Dense Set Of Points Research Articles

Multi-sensitivity and other stronger forms of sensitivity in non-autonomous discrete systems

In this paper we obtain different sufficient conditions for a non-autonomous discrete system to be multi-sensitivite. We study properties of a multi-sensitive non-autonomous system in detail. It is proved that on a compact metric space every finitely generated non-autonomous system which is topologically transitive having dense set of periodic points is thickly syndetically sensitive. We introduce and study the notion of totally sensitive non-autonomous systems. We also provide counter examples to support our results.

The Dynamical Mordell–Lang Conjecture for Skew-Linear Self-Maps. Appendix by Michael Wibmer

Abstract Let $k$ be an algebraically closed field of characteristic $0$, let $N\in{\mathbb{N}}$, let $g:{\mathbb{P}}^1{\longrightarrow } {\mathbb{P}}^1$ be a nonconstant morphism, and let $A:{\mathbb{A}}^N{\longrightarrow } {\mathbb{A}}^N$ be a linear transformation defined over $k({\mathbb{P}}^1)$, that is, for a Zariski-open dense subset $U\subset{\mathbb{P}}^1$, we have that for $x\in U(k)$, the specialization $A(x)$ is an $N$-by-$N$ matrix with entries in $k$. We let $f:{\mathbb{P}}^1\times{\mathbb{A}}^N{\dashrightarrow } {\mathbb{P}}^1\times{\mathbb{A}}^N$ be the rational endomorphism given by $(x,y)\mapsto (\,g(x), A(x)y)$. We prove that if $g$ induces an automorphism of ${\mathbb{A}}^1\subset{\mathbb{P}}^1$, then each irreducible curve $C\subset{\mathbb{A}}^1\times{\mathbb{A}}^N$ that intersects some orbit $\mathcal{O}_f(z)$ in infinitely many points must be periodic under the action of $f$. Furthermore, in the case $g:{\mathbb{P}}^1{\longrightarrow } {\mathbb{P}}^1$ is an endomorphism of degree greater than $1$, then we prove that each irreducible subvariety $Y\subset{\mathbb{P}}^1\times{\mathbb{A}}^N$ intersecting an orbit $\mathcal{O}_f(z)$ in a Zariski dense set of points must be periodic. Our results provide the desired conclusion in the Dynamical Mordell–Lang Conjecture in a couple new instances. Moreover, our results have interesting consequences toward a conjecture of Rubel and toward a generalized Skolem–Mahler–Lech problem proposed by Wibmer in the context of difference equations. In the appendix it is shown that the results can also be used to construct Picard–Vessiot extensions in the ring of sequences.

Dynamical systems arising from random substitutions

Random substitutions are a natural generalisation of their classical ‘deterministic’ counterpart, whereby at every step of iterating the substitution, instead of replacing a letter with a predetermined word, every letter is independently replaced by a word from a finite set of possible words according to a probability distribution. We discuss the subshifts associated with such substitutions and explore the dynamical and ergodic properties of these systems in order to establish the groundwork for their systematic study. Among other results, we show under reasonable conditions that such systems are topologically transitive, have either empty or dense sets of periodic points, have dense sets of linearly repetitive elements, are rarely strictly ergodic, and have positive topological entropy.

Three counterexamples concerning the Northcott property of fields

We give three examples of fields concerning the Northcott property on elements of small height: The first one has the Northcott property but its Galois closure does not even satisfy the Bogomolov property. The second one has the Northcott property and is pseudo-algebraically closed, i.e. every variety has a dense set of rational points. The third one has bounded local degree at infinitely many rational primes but does not have the Northcott property.

Characterization of pinna motion patterns in hipposiderid bats

Hipposiderid bats have a set of highly differentiated pinna muscles that support different pinna motion patterns during biosonar behaviors. It has been shown that these bats' pinna motions fall into two separate categories: Rigid motions that change only pinna orientation and non-rigid motions that also change pinna shape. It remains unclear if further subdivisions of these two categories (e.g., different orientations for rigid motions and different deformation patterns for non-rigid motions) can be made. In order to investigate this question, experiments have been conducted where the positions of a dense set of landmark points (50–80 per pinna) were reconstructed based on footage from an array of four high-speed video cameras. The resulting point trajectory data (positions as a function of time) was clustered to facilitate the detection of patterns. Clustering revealed a structure of coherent surface patches for rigid as well as non-rigid motion. For the rigid motion pilot data set, these patches followe...

블록 정합 재작업 시수 예측 시스템에 관한 연구

In order to evaluate the precision degree of the blocks on the dock, the shipyards recently started to use the point cloud approaches using the 3D scanners. However, they hesitate to use it due to the limited time, cost, and elaborative effects for the post-works. Although it is somewhat traditional instead, they have still used the electro-optical wave devices which have a characteristic of having less dense point set (usually 1 point per meter) around the contact section of two blocks. This paper tried to expand the usage of point sets. Our approach can estimate the rework time to weld between the Pre-Erected(PE) Block and Erected(ER) block as well as the precision of block construction. In detail, two algorithms were applied to increase the efficiency of estimation process. The first one is K-mean clustering algorithm which is used to separate only the related contact point set from others not related with welding sections. The second one is the Concave hull algorithm which also separates the inner point of the contact section used for the delayed outfitting and stiffeners section, and constructs the concave outline of contact section as the primary objects to estimate the rework time of welding. The main purpose of this paper is that the rework cost for welding is able to be obtained easily and precisely with the defective point set. The point set on the blocks’ outline are challenging to get the approximated mathematical curves, owing to the lots of orthogonal parts and lack of number of point. To solve this problems we compared the Radial based function-Multi-Layer(RBF-ML) and Akima interpolation method. Collecting the proposed methods, the paper suggested the noble point matching method for minimizing the rework time of block-welding on the dock, differently the previous approach which had paid the attention of only the degree of accuracy.

Efficient and Accurate Hausdorff Distance Computation Based on Diffusion Search

The Hausdorff distance (HD) between two point sets is widely used in similarity measures, but the high computational cost of HD algorithms restrict their practical use. In this paper, we analyze the time complexity to compute an accurate Hausdorff distance and find that reducing the iterations of the inner loop significantly contributes in reducing the average time cost. Based on the observation that the nearest neighbor (NN) of the breakpoint in the current inner loop suggests a higher probability to break the next inner loop, we present a novel and efficient approach for computing the accurate Hausdorff distance based on a diffusion search. The current breakpoint is recorded as the diffusion center of the next inner loop so that the efficiency of the HD computation can be significantly improved without scanning every point. According to the type of 3-D model (sparse and dense point sets), a novel HD computation framework consisting of two specific diffusion search methods is proposed. First, a Z-order-based HD algorithm (ZHD) for a sparse point sets is proposed. Second, to avoid the low efficiency of a diffusion search when computing the Hausdorff distance between dense point sets with the ZHD algorithm, an octree-based HD algorithm (OHD) is proposed. Evaluation results demonstrate that the ZHD algorithm and the OHD algorithm can greatly reduce the time complexity of HD computations for sparse and dense point sets, respectively. In addition, we conduct several comparative experiments against the most famous HD computation methods. Experimental results show that the proposed approach achieves performance as good as the most efficient available algorithm and exhibits better performance in dealing with spatial data that is highly overlapping.

Quantification of fast pinna motions in rhinolophid and hipposiderid bats

As part of their biosonar behaviors, rhinolophid (family Rhinolophidae) and hipposiderid bats (family Hipposideridae) both show conspicuous motions of their outer ears (pinna). These motions coincide with pulse emission and echo reception in time and could hence have a functional relevance for the encoding of sensory information. However, a quantitative in-depth characterization of these motions is still needed to derive detailed hypotheses for their function. To accomplish this, dense sets of landmark points have been placed on the pinna to provide for dense spatial coverage of its surface over the course of a motion cycle. Occlusion-free stereo tracking of the landmarks was accomplished with an array of four high-speed video cameras. Customized methods based on motion prediction have been used to track landmark points across video frames. The results have been used to construct accurate, continuous estimates of pinna surface motion. These estimates reveal that the pinna surface is subject to heterogeneous patterns of displacements and velocities within each motion cycle. Experiments with simplified robotic reproductions to understand the acoustic implications of these pinna surface motions are currently in progress. Once the signal transformations that result from the pinna motions are understood, the question of functional relevance can be addressed.

MONITORING AND EVALUATION OF A LONG-SPAN RAIWAY BRIDGE USING SENTINEL-1 DATA

Abstract. This paper is focused on displacement monitoring of a bridge, which is one of the key aspects of its structural health monitoring. A simplified Persistent Scatterer Interferometry (PSI) approach is used to monitor the displacements of the Nanjing Dashengguan Yangtze River High-speed Railway Bridge (China). This bridge is 1272 m long and hosts a total of 6 railway lines. The analysis was based on a set of twenty-nine Sentinel-1A images, acquired from April 2015 to August 2016. A dense set of measurement points were selected on the bridge. The PSI results show a maximum longitudinal displacement of 150 mm, on each side of the bridge. The displacements are strongly correlated with the temperature, showing that they are due to thermal expansion. Using the PSI results, the Coefficient of Thermal Expansion (CTE) of the whole bridge was estimated. The result agrees well with the CTE of the bridge materials. Using a regression model, the PSI-measured displacements were compared with in-situ measurements. The paper proposes a procedure to assess the performance of the movable bearings of the bridge, which is based on the PSI measurements.

A Note on Sensitivity in Uniform Spaces

In this paper, the notions of periodic point are compared, and the sensitivity of semigroup actions on Hausdorff uniform spaces is studied. We show that for an action of a semigroup on a compact uniform space, if it is syndetically transitive and not minimal, then it is syndetically sensitive. We point out that if an action of a semigroup on a uniform space (does not need to be compact) is topologically transitive, not minimal, and has a dense set of s-periodic points, then it is syndetically sensitive. Additionally, we prove that if an action of a monoid on a uniform space (does not need to be compact) is topologically transitive, not minimal, and has a dense set of FM-periodic points, then it is syndetically sensitive.

The shape variational autoencoder: A deep generative model of part‐segmented 3D objects

AbstractWe introduce a generative model of part‐segmented 3D objects: the shape variational auto‐encoder (ShapeVAE). The ShapeVAE describes a joint distribution over the existence of object parts, the locations of a dense set of surface points, and over surface normals associated with these points. Our model makes use of a deep encoder‐decoder architecture that leverages the part‐decomposability of 3D objects to embed high‐dimensional shape representations and sample novel instances. Given an input collection of part‐segmented objects with dense point correspondences the ShapeVAE is capable of synthesizing novel, realistic shapes, and by performing conditional inference enables imputation of missing parts or surface normals. In addition, by generating both points and surface normals, our model allows for the use of powerful surface‐reconstruction methods for mesh synthesis. We provide a quantitative evaluation of the ShapeVAE on shape‐completion and test‐set log‐likelihood tasks and demonstrate that the model performs favourably against strong baselines. We demonstrate qualitatively that the ShapeVAE produces plausible shape samples, and that it captures a semantically meaningful shape‐embedding. In addition we show that the ShapeVAE facilitates mesh reconstruction by sampling consistent surface normals.

Chaotic extensions of continuous maps on compact manifolds

Let X be a compact connected Lipschitz manifold, with or without boundary. We show that for every continuous map and every nowhere dense closed subset K of X, there is a topologically transitive continuous map having a dense set of periodic points in X such that . Combined with a deep theorem of Sullivan, our result extends to all compact connected topological manifolds of dimension .

Indecomposability and Devaney’s chaoticity of semiflows with an arbitrary acting abelian topological semigroup

We prove that a semiflow with an arbitrary acting abelian topological semigroup is Devaney chaotic if and only if it is nonminimal, indecomposable and has a dense set of periodic points. This generalizes a result of X. Wang and Y. Huang.

Power-free values of polynomials on symmetric varieties

Given a symmetric variety Y defined over the rationals and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions under which the polynomial can be made r-free for a Zariski dense set of integral points on Y. We also establish an asymptotic counting formula for this set. In the special case that Y is a quadric hypersurface, we give explicit bounds on the size of r by combining the argument with a uniform upper bound for the density of integral points on general affine quadrics.

Transitive and series transitive maps on [formula omitted

Motivated by the behavior of topologically transitive homomorphisms of Polish abelian groups, we say a continuous map f:Rd→Rd is ‘series transitive’ if for any two nonempty open sets U,V⊂Rd, there exist x∈U and n∈N such that ∑j=0n−1fj(x)∈V. We show that any map on a discrete and closed subset of Rd can be extended to a mixing map of Rd, and use this result to produce a mixing map f:Rd→Rd (for each d∈N) which is also series transitive. We have examples to say that transitivity and series transitivity are independent properties for continuous self-maps of Rd. We also construct a chaotic map (i.e., a transitive map with a dense set of periodic points) f:Rd→Rd such that f is arbitrarily close to and asymptotic to the identity map. Finally, we make a few observations about topological transitivity of continuous homomorphisms of Polish abelian groups.

Weakly mixing proximal topological models for ergodic systems and applications

In this paper it is shown that every non-periodic ergodic system has two topologically weakly mixing, fully supported models: one is non-minimal but has a dense set of minimal points; and the other one is proximal. Also for independent interests, for a given Kakutani-Rokhlin tower with relatively prime column heights, it is demonstrated how to get a new taller Kakutani-Rokhlin tower with same property, which can be used in Weiss's proof of the Jewett-Krieger's theorem and the proofs of our theorems. Applications of the results are given.

Induced dynamics on the hyperspaces

<p> </p><p>In this paper, we study the dynamics induced by finite commutative relation on the hyperspaces. We prove that the dynamics induced on the hyperspace by a non-trivial commutative family of continuous self maps cannot be transitive and hence cannot exhibit higher degrees of mixing. We also prove that the dynamics induced on the hyperspace by such a collection cannot have dense set of periodic points. We also give example to show that the induced dynamics in this case may or may not be sensitive.</p>

Optimization of Sample Points for Monitoring Arable Land Quality by Simulated Annealing while Considering Spatial Variations

With China’s rapid economic development, the reduction in arable land has emerged as one of the most prominent problems in the nation. The long-term dynamic monitoring of arable land quality is important for protecting arable land resources. An efficient practice is to select optimal sample points while obtaining accurate predictions. To this end, the selection of effective points from a dense set of soil sample points is an urgent problem. In this study, data were collected from Donghai County, Jiangsu Province, China. The number and layout of soil sample points are optimized by considering the spatial variations in soil properties and by using an improved simulated annealing (SA) algorithm. The conclusions are as follows: (1) Optimization results in the retention of more sample points in the moderate- and high-variation partitions of the study area; (2) The number of optimal sample points obtained with the improved SA algorithm is markedly reduced, while the accuracy of the predicted soil properties is improved by approximately 5% compared with the raw data; (3) With regard to the monitoring of arable land quality, a dense distribution of sample points is needed to monitor the granularity.

Tangent Estimation from Point Samples

Let $$\mathcal{M}$$M be an m-dimensional smooth compact manifold embedded in $$\mathbb {R}^d$$Rd, where m is a constant known to us. Suppose that a dense set of points are sampled from $$\mathcal{M}$$M according to a Poisson process with an unknown parameter. Let p be any sample point, let $$\varrho $$ź be the local feature size at p, and let $$\varrho \varepsilon $$źź be the distance from p to the $$(n+1)$$(n+1)th nearest sample point for some n between $$\left( {\begin{array}{c}m+1\\ 2\end{array}}\right) + 1$$m+12+1 and $$\left( {\begin{array}{c}d+1\\ 2\end{array}}\right) $$d+12. Using the n sample points nearest to p, we can estimate the tangent space at p and it holds with probability $$1 - O(n^{-1/3})$$1-O(n-1/3) that the angular error is $$O(\varepsilon ^2)$$O(ź2). The running time is bounded by the time to compute the thin SVD of an $$n \times \left( {\begin{array}{c}d+1\\ 2\end{array}}\right) $$n?d+12 matrix and the full SVD of an $$n \times d$$n?d matrix, which is usually $$O(d^2n^2)$$O(d2n2) in practice. We implemented the algorithm and experimentally verified its effectiveness on both noiseless and noisy data.

Old wine in fractal bottles I: Orthogonal expansions on self-referential spaces via fractal transformations

Our results and examples show how transformations between self-similar sets may be continuous almost everywhere with respect to measures on the sets and may be used to carry well known notions from analysis and functional analysis, for example flows and spectral analysis, from familiar settings to new ones. The focus of this paper is on a number of surprising applications including what we call fractal Fourier analysis, in which the graphs of the basis functions are Cantor sets, discontinuous at a countable dense set of points, yet have good approximation properties. In a sequel, the focus will be on Lebesgue measure-preserving flows whose wave-fronts are fractals. The key idea is to use fractal transformations to provide unitary transformations between Hilbert spaces defined on attractors of iterated function systems.