Related papers: Efficient construction of contact coordinates for …

We give a model-independent construction of directed univalent cocartesian fibrations of $(\infty,1)$-categories, and prove a straightening equivalence against such fibrations. The key step is showing that cocartesian fibrations descend…

Constant dimension codes (CDCs) have become an important object in coding theory due to their application in random network coding. The multilevel construction is one of the most effective ways to construct constant dimension codes. The…

An integral geometric curvature is defined as the index expectation K(x) = E[i(x)] if a probability measure m is given on vector fields on a Riemannian manifold or on a finite simple graph. Such curvatures are local, satisfy Gauss-Bonnet…

In this work, we present a new approach to the construction of variational integrators. In the general case, the estimation of the action integral in a time interval $[q_k,q_{k+1}]$ is used to construct a symplectic map $(q_k,q_{k+1})\to…

Local connection forms provide a very useful tool for handling connections on principal bundles, because they ignore any complexities of the total space and, essentially, involve only two fundamental features of the structure group, namely…

The L\'evi-Civita connection of a Riemannian manifold is a metric (compatible) linear connection, uniquely determined by its vanishing torsion. It is extremal in the sense that it has minimal torsion at each point. We can extend this idea…

In this paper, we propose a method to build molecular cages designed to capture a specific substrate. We model a cage as a graph of atoms with coordinates in space, and several constraints on their edges (degree, length and angle). We use a…

In this paper, we present the design and implementation of a robust motion formation distributed control algorithm for a team of mobile robots. The primary task for the team is to form a geometric shape, which can be freely translated and…

Optimized spatial partitioning algorithms are the corner stone of many successful experimental designs and statistical methods. Of these algorithms, the Centroidal Voronoi Tessellation (CVT) is the most widely utilized. CVT based methods…

We introduce a corrective function to compensate errors in contact area computations coming from mesh discretization. The correction is based on geometrical arguments and requires only one additional quantity to be computed: the length of…

A PhD thesis written under supervision of Pawel Nurowski and defended at the Faculty of Physics of the University of Warsaw. We adress the problems of local equivalence and geometry of third order ODEs modulo contact, point and…

We consider random quantum circuits (RQC) on arbitrary connected graphs whose edges determine the allowed $2$-qudit interactions. Prior work has established that such $n$-qudit circuits with local dimension $q$ on 1D, complete, and…

This paper explores a full generalization of the classical corner-vector method for constructing weighted spherical designs, which we call the {\it generalized corner-vector method}. First we establish a uniform upper bound for the degree…

In a contact manifold (M^5, alpha), we consider almost complex structures J which satisfy, for any vector v in the horizontal distribution, d alpha (v,Jv) = 0. We prove that integral cycles whose approximate tangent planes have the property…

First-order logic is known to have limited expressive power over finite structures. It enjoys in particular the locality property, which states that first-order formulae cannot have a global view of a structure. This limitation ensures on…

This work proposes multi-agent systems setting for concurrent engineering system design optimization and gradually paves the way towards examining graph theoretic constructs in the context of multidisciplinary design optimization problem.…

We propose a model of the functional architecture of curvature-sensitive cells in the primary visual cortex. The model accounts for the modular and hierarchical organization of the cortex, the horizontal connectivity, and the shape of…

This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a…

In this paper, we consider the optimal coordination of automated vehicles at intersections under fixed crossing orders. We formulate the problem using direct optimal control and exploit the structure to construct a semi-distributed…

We propose a new algorithm solving the extended gcd problem, which provides a solution minimizing one of the two coordinates. The algorithm relies on elementary arithmetic properties.