Fasting initiates a coordinated metabolic response to preserve energy balance. As glycogen stores are depleted, the body transitions to mobilizing fatty acids from adipose tissue and generating ketone bodies in the liver to sustain the function of vital organs. A network of hormonal signals and transcriptional programs coordinate these adaptations. Among these, the hepatokine fibroblast growth factor 21 (FGF21) is strongly upregulated during fasting and has been proposed as a key mediator of the fasting response. To investigate the physiological functions of FGF21, we study mice with hepatocyte-specific deletion of Fgf21. Although the liver is the primary source of circulating FGF21 during fasting, its absence in hepatocytes does not alter typical fasting-induced gene expression or key metabolic pathways such as hepatic gluconeogenesis, adipose tissue lipolysis, or ketone production. Instead, we uncover a distinct role for FGF21 in promoting protein appetite following a fast. These findings challenge the conventional view of hepatocyte-produced FGF21 as a fasting-acting hormone and reveal a more specialized function in guiding nutrient selection after energy depletion.
In this paper we study meromorphic solutions of linear shift difference equations with coefficients in C (x) involving the operator rho: y(x) bar right arrow y(x + h), for some h is an element of C*. We prove that if f is a solution of an algebraic differential equation, then f belongs to a ring that is generated by periodic functions and exponentials. Our proof is based on the parametrized difference Galois theory initiated by Hardouin and Singer. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves. The rational abelianization of the Johnson kernel has been computed by Dimca, Hain and Papadima, and a more explicit form was subsequently provided by Morita, Sakasai and Suzuki. Based on these results, Nozaki, Sato and Suzuki used the theory of finite-type invariants of 3-manifolds to prove that the torsion subgroup of the abelianized Johnson kernel is non-trivial. In this paper, we give a purely 2-dimensional proof of the non-triviality of this torsion subgroup and provide a lower bound for its cardinality. Our main tool is the action of the mapping class group on the Malcev Lie algebra of the fundamental group of the surface. Using the same infinitesimal techniques, we also provide an alternative diagrammatic description of the rational abelianized Johnson kernel, and we include in the results the case of an oriented surface with one boundary component.
We propose a new method for obtaining complete asymptotic expansions in a systematic manner, which is suitable for counting sequences of various graph families in dense regime. The core idea is to encode the two-dimensional array of expansion coefficients into a special bivariate generating function, which we call a coefficient generating function. We show that coefficient generating functions possess certain general properties that make it possible to express asymptotics in a short closed form. Also, in most scenarios, we indicate a combinatorial meaning of the involved coefficients. Applications of our method include asymptotics of connected graphs, irreducible tournaments, strongly connected digraphs, 2-SAT formulae and contradictory strongly connected implication digraphs. Moreover, due to its flexibility, the method allows to treat a wide range of structural variations, including fixing the numbers of connected, irreducible, strongly connected and contradictory components, as well as source-like, sink-like and isolated ones, or adding weights and marking variables.
We consider the problem of symbolic integration of $\int G(x,y(x)) dx$ where $G$ is rational and $y(x)$ is a non algebraic solution of a differential equation $y'(x)=F(x,y(x))$ with $F$ rational. As $y$ is transcendental, the Galois action generates a family of parametrized integrals $I(x,h)=\int G(x,y(x,h)) dx$. We prove that $I(x,h)$ is either differentially transcendental or up to parametrization change satisfies a linear differential equation in $h$ with constant coefficients, called a telescoper. This notion generalizes elementary integration. We present an algorithm to compute such telescoper given a priori bound on their order and degree $\hbox{ord},N$ with complexity $\tilde{O}(N^{\omega+1} \hbox{ord}^{\omega-1}+N\hbox{ord}^{\omega+3})$. For the specific foliation $y=\ln x$, a more complete algorithm without an a priori bound is presented. Oppositely, non existence of telescoper is proven for a classical planar Hamiltonian system. As an application, we present an algorithm which always finds, if they exist, the Liouvillian solutions of a planar rational vector field, given a bound large enough for some notion of complexity height.
