Cache-Oblivious Persistence

Partial persistence is a general transformation that takes a data structure and allows queries to be executed on any past state of the structure. The cache-oblivious model is the leading model of a modern multi-level memory hierarchy.We present the first general transformation for making cache-oblivious model data structures partially persistent

Schwinger pair creation in Dirac semimetals in the presence of external magnetic and electric fields

We discuss the Schwinger pair creation process for the system of massless Dirac fermions in the presence of constant external magnetic and electric fields. The pair production rate remains finite unlike the vacuum decay rate. In the recently discovered Dirac semimetals, where the massless Dirac fermions emerge, this pair production may be observed experimentally through the transport properties. We estimate its contribution to the ordinary conductivity of the semimetals.Comment: Latex, 8 page

A general framework for Noetherian well ordered polynomial reductions

Polynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an efficient design of the related algorithm have been solidly established. This paper presents a general definition of polynomial reduction structure, studies its features and highlights the aspects needed in order to grant and to efficiently test the main properties (noetherianity, confluence, ideal membership). The most significant aspect of this analysis is a negative reappraisal of the role of the notion of term order which is usually considered a central and crucial tool in the theory. In fact, as it was already established in the computer science context in relation with termination of algorithms, most of the properties can be obtained simply considering a well-founded ordering, while the classical requirement that it be preserved by multiplication is irrelevant. The last part of the paper shows how the polynomial basis concepts present in literature are interpreted in our language and their properties are consequences of the general results established in the first part of the paper.Comment: 36 pages. New title and substantial improvements to the presentation according to the comments of the reviewer

Novel approaches for constructing persistent Delaunay triangulations by applying different equations and different methods

“Delaunay triangulation and data structures are an essential field of study and research in computer science, for this reason, the correct choices, and an adequate design are essential for the development of algorithms for the efficient storage and/or retrieval of information. However, most structures are usually ephemeral, which means keeping all versions, in different copies, of the same data structure is expensive. The problem arises of developing data structures that are capable of maintaining different versions of themselves, minimizing the cost of memory, and keeping the performance of operations as close as possible to the original structure. Therefore, this research aims to aims to examine the feasibility concepts of Spatio-temporal structures such as persistence, to design a Delaunay triangulation algorithm so that it is possible to make queries and modifications at a certain time t, minimizing spatial and temporal complexity. Four new persistent data structures for Delaunay triangulation (Bowyer-Watson, Walk, Hybrid, and Graph) were proposed and developed. The results of using random images and vertex databases with different data (DAG and CGAL), proved that the data structure in its partial version is better than the other data structures that do not have persistence. Also, the full version data structures show an advance in the state of the technique. All the results will allow the algorithms to minimize the cost of memory”--Abstract, page iii

Development of the human bladder and ureterovesical junction.

The urinary bladder collects urine from the kidneys and stores it until the appropriate moment for voiding. The trigone and ureterovesical junctions are key to bladder function, by allowing one-way passage of urine into the bladder without obstruction. Embryological development of these structures has been studied in multiple animal models as well as humans. In this report we review the existing literature on bladder development and cellular signalling with particular focus on bladder development in humans. The bladder and ureterovesical junction form primarily during the fourth to eighth weeks of gestation, and arise from the primitive urogenital sinus following subdivision of the cloaca. The bladder develops through mesenchymal-epithelial interactions between the endoderm of the urogenital sinus and mesodermal mesenchyme. Key signalling factors in bladder development include shh, TGF-β, Bmp4, and Fgfr2. A concentration gradient of shh is particularly important in development of bladder musculature, which is vital to bladder function. The ureterovesical junction forms from the interaction between the Wolffian duct and the bladder. The ureteric bud arises from the Wolffian duct and is incorporated into the developing bladder at the trigone. It was previously thought that the trigonal musculature developed primarily from the Wolffian duct, but it has been shown to develop primarily from bladder mesenchyme. Following emergence of the ureters from the Wolffian ducts, extensive epithelial remodelling brings the ureters to their final trigonal positions via vitamin A-induced apoptosis. Perturbation of this process is implicated in clinical obstruction or urine reflux. Congenital malformations include ureteric duplication and bladder exstrophy