Improved bounds for the number of forests and acyclic orientations in the square lattice

In a recent paper Merino and Welsh (1999) studied several counting problems on the square lattice $L_n$. The authors gave the following bounds for the asymptotics of $f(n)$, the number of forests of $L_n$, and $\alpha(n)$, the number of acyclic orientations of $L_n$: $3.209912 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.84161$ and $22/7 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.70925$. In this paper we improve these bounds as follows: $3.64497 \leq \lim_{n\rightarrow\infty} f(n)^{1/n^2} \leq 3.74101$ and $3.41358 \leq \lim_{n\rightarrow\infty} \alpha(n) \leq 3.55449$. We obtain this by developing a method for computing the Tutte polynomial of the square lattice and other related graphs based on transfer matrices

Linear Momentum Density in Quasistatic Electromagnetic Systems

We discuss a couple of simple quasistatic electromagnetic systems in which the density of electromagnetic linear momentum can be easily computed. The examples are also used to illustrate how the total electromagnetic linear momentum, which may also be calculated by using the vector potential, can be understood as a consequence of the violation of the action-reaction principle, because a non-null external force is required to maintain constant the mechanical linear momentum. We show how one can avoid the divergence in the interaction linear electromagnetic momentum of a system composed by an idealization often used in textbooks (an infinite straight current) and a point charge.Comment: 22 pages, 5 figures, to appear in Eur. J. Phy

Selecting and monitoring pheromone traps in insect pest management

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IDOL regulates systemic energy balance through control of neuronal VLDLR expression.

Liver X receptors limit cellular lipid uptake by stimulating the transcription of Inducible Degrader of the LDL Receptor (IDOL), an E3 ubiquitin ligase that targets lipoprotein receptors for degradation. The function of IDOL in systemic metabolism is incompletely understood. Here we show that loss of IDOL in mice protects against the development of diet-induced obesity and metabolic dysfunction by altering food intake and thermogenesis. Unexpectedly, analysis of tissue-specific knockout mice revealed that IDOL affects energy balance, not through its actions in peripheral metabolic tissues (liver, adipose, endothelium, intestine, skeletal muscle), but by controlling lipoprotein receptor abundance in neurons. Single-cell RNA sequencing of the hypothalamus demonstrated that IDOL deletion altered gene expression linked to control of metabolism. Finally, we identify VLDLR rather than LDLR as the primary mediator of IDOL effects on energy balance. These studies identify a role for the neuronal IDOL-VLDLR pathway in metabolic homeostasis and diet-induced obesity