scholarly journals The Stellar decomposition: A compact representation for simplicial complexes and beyond

2021 ◽  
Author(s):  
Riccardo Fellegara ◽  
Kenneth Weiss ◽  
Leila De Floriani
Keyword(s):  
Simplicial Complexes ◽  
Compact Representation

Algebraic Shifting and Sequentially Cohen-Macaulay Simplicial Complexes

10.37236/1245 ◽  
1996 ◽  
Vol 3 (1) ◽  
Author(s):  
Art M. Duval
Keyword(s):  
Simplicial Complex ◽  
Simplicial Complexes ◽  
Pure Case ◽  
Definition Of ◽  
Algebraic Shifting

Björner and Wachs generalized the definition of shellability by dropping the assumption of purity; they also introduced the $h$-triangle, a doubly-indexed generalization of the $h$-vector which is combinatorially significant for nonpure shellable complexes. Stanley subsequently defined a nonpure simplicial complex to be sequentially Cohen-Macaulay if it satisfies algebraic conditions that generalize the Cohen-Macaulay conditions for pure complexes, so that a nonpure shellable complex is sequentially Cohen-Macaulay. We show that algebraic shifting preserves the $h$-triangle of a simplicial complex $K$ if and only if $K$ is sequentially Cohen-Macaulay. This generalizes a result of Kalai's for the pure case. Immediate consequences include that nonpure shellable complexes and sequentially Cohen-Macaulay complexes have the same set of possible $h$-triangles.

scholarly journals Homological percolation transitions in growing simplicial complexes

2021 ◽  
Vol 31 (4) ◽  
pp. 041102
Author(s):  
Y. Lee ◽  
J. Lee ◽  
S. M. Oh ◽  
D. Lee ◽  
B. Kahng
Keyword(s):  
Simplicial Complexes

scholarly journals Method for designing multi-input system identification signals using a compact time-frequency representation

2021 ◽  
Author(s):  
Mathias Stefan Roeser ◽  
Nicolas Fezans
Keyword(s):  
System Identification ◽  
Design Method ◽  
Flight Test ◽  
Compact Representation ◽  
Time Frequency ◽  
Stability And Control ◽  
Frequency Representation ◽  
Aerodynamic Parameters ◽  
Definition Of ◽  
And Control

AbstractA flight test campaign for system identification is a costly and time-consuming task. Models derived from wind tunnel experiments and CFD calculations must be validated and/or updated with flight data to match the real aircraft stability and control characteristics. Classical maneuvers for system identification are mostly one-surface-at-a-time inputs and need to be performed several times at each flight condition. Various methods for defining very rich multi-axis maneuvers, for instance based on multisine/sum of sines signals, already exist. A new design method based on the wavelet transform allowing the definition of multi-axis inputs in the time-frequency domain has been developed. The compact representation chosen allows the user to define fairly complex maneuvers with very few parameters. This method is demonstrated using simulated flight test data from a high-quality Airbus A320 dynamic model. System identification is then performed with this data, and the results show that aerodynamic parameters can still be accurately estimated from these fairly simple multi-axis maneuvers.

scholarly journals Conditional out-of-distribution generation for unpaired data using transfer VAE

2020 ◽  
Vol 36 (Supplement_2) ◽  
pp. i610-i617
Author(s):  
Mohammad Lotfollahi ◽  
Mohsen Naghipourfar ◽  
Fabian J Theis ◽  
F Alexander Wolf
Keyword(s):  
Single Cell ◽  
Generative Models ◽  
Response To Treatment ◽  
High Dimensional ◽  
Compact Representation ◽  
Hair Color ◽  
Great Success ◽  
Cell Type ◽  
Style Transfer ◽  
Cell Type Specific

Abstract Motivation While generative models have shown great success in sampling high-dimensional samples conditional on low-dimensional descriptors (stroke thickness in MNIST, hair color in CelebA, speaker identity in WaveNet), their generation out-of-distribution poses fundamental problems due to the difficulty of learning compact joint distribution across conditions. The canonical example of the conditional variational autoencoder (CVAE), for instance, does not explicitly relate conditions during training and, hence, has no explicit incentive of learning such a compact representation. Results We overcome the limitation of the CVAE by matching distributions across conditions using maximum mean discrepancy in the decoder layer that follows the bottleneck. This introduces a strong regularization both for reconstructing samples within the same condition and for transforming samples across conditions, resulting in much improved generalization. As this amount to solving a style-transfer problem, we refer to the model as transfer VAE (trVAE). Benchmarking trVAE on high-dimensional image and single-cell RNA-seq, we demonstrate higher robustness and higher accuracy than existing approaches. We also show qualitatively improved predictions by tackling previously problematic minority classes and multiple conditions in the context of cellular perturbation response to treatment and disease based on high-dimensional single-cell gene expression data. For generic tasks, we improve Pearson correlations of high-dimensional estimated means and variances with their ground truths from 0.89 to 0.97 and 0.75 to 0.87, respectively. We further demonstrate that trVAE learns cell-type-specific responses after perturbation and improves the prediction of most cell-type-specific genes by 65%. Availability and implementation The trVAE implementation is available via github.com/theislab/trvae. The results of this article can be reproduced via github.com/theislab/trvae_reproducibility.

Hardware-Accelerated Dual-Split Trees

2020 ◽  
Vol 3 (2) ◽  
pp. 1-21
Author(s):  
Daqi Lin ◽  
Elena Vasiou ◽  
Cem Yuksel ◽  
Daniel Kopta ◽  
Erik Brunvand
Keyword(s):  
Ray Tracing ◽  
Hardware Acceleration ◽  
Memory Storage ◽  
Compact Representation ◽  
Space Partitioning ◽  
Data Movement ◽  
Bounding Volume ◽  
Bounding Boxes ◽  
Split Trees ◽  
Bounding Volume Hierarchies

Bounding volume hierarchies (BVH) are the most widely used acceleration structures for ray tracing due to their high construction and traversal performance. However, the bounding planes shared between parent and children bounding boxes is an inherent storage redundancy that limits further improvement in performance due to the memory cost of reading these redundant planes. Dual-split trees can create identical space partitioning as BVHs, but in a compact form using less memory by eliminating the redundancies of the BVH structure representation. This reduction in memory storage and data movement translates to faster ray traversal and better energy efficiency. Yet, the performance benefits of dual-split trees are undermined by the processing required to extract the necessary information from their compact representation. This involves bit manipulations and branching instructions which are inefficient in software. We introduce hardware acceleration for dual-split trees and show that the performance advantages over BVHs are emphasized in a hardware ray tracing context that can take advantage of such acceleration. We provide details on how the operations needed for decoding dual-split tree nodes can be implemented in hardware and present experiments in a number of scenes with different sizes using path tracing. In our experiments, we have observed up to 31% reduction in render time and 38% energy saving using dual-split trees as compared to binary BVHs representing identical space partitioning.

A Method Based on Support Vector Machine for Feature Selection of Latent Semantic Features

2011 ◽  
Vol 181-182 ◽  
pp. 830-835
Author(s):  
Min Song Li
Keyword(s):  
Support Vector Machine ◽  
Text Categorization ◽  
Latent Semantic Indexing ◽  
Classification Performance ◽  
Compact Representation ◽  
Support Vector ◽  
Semantic Features ◽  
Semantic Indexing ◽  
Feature Extraction Method ◽  
Feature Subspace

Latent Semantic Indexing(LSI) is an effective feature extraction method which can capture the underlying latent semantic structure between words in documents. However, it is probably not the most appropriate for text categorization to use the method to select feature subspace, since the method orders extracted features according to their variance,not the classification power. We proposed a method based on support vector machine to extract features and select a Latent Semantic Indexing that be suited for classification. Experimental results indicate that the method improves classification performance with more compact representation.

scholarly journals CGCI-SIFT: A More Efficient and Compact Representation of Local Descriptor

2013 ◽  
Vol 13 (3) ◽  
pp. 132-141 ◽  
Author(s):  
Dongliang Su ◽  
Jian Wu ◽  
Zhiming Cui ◽  
Victor S. Sheng ◽  
Shengrong Gong
Keyword(s):  
Peripheral Region ◽  
Intensity Difference ◽  
Compact Representation ◽  
Interest Point ◽  
Local Descriptor ◽  
Geometric Transformations ◽  
Intensity Information ◽  
Matching Efficiency ◽  
Inner Region ◽  
Better Than

This paper proposes a novel invariant local descriptor, a combination of gradient histograms with contrast intensity (CGCI), for image matching and object recognition. Considering the different contributions of sub-regions inside a local interest region to an interest point, we divide the local interest region around the interest point into two main sub-regions: an inner region and a peripheral region. Then we describe the divided regions with gradient histogram information for the inner region and contrast intensity information for the peripheral region respectively. The contrast intensity information is defined as intensity difference between an interest point and other pixels in the local region. Our experimental results demonstrate that the proposed descriptor performs better than SIFT and its variants PCA-SIFT and SURF with various optical and geometric transformations. It also has better matching efficiency than SIFT and its variants PCA-SIFT and SURF, and has the potential to be used in a variety of realtime applications.

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