Classical theta constants vs. lattice theta series, and super string partition functions

Recently, various possible expressions for the vacuum-to-vacuum superstring amplitudes has been proposed at genus $g=3,4,5$. To compare the different proposals, here we will present a careful analysis of the comparison between the two main technical tools adopted to realize the proposals: the classical theta constants and the lattice theta series. We compute the relevant Fourier coefficients in order to relate the two spaces. We will prove the equivalence up to genus 4. In genus five we will show that the solutions are equivalent modulo the Schottky form and coincide if we impose the vanishing of the cosmological constant.Comment: 21 page

Testing Taylor’s Law in Urban Population Dynamics Worldwide with Simultaneous Equation Models

Knowledge of long-term population trends is still incomplete at the global scale. In this perspective, human and animal ecology has intensively studied the relationship between the Mean (M) size and the Variance (V) of specific attributes of subpopulations within a given regional system. One of the best-known relationships between these two attributes suitable to describe long-term population trends is governed by Taylor’s law (TL). The present article contributes to the recent literature on population trends worldwide by testing the long-term relationship (1950–2015) between the overall variance and mean in the total population of 1857 metropolitan agglomerations in 155 countries classified into 9 world macro-regions. To estimate the unknown parameter(s) of the V–M relation we made use of a simultaneous equation system using both linear (classical TL) and quadratic specifications, with the aim of ascertaining a wide range of simplified (or more complex) association rules between the two dimensions of demographic change. The empirical results show that TL is verified in all nine cases, although a quadratic relationship provides slightly better results than the classical, linear relationship. More specifically, similar estimates for both linear and quadratic relationships were characteristic of ‘new’ demographic continents with more recent and intense urbanization processes (the Americas, and African and Asian countries). The predominance of quadratic relationships characterized regions with long-established urbanization processes, such as Europe, Russia, and, partly, China and the Middle East. The relevance of the TL for a refined understanding of urbanization mechanisms worldwide, and the importance of a quadratic term for distinguishing metropolitan systems that have experienced different development paths, were finally discussed

LSD: Lyman-break galaxies Stellar populations and Dynamics. I: Mass, metallicity and gas at z~3.1

We present the first results of a project, LSD, aimed at obtaining spatially-resolved, near-infrared spectroscopy of a complete sample of Lyman-Break Galaxies at z~3. Deep observations with adaptive optics resulted in the detection of the main optical lines, such as [OII], Hbeta and [OIII], which are used to study sizes, SFRs, morphologies, gas-phase metallicities, gas fractions and effective yields. Optical, near-IR and Spitzer/IRAC photometry is used to measure stellar mass. We obtain that morphologies are usually complex, with the presence of several peaks of emissions and companions that are not detected in broad-band images. Typical metallicities are 10-50% solar, with a strong evolution of the mass-metallicity relation from lower redshifts. Stellar masses, gas fraction, and evolutionary stages vary significantly among the galaxies, with less massive galaxies showing larger fractions of gas. In contrast with observations in the local universe, effective yields decrease with stellar mass and reach solar values at the low-mass end of the sample. This effect can be reproduced by gas infall with rates of the order of the SFRs. Outflows are present but are not needed to explain the mass-metallicity relation. We conclude that a large fraction of these galaxies are actively creating stars after major episodes of gas infall or merging.Comment: MNRAS, in pres

The vanishing of two-point functions for three-loop superstring scattering amplitudes

In this paper we show that the two-point function for the three-loop chiral superstring measure ansatz proposed by Cacciatori, Dalla Piazza, and van Geemen vanishes. Our proof uses the reformulation of ansatz in terms of even cosets, theta functions, and specifically the theory of the $\Gamma_{00}$ linear system on Jacobians introduced by van Geemen and van der Geer. At the two-loop level, where the amplitudes were computed by D'Hoker and Phong, we give a new proof of the vanishing of the two-point function (which was proven by them). We also discuss the possible approaches to proving the vanishing of the two-point function for the proposed ansatz in higher genera

The (Evolving) vineyard\u2019s age structure in the valencian community, Spain. A new demographic approach for rural development and landscape analysis

Vineyards have assumed a key role as rural landmarks in recent decades. Investigating vineyard dynamics and contexts may reveal various economic, cultural, and environmental aspects of rural landscapes, which can be linked to land-use changes and major soil degradation processes, including soil erosion. As a contribution to rural landscape studies, the purpose of this work is to investigate the spatial distribution of vineyard plots in the Valencian community, located in the eastern area of the Iberian Peninsula, focusing on the final product, the type of vineyard and how long each vineyard has been settled over time. The work provides a comprehensive analysis of a wine-growing landscape, considering strategic (spatial) assets in present and past times. Vineyards were interpreted as a distinctive landmarks that give value to local economies, basic knowledge of how long different types of wine plots have been present in the Valencian community is useful when estimating their degree of sustainability and formulating suggestions, policies, and strategies to prevent processes of landscape degradation at various spatial scales

Retrieving cosmological information from small-scale CMB foregrounds. I. The thermal Sunyaev Zel'dovich effect

We propose a new analysis of small-scale cosmic microwave background (CMB) data by introducing the cosmological dependency of the foreground signals, focussing first on the thermal Sunyaev-Zel’dovich (tSZ) power spectrum, derived from the halo model. We analyse the latest observations by the South Pole Telescope (SPT) of the high-ℓ power (cross) spectra at 95, 150, and 220 GHz, as the sum of CMB and tSZ signals, both depending on cosmological parameters and remaining contaminants. In order to perform faster analyses, we propose a new tSZ modelling based on machine learning algorithms (namely Random Forest). We show that the additional information contained in the tSZ power spectrum tightens constraints on cosmological and tSZ scaling relation parameters. We combined for the first time the Planck tSZ data with SPT high-ℓ to derive new constraints. Finally, we show how the amplitude of the remaining kinetic SZ power spectrum varies depending on the assumptions made on both tSZ and cosmological parameters. These results show the importance of a thorough modelling of foregrounds in the cosmological analysis of small-scale CMB data. Reliable constraints on cosmological parameters can only be achieved once other significant foregrounds, such as the kinetic SZ and the cosmic infrared background (CIB), are also properly accounted fo

On the decomposition of finite-valued streaming string transducers

We prove the following decomposition theorem: every 1-register streaming string transducer that associates a uniformly bounded number of outputs with each input can be effectively decomposed as a finite union of functional 1-register streaming string transducers. This theorem relies on a combinatorial result by Kortelainen concerning word equations with iterated factors. Our result implies the decidability of the equivalence problem for the considered class of transducers. This can be seen as a first step towards proving a more general decomposition theorem for streaming string transducers with multiple registers