Set Of Tiles Research Articles

Tiling and weak tiling in (Zp)d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\mathbb {Z}_p)^d$$\\end{document}

We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary p-groups (Zp)d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\mathbb {Z}_p)^d$$\\end{document}, we introduce an averaging procedure that leads to a natural object of study: a 4-tuple of functions which can be regarded as a common generalization of tiles and spectral sets. We characterize such 4-tuples for d=1,2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=1, 2$$\\end{document}, and prove some partial results for d=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=3$$\\end{document}.

Robust and Flexible Sliding Tactile Sensor for Surface Pattern Perception and Recognition

Perceiving surface characteristics through tactile interaction typically requires high‐resolution devices or precise spatial scanning to record and analyze a significant amount of information. However, most available tactile sensors require complicated technological processes, redundant layouts, and data acquisition circuits, which limits their ability to provide a real‐time static perception and feedback for potential applications such as robotic manipulation. Drawing inspiration from the sliding tactile (ST) perception mode of the human fingertip, a robust and flexible ST sensor with a low array density of 2.7 cells cm−2 is reported. This innovative sensor has a soft and cambered configuration that allows it to rapidly and accurately recognize the 3D surface features of objects, including grooves as small as 500 μm. Benefiting from the strong correlation between collected electronic responding and local deformation of sensing cell, the ST sensor can adaptively reconstruct surface patterns with the assistance of deep learning, even on unstructured objects. The pattern recognition system based on the robot is demonstrated by accurately classifying a set of mahjong tiles with nearly 100% accuracy, surpassing human tactile perception capabilities in the same task.

Generating Loop Patterns with a Genetic Algorithm and a Probabilistic Cellular Automata Rule

The objective is to find a Cellular Automata (CA) rule that can generate “loop patterns”. A loop pattern is given by ones on a zero background showing loops. In order to find out how loop patterns can be locally defined, tentative loop patterns are generated by a genetic algorithm in a preliminary stage. A set of local matching tiles is designed and checked whether they can produce the aimed loop patterns by the genetic algorithm. After having approved a certain set of tiles, a probabilistic CA rule is designed in a methodical way. Templates are derived from the tiles, which then are used in the CA rule for matching. In order to drive the evolution to the desired patterns, noise is injected if the templates do not match or other constraints are not fulfilled. Simulations illustrate that loops and connected loops can be evolved by the CA rule.

Counting Traversing Hamiltonian Cycles in Tiled Graphs

Recently, the problem of counting Hamiltonian cycles in 2-tiled graphs was resolved by Vegi Kalamar, Bokal, and Žerak. In this paper, we continue our research on generalized tiled graphs. We extend algorithms on counting traversing Hamiltonian cycles from 2-tiled graphs to generalized tiled graphs. We further show that, similarly as for 2-tiled graphs, for a fixed finite set of tiles, counting traversing Hamiltonian cycles can be performed in linear time with respect to the size of such graph, implying that counting traversing Hamiltonian cycles in tiled graphs is fixed-parameter tractable.

Seismic Tiles, a data format to facilitate analytics on seismic reflectors

Seismic Tiles is a new concept for representing seismic reflectors and attributes derived from seismic data, which makes it easy to automate seismic interpretation and analysis in general. Many subsurface problems can now be solved mostly automatically by computers, instead of mostly manually by humans, enabling the disruption of seismic interpretation at a scale similar to the disruption of road navigation facilitated by the closely analogous Google Map-style data structure. Some examples where this has been successfully implemented include screening for amplitude-variation-with-offset anomalies to identify prospects, automatic characterization of 4D effects according to rock physics modeling, and identifying faults and horizons verified by structural logic. Automation takes place not via machine learning but by direct and transparent application of well-known geophysical and geologic logic. This is achieved by automatically detecting all reflectors in the seismic data set and representing them by a set of tiles, which are small rectangular surfaces typically 200 m × 200 m in size. Tiles are calculated on a regular grid in lateral coordinates via a local 3D linear Radon transform. A set of tiles combine to describe a reflector surface, similar to how tiles in a bathroom combine to describe the walls and floor. Any attribute, from any seismic cube or other data sets, can be automatically extracted and assigned to the tiles and thus used in the logic. This logic can include the geometry of the tile itself and how it relates to tiles in the neighborhood, thus allowing easy implementation of any kind of interpretation logic that involves seismic reflectors. As the tile geometry and attributes are exposed to man and machine in a simple tabular data format, implementing logic using Seismic Tiles is easy, and much easier than applying logic directly on input in the form of raw seismic data.

Bounded Wang tilings with integer programming and graph-based heuristics

Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging applications in materials engineering, we consider the bounded version of the tiling problem and offer four integer programming formulations to construct valid or nearly-valid Wang tilings: a decision, maximum-rectangular tiling, maximum cover, and maximum adjacency constraint satisfaction formulations. To facilitate a finer control over the resulting tilings, we extend these programs with tile-based, color-based, packing, and variable-sized periodic constraints. Furthermore, we introduce an efficient heuristic algorithm for the maximum-cover variant based on the shortest path search in directed acyclic graphs and derive simple modifications to provide a 1/2 approximation guarantee for arbitrary tile sets, and a 2/3 guarantee for tile sets with cyclic transducers. Finally, we benchmark the performance of the integer programming formulations and of the heuristic algorithms showing that the heuristics provide very competitive outputs in a fraction of time. As a by-product, we reveal errors in two well-known aperiodic tile sets: the Knuth tile set contains a tile unusable in two-way infinite tilings, and the Lagae corner tile set is not aperiodic.

Aharonov-Bohm cages, flat bands, and gap labeling in hyperbolic tilings

Aharonov-Bohm caging is a localization mechanism stemming from the competition between the geometry and the magnetic field. Originally described for a tight-binding model in the dice lattice, this destructive interference phenomenon prevents any wavepacket spreading away from a strictly confined region. Accordingly, for the peculiar values of the field responsible for this effect, the energy spectrum consists of a discrete set of highly degenerate flat bands. In the present work, we show that Aharonov-Bohm cages are also found in an infinite set of hyperbolic dice tilings defined on a negatively curved hyperbolic plane. We detail the construction of these tilings and compute their Hofstadter butterflies by considering periodic boundary conditions on high-genus surfaces. As recently observed for some regular hyperbolic tilings, these butterflies do not manifest the self-similar structure of their Euclidean counterparts but still contain some gaps. We also consider the energy spectrum of hyperbolic kagome tilings (which are the dual of hyperbolic dice tilings), which displays interesting features, such as highly degenerate states arising for some particular values of the magnetic field. For these two families of hyperbolic tilings, we compute the Chern number in the main gaps of the Hofstadter butterfly and propose a gap labeling inspired by the Euclidean case. Finally, we also study the triangular Husimi cactus, which is a limiting case in the family of hyperbolic kagome tilings, and we derive an exact expression for its spectrum versus magnetic flux.

The density and minimal gap of visible points in some planar quasicrystals

It has previously been observed that the limiting gap distribution of the directions to visible points of planar quasicrystals may vanish near zero, that is, there exist planar quasicrystals with a positive limiting minimal normalised gap between the angles of visible points. The exact values of these limiting minimal normalised gaps have not been determined. In this paper we give explicit formulas for the densities of visible points for planar quasicrystals from several families, which include the Ammann–Beenker point set and the vertex sets of some rhombic Penrose tilings. Combining these results with a known characterisation of the limiting minimal gap in terms of a probability measure on an associated homogeneous space of quasicrystals, we give explicit values of the limiting minimal normalised gap between the angles of visible points for several families of planar quasicrystals, in particular, for the Ammann–Beenker point set and for the vertex sets of some rhombic Penrose tilings. We also compare our results with numerical observations.

Replication of Arbitrary Hole-Free Shapes via Self-assembly with Signal-Passing Tiles

In this paper, we investigate the abilities of systems of self-assembling tiles which can each pass a constant number of signals to their immediate neighbors to create replicas of input shapes. Namely, we work within the Signal-passing Tile Assembly Model (STAM), and we provide a universal STAM tile set which is capable of creating unbounded numbers of assemblies of shapes identical to those of input assemblies. The shapes of the input assemblies can be arbitrary 2-dimensional hole-free shapes. This improves previous shape replication results in self-assembly that required models in which multiple assembly stages and/or bins were required, and the shapes which could be replicated were more constrained, as well as a previous version of this result that required input shapes to be represented at scale factor 2.

Spirals in Periodic Tilings

Spiral tilings, as appealing as they are for their aesthetics, have not been studied well mathematically. One of the difficulties in this area of tiling theory is providing a mathematical definition of spiral tilings. A recently published attempt at providing a formal definition distinguishes a so-called L-spiral tiling (L-tiling) and an S-spiral tiling (S-tiling), with the two types being characterized by special properties of tile set partitions. Based on these existing definitions, we investigate the spiral structure in periodic tilings. Unlike spiral tilings, periodic tilings lend themselves easily to a definition and have been well studied. We first prove that it is not possible for periodic tilings to be S-tilings. We then study a subset of periodic tilings that can be L-tilings. In particular, we demonstrate that there exist examples for each type of isohedral tilings (a subset of periodic monohedral tilings) that are L-spirable.

Evaluation of SRGAN Algorithm for Superresolution of Satellite Imagery on Different Sensors

Abstract. In recent years, deep learning has quickly evolved to be the go-to solution for any kind of analysis of non-linear data. One such use has been that of Generative Adversarial Networks (GAN) in the field of Computer Vision. GAN models have a variety of applications for image processing, specifically, super-resolution of images. A lot of work has been done to enhance or upscale generic RGB imagery such as the ones taken from a mobile or digital camera. However, in the field of remote sensing, it presents challenges like preserving the spatial resolution of the sensor, which is affected by a wider pixel value range and relation of a pixel to ground sampling distance (GSD). From data preparation to enhancing a complete set of tiles at scale, the upsampling/downsampling requires the ratio of number pixels to the actual area in geography to be preserved. SRGAN model has been proven to be effective for interpolating the pixels based on context. However, it was observed that the same algorithm with or without parameter tuning behaves differently based on the sensor source and target resolution. We evaluate the performance of the model from 10m to 2.5m and 2.4m to 0.6m resolution. The comparison will enable better decision making when using the enhanced images for LULC classification, segmentation, and object detection.

EXPERIMENTS AND USED EVALUATION METRICS USED IN THE DEVELOPMENT OF A LANGUAGE-INDEPENDENT INCREASE DETECTOR

Experiments and evaluation metrics play an important role in the development of a language-independent incremental detector (MRIP), which will allow to analyze the results of the development and the suitability of the developed algorithm and device. The experiments will also provide an answer to the question of evaluating the performance of the developed detector and comparing it with the commercial SIG approach to clone detection, to explore the benefits that the incremental approach can offer. To get an idea of the performance of MNIDP, it is proposed to run it for five software systems (open source), measuring the requirements for time and memory. Also, to answer the question of expanding and improving the initial approach, by using locally sensitive hashing (LCH), there is a need to measure the performance of the proposed expansion on the basis of LCH and compare it with the performance of MNIP. The experiments conducted in the study provided some useful information based on the evaluation of the effectiveness of the proposed expansion on the basis of LCH. More specifically, in some cases, compared to the implementation of MNIDP, the stage of creating an index in the approach based on LCH was two, and in some cases three times slower. A possible reason for this may be the complexity of the MinHash operation, which is a significant part of the overall LCH scheme. This becomes obvious when you consider that the hashing of each tile for each set of tiles during MinHashing must be performed by k-based hash functions. It was assumed that the process of incremental implementation step on the basis of MNIDP will be much slower, due to the calculation of index records on the fly. However, in the course of the study, opposite results were obtained. In practice, this was justified by the fact that the similarity threshold used did not cause a large number of matches between the source files. To gain a better understanding of its behavior, there is a need for further research into the relationship of runtime required for the incremental implementation step flow based on the LCH and the similarity threshold.

Enumerating Isotopy Classes of Tilings Guided by the Symmetry of Triply Periodic Minimal Surfaces

We present a technique for the enumeration of all isotopically distinct ways of tiling a hyperbolic surface of finite genus, possibly nonorientable and with punctures and boundary. This generalizes the enumeration using Delaney--Dress combinatorial tiling theory of combinatorial classes of tilings to isotopy classes of tilings. To accomplish this, we derive an action of the mapping class group of the orbifold associated to the symmetry group of a tiling on the set of tilings. We explicitly give descriptions and presentations of semipure mapping class groups and of tilings as decorations on orbifolds. We apply this enumerative result to generate an array of isotopically distinct tilings of the hyperbolic plane with symmetries generated by rotations that are commensurate with the three-dimensional symmetries of the primitive, diamond, and gyroid triply periodic minimal surfaces, which have relevance to a variety of physical systems.

3coSoKu and its declarative modeling

Abstract In this paper, we analyze the physical puzzle IcoSoKu, a game about placing some given triangular tiles on the faces of an icosahedron in order to fill the capacities of its vertices, and we propose its generalization called 3coSoKu, admitting an arbitrary playing field with triangular faces, arbitrary capacities and an arbitrary set of triangular tiles. First, we prove the strong NP-completeness of 3coSoKu, even when the playing field is a convex polyhedron with equilateral triangles as faces. Second, we encode 3coSoKu both in the constraint modeling language MiniZinc and in the logic programming paradigm known as Answer Set Programming and we develop a visual tool for an accessible interface to the solver. Finally, we use our encodings to verify experimentally that every initial state for IcoSoKu admits a solution.

Geography of Legendrian knot mosaics

In this paper, mosaic tiles have been used to build knots and define invariants since they were introduced by Lomonaco and Kauffman to describe quantum knots. In this paper, we propose a modified set of tiles to describe the front projections of Legendrian knots. We explore the effect of stabilization on the mosaic number of a Legendrian knot by defining and classifying “two-cell” stabilizations. Inspired by a construction of Ludwig et al. in 2013, we provide an infinite family of Legendrian unknots whose mosaic numbers are realized only in non-reduced projections. Finally, we provide a census of known mosaic numbers for Legendrian unknots and trefoils.

Online recognition of magnetic tile defects based on UPM-DenseNet

The detection of surface defects of magnetic tile has a crucial impact on the quality of the motor; however, owing to the large difference in the scale of the surface defects of magnetic tile and the complex background texture, it is difficult for the convolutional neural network to extract the characteristics of the defect itself, and the phenomenon that small defects easily lose features in forward propagation further increases the difficulty of extracting features from the network model. As a result, the accuracy and robustness of surface defect detection based on machine vision are low. Aiming at the above problems, this paper proposes a UPM-DenseNet two-stage detection model. First, the original image data are generated through the positioning network to generate areas where defects may exist, and the influence of complex backgrounds is eliminated to a feasible extent. Then, the obtained feature map is used as the input of the classification network. Finally, the online recognition of the magnetic tile defect is completed through the classification network. To enhance the neural network’s ability to recognize regions of interest for defects of different scales, a plug-and-play feature restoration module is further proposed. The experimental results on the defective set of magnetic tiles show that UPM-DenseNet was effective for different kinds of defects. Under normal, out-of-focus and, noise conditions, the sparse classification accuracy of this method was 96.385%, 95.107%, and 84.47%, respectively. Compared with mainstream network frameworks, it increased by 1.037%, 0.83%, and 1.531%, respectively. The average area under the curve of various defects reached 0.9863, and the average detection speed was 11.109 FPS, both of which meet the accuracy and speed requirements for the detection of small defects on the surface of the magnetic tile in industrial production.

Pointwise periodic maps with quantized first integrals

We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete, thus quantized. Furthermore, the level sets are bounded sets whose interior is formed by a finite number of open tiles of certain regular or uniform tessellations. The action of the maps on each invariant set of tiles is described geometrically.

Sub‐bitstream packing based lightweight tiled streaming for 6 degree of freedom immersive video

The MPEG immersive video (MIV) has been designed to remove the redundancies of multi-view videos and merge the residuals into two textures and two geometry videos; therefore, four bitstreams and video decoders are required to provide six degrees of freedom (6DoF) in virtual reality (VR) in MIV. This letter proposes a sub-bitstream packing method and realisation in tiled streaming for MIV to provide a single bitstream for legacy systems that have a single decoder without an increase in the server-side storage. The proposed method divided the input videos into tiles in the compressed-domain to accomplish two goals: (i) generate a merged bitstream using the existing four bitstreams for legacy systems and (ii) improve the quality of an immersive video by disabling the deblocking filter. For a player with one or few numbers of decoders, the extracted tile sub-streams were merged by the proposed four specific mixed-quality tiling and packing methods using a motion-constrained tile set (MCTS), while complying with the high-efficiency video coding (HEVC) standard. Experimental results demonstrated that the proposed sub-stream packing method required a single decoder and exhibited 17.40% decoding time and 0.81% bjontegaard-delta rate (BD-rate) savings on Y-PSNR saving compared to the non-tiled streaming method.

Optimization and Inverse Design of Floor Tile Airflow Distributions in Data Centers Using Response Surface Method

Abstract Computational fluid dynamics (CFD) has become a popular tool compared to experimental measurement for thermal management in data centers. However, it is very time-consuming and resource-intensive when used to model large-scale data centers, and often unrealistic for real-time thermal analyses. In addition, it is prohibitive to use CFD for the optimization process where thousands of designs need to be generated. Floor tile airflow distribution control is a key technique for maintaining a sufficient cold air delivery to variable thermal loadings of server cabinets. Regular practice of deploying a set of identical floor tiles may not result in the best solution for airflow uniformity through tiles. In this paper, an optimization procedure based on response surface methodology (RSM) is proposed to find the best arrangement of mixed-porosity floor tiles for different targeted tile airflow distributions. Fast-approximation RSM based on radial basis function (RBF) allows thousands of designs to be generated for the optimization process which uses a genetic algorithm as its main solver. The method shows proven success in maximizing floor tile airflow uniformity, and in the inverse design optimization where various tile airflow distribution topologies, i.e., linear, parabolic, and sinusoidal shapes are targeted. For the considered data center and aisle configuration, the improvement over the all-uniform-tile design is 55% in terms of standard deviation to the average tile airflow rate, whereas 90%, 91%, and 94% in root-mean-square error (RMSE) for the linear, parabolic, and sinusoidal floor tile airflow distribution objectives, respectively.

On the effects of hierarchical self-assembly for reducing program-size complexity

In this paper we present a series of results which show separations between the standard seeded model of self-assembly, Winfree's abstract Tile Assembly Model (aTAM), and the “seedless” 2-Handed Assembly Model (2HAM), which incorporates the dynamics of hierarchical self-assembly. In particular, we focus on the problem of self-assembling various shapes while minimizing the sizes of tile sets, or “programs”, in each of these models in order to compare and contrast the models. A high-level overview of a subset of these results was presented in a paper by the authors in STACS 2013, but in this version we expand and improve the set of results related to showing separations between the two models according to their abilities to self-assemble various shapes. We exhibit classes of finite shapes that can be self-assembled more efficiently in each model. We also demonstrate infinite shapes that can self-assemble in one model but not in the other, as well as a shape which cannot self-assemble in either model.