1,720,985 research outputs found
ORIENTED MANIFOLDS WITH COMPACT SUPPORT AND COHOMOLOGY ALGEBRA
Get PDFThe cohomology of with compact supports is the graded algebra....... Keywords: Compact manifold, cohomology, graded algebra, isomorphism, bilinear map
A Geometric Study on Ramanujan's Modular Equations and Hecke Groups
Get PDFTohoku University博士（情報科学）博士学位論文 (Thesis(doctor))doctoral thesi
Control of constraint weights for an autonomous camera
Get PDFConstraint satisfaction based techniques for camera control has the flexibility to add new constraints easily to increase the quality of a shot. We address the problem of deducing and adjusting constraint weights at run time to guide the movement of the camera in an informed and controlled way in response to the requirement of the shot. This enables the control of weights at the frame level. We analyze the mathematical representation of the cost structure of the domain of constraint search so that the constraint solver can search the domain efficiently. We start with a simple tracking shot of a single target. The cost structure of the domain of search suggests the use of a binary search which searches along a curve for 2D and on a surface for 3D by utilizing the information about the cost structure. The problems of occlusion and collision avoidance have also been addressed
On Ramanujan's modular equations and Hecke groups
No full textInspired by the work of Ramanujan, many people have studied generalized modular equations and the numerous identities found by Ramanujan. These identities known as modular equations can be transformed into polynomial equations. There is no developed theory about how to find the degrees of these polynomial modular equations explicitly. In this paper, we determine the degrees of the polynomial modular equations explicitly and study the relation between Hecke groups and modular equations in Ramanujan's theories of signatures 2, 3, and 4
Appley: Approximate Shapley Values for Model Explainability in Linear Time
Get PDFWe have seen complex deep learning models outperforming human benchmarks in many areas (e.g. computer vision, natural language processing). Clever architectures and higher model complexity are two of the major drivers of such outstanding performances. Higher model complexity generally makes the decision-making process of a model opaque to human perception. But understanding the decision-making process is very important for many reasons including enhancing trust in the model\u27s prediction, improving model robustness, gaining actionable insight from why a model made a particular prediction, and discovering new knowledge about a problem. Model explainability has been an active area of research for some time now, but the problem is still far from being solved. An established way of model explanation (also known as variable attribution) is to assign a score to each variable, which represents the importance of the variable in a particular prediction of a model. In a lot of techniques, the scoring process involves distributing the output to each variable. This approach becomes challenging when the model is complex and consists of a high degree of interaction terms. A coalition game theoretic approach called Shapley Value provides a fair way to tackle the challenge. However, the growth of computation time of the exact Shapley Values is exponential in the number of variables. Hence, it is common to use approximations as opposed to the exact Shapley Values as attribution for relatively larger problems. There has been a lot of progress in the Shapley Value approximation techniques for variable attribution in recent years. However, there is still a lot of room for improvement, especially for complex models. In this manuscript, we propose a novel variable attribution technique called Appley (short for Approximate Shapley) by approximating the Shapley Values in linear time. We show that the Appley\u27\u27 attributions are generally closer to the exact Shapley Values than a few existing state-of-the-art attribution techniques
ORIENTATION OF MANIFOLDS AND SMOOTH FIBRE BUNDLES
Get PDFFor a smooth fibre bundle ......More details can be found in the full paper. Keywords: Smooth fibre bundle, manifold, vector bundle, bundle isomorphism, bundle orientation, graded subalgebra
Artificial Intelligence Based Tool Condition Monitoring in Machining
Get PDFIn a manufacturing environment, gradual and catastrophic failure of a cutting tool are common faults associated with a machining process. Left unmonitored these failures exhibit a high likelihood of triggering workpiece surface quality issues and reducing the overall productivity of the process. This research offers a comprehensive study of the design, development and implementation of a low-cost artificially intelligent (AI) tool condition monitoring (TCM) system for the turning operation of different workpiece material. As the characteristics of the signals from the fusion of multiple sensors differ from each individual sensor, fast Fourier transform (FFT) and wavelet transform (WT) were used to identify signal features which provided the most useful information about the cutting tool conditions. Pearson correlation coefficients (PCC) and principal component analysis (PCA) singled out the most sensitive features from the sensor fusion signals which play a pivotal role in monitoring gradual tool wear (flank wear) progression during machining. Experimental results indicated that the total harmonic distortion (THD), crest factor of the spindle motor current and certain spectral features from the vibration sensor signal had a significant correlation with cutting tool flank wear under different cutting conditions and when machining different materials. Furthermore, a data-driven artificial neural network (ANN) and an adaptive neuro-fuzzy inference system (ANFIS) were studied to investigate their prediction accuracy for cutting tool conditions (tool wear). The ANFIS prediction model outperformed the ANN prediction in terms of accuracy. As a result, the developed (trained and validated) ANFIS based TCM system was implemented in the material turning process. In addition, the adaptability of the supervised ANFIS based TCM system was shown to further increase the reliability of tool wear prediction.ThesisMaster of Applied Science (MASc
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