The Upgrade II of the LHCb detector, foreseen for 2031, will operate at an instantaneous luminosity of 1.5 x 10$^{34}$ cm$^{-2}$s$^{-1}$, accumulating a sample of more than 300 fb$^{-1}$. To cope with the estimated pile-up of 42 and 200 charged parti...
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Unity 5.3 Vertex Painter (⭐ 923)
This contribution is mainly based on joint papers with Lepowsky and Milas, and some parts of these papers are reproduced here. These papers further extended works by Lepowsky and by Milas. Following our joint papers, I explain the general principle...
The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. Very often the problem is studied for restricted families of graph such as vertex-transitive or Cayley graphs...
A $k$-permutation family on $n$ vertices is a set system consisting of the intervals of $k$ permutations of the integers $1$ through $n$. The discrepancy of a set system is the minimum over all red-blue vertex colorings of the maximum difference betw...
An edge coloring $c$ of a graph $G$ is a royal $k$-edge coloring of $G$ if the edges of $G$ are assigned nonempty subsets of the set $\{1, 2, \ldots, k\}$ in such a way that the vertex coloring obtained by assigning the union of the colors of the inc...
Graph neural networks have become one of the most important techniques to solve machine learning problems on graph-structured data. Recent work on vertex classification proposed deep and distributed learning models to achieve high performance and sca...
The $m \times n$ king graph consists of all locations on an $m \times n$ chessboard, where edges are legal moves of a chess king. %where each vertex represents a square on a chessboard and each edge is a legal move. Let $P_{m \times n}(z)$ denote its...
ALEPH and DELPHI were the first experiments operating a silicon vertex detector at LEP. During the past 10 years of data taking the DELPHI Silicon Tracker was upgraded three times to follow the different tracking requirements for LEP 1 and LEP 2 as...
In this paper we examine the behavior of lifts of Brauer characters in p-solvable groups where p is an odd prime. In the main result, we show that if φ\in IBrp(G) is a Brauer character of a solvable group such that φhas an abelian vertex subgroup Q...
In the Independent set problem, the input is a graph $G$, every vertex has a non-negative integer weight, and the task is to find a set $S$ of pairwise non-adjacent vertices, maximizing the total weight of the vertices in $S$. We give an $n^{O (\log^...
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Let $spex(n,H_{minor})$ denote the maximum spectral radius of $n$-vertex $H$-minor free graphs. The problem on determining this extremal value can be dated back to the early 1990s. Up to now, it has been solved for $n$ sufficiently large and some spe...
We introduce the notion of colorful minors, which generalizes the classical concept of rooted minors in graphs. A $q$-colorful graph is defined as a pair $(G, χ),$ where $G$ is a graph and $χ$ assigns to each vertex a (possibly empty) subset of at...
Hybrid pixel detectors have been invented for the LHC to make tracking and vertexing possible at all in LHC's radiation intense environment. The LHC pixel detectors have meanwhile very successfully fulfilled their promises and R\&D for the planned HL...
Pixel detectors for precise particle tracking in high energy physics have been developed to a level of maturity during the past decade. Three of the LHC detectors will use vertex detectors close to the interaction point based on the hybrid pixel te...
The exploration of weakly toll convexity is the focus of this investigation. A weakly toll walk is any walk $W: u, w_1, \ldots , w_{k-1}, v$ between $u$ and $v$ such that $u$ is adjacent only to the vertex $w_1$, which can appear more than once in th...
The one loop 3-point vertex functions of QCD in the maximal abelian gauge (MAG) are evaluated at the fully symmetric point at one loop. As a consequence the theory is renormalized in the various momentum (MOM) schemes which are defined by the trivale...
The hedgehog $H_t$ is a 3-uniform hypergraph on vertices $1,\dots,t+\binom{t}{2}$ such that, for any pair $(i,j)$ with $1\le i<j\le t$, there exists a unique vertex $k>t$ such that $\{i,j,k\}$ is an edge. Conlon, Fox, and Rödl proved that the two-co...