On the Coble quartic

We review and extend the known constructions relating Kummer threefolds, G¨opel systems, theta constants and their derivatives, and the GIT quotient for 7 points in P^2 to obtain an explicit expression for the Coble quartic. The Coble quartic was recently determined completely in [RSSS12], where it was computed completely explicitly, as a polynomial with 372060 monomials of bidegree (28, 4) in theta constants of the second order and theta functions of the second order, respectively. Our expression is in terms of products of theta constants with characteristics corresponding to G¨opel systems, and is a polynomial with 134 terms. Our approach is based on the beautiful geometry studied by Coble and further investigated by Dolgachev and Ortland and highlights the geometry and combinatorics of syzygetic octets of characteristics, and the corresponding representations of Sp(6, F_2). One new ingredient is the relationship of G¨opel systems and Jacobian determinants of theta functions. In genus 2, we similarly obtain a short explicit equation for the universal Kummer surface, and relate modular forms of level two to binary invariants of six points on P^

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

Disentangling Biomolecular Corona Interactions With Cell Receptors and Implications for Targeting of Nanomedicines

Nanoparticles are promising tools for nanomedicine in a wide array of therapeutic and diagnostic applications. Yet, despite the advances in the biomedical applications of nanomaterials, relatively few nanomedicines made it to the clinics. The formation of the biomolecular corona on the surface of nanoparticles has been known as one of the challenges toward successful targeting of nanomedicines. This adsorbed protein layer can mask targeting moieties and creates a new biological identity that critically affects the subsequent biological interactions of nanomedicines with cells. Extensive studies have been directed toward understanding the characteristics of this layer of biomolecules and its implications for nanomedicine outcomes at cell and organism levels, yet several aspects are still poorly understood. One aspect that still requires further insights is how the biomolecular corona interacts with and is "read" by the cellular machinery. Within this context, this review is focused on the current understanding of the interactions of the biomolecular corona with cell receptors. First, we address the importance and the role of receptors in the uptake of nanoparticles. Second, we discuss the recent advances and techniques in characterizing and identifying biomolecular corona-receptor interactions. Additionally, we present how we can exploit the knowledge of corona-cell receptor interactions to discover novel receptors for targeting of nanocarriers. Finally, we conclude this review with an outlook on possible future perspectives in the field. A better understanding of the first interactions of nanomaterials with cells, and -in particular -the receptors interacting with the biomolecular corona and involved in nanoparticle uptake, will help for the successful design of nanomedicines for targeted delivery

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

Long-term urbanization dynamics and the evolution of green/blue areas in eastern europe: Insights from Romania

Urbanization is a dynamic process performed at the expense of natural and/or semi-natural areas, with direct impacts on the ecosystem services provided to human society. The increasing population density in urban areas and the associated demand for housing and public services have led to progressive changes in the structure, architecture, and design of urban areas. The present study analyzes long-term urban development in Western Romania, focusing on green/blue areas’ strategies in Timisoara over centuries. The empirical results of a literature review carried out with a historical perspective have delineated the time periods that favored “urban green development” (1716–1918 and 1918–1940) and those restricting their development (1940–2000), as well as the factors that influenced long-term urbanization dynamics and the evolution of green/blue areas. These factors can be generalized to other socioeconomic contexts in Eastern Europe. Characteristic issues of this geographical area impacting the evolution of urban green/blue areas include (i) common historical aspects (e.g., the influence of geo-political and strategic dimensions, the dominations of former great empires such as the Turkish empire and the communist period) and (ii) population migration after 1990

An explicit solution to the weak Schottky problem

We give an explicit weak solution to the Schottky problem, in the spirit of Riemann and Schottky. For any genus g, we write down a collection of polynomials in genus g theta constants such that their common zero locus contains the locus of Jacobians of genus g curves as an irreducible component. These polynomials arise by applying a specific Schottky-Jung proportionality to an explicit collection of quartic identities for genus g - 1 theta constants

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

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

Therapeutic approach in glioblastoma multiforme with primitive neuroectodermal tumor components: case report and review of the literature

Glioblastoma multiforme (GBM) is the most common and aggressive malignant glioma that is treated with first-line therapy, using surgical resection followed by local radiotherapy and concomitant/adjuvant temozolomide (TMZ) treatment. GBM is characterised by a high local recurrence rate and a low response to therapy. Primitive neuroectodermal tumour (PNET) of the brain revealed a low local recurrence rate; however, it also exhibited a high risk of cerebrospinal fluid (CSF) dissemination. PNET is treated with surgery followed by craniospinal irradiation (CSI) and platinum-based chemotherapy in order to prevent CSF dissemination. GBM with PNET-like components (GBM/PNET) is an emerging variant of GBM, characterised by a PNET-like clinical behaviour with an increased risk of CSF dissemination; it also may benefit from platinum-based chemotherapy upfront or following failure of GBM therapy. The results presented regarding the management of GBM/PNET are based on case reports or case series, so a standard therapeutic approach for GBM/PNET is not defined, constituing a challenging diagnostic and therapeutic dilemma. In this report, a case of a recurrent GBM/PNET treated with surgical resection and radiochemotherapy as Stupp protocol, and successive platinum-based chemotherapy due to the development of leptomeningeal dissemintation and an extracranial metastasis, is discussed. A review of the main papers regarding this rare GBM variant and its therapeutic approach are also reported. In conclusion, GBM/PNET should be treated with a multimodal approach including surgery, chemoradiotherapy, and/or the early introduction of CSI and platinum-based chemotherapy upfront or at recurrence

Demographic Change and the Urban–Rural Divide: Understanding the Role of Density and Agglomeration in Fertility Transitions

Assuming fertility variations across urban–rural gradients, our study focuses on the traditional polarization in urban and rural fertility, offering a refined interpretation of demographic processes associated with population density. More specifically, we tested the intimate relationship between local fertility and population density, comparing the outcomes of a classical urban–rural model (reflecting a linear relationship between the two variables) with those of a more complex quadratic model (implying the so-called ‘suburban fertility hypothesis’) in Greece. We considered fertility dynamics in three districts (urban, suburban, and rural) of 51 Greek prefectures for the last two decades (2000–2009 and 2010–2019) and controlled for the diverging impact of local contexts at different population density levels. Taken as a measure of ‘maturity’ of regional systems, urban fertility surpassed rural fertility in almost all prefectures of Greece. An additional sign of maturity in metropolitan systems indicates that suburban birth rates are higher than urban birth rates in prefectures with high population density (Athens, Thessaloniki, Heraklion, and Patras). The regression outcomes document a specific response of fertility to regional development, evidencing a spatially differentiated shift from classical urban–rural disparities toward a more complex model with the emergence of suburban poles. From this perspective, fertility divides reflect the evolutions of socioeconomic forces (more or less rapidly) along the urban gradient