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We call a class $\mathcal{M}$ of matroids hereditary if it is closed under flats. We denote by $\mathcal{M}^{ext}$ the class of matroids $M$ that is in $\mathcal{M}$, or has an element $e$ such that $M \backslash e$ is in $\mathcal{M}$. We prove that if $\mathcal{M}$ has finitely many forbidden flats, then so does $\mathcal{M}^{ext} $., Comment: 2 pages

A class $\mathcal{G}$ of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by $G^{epex}$ the class of graphs that are at most one edge away from being in $\mathcal{G}$. We note that $G^{epex}$ is hereditary and prove that if a hereditary class $\mathcal{G}$ has finitely many forbidden induced subgraphs, then so does $G^{epex}$. The hereditary class of cographs consists of all graphs $G$ that can be generated from $K_1$ using complementation and disjoint union. Cographs are precisely the graphs that do not have the $4$-vertex path as an induced subgraph. For the class of edge-apex cographs our main result bounds the order of such forbidden induced subgraphs by 8 and finds all of them by computer search., Comment: 10 pages, 4 figures

A class $\mathcal{G}$ of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by $\mathcal{G}^\mathrm{apex}$ the class of graphs $G$ that contain a vertex $v$ such that $G-v$ is in $\mathcal{G}$. We prove that if a hereditary class $\mathcal{G}$ has finitely many forbidden induced subgraphs, then so does $\mathcal{G}^\mathrm{apex}$. The hereditary class of cographs consists of all graphs $G$ that can be generated from $K_1$ using complementation and disjoint union. A graph is an apex cograph if it contains a vertex whose deletion results in a cograph. Cographs are precisely the graphs that do not have the $4$-vertex path as an induced subgraph. Our main result finds all such forbidden induced subgraphs for the class of apex cographs., Comment: 11 pp., 7 figures

The rapid increase in demand for wireless controlled Smart Lighting has created a need to automate the mapping between the identifiers for individual light sources and their physical locations. To control Smart Lights, their IDs and physical locations relative to each other must be determined. Nowadays, skilled technicians perform this process manually, which requires a lot of effort, is time-consuming, and incurs high costs, particularly with non-stationary lights. Visible Light Communication has been presented as a possible solution to this problem. This paper presents an approach based on Visible Light Communication that leverages Machine Learning to automate the mapping process between the identifiers and the relative physical location of Smart Lights. We show that our approach provides a better location-mapping performance compared to existing methods.

A graph that can be generated from $K_1$ using joins and 0-sums is called a cograph. We define a sesquicograph to be a graph that can be generated from $K_1$ using joins, 0-sums, and 1-sums. We show that, like cographs, sesquicographs are closed under induced minors. Cographs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. We obtain an analogue of this result for sesquicographs, that is, we find those non-sesquicographs for which every proper induced subgraph is a sesquicograph.

In large wind farms, wake distribution behind a wind turbine causes a considerable reduction of wind velocity for downstream wind turbines, resulting in a significant amount of power loss. Therefore, it is very crucial to predict wind turbine wakes efficiently. Thus, we propose a large-eddy simulation (LES) methodology, which takes the vorticity stretching to model transients in wind turbine wakes. In addition, we present an improved actuator disk model, which accounts for two-way feedback between the atmosphere and the wakes. First, we show that the vertical profile of the mean wind predicted with the new model has an excellent agreement with experimental measurements. Next, we validate the predicted Reynolds stresses against wind tunnel data and show that the dispersive stresses account for about 40% of Reynolds stresses. Finally, we show that the proposed LES method accurately predicts the characteristics of wind turbine wakes. Comparing the LES results with previously reported data, we have found that the new LES framework accurately predicts the flow statistics in both the near-wake and the far-wake regions., Comment: 24 pages, 18 figures

In large eddy simulation of atmospheric boundary layer flows over wind farms, wall-layer models are generally imposed for the surface fluxes without considering the spatial variability of the surface roughness. In this study, we consider the near-surface model in conjunction with square of the velocity gradient tensor to model the adaptive dissipation of turbulence production. The surface roughness is incorporated through Monin-Obhukhov similarity theory for the computational cells immediately adjacent to the Earth's surface. The underlying proposed near-surface model captures the significant amount of Reynolds stresses in the near-surface and is able to maintain the log-law profile in wind farms. The present study indicates that the suggested `near-surface model' is relatively robust in comparison to the classical `near-wall model'.

The class of cographs or complement-reducible graphs is the class of graphs that can be generated from $K_1$ using the operations of disjoint union and complementation. By analogy, this paper introduces the class of binary comatroids as the class of matroids that can be generated from the empty matroid using the operations of direct sum and taking complements inside of binary projective space. We show that a proper flat of a binary comatroid is a binary comatroid. Our main result identifies those binary non-comatroids for which every proper flat is a binary comatroid. The paper also proves the corresponding results for ternary matroids., Comment: 26 pages, 10 figures

A graph in which every connected induced subgraph has a disconnected complement is called a cograph. Such graphs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. We define a $2$-cograph to be a graph in which the complement of every $2$-connected induced subgraph is not $2$-connected. We show that, like cographs, $2$-cographs can be recursively defined. But, unlike cographs, $2$-cographs are closed under induced minors. We characterize the class of non-$2$-cographs for which every proper induced minor is a $2$-cograph. We further find the finitely many members of this class whose complements are also induced-minor-minimal non-$2$-cographs., Comment: 32 pages

It follows by Bixby's Lemma that if $e$ is an element of a $3$-connected matroid $M$, then either ${\rm co}(M\delete e)$, the cosimplification of $M\delete e$, or ${\rm si}(M/e)$, the simplification of $M/e$, is $3$-connected. A natural question to ask is whether $M$ has an element $e$ such that both ${\rm co}(M\delete e)$ and ${\rm si}(M/e)$ are $3$-connected. Calling such an element "elastic", in this paper we show that if $|E(M)|\ge 4$, then $M$ has at least four elastic elements provided $M$ has no $4$-element fans and, up to duality, $M$ has no $3$-separating set $S$ that is the disjoint union of a rank-$2$ subset and a corank-$2$ subset of $E(M)$ such that $M|S$ is isomorphic to a member or a single-element deletion of a member of a certain family of matroids., Comment: 20 pages, 1 figure. The main result (Theorem 1) in the original paper is incorrect. In particular, as well as 4-element fans, there is also a family of exceptions. An error in one of the earlier lemmas was missed. We have corrected the paper

In 2004, Ehrenfeucht, Harju, and Rozenberg showed that any graph on a vertex set $V$ can be obtained from a complete graph on $V$ via a sequence of the operations of complementation, switching edges and non-edges at a vertex, and local complementation. The last operation involves taking the complement in the neighbourhood of a vertex. In this paper, we consider natural generalizations of these operations for binary matroids and explore their behaviour. We characterize all binary matroids obtainable from the binary projective geometry of rank $r$ under the operations of complementation and switching. Moreover, we show that not all binary matroids of rank at most $r$ can be obtained from a projective geometry of rank $r$ via a sequence of the three generalized operations. We introduce a fourth operation and show that, with this additional operation, we are able to obtain all binary matroids., Comment: Fixed an error in the proof of Theorem 5.3. Adv. in Appl. Math. (2020)