In this article we describe a program -- called planar_draw -- to draw maps on oriented surfaces in the plane. The drawings are coded as tikz files that can easily be manipulated and used in latex documents. Next to plane maps -- a case for which already several programs exist -- the program allows to draw maps of genus at least one inside a fundamental polygon or with non-contractible cycles displayed as disjoint cycles that have to be identified. Several options allow to tailor the output for individual needs -- e.g.\ by forcing some edges to be completely inside the fundamental polygon. In combination with a program embedding graphs, the tool can also be used for graphs that do not already come with an embedding in an orientable surface.
In this paper, we provide the first known infinite family of simple graphs, each of which is the skeleton of a chiral map, a skeleton of a reflexible map on an orientable surfaces, as well as a skeleton of a reflexible map on a non-orientable surface. This family consists of all lexicographic product $C_n[mK_1]$, where $m\ge 3$, $n = sm$, with $s$ an integer not divisible by $4$. This answers a question posed in [S.\ Wilson, Families of regular graphs in regular maps, {\em Journal of Combinatorial Theory, Series B} 85 (2002), 269--289].
The problems in our teaching on object-oriented programming are analyzed, and the basic ideas, causes and methods of the reform are discussed on the curriculum, theoretical teaching and practical classes. Our practice shows that these reforms can improve students' understanding of object-oriented to enhance students' practical ability and innovative ability.
In the subfamily Stomoxyinae there are currently 18 recognized Stomoxys species, plus two subspecies. Most Stomoxys knowledge was gained through studies with S. calcitrans, a cosmopolitan species, economic pest, and vector. Other Stomoxys spp. are known only from a few trapped adult specimens. Herein, the Stomoxys spp. have been grouped by their ecological diversity, global distribution, and phylogeny and phylogeography. Seven species are dependent to some degree on humans and their activities, particularly animal production. Eleven species are dependent on wildlife to some degree for their development, and little is known about their biology in many cases. Global distributions include one cosmopolitan species (S. calcitrans), twelve species found only in Africa, four species only in Asia, and one species (S. sitiens) in Africa and Asia. Most genetic studies on Stomoxys calcitrans showed little variation in North America, possibly due to the adults’ long range flight capability. Phylogeographic analysis of S. calcitrans showed a differentiation between Oriental populations (first lineage) and populations from Afrotropical, Palearctic, Nearctic, Neotropical and Oceanian regions (second lineage). Genetic studies were followed by sequencing of the Stomoxys calcitrans genome and phylogenetic studies of the Stomoxys genus using 10 of the known species. Phylogenetic relationships were established.
ABSTRACT The debate on Orientalist representations of Islam and/or Muslims has been rampant in academic literature since Edward Said’s publication of his seminal work Orientalism (1978). The articulation of this discourse however has transformed in due course. It has manifested into its new variant ‘neo-Orientalism’, which has gained prominence in the post-9/11 era. In this paper, I discuss the transition from Orientalism to neo-Orientalism, and argue that this new mode of representation does not exclusively result from the 9/11 events and the subsequent War on Terror, but also from the portrayals of Muslims in the last quarter of the twentieth century. These portrayals, disseminated with great intensity by people in the media, journalists, politicians, and Orientalist academics, as well as in literary and cultural productions, continue to reify narratives about Islam and Muslim societies. This paper concludes with the dynamics Orientalism holds and reveals the role authors of the Middle East and South Asia play in disseminating neo-Orientalist discourses with the often-detrimental effect of catering to and promoting modern-day Islamophobia in contemporary Western societies. This is briefly illustrated on the examples of Nadeem Aslam’s Maps for Lost Lovers (2004), Qaisra Shahraz’s The Holy Woman (2001), and Uzma Aslam Khan’s Trespassing (2003).
We give an algorithm to calculate the minimal and maximal genus of the orientable closed surface where a graph $G$ can be embedded. For this, we construct some special branched coverings of the 2-sphere. We apply this algorithm to calculate the orientable genus and maximal genus of some Snarks graphs.
We calculate the cobordism ring $Ω^{C_2}_*$ of stably almost complex manifolds with involution, and investigate the $C_2$-spectrum $Ω_{C_2}$ which represents it. We introduce the notion of a geometrically oriented $C_2$-spectrum, which extends the notion of a complex oriented $C_2$-spectrum, and of which $Ω_{C_2}$ is the universal example. Examples, in addition to $Ω_{C_2}$, include the Eilenberg-Maclane spectrum $H \underline{\mathbb{Z}}_{C_2}$ and the connective cover $k_{C_2}$ of $C_2$-equivariant $K$-theory. On the algebraic side, we define and study filtered $C_2$-equivariant formal group laws, which are the algebraic structures determined by geometrically oriented $C_2$-spectra. We prove some of the fundamental properties of filtered $C_2$-equivariant formal group laws, as well as a universality statement for the filtered $C_2$-equivariant formal group law determined by $Ω_{C_2}$.
Sarah Arpin, Mingjie Chen, Kristin E. Lauter
et al.
The paper concerns several theoretical aspects of oriented supersingular $\ell$-isogeny volcanoes and their relationship to closed walks in the supersingular $\ell$-isogeny graph. Our main result is a bijection between the rims of the union of all oriented supersingular $\ell$-isogeny volcanoes over $\overline{\mathbb{F}}_p$ (up to conjugation of the orientations), and isogeny cycles (non-backtracking closed walks which are not powers of smaller walks) of the supersingular $\ell$-isogeny graph over $\overline{\mathbb{F}}_p$. The exact proof and statement of this bijection are made more intricate by special behaviours arising from extra automorphisms and the ramification of $p$ in certain quadratic orders. We use the bijection to count isogeny cycles of given length in the supersingular $\ell$-isogeny graph exactly as a sum of class numbers of these orders, and also give an explicit upper bound by estimating the class numbers.
We construct a new family of minimal non-orientable matroids of rank three. Some of these matroids embed in Desarguesian projective planes. This answers a question of Ziegler: for every prime power $q$, find a minimal non-orientable submatroid of the projective plane over the $q$-element field.
Oriented object detection is a practical and challenging task in remote sensing image interpretation. Nowadays, oriented detectors mostly use horizontal boxes as intermedium to derive oriented boxes from them. However, the horizontal boxes are inclined to get small Intersection-over-Unions (IoUs) with ground truths, which may have some undesirable effects, such as introducing redundant noise, mismatching with ground truths, detracting from the robustness of detectors, etc. In this paper, we propose a novel Anchor-free Oriented Proposal Generator (AOPG) that abandons horizontal box-related operations from the network architecture. AOPG first produces coarse oriented boxes by a Coarse Location Module (CLM) in an anchor-free manner and then refines them into high-quality oriented proposals. After AOPG, we apply a Fast R-CNN head to produce the final detection results. Furthermore, the shortage of large-scale datasets is also a hindrance to the development of oriented object detection. To alleviate the data insufficiency, we release a new dataset on the basis of our DIOR dataset and name it DIOR-R. Massive experiments demonstrate the effectiveness of AOPG. Particularly, without bells and whistles, we achieve the accuracy of 64.41%, 75.24% and 96.22% mAP on the DIOR-R, DOTA and HRSC2016 datasets respectively. Code and models are available at https://github.com/jbwang1997/AOPG.
To any Frobenius superalgebra $A$ we associate an oriented Frobenius Brauer category and an affine oriented Frobenius Brauer category. We define natural actions of these categories on categories of supermodules for general linear Lie superalgebras $\mathfrak{gl}_{m|n}(A)$ with entries in $A$. These actions generalize those on module categories for general linear Lie superalgebras and queer Lie superalgebras, which correspond to the cases where $A$ is the ground field and the two-dimensional Clifford superalgebra, respectively.
Let $D$ be a weighted oriented graph with the underlying graph $G$ when vertices with non-trivial weights are sinks and $I(D), I(G) $ be the edge ideals corresponding to $D$ and $G,$ respectively. We give explicit description of the symbolic powers of $I(D)$ using the concept of strong vertex covers. We show that the ordinary and symbolic powers of $I(D)$ and $I(G)$ behave in a similar way. We provide a description for symbolic powers and Waldschmidt constant of $I(D)$ for certain classes of weighted oriented graphs. When $D$ is a weighted oriented odd cycle we compute $\reg (I(D)^{(s)}/I(D)^s)$ and prove $\reg I(D)^{(s)}\leq\reg I(D)^s$ and show that equality holds when there is only one vertex with non-trivial weight.
Control of molecular rotations by laser fields is an active area of research focusing on the alignment/orientation of otherwise isotropic molecular samples. Oriented molecules are useful in many applications, such as molecular orbital tomography, femtosecond imaging of molecular structure, dynamics and chemical reaction control. In this work, we present a novel, previously unreported phenomenon appearing in thermal ensembles of non-linear polar molecules excited by a single THz pulse. We find that the induced orientation lasts long after the excitation pulse is over. In the case of symmetric-top molecules, the ensemble averaged orientation remains indefinitely constant after the pulse, whereas in the case of asymmetric-top molecules the orientation persists for a long time after the end of the pulse. We discuss the underlying mechanism, study its non-monotonous temperature dependence, and show that there exists an optimal temperature for the maximal residual orientation. The persistent orientation implies long lasting macroscopic dipole moment, which may be probed by second (or higher order) harmonic generation.
The purpose of this study is to analyse two related topics: the Rumin cohomology and the $\mathbb{H}$-orientability in the Heisenberg group $\mathbb{H}^n$. In the first three chapters we carefully describe the Rumin cohomology with particular emphasis at the second order differential operator $D$, giving examples in the cases $n=1$ and $n=2$. We also show the commutation between all Rumin differential operators and the pullback by a contact map and, more generally, describe pushforward and pullback explicitly in different situations. Differential forms can be used to define the notion of orientability; indeed in the fourth chapter we define the $\mathbb{H}$-orientability for $\mathbb{H}$-regular surfaces and we prove that $\mathbb{H}$-orientability implies standard orientability, while the opposite is not always true. Finally we show that, up to one point, a Möbius strip in $\mathbb{H}^1$ is a $\mathbb{H}$-regular surface and we use this fact to prove that there exist $\mathbb{H}$-regular non-$\mathbb{H}$-orientable surfaces, at least in the case $n=1$. This opens the possibility for an analysis of Heisenberg currents mod $2$.
We construct a new polynomial invariant of maps (graphs embedded in a compact surface, orientable or non-orientable), which contains as specializations the Krushkal polynomial, the Bollobás--Riordan polynomial, the Las Vergnas polynomial, and their extensions to non-orientable surfaces, and hence in particular the Tutte polynomial. Other evaluations include the number of local flows and local tensions taking non-identity values in a given finite group.