Performance evaluation of SIFT against common image deformations on iban plaited mat motif images

Decorative plaited mat is one of the many examples of rich plait work often seen on Borneo handicraft products. The plaited mats are decorated with simple and complex motif designs; each has its own special meaning and taboos. The motif designs are used as a reflection of environment and the traditional beliefs in the Iban community. In line with efforts from UNESCO’s and Sarawak Government’s, digitization, and the use of IR4.0 technologies to preserve and promote this cultural heritage is encouraged. Towards this end goal, we present a novel image dataset containing 10 Iban plaited mat motif classes. The plaited mat motifs are made of diagonal and symmetrical shapes, as well as geometric and non-geometric patterns. Classification’s accuracy using scale-invariant feature transform (SIFT) features was evaluated against 6 common image deformations: zoom+rotation, viewpoint, image blur, JPEG compression, scale and illumination, across multiple threshold values. Varying degrees of each deformation were applied to a digitally cleaned (and cropped) image of each mat motif class. We used RANSAC to remove outliers from the noisy SIFT matching result. The optimal threshold value is 2.0e-2 with a reported 100.0% matching accuracy for the scale change and zoom+rotation set.

Metabolic impact of weight variations in Icelandic horses

Background Insulin dysregulation (ID) is an equine endocrine disorder, which is often accompanied by obesity and various metabolic perturbations. The relationship between weight variations and fluctuations of the insulin response to oral glucose tests (OGT) as well as the metabolic impact of ID have been described previously. The present study seeks to characterize the concomitant metabolic impact of variations in the insulin response and bodyweight during repeated OGTs using a metabolomics approach. Methods Nineteen Icelandic horses were subjected to five OGTs over one year and their bodyweight, insulin and metabolic response were monitored. Analysis of metabolite concentrations depending on time (during the OGT), relative bodyweight (rWeight; defined as the bodyweight at one OGT divided by the mean bodyweight across all OGTs) and relative insulin response (rAUCins; defined accordingly from the area under the insulin curve during OGT) was performed using linear models. Additionally, the pathways significantly associated with time, rWeight and rAUCins were identified by rotation set testing. Results The results suggested that weight gain and worsening of ID activate distinct metabolic pathways. The metabolic profile associated with weight gain indicated an increased activation of arginase, while the pathways associated with time and rAUCins were consistent with the expected effect of glucose and insulin, respectively. Overall, more metabolites were significantly associated with rWeight than with rAUCins.

Non-existence of sublinear diffusion for a class of torus homeomorphisms

We prove that, if f is a homeomorphism of the 2-torus isotopic to the identity whose rotation set is a non-degenerate segment and f has a periodic point, then it has uniformly bounded deviations in the direction perpendicular to the segment.

Generic rotation sets

Let $(X,T)$ be a topological dynamical system. Given a continuous vector-valued function $F \in C(X, \mathbb {R}^{d})$ called a potential, we define its rotation set $R(F)$ as the set of integrals of F with respect to all T-invariant probability measures, which is a convex body of $\mathbb {R}^{d}$ . In this paper we study the geometry of rotation sets. We prove that if T is a non-uniquely ergodic topological dynamical system with a dense set of periodic measures, then the map $R(\cdot )$ is open with respect to the uniform topologies. As a consequence, we obtain that the rotation set of a generic potential is strictly convex and has $C^{1}$ boundary. Furthermore, we prove that the map $R(\cdot )$ is surjective, extending a result of Kucherenko and Wolf.

On the rotation sets of generic homeomorphisms on the torus

We study the rotation sets for homeomorphisms homotopic to the identity on the torus $\mathbb T^d$ , $d\ge 2$ . In the conservative setting, we prove that there exists a Baire residual subset of the set $\text {Homeo}_{0, \lambda }(\mathbb T^2)$ of conservative homeomorphisms homotopic to the identity so that the set of points with wild pointwise rotation set is a Baire residual subset in $\mathbb T^2$ , and that it carries full topological pressure and full metric mean dimension. Moreover, we prove that for every $d\ge 2$ the rotation set of $C^0$ -generic conservative homeomorphisms on $\mathbb T^d$ is convex. Related results are obtained in the case of dissipative homeomorphisms on tori. The previous results rely on the description of the topological complexity of the set of points with wild historic behavior and on the denseness of periodic measures for continuous maps with the gluing orbit property.

A condition that implies full homotopical complexity of orbits for surface homeomorphisms

We consider closed orientable surfaces $S$ of genus $g>1$ and homeomorphisms $f:S\rightarrow S$ isotopic to the identity. A set of hypotheses is presented, called a fully essential system of curves $\mathscr{C}$ and it is shown that under these hypotheses, the natural lift of $f$ to the universal cover of $S$ (the Poincaré disk $\mathbb{D}$), denoted by $\widetilde{f},$ has complicated and rich dynamics. In this context, we generalize results that hold for homeomorphisms of the torus isotopic to the identity when their rotation sets contain zero in the interior. In particular, for $C^{1+\unicode[STIX]{x1D716}}$ diffeomorphisms, we show the existence of rotational horseshoes having non-trivial displacements in every homotopical direction. As a consequence, we found that the homological rotation set of such an $f$ is a compact convex subset of $\mathbb{R}^{2g}$ with maximal dimension and all points in its interior are realized by compact $f$-invariant sets and by periodic orbits in the rational case. Also, $f$ has uniformly bounded displacement with respect to rotation vectors in the boundary of the rotation set. This implies, in case where $f$ is area preserving, that the rotation vector of Lebesgue measure belongs to the interior of the rotation set.

Deviations in the Franks–Misiurewicz conjecture

We show that if there exists a counter example for the rational case of the Franks–Misiurewicz conjecture, then it must exhibit unbounded deviations in the complementary direction of its rotation set.

On the computability of rotation sets and their entropies

Let$f:X\rightarrow X$be a continuous dynamical system on a compact metric space$X$and let$\unicode[STIX]{x1D6F7}:X\rightarrow \mathbb{R}^{m}$be an$m$-dimensional continuous potential. The (generalized) rotation set$\text{Rot}(\unicode[STIX]{x1D6F7})$is defined as the set of all$\unicode[STIX]{x1D707}$-integrals of$\unicode[STIX]{x1D6F7}$, where$\unicode[STIX]{x1D707}$runs over all invariant probability measures. Analogous to the classical topological entropy, one can associate the localized entropy$\unicode[STIX]{x210B}(w)$to each$w\in \text{Rot}(\unicode[STIX]{x1D6F7})$. In this paper, we study the computability of rotation sets and localized entropy functions by deriving conditions that imply their computability. Then we apply our results to study the case where$f$is a subshift of finite type. We prove that$\text{Rot}(\unicode[STIX]{x1D6F7})$is computable and that$\unicode[STIX]{x210B}(w)$is computable in the interior of the rotation set. Finally, we construct an explicit example that shows that, in general,$\unicode[STIX]{x210B}$is not continuous on the boundary of the rotation set when considered as a function of$\unicode[STIX]{x1D6F7}$and$w$. In particular,$\unicode[STIX]{x210B}$is, in general, not computable at the boundary of$\text{Rot}(\unicode[STIX]{x1D6F7})$.

Homotopical complexity of a billiard flow on the 3D flat torus with two cylindrical obstacles

We study the homotopical rotation vectors and the homotopical rotation sets for the billiard flow on the unit flat torus with two disjoint and orthogonal toroidal (cylindrical) scatterers removed from it. The natural habitat for these objects is the infinite cone erected upon the Cantor set $\text{Ends}(G)$ of all ‘ends’ of the hyperbolic group $G=\unicode[STIX]{x1D70B}_{1}(\mathbf{Q})$. An element of $\text{Ends}(G)$ describes the direction in (the Cayley graph of) the group $G$ in which the considered trajectory escapes to infinity, whereas the height function $s$ ($s\geq 0$) of the cone gives us the average speed at which this escape takes place. The main results of this paper claim that the orbits can only escape to infinity at a speed not exceeding $\sqrt{3}$ and, in any direction $e\in \text{Ends}(\unicode[STIX]{x1D70B}_{1}({\mathcal{Q}}))$, the escape is feasible with any prescribed speed $s$, $0\leq s\leq 1/(\sqrt{6}+2\sqrt{3})$. This means that the radial upper and lower bounds for the rotation set $R$ are actually pretty close to each other. Furthermore, we prove the convexity of the set $\mathit{AR}$ of constructible rotation vectors, and that the set of rotation vectors of periodic orbits is dense in $\mathit{AR}$. We also provide effective lower and upper bounds for the topological entropy of the studied billiard flow.

The local rotation set is an interval

Let $\text{Homeo}_{0}(\mathbb{R}^{2};0)$ be the set of all homeomorphisms of the plane that are isotopic to the identity and which fix zero. Recently, in Le Roux [L’ensemble de rotation autour d’un point fixe. Astérisque (350) (2013), 1–109], Le Roux gave the definition of the local rotation set of an isotopy$I$ in $\text{Homeo}_{0}(\mathbb{R}^{2};0)$ from the identity to a homeomorphism $f$ and he asked if this set is always an interval. In this article, we give a positive answer to this question and to the analogous question in the case of the open annulus.