Comment on "The N = 3 Weyl Multiplet in Four Dimensions"

N = 3 Weyl multiplet in four dimensions was first constructed in J van Muiden et al (2017) where the authors used the current multiplet approach to obtain the linearized transformation rules and completed the nonlinear variations using the superconformal algebra. The multiplet of currents was obtained by a truncation of the multiplet of currents for the N = 4 vector multiplet. While the procedure seems to be correct, the result suffers from several inconsistencies. The inconsistencies are observed in the transformation rules as well as the field dependent structure constants in the corresponding soft algebra. We take a different approach, and compute the transformation rule as well as the corresponding soft algebra by demanding consistency.Comment: 7 pages, text revision

The H-Line Signed Graph of a Signed Graph

For standard terminology and notion in graph theory we refer the reader to Harary; the non-standard will be given in this paper as and when required. We treat only finite simple graphs without self loops and isolates

Multilingual Language Processing From Bytes

We describe an LSTM-based model which we call Byte-to-Span (BTS) that reads text as bytes and outputs span annotations of the form [start, length, label] where start positions, lengths, and labels are separate entries in our vocabulary. Because we operate directly on unicode bytes rather than language-specific words or characters, we can analyze text in many languages with a single model. Due to the small vocabulary size, these multilingual models are very compact, but produce results similar to or better than the state-of- the-art in Part-of-Speech tagging and Named Entity Recognition that use only the provided training datasets (no external data sources). Our models are learning "from scratch" in that they do not rely on any elements of the standard pipeline in Natural Language Processing (including tokenization), and thus can run in standalone fashion on raw text

Graph Editing to a Given Neighbourhood Degree List is Fixed-Parameter Tractable

Graph editing problems have a long history and have been widely studied, with applications in biochemistry and complex network analysis. They generally ask whether an input graph can be modified by inserting and deleting vertices and edges to a graph with the desired property. We consider the problem \textsc{Graph-Edit-to-NDL} (GEN) where the goal is to modify to a graph with a given neighbourhood degree list (NDL). The NDL lists the degrees of the neighbours of vertices in a graph, and is a stronger invariant than the degree sequence, which lists the degrees of vertices. We show \textsc{Graph-Edit-to-NDL} is NP-complete and study its parameterized complexity. In parameterized complexity, a problem is said to be fixed-parameter tractable with respect to a parameter if it has a solution whose running time is a function that is polynomial in the input size but possibly superpolynomial in the parameter. Golovach and Mertzios [ICSSR, 2016] studied editing to a graph with a given degree sequence and showed the problem is fixed-parameter tractable when parameterized by $\Delta+\ell$, where $\Delta$ is the maximum degree of the input graph and $\ell$ is the number of edits. We prove \textsc{Graph-Edit-to-NDL} is fixed-parameter tractable when parameterized by $\Delta+\ell$. Furthermore, we consider a harder problem \textsc{Constrained-Graph-Edit-to-NDL} (CGEN) that imposes constraints on the NDLs of intermediate graphs produced in the sequence. We adapt our FPT algorithm for \textsc{Graph-Edit-to-NDL} to solve \textsc{Constrained-Graph-Edit-to-NDL}, which proves \textsc{Constrained-Graph-Edit-to-NDL} is also fixed-parameter tractable when parameterized by $\Delta+\ell$. Our results imply that, for graph properties that can be expressed as properties of NDLs, editing to a graph with such a property is fixed-parameter tractable when parameterized by $\Delta+\ell$. We show that this family of graph properties includes some well-known graph measures used in complex network analysis