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We discuss the interrelationship between the treatment of the elderly, the nature of production, and the transmission of culture. Respect for the elderly is endogenous. Parents cultivate an interest in consuming culture in their children; when they are older, children compensate their elders proportional to the degree to which their interests were previously cultivated. We show that this model is functionally equivalent to one in which cultural goods are transferred across generations. We focus on the relative well-being of the elderly and use the model to explain patterns in their relative well-being across societies. An important theme is that the cultivation of culture and norms for the respect and support of the elderly bear a nonlinear relationship with many economic variables, such as capital and or land intensity in production. We also discuss the interaction of property rights with production, assets such as productive resources, and relative treatment of the elderly. Insecurity of some types of property rights, such as rights over output, may benefit the elderly, while secure rights over productive resources may also benefit the elderly. We discuss how the elderly could be affected by demographic, technological and policy changes in both developing and developed economies.

We show that, under suitable hypotheses, the foundation of a generalized parallel connection of matroids is the relative tensor product of the foundations. Using this result, we show that the foundation of a 2-sum of matroids is the absolute tensor product of the foundations, and that the foundation of a matroid is invariant under segment-cosegment exchange.

We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle. They from a ring-like counterpart to the field-like category of idylls introduced by the first and third author. The first part of the paper is dedicated to establishing fundamental properties of bands analogous to basic facts in commutative algebra. In particular, we introduce various kinds of ideals in a band and explore their properties, and we study localization, quotients, limits, and colimits. The second part of the paper studies band schemes. After giving the definition, we present some examples of band schemes, along with basic properties of band schemes and morphisms thereof, and we describe functors into some other scheme theories. In the third part, we discuss some ``visualizations'' of band schemes, which are different topological spaces that one can functorially associate to a band scheme $X$., Comment: 61 pages

New radio (NR) positioning in the Third Generation Partnership Project (3GPP) Release 18 (Rel-18) enables 5G-advanced networks to achieve ultra-high accuracy positioning without dependence on global navigation satellite systems (GNSS) with key enablers such as the carrier phase positioning technique, standardized for the first time in a cellular communications standard and setting a new baseline for future generations. In addition, Rel-18 NR supports positioning functionalities for reduced capability (RedCap) user equipment and bandwidth aggregation for positioning measurements. Moreover, the low power solutions are designed for low power high accuracy positioning use cases. Lastly, sidelink-based positioning is introduced in Rel-18. This article constitutes a comprehensive treatment of the Rel-18 NR positioning enhancements crucial for the development of next-generation networks.

Historians and political economists have long debated the processes that led land in frontier regions, managed commons, and a variety of customary landholding regimes to be enclosed and transformed into more exclusive forms of private property. Using the framework of aggregative games, we examine land-holding regimes where access to land is established via possession and use, and then explore the factors that may initiate decentralized privatization processes. Factors including population density, potential for technology improvement, enclosure costs, shifts in group cohesion and bargaining power, or the policy and institutional environment determine the equilibrium mix of property regimes. While decentralized processes yield efficient enclosure and technological transformation in some circumstances, in others, the outcomes fall short of second-best. This stems from the interaction of different spillover effects, leading to inefficiently low rates of enclosure and technological transformation in some cases and excessive enclosure in others. Implementing policies to strengthen customary governance, compensate displaced stakeholders, or subsidize/tax enclosure can realign incentives. However, addressing one market failure while overlooking others can worsen outcomes. Our analysis offers a unified framework for evaluating claimed mechanisms and processes across Neoclassical, neo-institutional, and Marxian interpretations of enclosure processes.

In this sequel to "Foundations of matroids - Part 1", we establish several presentations of the foundation of a matroid in terms of small building blocks. For example, we show that the foundation of a matroid M is the colimit of the foundations of all embedded minors of M isomorphic to one of the matroids $U^2_4$, $U^2_5$, $U^3_5$, $C_5$, $C_5^\ast$, $U^2_4\oplus U^1_2$, $F_7$, $F_7^\ast$, and we show that this list is minimal. We establish similar minimal lists of building blocks for the classes of 2-connected and 3-connected matroids. We also establish a presentation for the foundation of a matroid in terms of its lattice of flats. Each of these presentations provides a useful method to compute the foundation of certain matroids, as we illustrate with a number of concrete examples. Combining these techniques with other results in the literature, we are able to compute the foundations of several interesting classes of matroids, including whirls, rank-2 uniform matroids, and projective geometries. In an appendix, we catalogue various 'small' pastures which occur as foundations of matroids, most of which were found with the assistance of a computer, and we discuss some of their interesting properties., Comment: 77 pages

The determinant of a skew-symmetric matrix has a canonical square root given by the Pfaffian. Similarly, the resultant of two reciprocal polynomials of even degree has a canonical square root given by their reciprocant. Computing the reciprocant of two cyclotomic polynomials yields a short and elegant proof of the Law of Quadratic Reciprocity., Comment: 10 pages. v2: Rewrote Appendix B, fixed miscellaneous typos

We give a new proof, along with some generalizations, of a folklore theorem (attributed to Laurent Lafforgue) that a rigid matroid (i.e., a matroid with indecomposable basis polytope) has only finitely many projective equivalence classes of representations over any given field., Comment: 11 pages. v2: Generalized Theorem 2.3, made some minor expository changes

The Jacobian group (also called the sandpile group, Picard group, or critical group) of a graph or, more generally, of a regular matroid has been well studied. Sixth-root-of-unity matroids, also called complex unimodular matroids, are generalizations of regular matroids. This paper provides a definition, and establishes some basic properties, of the Jacobian group of a sixth-root-of-unity matroid.

This document presents an overview of the bayesmixedlogit and bayesmixedlogitwtp Stata packages. It mirrors closely the helpfile obtainable in Stata (i.e., through help bayesmixedlogit or help bayesmixedlogitwtp). Further background for the packages can be found in Baker(2014).

Let $r \leqslant n$ be nonnegative integers, and let $N = \binom{n}{r} - 1$. For a matroid $M$ of rank $r$ on the finite set $E = [n]$ and a partial field $k$ in the sense of Semple--Whittle, it is known that the following are equivalent: (a) $M$ is representable over $k$; (b) there is a point $p = (p_J) \in {\bf P}^N(k)$ with support $M$ (meaning that $\text{Supp}(p) := \{J \in \binom{E}{r} \; \vert \; p_J \ne 0\}$ of $p$ is the set of bases of $M$) satisfying the Grassmann-Pl\"ucker equations; and (c) there is a point $p = (p_J) \in {\bf P}^N(k)$ with support $M$ satisfying just the 3-term Grassmann-Pl\"ucker equations. Moreover, by a theorem of P. Nelson, almost all matroids (meaning asymptotically 100%) are not representable over any partial field. We prove analogues of these facts for Lagrangian orthogonal matroids in the sense of Gelfand-Serganova, which are equivalent to even Delta-matroids in the sense of Bouchet., Comment: 13 pages

Given a tract $F$ in the sense of Baker and Bowler and a matrix $A$ with entries in $F$, we define several notions of rank for $A$. In this way, we are able to unify and find conceptually satisfying proofs for various results about ranks of matrices that one finds scattered throughout the literature.