We consider fiber-preserving, orientation-reversing involutions on orientable Seifert fibered 3-manifolds and the conditions on a manifold for admissibility of such involutions. We construct a class $Ψ$ of fiber-preserving, orientation-reversing involutions that act trivially on the base. Each element of $Ψ$ is obtained by extending a product involution across Seifert pieces of type $V(2,2;-1)$ - a solid torus with three fibers filled according to Seifert invariants $(2,1)$, $(2,1)$, and $(1,-1)$. We show that $Ψ$ forms a single conjugacy class under fiber-preserving diffeomorphisms. Our main result establishes that any fiber-preserving, orientation-reversing involution factors as $ψ\circ g$, where $g$ is fiber-preserving and orientation-preserving and $ψ\inΨ$, thus reducing the problem to the previously known orientation-preserving case. Through the orientable base-space double covering, we further extend the classification to manifolds with non-orientable base orbifold.
Let S denote a Steiner triple system on an n-element set. An orientation of S is an assignment of a cyclic ordering to each of the triples in S. From an oriented Steiner triple system, one can define an anticommutative bilinear operation on Rn resembling the cross product. We call this bilinear operation a Steiner product. We classify the oriented Steiner triple systems on sets of size 7 and 9 and investigate the dynamics of their associated Steiner products.
Let $F$ and $G$ be simple finite oriented graphs (without symmetric arcs). A graph $G$ is called $F$-irregular if any two distinct vertices in $G$ belong to a different number of subgraphs of $G$ isomorphic to $F$. In this paper, we investigate the problem of the existence of $\overrightarrow{C_n}$-irregular graphs, where $\overrightarrow{C_n}$ is an oriented circle of order $n$ (a strongly connected oriented graph that is formed from a simple undirected cycle $C_n$ on $n$ vertices by orienting each of its edges). For every integer $n \ge 3$, we prove that there exists an infinite family of $\overrightarrow{C_n}$-irregular graphs. In addition, we show that the order of a non-trivial $\overrightarrow{C_3}$-irregular graph can be any integer not less than $10$ and nothing else. We also construct $\overrightarrow{C_4}$-irregular graphs of any order starting from $7$ and prove that there is no non-trivial $\overrightarrow{C_4}$-irregular graph of order less than $7$.
We provide a short proof of a conic version of the colorful Carathéodory theorem for oriented matroids. Holmsen's extension of the colorful Carathéodory theorem to oriented matroids (Advances in Mathematics, 2016) already encompasses several generalizations of the original result, but not its conic version. Our approach relies on a common generalization of Sperner's lemma and Meshulam's lemma-two closely related results from combinatorial topology that have found a number of applications in discrete geometry and combinatorics. This generalization may be of independent interest. Using a similar approach, we also establish the following colorful theorem for topes, whose special geometric case had not been considered before: Given $n$ topes from a uniform oriented matroid with $n$ elements, if they agree on some element, then there is a way to select a distinct element from each tope, together with its sign, so as to form another tope of the oriented matroid. Motivated by this theorem, we further explore other conditions leading to the same conclusion.
Via mechanisms not accessible at equilibrium, self-propelled particles can form phases with positional order, such as crystals, and with orientational order, such as polar flocks. However, the interplay between these two types of order remains relatively unexplored. Here, we address this point by studying crystals of active particles that turn either towards or away from each other, which can be experimentally realised with phoretic or Janus colloids or with elastically-coupled walker robots. We show that, depending on how these interactions vary with interparticle distance, the particles align along directions determined by the underlying crystalline lattice. To explain the results, we map the orientational dynamics of the active crystal onto a lattice of spins that interact via (anti-)ferromagnetic alignment with each other plus nematic alignment with the lattice directions. Our findings indicate that orientational and positional order can be strongly coupled in active crystals, thus suggesting strategies to control orientational order by engineering the underlying crystalline lattice.
Spencer M. Richards, Navid Azizan, Jean-Jacques Slotine
et al.
Real-time adaptation is imperative to the control of robots operating in complex, dynamic environments. Adaptive control laws can endow even nonlinear systems with good trajectory tracking performance, provided that any uncertain dynamics terms are linearly parameterizable with known nonlinear features. However, it is often difficult to specify such features a priori, such as for aerodynamic disturbances on rotorcraft or interaction forces between a manipulator arm and various objects. In this paper, we turn to data-driven modeling with neural networks to learn, offline from past data, an adaptive controller with an internal parametric model of these nonlinear features. Our key insight is that we can better prepare the controller for deployment with control-oriented meta-learning of features in closed-loop simulation, rather than regression-oriented meta-learning of features to fit input-output data. Specifically, we meta-learn the adaptive controller with closed-loop tracking simulation as the base-learner and the average tracking error as the meta-objective. With both fully-actuated and underactuated nonlinear planar rotorcraft subject to wind, we demonstrate that our adaptive controller outperforms other controllers trained with regression-oriented meta-learning when deployed in closed-loop for trajectory tracking control.
Detecting robust keypoints from an image is an integral part of many computer vision problems, and the characteristic orientation and scale of keypoints play an important role for keypoint description and matching. Existing learning-based methods for keypoint detection rely on standard translation-equivariant CNNs but often fail to detect reliable keypoints against geometric variations. To learn to detect robust oriented keypoints, we introduce a self-supervised learning framework using rotation-equivariant CNNs. We propose a dense orientation alignment loss by an image pair generated by synthetic transformations for training a histogram-based orientation map. Our method outperforms the previous methods on an image matching benchmark and a camera pose estimation benchmark.
Anisotropic particles oriented in a specific direction can act as artificial atoms and molecules, and their controlled assembly can result in a wide variety of ordered structures. Towards this, we demonstrate the orientation transitions of uncharged peanut-shaped polystyrene colloids, suspended in a non-ionic aprotic polar solvent, near a flat surface whose potential is static or time-varying. The charged surface is coated with an insulating dielectric layer to suppress electric currents. The transition between several orientation states such as random, normal or parallel orientation with respect to the surface, is examined for two different colloid sizes at low-frequency ($\sim 10-350$ kHz) or static fields, and at small electric potentials. In time-varying (AC) field, a detailed phase diagram in the potential-frequency plane indicating the transition between particles parallel or normal to the surface is reported. We next present the first study of orientation switching in static (DC) fields, where no electro-osmotic or other flow is present. A reversible change between the two colloidal states is explained by a theory showing that the sum of electrostatic and gravitational energies of the colloid is bistable. The number of colloids in each of the two states depends on the external potential, particle and solvent permittivities, particle aspect ratio, and distance from the electrode.
Deep Convolutional Neural Networks (DCNNs) are capable of obtaining powerful image representations, which have attracted great attentions in image recognition. However, they are limited in modeling orientation transformation by the internal mechanism. In this paper, we develop Orientation Convolution Networks (OCNs) for image recognition based on the proposed Landmark Gabor Filters (LGFs) that the robustness of the learned representation against changed of orientation can be enhanced. By modulating the convolutional filter with LGFs, OCNs can be compatible with any existing deep learning networks. LGFs act as a Gabor filter bank achieved by selecting $ p $ $ \left( \ll n\right) $ representative Gabor filters as andmarks and express the original Gabor filters as sparse linear combinations of these landmarks. Specifically, based on a matrix factorization framework, a flexible integration for the local and the global structure of original Gabor filters by sparsity and low-rank constraints is utilized. With the propogation of the low-rank structure, the corresponding sparsity for representation of original Gabor filter bank can be significantly promoted. Experimental results over several benchmarks demonstrate that our method is less sensitive to the orientation and produce higher performance both in accuracy and cost, compared with the existing state-of-art methods. Besides, our OCNs have few parameters to learn and can significantly reduce the complexity of training network.
The Thief Orienteering Problem (ThOP) is a multi-component problem that combines features of two classic combinatorial optimization problems: Orienteering Problem and Knapsack Problem. The ThOP is challenging due to the given time constraint and the interaction between its components. We propose an Ant Colony Optimization algorithm together with a new packing heuristic to deal individually and interactively with problem components. Our approach outperforms existing work on more than 90% of the benchmarking instances, with an average improvement of over 300%.
The orientation and stability of the reconnection x-line in asymmetric geometry is studied using three-dimensional (3D) particle-in-cell simulations. We initiate reconnection at the center of a large simulation domain to minimize the boundary effect. The resulting x-line has sufficient freedom to develop along an optimal orientation, and it remains laminar. Companion 2D simulations indicate that this x-line orientation maximizes the reconnection rate. The divergence of the non-gyrotropic pressure tensor breaks the frozen-in condition, consistent with its 2D counterpart. We then design 3D simulations with one dimension being short to fix the x-line orientation, but long enough to allow the growth of the fastest growing oblique tearing modes. This numerical experiment suggests that reconnection tends to radiate secondary oblique tearing modes if it is externally (globally) forced to proceed along an orientation not favored by the local physics. The development of oblique structure easily leads to turbulence inside small periodic systems.
In [Jo14] and [Jo18] Vaughan Jones introduced a construction which yields oriented knots and links from elements of the oriented Thompson group $\vec{F}$. In this paper we prove, by analogy with Alexander's classical theorem establishing that every knot or link can be represented as a closed braid, that given an oriented knot/link $\vec{L}$, there exists an element $g$ in $\vec{F}$ whose closure $\vec{\mathcal{L}}(g)$ is $\vec L$.
Motivated by the conjecture of Hartsfield and Ringel on antimagic labelings of undirected graphs, Hefetz, Mütze, and Schwartz initiated the study of antimagic labelings of digraphs in 2010. Very recently, it has been conjectured in [Antimagic orientation of even regular graphs, J. Graph Theory, 90 (2019), 46-53.] that every graph admits an antimagtic orientation, which is a strengthening of an earlier conjecture of Hefetz, Mütze and Schwartz. In this paper, we prove that every $2d$-regular graph (not necessarily connected) admits an antimagic orientation, where $d\ge2$. Together with known results, our main result implies that the above-mentioned conjecture is true for all regular graphs.
Deep Convolutional Neural Networks (DCNN) have been proven to be effective for various computer vision problems. In this work, we demonstrate its effectiveness on a continuous object orientation estimation task, which requires prediction of 0 to 360 degrees orientation of the objects. We do so by proposing and comparing three continuous orientation prediction approaches designed for the DCNNs. The first two approaches work by representing an orientation as a point on a unit circle and minimizing either L2 loss or angular difference loss. The third method works by first converting the continuous orientation estimation task into a set of discrete orientation estimation tasks and then converting the discrete orientation outputs back to the continuous orientation using a mean-shift algorithm. By evaluating on a vehicle orientation estimation task and a pedestrian orientation estimation task, we demonstrate that the discretization-based approach not only works better than the other two approaches but also achieves state-of-the-art performance. We also demonstrate that finding an appropriate feature representation is critical to achieve a good performance when adapting a DCNN trained for an image recognition task.
Abstract This study contributes to the history of paper in Central Asia during the first millennium C.E. and aims to create a typology of paper based on a systematic study of Chinese manuscript collections found along the Silk Roads. The further aspect of this study aims to improve our knowledge of archaeometric research considered with the revision and test of scientific methodology which can then be used for historical and philological scholarship. By using fibre analysis and the technological study of paper combined with codicological and textual information, research has aimed to explore the possibilities for dating these materials, and fingerprinting their places of origin. The fact that many of Chinese manuscripts being studied (which are the oldest preserved and dated artefacts from Central Asia) are fixed in time by dates mentioned in colophons makes them valuable and reliable references for building a typology of paper and for comparative study of any yet to be discovered papers from that region. A sample of studied manuscripts comprises a total of 182 Chinese manuscripts selected from the Dunhuang Collection in the British Library in London, the Bibliothèque Nationale de France in Paris (BnF), the Institute of Oriental Manuscripts in St. Petersburg, and the Turfan collection in the Berlin Brandenburg Academy of Sciences (BBAW) and the Berlin State Library (StaBi).
Typestate-oriented programming is an extension of the OO paradigm in which objects are modeled not just in terms of interfaces but also in terms of their usage protocols, describing legal sequences of method calls, possibly depending on the object's internal state. We argue that the Actor Model allows typestate-OOP in an inherently distributed setting, whereby objects/actors can be accessed concurrently by several processes, and local entities cooperate to carry out a communication protocol. In this article we illustrate the approach by means of a number of examples written in Scala Akka. We show that Scala's abstractions support clean and natural typestate-oriented actor programming with the usual asynchronous and non-blocking semantics. We also show that the standard type system of Scala and a typed wrapping of usual (untyped) Akka's ActorRef are enough to provide rich forms of type safety so that well-typed actors respect their intended communication protocols. This approach draws on a solid theoretical background, consisting of a sound behavioral type system for the Join Calculus, that is a foundational calculus of distributed asynchronous processes whose semantics is based on the Chemical Abstract Machine, that unveiled its strong connections with typestate-oriented programming of both concurrent objects and actors.
Motivated by an old conjecture of P. Erdős and V. Neumann-Lara, our aim is to investigate digraphs with uncountable dichromatic number and orientations of undirected graphs with uncountable chromatic number. A graph has uncountable chromatic number if its vertices cannot be covered by countably many independent sets, and a digraph has uncountable dichromatic number if its vertices cannot be covered by countably many acyclic sets. We prove that consistently there are digraphs with uncountable dichromatic number and arbitrarily large digirth; this is in surprising contrast with the undirected case: any graph with uncountable chromatic number contains a 4-cycle. Next, we prove that several well known graphs (uncountable complete graphs, certain comparability graphs, and shift graphs) admit orientations with uncountable dichromatic number in ZFC. However, we show that the statement "every graph $G$ of size and chromatic number $ω_1$ has an orientation $D$ with uncountable dichromatic number" is independent of ZFC.