Enumerating the Configurations in the n-Dimensional Orthogonal Polytopes Through Pólya's Countings and A Concise Representation

2006 ◽  
Author(s):  
Ricardo Perez-Aguila
Keyword(s):  
Concise Representation ◽  
Orthogonal Polytopes

A Krasnosel’skii-type theorem for certain orthogonal polytopes starshaped via k-staircase paths

2020 ◽  
Vol 20 (2) ◽  
pp. 169-177 ◽  
Author(s):  
Marilyn Breen
Keyword(s):  
Type Theorem ◽  
Common Point ◽  
Finite Family ◽  
Intersection Graph ◽  
Axis Parallel ◽  
Orthogonal Polytopes

AbstractLet 𝒞 be a finite family of distinct axis-parallel boxes in ℝd whose intersection graph is a tree, and let S = ⋃{C : C in 𝒞}. If every two points of S see a common point of S via k-staircase paths, then S is starshaped via k-staircase paths. Moreover, the k-staircase kernel of S will be convex via k-staircases.

scholarly journals A generalization of t-SNE and UMAP to single-cell multimodal omics

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Van Hoan Do ◽  
Stefan Canzar
Keyword(s):  
Dimensionality Reduction ◽  
Single Cell ◽  
Cell Types ◽  
High Dimensional ◽  
Omics Data ◽  
Relative Contribution ◽  
Reduction Techniques ◽  
Dimensionality Reduction Techniques ◽  
Concise Representation ◽  
Cellular Identity

AbstractEmerging single-cell technologies profile multiple types of molecules within individual cells. A fundamental step in the analysis of the produced high-dimensional data is their visualization using dimensionality reduction techniques such as t-SNE and UMAP. We introduce j-SNE and j-UMAP as their natural generalizations to the joint visualization of multimodal omics data. Our approach automatically learns the relative contribution of each modality to a concise representation of cellular identity that promotes discriminative features but suppresses noise. On eight datasets, j-SNE and j-UMAP produce unified embeddings that better agree with known cell types and that harmonize RNA and protein velocity landscapes.

scholarly journals A Concise Representation for Detailed Sentiment Analysis

2015 ◽  
Vol 97 (1) ◽  
pp. 35-45
Author(s):  
Victor M. Morales ◽  
Saúl León ◽  
Maya Carrillo ◽  
Aurelio López-López ◽  
Luis Enrique Colmenares-Guillen
Keyword(s):  
Sentiment Analysis ◽  
Concise Representation

scholarly journals Capturing User Intent when Brushing In Scatterplots

2020 ◽  
Author(s):  
Kiran Gadhave ◽  
Jochen Görtler ◽  
Oliver Deussen ◽  
Miriah Meyer ◽  
Jeff Phillips ◽  
...  
Keyword(s):  
Visualization Tool ◽  
Domain Experts ◽  
User Intent ◽  
Selection Accuracy ◽  
Provenance Data ◽  
Potential Benefits ◽  
Concise Representation ◽  
Mixed Initiative ◽  
Selection Of

Being able to capture or predict a user's intent behind a brush in a visualization tool has important implications in two scenarios. First, predicting intents can be used to auto-complete a partial selection in a mixed-initiative approach, with potential benefits to selection speed, correctness, and confidence. Second, capturing the intent of a selection can be used to improve recall, reproducibility, and even re-use. Augmenting provenance logs with semi-automatically captured intents makes it possible to save the reasoning behind selections. In this paper, we introduce a method to infer intent for selections and brushes in scatterplots. We first introduce a taxonomy of types of patterns that users might specify, which we elicited in a formative study conducted with professional data analysts and scientists. Based on this, we identify algorithms that can classify these patterns, and introduce various approaches to score the match of each pattern to an analyst's selection of items. We introduce a system that implements these methods for scatterplots and ranks alternative patterns against each other. Analysts then can use these predictions to auto-complete partial selections, and to conveniently capture their intent and provide annotations, thus making a concise representation of that intent available to be stored as provenance data. We evaluate our approach using interviews with domain experts and in a quantitative crowd-sourced study, in which we show that using auto-complete leads to improved selection accuracy for most types of patterns.

Stability of Vlasov equilibria. Part 1. General theory

1982 ◽  
Vol 27 (1) ◽  
pp. 13-24 ◽  
Author(s):  
K. R. Symon ◽  
C. E. Seyler ◽  
H. R. Lewis
Keyword(s):  
Distribution Function ◽  
General Theory ◽  
Linear Stability ◽  
Vlasov Equation ◽  
Stability Problem ◽  
Dispersion Matrix ◽  
Initial Value ◽  
Spectral Matrix ◽  
Concise Representation ◽  
The Stability

We present a general formulation for treating the linear stability of inhomogeneous plasmas for which at least one species is described by the Vlasov equation. Use of Poisson bracket notation and expansion of the perturbation distribution function in terms of eigenfunctions of the unperturbed Liouville operator leads to a concise representation of the stability problem in terms of a symmetric dispersion functional. A dispersion matrix is derived which characterizes the solutions of the linearized initial-value problem. The dispersion matrix is then expressed in terms of a dynamic spectral matrix which characterizes the properties of the unperturbed orbits, in so far as they are relevant to the linear stability of the system.

Concise Representation of Mass Spectrometry Images by Probabilistic Latent Semantic Analysis

2008 ◽  
Vol 80 (24) ◽  
pp. 9649-9658 ◽  
Author(s):  
Michael Hanselmann ◽  
Marc Kirchner ◽  
Bernhard Y. Renard ◽  
Erika R. Amstalden ◽  
Kristine Glunde ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Latent Semantic Analysis ◽  
Semantic Analysis ◽  
Probabilistic Latent Semantic Analysis ◽  
Concise Representation
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