established that for continuous variable systems, the Wigner function of a pure state has no negative values if and only if the state is Gaussian. Turning to mixed states, it might be surmised that only convex combinations of stabilizer states give rise to non-negative Wigner distributions. We refute this conjecture by means of a counter-example. Further, we give an axiomatic characterization which completely fixes the definition of the Wigner function and compare two approaches to stabilizer states for Hilbert spaces of prime-power dimensions. In the course of the discussion, we derive explicit formulas for the number of stabilizer codes defined on such systems.Comment: 17 pages, 3 figures; References updated. Title changed to match published version. See also quant-ph/070200

A classification of primitive permutation groups with finite stabilizers

We classify all infinite primitive permutation groups possessing a finite point stabilizer, thus extending the seminal Aschbacher-O'Nan-Scott Theorem to all primitive permutation groups with finite point stabilizers.Comment: Accepted in J. Algebra. Various changes, some due to the author, some due to suggestions from readers and others due to the comments of anonymous referee

Vertex-primitive groups and graphs of order twice the product of two distinct odd primes

A non-Cayley number is an integer n for which there exists a vertex-transitive graph on n vertices which is not a Cayley graph. In this paper, we complete the determination of the non-Cayley numbers of the form 2pq, where p, q are distinct odd primes. Earlier work of Miller and the second author had dealt with all such numbers corresponding to vertex-transitive graphs admitting an imprimitive subgroup of automorphisms. This paper deals with the primitive case. First the primitive permutation groups of degree 2pq are classified. This depends on the finite simple group classification. Then each of these groups G is examined to determine whether there are any non-Cayley graphs which admit G as a vertex-primitive subgroup of automorphisms, and admit no imprimitive subgroups. The outcome is that 2pq is a non-Cayley number, where

Lie algebras and 3-transpositions

We describe a construction of an algebra over the field of order 2 starting from a conjugacy class of 3-transpositions in a group. In particular, we determine which simple Lie algebras arise by this construction. Among other things, this construction yields a natural embedding of the sporadic simple group \Fi{22} in the group $^2E_6(2)$.Comment: 23 page

Real-world heart rate norms in the Health eHeart study.

Emerging technology allows patients to measure and record their heart rate (HR) remotely by photoplethysmography (PPG) using smart devices like smartphones. However, the validity and expected distribution of such measurements are unclear, making it difficult for physicians to help patients interpret real-world, remote and on-demand HR measurements. Our goal was to validate HR-PPG, measured using a smartphone app, against HR-electrocardiogram (ECG) measurements and describe out-of-clinic, real-world, HR-PPG values according to age, demographics, body mass index, physical activity level, and disease. To validate the measurements, we obtained simultaneous HR-PPG and HR-ECG in 50 consecutive patients at our cardiology clinic. We then used data from participants enrolled in the Health eHeart cohort between 1 April 2014 and 30 April 2018 to derive real-world norms of HR-PPG according to demographics and medical conditions. HR-PPG and HR-ECG were highly correlated (Intraclass correlation = 0.90). A total of 66,788 Health eHeart Study participants contributed 3,144,332 HR-PPG measurements. The mean real-world HR was 79.1 bpm ± 14.5. The 95th percentile of real-world HR was ≤110 in individuals aged 18-45, ≤100 in those aged 45-60 and ≤95 bpm in individuals older than 60 years old. In multivariable linear regression, the number of medical conditions, female gender, increasing body mass index, and being Hispanic was associated with an increased HR, whereas increasing age was associated with a reduced HR. Our study provides the largest real-world norms for remotely obtained, real-world HR according to various strata and they may help physicians interpret and engage with patients presenting such data

Generators of simple Lie algebras in arbitrary characteristics

In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property, and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.Comment: 26 pages, final version, to appear in Math. Z. Main improvements and corrections in Section 4.