Linear Independence and Rank. The Simple Image Set

2010 ◽  
pp. 127-148
Author(s):  
Peter Butkovič
Keyword(s):  
Linear Independence ◽  
Image Set

Oral Immune Activation by Disgust and Disease-Related Pictures

2015 ◽  
Vol 29 (3) ◽  
pp. 119-129 ◽  
Author(s):  
Richard J. Stevenson ◽  
Deborah Hodgson ◽  
Megan J. Oaten ◽  
Luba Sominsky ◽  
Mehmet Mahmut ◽  
...  
Keyword(s):  
Immune Response ◽  
Immune Responses ◽  
Innate Immune Response ◽  
Negative Control ◽  
Innate Immune ◽  
Innate Immune Responses ◽  
Immune Markers ◽  
Before And After ◽  
Secondary Analyses ◽  
Image Set

Abstract. Both disgust and disease-related images appear able to induce an innate immune response but it is unclear whether these effects are independent or rely upon a common shared factor (e.g., disgust or disease-related cognitions). In this study we directly compared these two inductions using specifically generated sets of images. One set was disease-related but evoked little disgust, while the other set was disgust evoking but with less disease-relatedness. These two image sets were then compared to a third set, a negative control condition. Using a wholly within-subject design, participants viewed one image set per week, and provided saliva samples, before and after each viewing occasion, which were later analyzed for innate immune markers. We found that both the disease related and disgust images, relative to the negative control images, were not able to generate an innate immune response. However, secondary analyses revealed innate immune responses in participants with greater propensity to feel disgust following exposure to disease-related and disgusting images. These findings suggest that disgust images relatively free of disease-related themes, and disease-related images relatively free of disgust may be suboptimal cues for generating an innate immune response. Not only may this explain why disgust propensity mediates these effects, it may also imply a common pathway.

LNTP-MDBN: Big Data Integrated Learning Framework for Heterogeneous Image Set Classification

2019 ◽  
Vol 15 (2) ◽  
pp. 227-236
Author(s):  
D. Franklin Vinod ◽  
V. Vasudevan
Keyword(s):  
Big Data ◽  
Medical Image ◽  
Research Study ◽  
Big Data Analytics ◽  
Learning Framework ◽  
Image Set Classification ◽  
Filtering Technique ◽  
Image Set ◽  
Hidden Patterns ◽  
Global Data

Background: With the explosive growth of global data, the term Big Data describes the enormous size of dataset through the detailed analysis. The big data analytics revealed the hidden patterns and secret correlations among the values. The major challenges in Big data analysis are due to increase of volume, variety, and velocity. The capturing of images with multi-directional views initiates the image set classification which is an attractive research study in the volumetricbased medical image processing. Methods: This paper proposes the Local N-ary Ternary Patterns (LNTP) and Modified Deep Belief Network (MDBN) to alleviate the dimensionality and robustness issues. Initially, the proposed LNTP-MDBN utilizes the filtering technique to identify and remove the dependent and independent noise from the images. Then, the application of smoothening and the normalization techniques on the filtered image improves the intensity of the images. Results: The LNTP-based feature extraction categorizes the heterogeneous images into different categories and extracts the features from each category. Based on the extracted features, the modified DBN classifies the normal and abnormal categories in the image set finally. Conclusion: The comparative analysis of proposed LNTP-MDBN with the existing pattern extraction and DBN learning models regarding classification accuracy and runtime confirms the effectiveness in mining applications.

Examples of theories of presheaf type

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
Finite Groups ◽  
Linear Independence ◽  
Geometric Theory ◽  
Vector Spaces ◽  
Linear Orders ◽  
Locally Finite ◽  
Strong Unit ◽  
Locally Finite Groups ◽  
Simplicial Sets ◽  
Separable Extensions

This chapter discusses several classical as well as new examples of theories of presheaf type from the perspective of the theory developed in the previous chapters. The known examples of theories of presheaf type that are revisited in the course of the chapter include the theory of intervals (classified by the topos of simplicial sets), the theory of linear orders, the theory of Diers fields, the theory of abstract circles (classified by the topos of cyclic sets) and the geometric theory of finite sets. The new examples include the theory of algebraic (or separable) extensions of a given field, the theory of locally finite groups, the theory of vector spaces with linear independence predicates and the theory of lattice-ordered abelian groups with strong unit.

scholarly journals Automatic Detection of Discrimination Actions from Social Images

Electronics ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 325
Author(s):  
Zhihao Wu ◽  
Baopeng Zhang ◽  
Tianchen Zhou ◽  
Yan Li ◽  
Jianping Fan
Keyword(s):  
Action Recognition ◽  
State Of The Art ◽  
Automatic Detection ◽  
Experimental Results ◽  
Practical Approach ◽  
Detection And Identification ◽  
Art Methods ◽  
Image Set ◽  
Social Images ◽  
Relationship Identification

In this paper, we developed a practical approach for automatic detection of discrimination actions from social images. Firstly, an image set is established, in which various discrimination actions and relations are manually labeled. To the best of our knowledge, this is the first work to create a dataset for discrimination action recognition and relationship identification. Secondly, a practical approach is developed to achieve automatic detection and identification of discrimination actions and relationships from social images. Thirdly, the task of relationship identification is seamlessly integrated with the task of discrimination action recognition into one single network called the Co-operative Visual Translation Embedding++ network (CVTransE++). We also compared our proposed method with numerous state-of-the-art methods, and our experimental results demonstrated that our proposed methods can significantly outperform state-of-the-art approaches.

scholarly journals Convergence properties of the Broyden-like method for mixed linear–nonlinear systems of equations

2021 ◽  
Author(s):  
Florian Mannel
Keyword(s):  
Linear Independence ◽  
Affine Subspace ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Convergence Properties ◽  
Initial Matrix ◽  
First Time ◽  
Special Case ◽  
Dimensional Mapping ◽  
Finite Number Of Iterations

AbstractWe consider the Broyden-like method for a nonlinear mapping $F:\mathbb {R}^{n}\rightarrow \mathbb {R}^{n}$ F : ℝ n → ℝ n that has some affine component functions, using an initial matrix B0 that agrees with the Jacobian of F in the rows that correspond to affine components of F. We show that in this setting, the iterates belong to an affine subspace and can be viewed as outcome of the Broyden-like method applied to a lower-dimensional mapping $G:\mathbb {R}^{d}\rightarrow \mathbb {R}^{d}$ G : ℝ d → ℝ d , where d is the dimension of the affine subspace. We use this subspace property to make some small contributions to the decades-old question of whether the Broyden-like matrices converge: First, we observe that the only available result concerning this question cannot be applied if the iterates belong to a subspace because the required uniform linear independence does not hold. By generalizing the notion of uniform linear independence to subspaces, we can extend the available result to this setting. Second, we infer from the extended result that if at most one component of F is nonlinear while the others are affine and the associated n − 1 rows of the Jacobian of F agree with those of B0, then the Broyden-like matrices converge if the iterates converge; this holds whether the Jacobian at the root is invertible or not. In particular, this is the first time that convergence of the Broyden-like matrices is proven for n > 1, albeit for a special case only. Third, under the additional assumption that the Broyden-like method turns into Broyden’s method after a finite number of iterations, we prove that the convergence order of iterates and matrix updates is bounded from below by $\frac {\sqrt {5}+1}{2}$ 5 + 1 2 if the Jacobian at the root is invertible. If the nonlinear component of F is actually affine, we show finite convergence. We provide high-precision numerical experiments to confirm the results.

Student attitudes towards linear algebra: an attempt to roll back the fog

2020 ◽  
Author(s):  
Barry J Griffiths ◽  
Samantha Shionis
Keyword(s):  
Student Perceptions ◽  
Linear Algebra ◽  
Student Attitudes ◽  
Linear Independence ◽  
Negative Emotions ◽  
Practical Applications ◽  
Key Concepts ◽  
The Subject ◽  
Roll Back

Abstract In this study, we look at student perceptions of a first course in linear algebra, focusing on two specific aspects. The first is the statement by Carlson that a fog rolls in once abstract notions such as subspaces, span and linear independence are introduced, while the second investigates statements made by several authors regarding the negative emotions that students can experience during the course. An attempt is made to mitigate this through mediation to include a significant number of applications, while continually dwelling on the key concepts of the subject throughout the semester. The results show that students agree with Carlson’s statement, with the concept of a subspace causing particular difficulty. However, the research does not reveal the negative emotions alluded to by other researchers. The students note the importance of grasping the key concepts and are strongly in favour of using practical applications to demonstrate the utility of the theory.

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