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1 
Modified Silhouette Score with Generalized Mean and Trimmed MeanZhang, Yiran January 2023 (has links)
The silhouette score is a widely used technique to evaluate the quality of a clustering result. One of the current issues with the silhouette score is its sensitivity to outliers, which can lead to misleading interpretations. This problem is caused by the silhouette score using the arithmetic mean to calculate the average intra and intercluster distances.
To address this issue, three modified silhouette scores are presented: GenSil, TrimSil, and extended TrimSil, which replace the arithmetic mean with the generalized mean, the trimmed mean and a modified trimmed mean, respectively. Experiments on both simulated and realworld datasets show that GenSil is the most effective method, significantly reducing the impact of outliers and achieving high silhouette scores with negative parameter values. TrimSil also improves silhouette scores but performs worse than GenSil, while the extended TrimSil outperforms TrimSil but is still less effective than GenSil. To further aid in selecting the optimal number of clusters with these modified silhouette scores, a more straightforward visualization technique, the silhouetteparameter plot, is also introduced. / Thesis / Master of Science (MSc)

2 
A flexible suite of programs for modelling the cortex with a meanfield schemeChang, YuanKuei January 2007 (has links)
The cerebral cortex contains many neurons. The neuron is part of the nervous system and it receives and transmits the electrical signals. These signals are significant to a human's behaviour. Since the neurons are charged, these charges produce electrical fields, so these neural signals can be measured by using scalp electrodes in electroencephalography (EEG). As long as the brain is not dead, the spontaneous activities of neurons will produce a series of EEG signals. There are many models that have been developed for simulating the cortical signal, and mostly each model is focused towards a different purpose or application. Often, a different computer code has to be written for each different application, and this can be inefficient. Therefore, this project aims to develop a software system for simulating cortical signals where the model used for the system can be changed easily. Furthermore, the system is requested to be versatile and easytouse for many applications. The developed system is written in MATLAB in response to a user requirement and mostly applies to any model which uses a meanfield approach. Only the specific inputs need to be modified for changing the model. This thesis details how this system is developed. The main limitation of the system is computational resources, much the same as other cortical modelling. However, all the user requirements had been satisfied. The system can simulate the response of the neurons for any condition and generate simulated EEG data to the user. The user can analyze the cortical activities using the standard signal processing techniques such as a power spectrum. This software is very helpful for the research of sleep and anaesthesia.

3 
Minimal Surfaces in threesphere with special spherical symmetryHynd, Ryan Charles 14 July 2004 (has links)
We introduce the notion of special spherical symmetry and
classify the complete regular minimal
surfaces in the three sphere having this symmetry. We also show that
the Clifford torus is the unique embedded minimal torus in
three sphere possessing special spherical symmetry.

4 
A Study on Frequency Estimation AlgorithmsHsieh, MengHong 30 August 2004 (has links)
Abstract
Under known signals environments, the problem of frequency estimation can be regarded as that of sinusoidal frequency estimation. Therefore, the frequency estimation of a single complex sinusoid signal in a white Gaussian noise channel is an important problem in the field of signal processing. Some of the applications include array signal processing, spectral estimation, carrier and clock synchronization for digital communications, Doppler rate estimation, and many others in radar and sonar systems.
Frequency estimations based on the information of phase have threshold effects. While the length of the observation data is fixed, the performance of the estimator will be degraded and the variance will not achieve CramerRao lower bound under the condition that signaltonoise ratio (SNR) is below a certain threshold.
In this thesis, two modified frequency estimation methods are proposed in additive white Gaussian noise channels. These two methods, estimating the frequency value by linearly combining the phase difference of correlated data, are basically extended from Kim¡¦s method. These estimators have lower complexity than optimal maximum likelihood estimator and attain as good performance at moderately high SNR¡¦s. These two methods, at high frequency values, yield a considerably lower variance threshold than Kay¡¦s method and Kim¡¦s method and remain unbiased.

5 
A new approach to the determination of a mean sea surface model using multisatellite altimeter dataKim, HyoJin 03 August 2015 (has links)
Models for the mean sea surface (MSS) are created by combining and interpolating on a specified spatial grid inhomogenous data sets from different satellites with different ground track coverage. There are various approaches in which the sea surface height (SSH) data from different satellites can be combined to create an accurate reference surface. The orbit errors (especially from the early missions) need to be reduced, and systematic biases between different satellites can be decreased by reprocessing them using the improved models and geophysical corrections. In this research, a new method for the data adjustment (or error reduction), which attempts to compensate for both longwavelength orbit errors and systematic biases, simultaneously and efficiently. The approach is based on using an accurate sea surface profile as a reference surface for the integration process.
The new data adjustment technique is based on alongtrack SSH gradients computed for each satellite, which are integrated alongtrack with initial values obtained by dual crossover computation with respect to an accurate set of sea surface heights. The accurate Jason1 SSH data were used to determine the reference surface, and a total of 5 different satellites (Geosat ERM, ERS2, T/P, Envisat and ERS1 geodetic mission) data were adjusted to the Jason1 SSH data. After editing, the new homogeneous SSH datasets were averaged into mean SSH profiles. Then, they were gridded into a 5minute resolution mean sea surface over the global ocean within ±60º latitudes, as defined by the Jason1 mean profile, using a 2D spline interpolation in tension with Green’s function approach.
The new gridded mean sea surface, named CSRMSS14 was validated by three comparisons. First, it was compared with two accurate altimeter data sets: 7year Jason1 and 8year Envisat mean profiles. Second, two recent MSS models, DNSC08 and DTU10, were compared to investigate the accuracy of CSRMSS14. Third, a somewhat independent test is obtained by comparing a 2year Jason2 mean profile with the three MSS models (CSRMSS14, DTU10 and DNSC08), since Jason2 data were not used in their construction. These three validations demonstrated that CSRMSS14 mean sea surface model obtained with this new approach is comparable in accuracy to DNSC08 and DTU10. / text

6 
Geometry of mean value sets for general divergence form uniformly elliptic operatorsAryal, Ashok January 1900 (has links)
Doctor of Philosophy / Department of Mathematics / Ivan Blank / In the Fermi Lectures on the obstacle problem in 1998, Caffarelli gave a proof of the mean value theorem which extends to general divergence form uniformly elliptic operators. In the general setting, the result shows that for any such operator L and at any point [chi]₀ in the domain, there exists a nested family of sets { D[subscript]r([chi]₀) } where the average over any of those sets is related to the value of the function at [chi]₀. Although it is known that the { D[subscript]r([chi]₀) } are nested and are comparable to balls in the sense that there exists c, C depending only on L such that B[subscript]cr([chi]₀) ⊂ D[subscript]r([chi]₀) ⊂ B[subscript]Cr([chi]₀) for all r > 0 and [chi]₀ in the domain, otherwise their geometric and topological properties are largely unknown. In this work we begin the study of these topics and we prove a few results about the geometry of these sets and give a couple of applications of the theorems.

7 
Mean value theoremsUnknown Date (has links)
"There is no more fundamental theorem in calculus than the meanvalue theorem. Much of the theory of calculus depends, either directly or indirectly, on this theorem. As a consequence of its importance, the theorem has been investigated by a number of mathematicians with the result that various modifications and extensions of the basic theorem have been made"Introduction. / "May 1956." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts." / Includes bibliographical references (leaf 17).

8 
The Mean Value Property for Harmonic Functions on Graphs and TreesFabio Zucca, Andreas.Cap@esi.ac.at 05 March 2001 (has links)
No description available.

9 
A statistical model for estimating mean annual and mean monthly flows at ungaged locationsSukheswalla, Zubin Rohinton 30 September 2004 (has links)
Prediction of flow is necessary for planning and management of water resources. The objective of this study is to estimate mean annual flows for the USA and mean monthly flows for the rivers of central Texas based on the precipitation and their watershed characteristics. Flow varies largely with topographic and climatic parameters and hence generalization of runoff models is difficult. This model aims at providing a prediction at
ungaged locations with very few parameters that are easily available and measurable.
Scatter in predicted data will be seen at the annual and monthly time scale in the range selected for each data. This model will work on annual and monthly means to reduce the scatter and produce better estimates.

10 
Means and Mean Value TheoremsBlummer, Raymond O. January 1951 (has links)
This study covers means, mean value theorems of the differential calculus, and mean value theorems of integral calculus.

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