Groups whose degree graph has three independent vertices

Let G be a finite group, and let cd(G) denote the set of degrees of the irreducible complex characters of G. This paper is a contribution to the study of the degree graph of G, that is, the prime graph built on the set cd(G). Namely, we characterize finite groups whose degree graph has three independent vertices (i.e., three vertices that are pairwise non-adjacent). Our result turns out to be a generalization of several previously-known theorems concerning the structure of the degree graph

On the character degree graph of solvable groups

Let G be a finite solvable group, and let 06(G) denote the prime graph built on the set of degrees of the irreducible complex characters of G. A fundamental result by P. P. P\ue1lfy asserts that the complement 06(G) of the graph 06(G) does not contain any cycle of length 3. In this paper we generalize P\ue1lfy\u2019s result, showing that 06(G) does not contain any cycle of odd length, whence it is a bipartite graph. As an immediate consequence, the set of vertices of 06(G) can be covered by two subsets, each inducing a complete subgraph. The latter property yields in turn that if n is the clique number of 06(G), then 06(G) has at most 2n vertices. This confirms a conjecture by Z. Akhlaghi and H. P. Tong-Viet, and provides some evidence for the famous \u3c1-\u3c3 conjecture by B. Huppert

Individualized dosing of aminoglycosides in neonates: mission accomplished or work in progress?

We have read with great interest the paper of Sherwin et al. on individualized dosing of amikacin based on a population pharmacokinetic and-dynamic (PKPD) study in 80 neonates [1]. To the very best of our knowledge, this is the first PD study (outcome indicator sepsis) of aminoglycosides in neonates. We fully support the clinical need to evaluate both PK and PD of drugs, including aminoglycosides in neonates. The recent review on aminoglycosides in neonates in this journal hereby illustrates that clinical pharmacologists are aware of and interested in the specific needs and characteristics of this patient population [2]. We are, however, intrigued by the dosing suggestions formulated by the authors: 15 mg/kg at 36-h intervals for neonates with a postmenstrual age (PMA)≤28 weeks, 14 mg/kg at 24-h intervals for neonate

Non-perturbative gauge/gravity correspondence in N=2 theories

We derive the exact supergravity profile for the twisted scalar field emitted by a system of fractional D3 branes at a Z2 orbifold singularity supporting N=2 quiver gauge theories with unitary groups and bifundamental matter. At the perturbative level this twisted field is "dual" to the gauge coupling but it is corrected non-perturbatively by an infinite tower of fractional D-instantons. The explicit microscopic description allows to derive the gravity profile from disk amplitudes computing the emission rate of the twisted scalar field in terms of chiral correlators in the dual gauge theory. We compute these quantum correlators using multi-instanton localization techniques and/or Seiberg-Witten analysis. Finally, we discuss a non-perturbative relation between the twisted scalar and the effective coupling of the gauge theory for some simple choices of the brane set ups.Comment: 42 pages. 3 figures, PDFLaTe

A single-photon transistor using nano-scale surface plasmons

It is well known that light quanta (photons) can interact with each other in nonlinear media, much like massive particles do, but in practice these interactions are usually very weak. Here we describe a novel approach to realize strong nonlinear interactions at the single-photon level. Our method makes use of recently demonstrated efficient coupling between individual optical emitters and tightly confined, propagating surface plasmon excitations on conducting nanowires. We show that this system can act as a nonlinear two-photon switch for incident photons propagating along the nanowire, which can be coherently controlled using quantum optical techniques. As a novel application, we discuss how the interaction can be tailored to create a single-photon transistor, where the presence or absence of a single incident photon in a ``gate'' field is sufficient to completely control the propagation of subsequent ``signal'' photons.Comment: 20 pages, 4 figure

Highly stable and efficient all-inorganic lead-free perovskite solar cells with native-oxide passivation

There has been an urgent need to eliminate toxic lead from the prevailing halide perovskite solar cells (PSCs), but the current lead-free PSCs are still plagued with the critical issues of low efficiency and poor stability. This is primarily due to their inadequate photovoltaic properties and chemical stability. Herein we demonstrate the use of the lead-free, allinorganic cesium tin-germanium triiodide (CsSn0.5Ge0.5I3) solid-solution perovskite as the light absorber in PSCs, delivering promising efficiency of up to 7.11%. More importantly, these PSCs show very high stability, with less than 10% decay in efficiency after 500 h of continuous operation in N2 atmosphere under one-sun illumination. The key to this striking performance of these PSCs is the formation of a full-coverage, stable native-oxide layer, which fully encapsulates and passivates the perovskite surfaces. The native-oxide passivation approach reported here represents an alternate avenue for boosting the efficiency and stability of lead-free PSCs