We discuss certain aspects of the formal calculus used to describe vertex algebras. In the standard literature on formal calculus, the expression (x + y)n, where n is not necessarily a nonnegative integer, is defined as the formal Taylor series given by the binomial series in nonnegative powers of the second-listed variable (namely, y). We present a viewpoint that for some purposes of generaliz...

When food availability is restricted to a particular time each day, mammals exhibit food-anticipatory activity (FAA), a daily increase in locomotor activity preceding the presentation of food. Considerable historical evidence suggests that FAA is driven by a food-entrainable circadian clock distinct from the master clock of the suprachiasmatic nucleus. Multiple food-entrainable circadian clocks...

Raphaëlle Pardossi-Piquard,1 Agnès Petit,1 Toshitaka Kawarai,2 Claire Sunyach,1 Cristine Alves da Costa,1 Bruno Vincent,1 Sabine Ring,3 Luciano D’Adamio,4,5 Jie Shen,6 Ulrike Müller,3 Peter St. George Hyslop,2 and Frédéric Checler1,* 1Institut de Pharmacologie Moléculaire et Cellulaire Centre National de la Recherche Scientifique UMR6097 CNRS/UNSA Valbonne 06560 France 2Centre for Research in N...

We introduce a general construction that takes as input a so-called stiff PRO and that outputs a Hopf algebra. Stiff PROs are particular PROs that can be described by generators and relations with precise conditions. Our construction generalizes the classical construction from operads to Hopf algebras of van der Laan. We study some of its properties and review some examples of application. We g...

When a rat is on a limited fixed-time food schedule with full access to a running wheel (activity-based anorexia model, ABA), its activity level will increase hours prior to the feeding period. This activity, called food-anticipatory activity (FAA), is a hypothesized parallel to the hyperactivity symptom in human anorexia nervosa. To investigate in depth the characteristics of FAA, we retrospec...

Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the equivalent Lagrangians play an important role because they admit the same Euler-Lagrange equations. By adding a total time derivative of a suitable function to a g...

OBJECTIVE To assess the intra-rater and inter-rater reliability for measuring femoral anteversion angle (FAA) by a radiographic method using three-dimensional computed tomography reconstruction (3D-CT). METHODS The study included 82 children who presented with intoeing gait. 3D-CT data taken between 2006 and 2014 were retrospectively reviewed. FAA was measured by 3D-CT. FAA is defined as the ...

Although free amino acids (FAA) account for a small fraction of total nitrogen in mammalian milk, they are more abundant in human milk than in most formulas, and may serve as a readily available source of amino acids for protein synthesis, as well as fulfill specific physiologic roles. We used reversed phase Ultra Performance Liquid Chromatography (UPLC) coupled to electrospray ionization tande...

In the paper, the author introduces the notions “multi-order logarithmic numbers” and “multi-order logarithmic polynomials”, establishes an explicit formula, an identity, and two recurrence relations by virtue of the Faà di Bruno formula and two identities of the Bell polynomials of the second kind in terms of the Stirling numbers of the first and second kinds, and constructs some determinantal...