arXiv research

No minimal chart of type (7) exists.

This paper studies minimal charts of a specific type to understand embedded surfaces in 4-space.

No minimal chart of type (2,3,2) exists.

No minimal chart of type (4,3) exists in 4-space.

Minimal charts of specific type contain unique subgraphs.

Let $Γ$ be a chart, and we denote by $Γ_m$ the union of all the edges of label $m$. A chart $Γ$ is of type $(3,2,2)$ if there exists a label $m$ such that $w(Γ)=7$, $w(Γ_m\capΓ_{m+1})=3$, $w(Γ_{m+1}\capΓ_{m+2})=2$, and $w(Γ_{m+2}\capΓ_{m+3})=2$ where $w(G)$ is the number of white vertices in $G$. In this paper, we prov…

Let $Γ$ be a chart. For each label $m$, we denote by $Γ_m$ the "subgraph" of $Γ$ consisting of all the edges of label $m$ and their vertices. Let $Γ$ be a minimal chart of type $(m;3,3)$. That is, a minimal chart $Γ$ has six white vertices, and both of $Γ_m\capΓ_{m+1}$ and $Γ_{m+1}\capΓ_{m+2}$ consist of three white ve…

Continuing the study of bounded geometry for Riemannian foliations, begun by Sanguiao, we introduce a chart-free definition of this concept. Our main theorem states that it is equivalent to a condition involving certain normal foliation charts. For this type of charts, it is also shown that the derivatives of the chang…

Charts are an excellent way to convey patterns and trends in data, but they do not facilitate further modeling of the data or close inspection of individual data points. We present a fully automated system for extracting the numerical values of data points from images of scatter plots. We use deep learning techniques t…

Stock market prediction is still a challenging problem because there are many factors effect to the stock market price such as company news and performance, industry performance, investor sentiment, social media sentiment and economic factors. This work explores the predictability in the stock market using Deep Convolu…

No minimal charts with exactly seven white vertices found.

In this paper, we give definitions of three kinds of minimal charts, and we investigate properties of minimal charts and establish fundamental theorems characterizing minimal charts. To classify charts with two or three crossings we use the fundamental theorems. In the future paper, we give an numeration of the charts …

Paper classifies surface-links using charts with specific properties.

The paper studies 4-charts with three crossings and their equivalence to a specific knot.

The Darboux theorem in symplectic geometry implies that any two points in a connected symplectic manifold have neighbourhoods symplectomorphic to each other. The impossibility of such a theorem in the more general multisymplectic framework appears to be, at least, folkloristic, but no explicit counterexample seems to e…

In this paper, we shall show a condition for that a chart is C-move equivalent to the product of two charts, the union of two charts $Γ^*$ and $Γ^{**}$ which are contained in disks $D^*$ and $D^{**}$ with $D^*\cap D^{**}=\emptyset$.

We classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in each of the distinguished holomorphic coordinate charts determined by the open …

Support Vector Data Description (SVDD) is a machine learning technique used for single class classification and outlier detection. SVDD based K-chart was first introduced by Sun and Tsung for monitoring multivariate processes when underlying distribution of process parameters or quality characteristics depart from Norm…

A method to fix radius distortion in generative models on curved spaces.

A branched covering surface-knot is a surface-knot in the form of a branched covering over an oriented surface-knot $F$, where we include the case when the covering has no branch points. A branched covering surface-knot is presented by a graph called a chart on a surface diagram of $F$. We can simplify a branched cover…

A 2-dimensional braid over an oriented surface-knot $F$ is presented by a graph called a chart on a surface diagram of $F$. We consider 2-dimensional braids obtained by an addition of 1-handles equipped with chart loops. We introduce moves of 1-handles with chart loops, called 1-handle moves, and we investigate how muc…

A branched covering surface-knot over an oriented surface-knot $F$ is a surface-knot in the form of a branched covering over $F$. A branched covering surface-knot over $F$ is presented by a graph called a chart on a surface diagram of $F$. For a branched covering surface-knot, an addition of 1-handles equipped with cha…

Dance Dance Revolution (DDR) is a popular rhythm-based video game. Players perform steps on a dance platform in synchronization with music as directed by on-screen step charts. While many step charts are available in standardized packs, players may grow tired of existing charts, or wish to dance to a song for which no …

New surfaces in 4-ball constructed from knits, described by charts.

Chart descriptions are a graphic method to describe monodromy representations of various topological objects. Here we introduce a chart description for hyperelliptic Lefschetz fibrations, and show that any hyperelliptic Lefschetz fibration can be stabilized by fiber-sum with certain basic Lefschetz fibrations.

Chart autoencoders learn latent features preserving manifold topology and geometry, with robust denoising capabilities.

We investigate minimal charts with loops, a simple closed curve consisting of edges of label $m$ containing exactly one white vertex. We shall show that there does not exist any loop in a minimal chart with exactly seven white vertices in this paper.

Channel charting (CC) has been proposed recently to enable logical positioning of user equipments (UEs) in the neighborhood of a multi-antenna base-station solely from channel-state information (CSI). CC relies on dimensionality reduction of high-dimensional CSI features in order to construct a channel chart that captu…

Classifies equivariant vector bundles over toric manifolds.

Introduces Hurewicz fibrations for embedding maps of orbifold charts.

Chart descriptions are a graphic method to describe monodromy representations of various topological objects. Here we introduce a chart description for genus-two Lefschetz fibrations, and show that any genus-two Lefschetz fibration can be stabilized by fiber-sum with certain basic Lefschetz fibrations.

Deep learning is an effective approach to solving image recognition problems. People draw intuitive conclusions from trading charts; this study uses the characteristics of deep learning to train computers in imitating this kind of intuition in the context of trading charts. The three steps involved are as follows: 1. B…

We give a combinatorial description of closed curves on oriented surfaces in terms of certain permutations, called charts. We describe automorphisms of curves in terms of charts and compute the total number of curves counted with appropriate weights. We also discuss relations between curves, Grothendieck dessins d'enfa…

We propose channel charting (CC), a novel framework in which a multi-antenna network element learns a chart of the radio geometry in its surrounding area. The channel chart captures the local spatial geometry of the area so that points that are close in space will also be close in the channel chart and vice versa. CC w…

Twisted $\operatorname{SL}_2 \mathbb{C}$ local systems on surfaces of finite type appear often in geometry and physics. Most of them arise geometrically as local systems of charts for pleated hyperbolic structures. Bonahon and Thurston's "shear-bend coordinates" parameterize these local systems of charts. On a surface …

Given a 2-crossing minimal chart $Γ$, a minimal chart with two crossings, set $α=\min\{~i~|~$there exists an edge of label $i$ containing a white vertex$\}$, and $β=\max\{~i~|~$there exists an edge of label $i$ containing a white vertex$\}$. In this paper we study the structure of a neighbourhood of $Γ_α\cupΓ_β$, and p…

The paper proves uniform Temple charts and applies them to null distance metrics.

This is the first step of the two steps to enumerate the minimal charts with two crossings. For a label $m$ of a chart $Γ$ we denote by $Γ_m$ the union of all the edges of label $m$ and their vertices. For a minimal chart $Γ$ with exactly two crossings, we can show that the two crossings are contained in $Γ_α\capΓ_β$ f…

In this paper, we find a holomorphic Darboux chart around any immersed noncompact holomorphic Legendrian curve in a complex contact manifold $(X,ξ)$. By using such a chart, we show that every holomorphic Legendrian immersion $R\to X$ from an open Riemann surface can be approximated on relatively compact subsets by holo…

A new control chart detects shifts in binary data streams quickly and reliably.

Unified framework for singular statistical models using observable charts.

This study evaluates the performances of CNN and LSTM for recognizing common charts patterns in a stock historical data. It presents two common patterns, the method used to build the training set, the neural networks architectures and the accuracies obtained.

In this paper we compute the minimal number of Darboux chart needed to cover a Hermitian symmetric space of compact type in terms of the degree of their embeddings in $\mathbb{C} P^N$. The proof is based on the recent work of Y. B. Rudyak and F. Schlenk [18] and on the symplectic geometry tool developed by the first au…

In this paper we try to design the necessary calculation needed for backtesting trading systems when only candle chart data are available. We lay particular emphasis on situations which are not or not uniquely decidable and give possible strategies to handle such situations.

The classic N p chart gives a signal if the number of successes in a sequence of inde- pendent binary variables exceeds a control limit. Motivated by engineering applications in industrial image processing and, to some extent, financial statistics, we study a simple modification of this chart, which uses only the most …

We employ a certain labeled finite graph, called a chart, in a closed oriented surface for describing the monodromy of a(n achiral) Lefschetz fibration over the surface. Applying charts and their moves with respect to Wajnryb's presentation of mapping class groups, we first generalize a signature formula for Lefschetz …

For an oriented surface link $F$ in $\mathbb{R}^4$, we consider a satellite construction of a surface link, called a 2-dimensional braid over $F$, which is in the form of a covering over $F$. We introduce the notion of an $m$-chart on a surface diagram $π(F)\subset \mathbb{R}^3$ of $F$, which is a finite graph on $π(F)…

New procedures connect braid charts, triplane diagrams, and braid movies for knotted surfaces.