Related papers: Array Orthogonality in Higher Dimensions
In order to apply nonstandard methods to modern algebraic geometry, as a first step in this paper we study the applications of nonstandard constructions to category theory. It turns out that many categorial properties are well behaved under…
Study of patterns on images is recognized as an important step in characterization and classification of image. The ability to efficiently analyze and describe image patterns is thus of fundamental importance. The study of syntactic methods…
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
In a previous paper, one of us pointed out that the anomalous dimension matrices for all physical processes that have been calculated to date are complex symmetric, if stated in an orthonormal basis. In this paper we prove this fact and…
The increasing application of deep-learning is accompanied by a shift towards highly non-linear statistical models. In terms of their geometry it is natural to identify these models with Riemannian manifolds. The further analysis of the…
A universally L^1 good sequence n_k is constructed with n_{k+1}-n_k tending to infinity. For ergodic transformations non-conventional ergodic averages of L^1 functions computed by using this sequence converge to the integral of the…
A successive vertex ordering of a graph is a linear ordering of its vertices in which every vertex except the first has at least one neighbour appearing earlier. Such orderings arise naturally in incremental growth and…
We characterize the existence of horizontal path lifts for general connections on arbitrary fiber bundles with a new property that also gives fresh insight into linear and $G$-connections.
We study the capability to learn and to generate long-range, power-law correlated sequences by a fully connected asymmetric network. The focus is set on the ability of neural networks to extract statistical features from a sequence. We…
Accurate lane topology is essential for autonomous driving, yet traditional methods struggle to model the complex, non-linear structures-such as loops and bidirectional lanes-prevalent in real-world road structure. We present SeqGrowGraph,…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
In a classical case, orthogonal polynomial sequences are in such a way that the $ n $th polynomial has the exact degree $n$. Such sequences are complete and form a basis of the space for any arbitrary polynomial. In this paper, we introduce…
Compacting orthogonal drawings is a challenging task. Usually algorithms try to compute drawings with small area or edge length while preserving the underlying orthogonal shape. We present a one-dimensional compaction algorithm that alters…
An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…
The motivation for using qualitative shape descriptions is as follows: qualitative shape descriptions can implicitly act as a schema for measuring the similarity of shapes, which has the potential to be cognitively adequate. Then, shapes…
A perfect matching in a hypergraph is a set of edges that partition the set of vertices. We study the complexity of deciding the existence of a perfect matching in orderable and separable hypergraphs. We show that the class of orderable…
In this paper, we study orthogonal colourings of random geometric graphs. Two colourings of a graph are orthogonal if they have the property that when two vertices receive the same colour in one colouring, then those vertices receive…
Correlation is a common technique for the detection of shifts. Its generalization to the multidimensional geometric correlation in Clifford algebras additionally contains information with respect to rotational misalignment. It has been…
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…
Reconstruction of directional fields is a need in many geometry processing tasks, such as image tracing, extraction of 3D geometric features, and finding principal surface directions. A common approach to the construction of directional…