Ferrari, Frank
Rivasseau, Vincent
Valette, Guillaume
We define a new large N limit for general {U}(N)<^>{R}$$\end{document} invariant tensor models, based on an enhanced large N scaling of the coupling constants. The resulting large N expansion is organized in terms of a half-integer associated with Feynman graphs that we call the index. This index has a natural interpretation in terms of the many matrix models embedded in the tensor model. Our new scaling can be shown to be optimal for a wide class of non-melonic interactions, which includes all the maximally single-trace terms. Our construction allows to define a new large D expansion of the sum over diagrams of fixed genus in matrix models with an additional , we identify in detail the leading order graphs for R a prime number. This slightly surprising condition is equivalent to the complete interaction being maximally single-trace.
A detailed study of the fragmentation reactions of an (n=3D4-8) ions containing only Ala residues has been carried out using collisional activation on an electrospray/QqToF instrument. Two distinct fragmentation pathways are observed. One, which we have called the "imine" pathway, involves initial elimination of an imine (a(n) -> b(n-1)) followed by elimination of Ala residues (b(n-1) -> b(n-2), etc.). This pathway most likely involves the protonated substituted imine R2C(=3D O)NH+=3D CHR1. The second pathway, which we have called the "amide" pathway, involves initial elimination of NH3 to form an a(n)* ion followed by elimination of Ala residues to form a series of a* ions (a(n)* a(n-2)*, etc.). This latter reaction sequence begins from a protonated C-terminal amide which has been identified by IRMPD studies as the major species present for the A-A-A-A a(4) ion (Bythell et al., 2010). The present results strongly indicate that the larger an ions fragment in a manner similar to that elucidated for the all-Ala a(4) ion and that the "amide" pathway is the dominant fragmentation channel for all the an ions studied in the present work. (C) 2015 Elsevier B.V. All rights reserved.
Inspired by the work of Zhefei He and Mingjin Wang which was published in the Journal of Inequalities and Applications in 2015, this paper further generalizes some related results to the case of multidimensional random variables. The resulting inequality for covariance is then applied to different multidimensional statistical distributions (multiuniform, multinomial, and multinormal). Coordinate dependence of the inequality is also examined. The obtained formulas could be useful for making estimates in multivariate statistics.
In this extended note we give a precise definition of fully extended topological field theories a la Lurie. Using complete n -fold Segal spaces as a model, we construct an (infinity, n)-category of n -dimensional bordisms, possibly with tangential structure. We endow it with a symmetric monoidal structure and show that we can recover the usual category of bordisms.
We study the distribution of solutions n to the congruence sigma(n) equivalent to a (mod n). After excluding obvious families of solutions, we show that the number of these n <= x is at most x(1/2+o(1)), as x -> infinity, uniformly for integers a with vertical bar a vertical bar = x(1/4). As a concrete example, the number of composite solutions n <= x to the congruence sigma(n) equivalent to 1 (mod n) is at most x(1/2+o(1)). These results are analogues of theorems established for the Euler phi-function by the third-named author.
High gain bidirectional dc-dc converter with high efficiency and high power density is a much desired circuit in any converter/inverter system. It is well known that switched capacitor circuits that are variants of the Dickson converter are suitable candidates for such a system. Modular design, absence of external magnetic components, and high efficiency are some of the features that make them suitable candidates. But, the inability to provide fractional and variable voltage gains at high efficiency during normal operation severely limits their application. It also leads to higher voltage stress in the overall system. The aim of this paper is twofold. First, a generalized modular switched capacitor converter, the "(n/m) X converter," which is a variant of the original Dickson converter is introduced. Using this generalized configuration, the converter can be designed for a required fractional gain. Next, two different methods to enable dynamic variation in gain with high efficiency using the (n/m) X converter are proposed. Detailed analysis, design steps, equivalent circuits, and experimental results for a 1 kW prototype of a variable (4/0.5) X boost converter validate the proposed theory. A peak measured efficiency of over 95% is achieved for the prototype. The design framework and analysis in this paper can be extended to a generic (n/m) X converter.
The phenomenon of toy unboxing describes rapidly scaling and commercialising videos featuring the opening, assembling and demonstration of children's toys, often by children, across social media platforms. This phenomenon has fostered concerns by parents and advocates around children's access to and participation in social media. This article provides a brief history of this phenomenon, noting the very limited scholarship on the issue while engaging with the new regulatory questions it provokes. We describe how these videos represent forms of creator labour and operate within the structural and material interests of social media entertainment (SME). SME refers to a proto-industry featuring professionalising-amateur content creators engaging in content innovation and media entrepreneurship across multiple social media platforms to aggregate global fan communities and incubate their own media brands. Our analysis accounts for how unboxing videos work for children both as agents and as small businesses and provides pointers to more nuanced regulatory approaches.
Computing the complexity of Markov bases is an extremely challenging problem; no formula is known in general and there are very few classes of toric ideals for which the Markov complexity has been computed. A monomial curve C in A(3) has Markov complexity m(C) two or three. Two if the monomial curve is complete intersection and three otherwise. Our main result shows that there is no d is an element of N such that m(C) <=3D d for all monomial curves C in A(4). The same result is true even if we restrict to complete intersections. We extend this result to all monomial curves in A(n), where n >=3D 4. (C) 2019 Elsevier B.V. All rights reserved.
Lever, Michael
McEntyre, Christopher J.
George, Peter M.
Chambers, Stephen T.
Choline metabolism is by oxidation to betaine, which is demethylated to N,N-dimethylglycine; dimethylglycine is oxidatively demethylated to sarcosine. This pathway is important for osmoregulation and as a source of methyl groups. We asked whether another metabolite was involved. We synthesized the N-oxide of dimethylglycine (DMGO) by oxidizing dimethylglycine with peracetic acid, and measured DMGO in human plasma and urine by HPLC-MS/MS with positive ion detection, using two chromatography procedures, based on ion exchange and HILIC separations. The molecular ion DMGOH(+) (m/z =3D 120) yielded four significant fragments (m/z =3D 103, 102, 58 and 42). The suspected DMGO peak in human body fluids showed all these fragments, and co-chromatographed with added standard DMGO in both HPLC systems. Typical plasma concentrations of DMGO are under 1 mu mol/l. They may be lower in metabolic syndrome patients. Urine concentrations are higher, and DMGO has a higher fractional clearance than dimethylglycine, betaine and choline. It was present in all of over 80 human urine and plasma samples assayed. Plasma DMGO concentrations correlate with plasma DMG concentrations, with betaine and choline concentrations, with the osmolyte myo-inositol, and strongly with urinary DMGO excretion. We conclude that DMGO is probably a normal human metabolite.