Related papers: Effective results in the three-dimensional minimal…
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are…
This is a very brief report on recent developments on the Dirichlet problem for the minimal surface system and minimal cones in Euclidean spaces. We shall mainly focus on two directions: (1) Further systematic developments after…
There is a growing need for better development methods and tools to keep up with the increasing complexity of new software systems. New types of user interfaces, the need for intelligent components, sustainability concerns, ... bring new…
In recent work we have shown how an accurate reduced model can be utilized to perform mesh refinement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity…
We use reduction maps to study the minimal model program. Our main result is that the existence of a good minimal model for a klt pair $(X,\Delta)$ can be detected on the base of the $(K_{X}+\Delta)$-trivial reduction map. Thus we show that…
We summarise the recent theoretical progress in few-body descriptions of the piNN system. Previous descriptions, both three- and four-dimensional, are shown to possess serious theoretical inconsistencies. We illustrate how three-dimensional…
Recent progress in nanofabrication and additive manufacturing have facilitated the building of nanometer-scale three-dimensional structures, that promise to lead to an emergence of new functionalities within a number of fields, compared to…
We show the validity of the relative dlt MMP over Q-factorial threefolds in all characteristics p>0. As a corollary, we generalise many recent results to low characteristics including: $W\mathcal{O}$-rationality of klt singularities,…
We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions.
The brain is a powerful tool used to achieve amazing feats. There have been several significant advances in neuroscience and artificial brain research in the past two decades. This article is a review of such advances, ranging from the…
The recent advancements in visual reasoning capabilities of large multimodal models (LMMs) and the semantic enrichment of 3D feature fields have expanded the horizons of robotic capabilities. These developments hold significant potential…
Human perception of 3D shapes goes beyond reconstructing them as a set of points or a composition of geometric primitives: we also effortlessly understand higher-level shape structure such as the repetition and reflective symmetry of object…
Over the last two decades, significant advances have been made in the design and analysis of fixed-parameter algorithms for a wide variety of graph-theoretic problems. This has resulted in an algorithmic toolbox that is by now…
This paper resolves several outstanding questions regarding the Minimal Model Program for klt threefolds in mixed characteristic. Namely termination for pairs which are not pseudo-effective, finiteness of minimal models and the Sarkisov…
In this short survey we concern ourselves with minimal codes, a classical object in coding theory. We will explain the relation between minimal codes and various other mathematical domains, in particular with finite projective geometry.…
Three-dimensional (3D) printed preoperative planning models serve a critical role in the success of many medical procedures. However, many of these models do not portray the patient's complete anatomy due to their monolithic and static…
We establish the minimal model program for log canonical and Q-factorial surfaces over excellent base schemes.
We investigate the three-dimensional formulation of a recently proposed operational arrival-time model. It is shown that within typical conditions for optical transitions the results of the simple one-dimensional version are generally…
Recent literature has witnessed significant interest towards 3D biometrics employing monocular vision for robust authentication methods. Motivated by this, in this work we seek to provide insight on recent development in the area of 3D…