Firm Size and Growth Rate Variance: the Effects of Data Truncation

This paper discusses the effects of the existence of natural and/or exogenously imposed thresholds in firm size distributions, on estimations of the relation between firm size and variance in firm growth rates. We explain why the results in the literature on this relationship are not consistent. We argue that a natural threshold (0 number of employees or 0 total sales) and/or the existence of truncating thresholds in the dataset, can lead to upwardly biased estimations of the relation. We show the potential impact of the bias on simulated data, suggest a methodology to improve these estimations, and present an empirical analysis based on a comprehensive dataset of Dutch manufacturing and service firms. The only stable relation between firm size and growth rate variance is negative regardless of how we define the measure of firm growth.firm growth, growth rates variance; truncation; thresholds

Thermodynamic transport theory of spin waves in ferromagnetic insulators

We use the Boltzmann transport theory in the relaxation time approximation to describe the thermal transport of spin waves in a ferromagnet. By treating spin waves as magnon excitations we are able to compute analytically and numerically the coefficients of the constitutive thermo-magnetic transport equations. As a main result, we find that the absolute thermo-magnetic power coefficient $\epsilon_M$, relating the gradient of the potential of the magnetization current and the gradient of the temperature, in the limit of low temperature and low field, is a constant $\epsilon_M = -0.6419 \, k_B/\mu_B$. The theory correctly describes the low-temperature and magnetic-field dependencies of spin Seebeck experiments. Furthermore, the theory predicts that in the limit of very low temperatures the spin Peltier coefficient $\Pi_M$, relating the heat and the magnetization currents, tends to a finite value which depends on the amplitude of the magnetic field. This indicates the possibility to exploit the spin Peltier effect as an efficient cooling mechanism in cryogenics.Comment: (v1) PDFLaTeX, 10 pages, 5 figures, 1 table, submitted to Phys. Rev. B; (v2) PDFLaTeX, 12 pages, 5 figures, 1 table; Secs. I, III, IV highly improved, old-Sec. VI splitted into two new Secs. VI-VII, references added, typos corrected, revised version re-submitted to Phys. Rev. B; (v3) PDFLaTeX, 12 pages, 5 figures, 1 table; Refs. [3], [27], [36] updated, final version published in Phys. Rev.

A Syntactic Model of Mutation and Aliasing

Traditionally, semantic models of imperative languages use an auxiliary structure which mimics memory. In this way, ownership and other encapsulation properties need to be reconstructed from the graph structure of such global memory. We present an alternative "syntactic" model where memory is encoded as part of the program rather than as a separate resource. This means that execution can be modelled by just rewriting source code terms, as in semantic models for functional programs. Formally, this is achieved by the block construct, introducing local variable declarations, which play the role of memory when their initializing expressions have been evaluated. In this way, we obtain a language semantics which directly represents at the syntactic level constraints on aliasing, allowing simpler reasoning about related properties. To illustrate this advantage, we consider the issue, widely studied in the literature, of characterizing an isolated portion of memory, which cannot be reached through external references. In the syntactic model, closed block values, called "capsules", provide a simple representation of isolated portions of memory, and capsules can be safely moved to another location in the memory, without introducing sharing, by means of "affine' variables. We prove that the syntactic model can be encoded in the conventional one, hence efficiently implemented.Comment: In Proceedings DCM 2018 and ITRS 2018 , arXiv:1904.0956

Generalized Mukai conjecture for special Fano varieties

Let X be a Fano variety of dimension n, pseudoindex i_X and Picard number \rho_X. A generalization of a conjecture of Mukai says that \rho_X(i_X-1)\le n. We prove that the conjecture holds if: a) X has pseudoindex i_X \ge \frac{n+3}{3} and either has a fiber type extremal contraction or does not have small extremal contractions b) X has dimension five.Comment: 19 page

Ideal Family Size and Fertility in Egypt: An Overview of Recent Trends

Egypt is already the most populous Arab country in the world with 93 million citizens in 2016 which may grow to about 120 million by 2030 if the same level of fertility continues. This paper aims to offer an overview of the evolution over time of the ideal number of children in Egypt, assessing previous researches and giving a particular emphasis on most recent data on such topic. In a context of raising fertility, whose causes are still unknown, we test the persistence of a high ideal number of children among younger cohorts