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The new formalism enables one to calculate matrix convolutions and other algebraic operations in matrix form.
We translate the matrix concept for designers and managers who are considering a matrix organization and argue that three factors are critical for its success: (1) Strong purpose: Only choose the matrix structure if there are strong reasons for doing so, (2) Alignment among contingencies: A matrix can only be successful if key contingencies are aligned with the matrix’s purpose, and (3) Management of junctions: The success of a matrix depends on how well activities at the junctions of the matrix are managed.
Although the detailed mechanisms of these specific matrix productions is not yet completely elucidated, the rapidly increasing knowledge on the regulation of specific matrix production process and deranged matrix production might represent a new area of crosstalk between cancer research and matrix biology.
We show that, for suitable choices of the matrix coefficients P and Q, it is possible to characterize by means of φ ( z ) well known matrix functions, namely the matrix square root, the matrix polar factor, the matrix sign and the geometric mean of two matrices.
In our results a nilpotent matrix and a symmetric matrix play an important role.
Journal ArticleDOI
01 Apr 1998-Automatica
41 Citations
This note proves that every Hurwitz-stable matrix can be expressed as the product of a symmetric positive-definite matrix and a generalised negative-definite matrix.
It is shown that this “modified” matrix measure has most of the properties of the usual matrix measure, and that many of the known applications of the usual matrix measure can therefore be carried over to the modified matrix measure.
The reason is that no transformation matrix, which transforms the Mastrovito matrix into a Toeplitz matrix, has been found.
Open accessJournal ArticleDOI
21 Citations
It is shown that our framework naturally extends the usual notion of (univariate) matrix functions and allows to unify existing results on linear matrix equations and derivatives of matrix functions.

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Various underground mining survey methods have been developed to accurately assess underground structures and objects. These methods include using artificial earthquake generators for underground surveys, computing forward and reverse propagation wave fields based on earthquake wave data for precise estimation of underground structures, employing horizontal directional drilling for engineering geological surveys to reduce drilling workload and costs, utilizing underground facility survey systems with transmission/reception antennae and display units for locating buried objects like pipes safely, and applying instruments like total stations, DistoX2, and digital cameras for surveying caves with methods such as polar and digital photogrammetry. Each method offers unique advantages in terms of accuracy, efficiency, and cost-effectiveness in conducting underground mining surveys.
What are convolution operations in image processing?
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Convolution operations in image processing involve applying a filter or kernel to an image to extract features or enhance certain characteristics. This process includes dividing the image into sub-images, performing convolution on these sub-images, and then combining the results to obtain the final convolution output. By convolving the image with a kernel, specific operations like smoothing, sharpening, noise reduction, and edge detection can be achieved. The convolution operation method typically entails multiplying elements of partial matrices from the image and the kernel, summing these products, and generating a convolution result. Utilizing convolutional neural networks in image processing allows for cutting the image into sub-images, independently convolving them, aggregating the results, and outputting the final processed image, enhancing system performance.
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4 answers
The difference between novelty and contribution of a research paper lies in their definitions and implications. Novelty refers to something new, original, or unusual, while contribution refers to the value or impact that the research adds to the field. Novelty is often considered a prerequisite for contribution, as research must offer new insights or understanding to be considered valuable. However, novelty alone is not sufficient to evaluate the contribution of a research paper. Contributions are evaluated based on criteria such as specificity of focus, proposed outcomes, logic, dialectic, rhetoric, and social-institutional argumentation. Contributions can also be framed in relation to the wider field or disciplinary matrix. Therefore, while novelty is about being new or original, contribution is about the value and impact that the research brings to the field.
How many replications on treatments must be done?
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The number of replications required for experiments varies depending on the specific context. In the case of maize hybrid competition experiments, it was found that at least 11 replications were needed to ensure a minimum significant level of 95% for grain yield. In the context of ecosystem experiments, substantial and sustained manipulations using multiple replicates produced significant results in the majority of simulated experiments. However, due to limitations such as high costs and scarcity of experimental ecosystems, it may not always be feasible to have an adequate number of replicates. In the field of psychotherapy clinical trials, there is a lack of direct replication attempts for trials with large effects, raising questions about the replicability of treatment superiority conclusions. The number of replicates required for studies on sperm production varies among species and end points, with some requiring a larger number of replicates than typically used in investigations.
How to write the information of a sonicater in published article?
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A published article on the information of a sonicater can be written by following a specific method and apparatus described in the abstract by Olsen et al.. The method involves using a sonic horn probe positioned in sonic energy transfer relationship to a film of liquid, which is streamed over the article. Sound waves transmitted through the liquid dislodge particles from the article, and the liquid carrying the dislodged particles is drained away. This process ensures that the liquid used as the sonication medium cannot recontaminate the article. Additionally, the article can be further cleaned using a subsequent sterilization means. This method and apparatus can be particularly useful for aseptic packaging of foodstuffs or other similar applications.
Is the film, The Matrix Buddhist in nature?
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The film, The Matrix, has been analyzed from various perspectives, including Buddhist interpretations. Scholars have noted the presence of Buddhist themes and concepts in the film, such as the exploration of hidden realities, the impermanence of the world, and the idea of selflessness as a means to transcend the material. The film also incorporates the Buddhist concept of skillful means, which is used by advanced practitioners to guide central characters on the path to wisdom. The parallels between The Matrix and Buddhist philosophy, particularly Mahayana Buddhism, are evident in the narrative and symbolism of the film.
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What causes cracks during cold forging metal matrix composite?
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Why eigenvalues and eigenvectors are used in machine learning?
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Eigenvalues and eigenvectors are used in machine learning because they provide valuable information about the structure and properties of data. Eigendecomposition, which involves factorizing a matrix into its eigenvalues and eigenvectors, allows for the reduction of data to a kernel matrix, which is used in various machine learning tasks. This approach has been shown to improve classifier performance in terms of accuracy and time compared to using Gram matrices. Eigenvectors also play a crucial role in methods such as spectral clustering, Independent Component Analysis (ICA), and topic models, where they help identify underlying patterns and structures in the data. Additionally, eigenvectors can be used to track the motion and dispersion of data points over time, enabling interpretability in machine learning models. Overall, eigenvalues and eigenvectors provide a powerful mathematical framework for understanding and analyzing complex datasets in machine learning applications.
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