arXiv research

Information mapping is a popular application of Multivoxel Pattern Analysis (MVPA) to fMRI. Information maps are constructed using the so called searchlight method, where the spherical multivoxel neighborhood of every voxel (i.e., a searchlight) in the brain is evaluated for the presence of task-relevant response patte…

Partial proof of a conjecture about knot concordance maps.

This paper proposes a new method for an optimized mapping of temporal variables, describing a temporal stream data, into the recently proposed NeuCube spiking neural network architecture. This optimized mapping extends the use of the NeuCube, which was initially designed for spatiotemporal brain data, to work on arbitr…

This paper investigates circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. We characterise the images of the curvature maps and establish several equivalent conditions regarding long time behaviors of Chow-Luo's combinatorial Ricci flows for these patterns. As consequences,…

A simple method makes Euclidean patterns look like Escher's art.

Uniform diameter bound for reflection group disk patterns.

We study the space of linear difference equations with periodic coefficients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations of points in the projective space. We define the notion of combinatorial Gale tr…

A novel method classifies wafer defects using topological data analysis.

An image pattern can be represented by a probability distribution whose density is concentrated on different low-dimensional subspaces in the high-dimensional image space. Such probability densities have an astronomical number of local modes corresponding to typical pattern appearances. Related groups of modes can join…

In this paper, we study the problem of locating a predefined sequence of patterns in a time series. In particular, the studied scenario assumes a theoretical model is available that contains the expected locations of the patterns. This problem is found in several contexts, and it is commonly solved by first synthesizin…

The recently introduced Tsetlin Machine (TM) has provided competitive pattern classification accuracy in several benchmarks, composing patterns with easy-to-interpret conjunctive clauses in propositional logic. In this paper, we go beyond pattern classification by introducing a new type of TMs, namely, the Regression T…

We consider circle packings and, more generally, Delaunay circle patterns - arrangements of circles arising from a Delaunay decomposition of a finite set of points - on surfaces equipped with a complex projective structure. Motivated by a conjecture of Kojima, Mizushima and Tan, we prove that the forgetful map sending …

Word embedding maps words into a low-dimensional continuous embedding space by exploiting the local word collocation patterns in a small context window. On the other hand, topic modeling maps documents onto a low-dimensional topic space, by utilizing the global word collocation patterns in the same document. These two …

In this paper, we investigate the multi-variate sequence classification problem from a multi-instance learning perspective. Real-world sequential data commonly show discriminative patterns only at specific time periods. For instance, we can identify a cropland during its growing season, but it looks similar to a barren…

For generic maps from compact surfaces with boundary into the plane we develop an explicit algorithm for minimizing both the number of cusps and the number of components of the singular locus. More precisely, we minimize among maps with fixed boundary conditions and prescribed singular pattern, by which we mean the com…

We introduce a mixed-effects model to learn spatiotempo-ral patterns on a network by considering longitudinal measures distributed on a fixed graph. The data come from repeated observations of subjects at different time points which take the form of measurement maps distributed on a graph such as an image or a mesh. Th…

New patterns on spheres and hyperbolic planes described by integrable systems.

CMC-1 surfaces linked via Möbius transformations between circle patterns.

A new method synthesizes expressions from characteristics using GAN for healthcare.

Analyzing large X-ray diffraction (XRD) datasets is a key step in high-throughput mapping of the compositional phase diagrams of combinatorial materials libraries. Optimizing and automating this task can help accelerate the process of discovery of materials with novel and desirable properties. Here, we report a new met…

The artificial neural network shows powerful ability of inference, but it is still criticized for lack of interpretability and prerequisite needs of big dataset. This paper proposes the Rule-embedded Neural Network (ReNN) to overcome the shortages. ReNN first makes local-based inferences to detect local patterns, and t…

Consider an oriented curve $Γ$ in a domain $D$ in the plane $\boldsymbol R^2$. Thinking of $D$ as a piece of paper, one can make a curved folding in the Euclidean space $\boldsymbol R^3$. This can be expressed as the image of an "origami map" $Φ:D\to \boldsymbol R^3$ such that $Γ$ is the singular set of $Φ$, the word "…

Using a simplistic model of juggling based on physics, a natural map is constructed from the set of periodic juggling patterns (or site swaps) to links. We then show that all topological links can be juggled.

3D manifolds can map to a plane with specific curve patterns.

Research studies have shown that a large proportion of hazards remain unrecognized, which expose construction workers to unanticipated safety risks. Recent studies have also found that a strong correlation exists between viewing patterns of workers, captured using eye-tracking devices, and their hazard recognition perf…

Comprehending complex systems by simplifying and highlighting important dynamical patterns requires modeling and mapping higher-order network flows. However, complex systems come in many forms and demand a range of representations, including memory and multilayer networks, which in turn call for versatile community-det…

A novel framework infers causal direction from symbolic sequences using pattern entropy.

ALT improves TSC by capturing complex patterns in time series data.

Study circle patterns and polyhedral surfaces in hyperbolic ends, proving manifold properties.

Embeds hyperbolic plane into 3D space with detailed geometric analysis.

Research reveals simplicity bias in random logistic map, impacting data analysis and forecasting.

The present study deals with the analysis and mapping of Swiss franc interest rates. Interest rates depend on time and maturity, defining term structure of the interest rate curves (IRC). In the present study IRC are considered in a two-dimensional feature space - time and maturity. Geostatistical models and machine le…

In order to decode the human brain, Multivariate Pattern (MVP) classification generates cognitive models by using functional Magnetic Resonance Imaging (fMRI) datasets. As a standard pipeline in the MVP analysis, brain patterns in multi-subject fMRI dataset must be mapped to a shared space and then a classification mod…

The excited states of polyatomic systems are rather complex, and often exhibit meta-stable dynamical behaviors. Static analysis of reaction pathway often fails to sufficiently characterize excited state motions due to their highly non-equilibrium nature. Here, we proposed a time series guided clustering algorithm to ge…

The paper studies how grid cell patterns emerge in neural networks.

A polyhedral map is called $\{p, q\}$-equivelar if each face has $p$ edges and each vertex belongs to $q$ faces. In 1983, it was shown that there exist infinitely many geometrically realizable $\{p, q\}$-equivelar polyhedral maps if $q > p = 4$, $p > q = 4$ or $q - 3 > p = 3$. It was shown in 2001 that there exist infi…

The detection of interesting patterns in large high-dimensional datasets is difficult because of their dimensionality and pattern complexity. Therefore, analysts require automated support for the extraction of relevant patterns. In this paper, we present FDive, a visual active learning system that helps to create visua…

Given a triangulation of a closed surface, we consider a cross ratio system that assigns a complex number to every edge satisfying certain polynomial equations per vertex. Every cross ratio system induces a complex projective structure together with a circle pattern on the closed surface. In particular, there is an ass…

In this paper are studied the simplest patterns of axial curvature lines (along which the normal curvature vector is at a vertex of the ellipse of curvature) near a critical point of a surface mapped into R4. These critical points, where the rank of the mapping drops from 2 to 1, occur isolated in generic one parameter…

We study the closed group of homeomorphisms of the boundary of real hyperbolic space generated by a cocompact Kleinian group $G_1$ and a quasiconformal conjugate $h^{-1}G_2 h$ of a cocompact group $G_2$. We show that if the conjugacy $h$ is not conformal then this group contains a non-trivial one parameter subgroup. Th…

Extends DAMs to Gaussian distributions for efficient pattern storage and retrieval.

ActiLabel learns activity patterns across diverse sensor devices.

Discrete conformal maps on surfaces with vertex decorations are studied.

A knot in a solid torus defines a map on the set of (smooth or topological) concordance classes of knots in $S^3$. This set admits a group structure, but a conjecture of Hedden suggests that satellite maps never induce interesting homomorphisms: we give new evidence for this conjecture in both categories. First, we use…

Spatially-aware metrics improve uncertainty evaluation in segmentation.

Here we present DIVE: Data-driven Inference of Vertexwise Evolution. DIVE is an image-based disease progression model with single-vertex resolution, designed to reconstruct long-term patterns of brain pathology from short-term longitudinal data sets. DIVE clusters vertex-wise biomarker measurements on the cortical surf…

Reconstructing network connectivity from the collective dynamics of a system typically requires access to its complete continuous-time evolution although these are often experimentally inaccessible. Here we propose a theory for revealing physical connectivity of networked systems only from the event time series their i…

Chaos in cerebellar cells enhances complexity of neural patterns.