scispace - formally typeset
Search or ask a question

Answers from top 5 papers

More filters
Papers (5)Insight
Furthermore, it is possible to predict an optional release process when the amount of matrix and composition of matrix system were defined.
Open accessProceedings ArticleDOI
03 Oct 2011
26 Citations
On the other hand, our results also provide the first guarantees for (a) deterministic matrix completion, and (b) recovery when we observe a vanishing fraction of entries of a corrupted matrix.
Our unified result also provides the first guarantees for 1) recovery when we observe a vanishing fraction of entries of a corrupted matrix, and 2) deterministic matrix completion.
When the matrix slices of the original tensor are highly correlated, we expect the corresponding sum of matrix ranks from all framelet transformed matrix frontal slices would be small, and the resulting tensor completion can be performed much better.
It is proved that the theorems being valid in the exiting matrix game with IVIFNs are still true when the general aggregation operator is used in the proposed matrix game with IVIFNs.

See what other people are reading

What is power flow analysis?
5 answers
What are the limitation of environmental performance and communication matrix framework?
5 answers
The limitations of the environmental performance and communication matrix framework include challenges related to robust environmental disturbances affecting system performance, missing measurements due to network connectivity, power consumption, and storage capacity constraints in Wireless Sensor Networks (WSNs), and the need for effective communication strategies to promote pro-environmental behavior in industrial settings. Additionally, the framework's effectiveness in communicating environmental efforts to customers, especially in B2B communications, is crucial for companies aiming to enhance their sustainable supplier brand image. These limitations highlight the importance of addressing environmental challenges, optimizing network performance, and implementing tailored communication strategies to effectively convey environmental performance in various contexts.
What is the mathematical background necessary to understand the level set method?
5 answers
To understand the level-set method, one needs a foundation in convex optimization with a focus on strong duality as a necessary condition for the method's success. Additionally, knowledge of degenerate nonlinear second-order differential equations on Euclidean space is crucial, particularly regarding the regularity of solutions and their twice differentiable nature in classical settings. Understanding the interplay between analysis and geometry is essential for proving fine analytical properties in such scenarios. Moreover, familiarity with numerical approaches for simulating magnetic phenomena using the level-set method, including the coupling mechanism between magnetic fields and mechanical systems, is beneficial. Finally, expertise in topology optimization procedures based on the level-set method for solving inverse problems, such as acoustic wave propagation, is valuable, especially in identifying obstacles within a background medium without requiring initial guesses or reinitialization procedures.
Can infinite robust control be effectively applied to real-world control problems, and if so, what are some examples?
5 answers
Infinite robust control can be effectively applied to real-world control problems, as demonstrated by various research studies. For instance, a novel robust controller in the Linear Matrix Inequality framework was proposed for a single-machine infinite bus system, accommodating parameter uncertainties and time delays without linearizing the system. Additionally, a control-limits aware robust safe control framework was developed for systems with uncertain dynamic models, ensuring safety under bounded state-dependent uncertainties and control limits. These examples showcase the practical applicability of infinite robust control in addressing uncertainties and ensuring system safety in real-world control applications.
How to do convex optimization on 3d cross-section to 2d image registration?
5 answers
Convex optimization for 3D cross-section to 2D image registration involves aligning volumetric 3D images with planar 2D images through various methods. One approach involves utilizing a hyperelastic deformation regularization suitable for biological materials, estimating out-of-plane deformation based on out-of-focus blur in 2D microscopy images, and employing a coarse-to-fine optimization strategy with higher-order optimization methods. Another method includes template matching for rough matching followed by accurate optimization using a gradient descent algorithm to achieve precise registration results efficiently. Additionally, a technique incorporates determining local 2D displacement information and motion parameters of a 3D motion model to describe the movement of the target region between image dataset acquisition and x-ray imaging, aiding in the registration process.
How to use simplex constraint inputs in bayesian optimization?
4 answers
To utilize simplex-constrained inputs in Bayesian optimization, one can leverage Gaussian process models in the joint space of design and uncertain variables, as discussed in. By correlating constraints in the GP model and employing a two-step acquisition function, relevant optimization variables associated with uncertain samples can be identified efficiently. Additionally, incorporating threshold functions, rectified linear, and rectified polynomial activation functions in neural architectures can aid in Bayesian compressive sensing of simplex-constrained sparse stochastic vectors, as outlined in. This approach allows for faster solutions in the low-measurement regime and robustness to small model mismatches, offering superior approximations with fewer parameters compared to standard architectures in supervised learning scenarios.
What are the factors affecting the shape of the density curve for light hazard?
5 answers
The shape of the density curve for light hazard can be influenced by various factors. In the context of laser irradiation on a spherical target, the radiation pressure generates a nonmonotonic density profile with an overdense bump in the underdense region, which is the stable solution under specific conditions. Probability density functions and hazard functions are interrelated, with specific shapes such as increasing, decreasing, unimodal, anti-unimodal, and more, impacting each other. Nonparametric maximum likelihood estimation methods consider decreasing density and constraints on hazard functions like increasing, convex, or bathtub-shaped, affecting the shape of the density curve. Perturbations to meteoroid shape or atmospheric density can also alter the light curve, with changes in mass distribution affecting the symmetry and curvature of the emitted light intensity.
However, AKF remains challenge to nonlinear systems of finding optimal solutions when faced with model parameter uncertainties
5 answers
The challenge of finding optimal solutions for nonlinear systems with model parameter uncertainties can be addressed through innovative optimization methods. One such approach involves jointly optimizing a nominal trajectory and an error feedback to handle uncertainties effectively. By reformulating uncertain nonlinear systems as linear time-varying systems, tools from system level synthesis can be applied to convexly bound uncertainties, leading to a tractable optimization problem. Additionally, incorporating uncertainties into a feedback loop via model predictive control can enhance the performance of control strategies in the presence of initial condition uncertainties. These methods offer efficient ways to handle uncertainties and optimize solutions for nonlinear systems, showcasing advancements in addressing challenges posed by model parameter uncertainties.
What does "linear" mean in linear algebra?
5 answers
In linear algebra, the term "linear" refers to the properties of additivity and homogeneity that linear operators and functions exhibit. Linear algebra plays a crucial role in various fields like numerical computing, functional analysis, and quantum programming language design. Linear algebra algorithms form the foundation of numerical computations, with matrices and vectors being fundamental components in solving complex problems efficiently. Linear operators are essential in functional analysis and vector space theory, providing a mathematical framework for numerical mathematics, differential equations, and mathematical physics. Additionally, in the context of linear logic extensions, linearity in the algebraic sense is explored, particularly in defining a logic system with quantum programming language as its proof language. Linear process algebra focuses on behavior and operations like tensor product, sum, sequence, and choice, akin to linear logic but emphasizing behavior over proof structures.
How to calculate the stiffness matrix components of an orthotropic material?
5 answers
To calculate the stiffness matrix components of an orthotropic material, various methods can be employed. One approach involves establishing a stiffness equation and utilizing magnetic-structural simulations with the finite element method to validate the shear modulus components. Another method utilizes numerical techniques to calculate the tangent stiffness matrix, crucial for determining the equilibrium state in material models. Additionally, a finite element stiffness matrix simulation method based on a GPU terminal can be implemented, reducing the computational load by splitting the rigidity matrix and utilizing GPU processing power. Furthermore, an element stiffness matrix calculating system on an Android platform offers a practical solution, incorporating calculations of element stiffness matrix and coordinate transformation matrix for efficient analysis in civil engineering applications. These methods collectively provide insights into effectively determining the stiffness matrix components of orthotropic materials.
What is maximum variation sampling qualitative?
4 answers
Maximum variation sampling qualitative refers to a technique that aims to select a subset of data from a larger dataset in a way that maximizes the diversity and dissimilarity among the chosen samples. This method is particularly useful in scenarios where the goal is to capture the broadest range of variation present in the data. The approach often involves utilizing statistical measures such as entropy, variance, and standard deviation to quantify the diversity within the dataset. Maximum variation sampling can be implemented using optimization algorithms like genetic algorithms, which excel in handling large datasets and complex search spaces. The ultimate objective of maximum variation sampling is to ensure that the selected subset represents the full spectrum of variability present in the original dataset, making it a valuable tool in data science and optimization problems.