Sensitivity Analysis of the Risk of Forecasting for Autoregressive Time Series with Missing Values

2000 Mathematics Subject Classification: 62M20, 62M10, 62-07.

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

Time to Extinction in Branching Processes and its Application in Epidemiology

2010 Mathematics Subject Classification: Primary 60J80; Secondary 92D30.

Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates

2000 Mathematics Subject Classification: 35B40, 35L15.

Remarks on blow up time for solutions of a nonlinear diffusion system with time dependent coefficients

2000 Mathematics Subject Classification: 35K55, 35K60.

Növelhető-e a csőd-előrejelző modellek előre jelző képessége az új klasszifikációs módszerek nélkül? (Can the predictive capacity of bankruptcy forecasting models be increased without new classification methods?)

A Bázel–2. tőkeegyezmény bevezetését követően a bankok és hitelintézetek Magyarországon is megkezdték saját belső minősítő rendszereik felépítését, melyek karbantartása és fejlesztése folyamatos feladat. A szerző arra a kérdésre keres választ, hogy lehetséges-e a csőd-előrejelző modellek előre jelző képességét növelni a hagyományos matematikai-statisztikai módszerek alkalmazásával oly módon, hogy a modellekbe a pénzügyi mutatószámok időbeli változásának mértékét is beépítjük. Az empirikus kutatási eredmények arra engednek következtetni, hogy a hazai vállalkozások pénzügyi mutatószámainak időbeli alakulása fontos információt hordoz a vállalkozás jövőbeli fizetőképességéről, mivel azok felhasználása jelentősen növeli a csődmodellek előre jelző képességét. A szerző azt is megvizsgálja, hogy javítja-e a megfigyelések szélsőségesen magas vagy alacsony értékeinek modellezés előtti korrekciója a modellek klasszifikációs teljesítményét. ______ Banks and lenders in Hungary also began, after the introduction of the Basel 2 capital agreement, to build up their internal rating systems, whose maintenance and development are a continuing task. The author explores whether it is possible to increase the predictive capacity of business-failure forecasting models by traditional mathematical-cum-statistical means in such a way that they incorporate the measure of change in the financial indicators over time. Empirical findings suggest that the temporal development of the financial indicators of firms in Hungary carries important information about future ability to pay, since the predictive capacity of bankruptcy forecasting models is greatly increased by using such indicators. The author also examines whether the classification performance of the models can be improved by correcting for extremely high or low values before modelling.

A közszolgálati szervezetek értékelési módszereinek osztályozása (Classification of evaluation methods of public sector organizations)

Az utóbbi évtizedekben egyre gyakrabban merült fel a közszolgálati szervezetek értékelésének igénye, és egyre újabb módszerek jelentek meg, amelyek felvetették ezek rendszerezésének szükségességét mind a gyakorlatban, mind a kutatásokban. A szerző a szakirodalomban fellelhető osztályozási kísérleteknek és az értékelés szakterülete szempontjainak figyelembevételével javaslatot tesz a közszolgálati szervezetek értékelési módszereinek osztályozási keretrendszerére. Az osztályozási szempontok között szerepel az értékelő helyzete, az értékelés szerepe és a megismerés módszere. Az osztályozási keretrendszer tartalmát a szerző példákkal is illusztrálja, amely jelzi a modell gyakorlati alkalmazhatóságát. Ugyanakkor a keretrendszer a kutatások fókuszának és érvényességi körének meghatározásában is segítséget nyújthat. _____ In the last decades the need of the evaluation of public sector organizations has emerged more and more often, and many new methods have shown up that has raised the need of their classification in practice and in research, as well. Based on literature review and the literature of evaluation the author makes a proposal on the classification framework of the evaluation methods of public sector organizations. The dimensions of the classification include the situation of evaluator, the role of evaluation and the approach of knowledge. The author illustrates the content of the framework with examples referring to the applicability of the model in practice. At the same time, the framework is also useful in determining the focus or the scope of research projects.

Statistical analysis and optimal classification of blood cell populations using Gaussian distributions

This dissertation develops a new figure of merit to measure the similarity (or dissimilarity) of Gaussian distributions through a novel concept that relates the Fisher distance to the percentage of data overlap. The derivations are expanded to provide a generalized mathematical platform for determining an optimal separating boundary of Gaussian distributions in multiple dimensions. Real-world data used for implementation and in carrying out feasibility studies were provided by Beckman-Coulter. It is noted that although the data used is flow cytometric in nature, the mathematics are general in their derivation to include other types of data as long as their statistical behavior approximate Gaussian distributions. ^ Because this new figure of merit is heavily based on the statistical nature of the data, a new filtering technique is introduced to accommodate for the accumulation process involved with histogram data. When data is accumulated into a frequency histogram, the data is inherently smoothed in a linear fashion, since an averaging effect is taking place as the histogram is generated. This new filtering scheme addresses data that is accumulated in the uneven resolution of the channels of the frequency histogram. ^ The qualitative interpretation of flow cytometric data is currently a time consuming and imprecise method for evaluating histogram data. This method offers a broader spectrum of capabilities in the analysis of histograms, since the figure of merit derived in this dissertation integrates within its mathematics both a measure of similarity and the percentage of overlap between the distributions under analysis. ^

Multidimensional classification and diagnosis of leukemia in flow cytometry

This research is to establish new optimization methods for pattern recognition and classification of different white blood cells in actual patient data to enhance the process of diagnosis. Beckman-Coulter Corporation supplied flow cytometry data of numerous patients that are used as training sets to exploit the different physiological characteristics of the different samples provided. The methods of Support Vector Machines (SVM) and Artificial Neural Networks (ANN) were used as promising pattern classification techniques to identify different white blood cell samples and provide information to medical doctors in the form of diagnostic references for the specific disease states, leukemia. The obtained results prove that when a neural network classifier is well configured and trained with cross-validation, it can perform better than support vector classifiers alone for this type of data. Furthermore, a new unsupervised learning algorithm---Density based Adaptive Window Clustering algorithm (DAWC) was designed to process large volumes of data for finding location of high data cluster in real-time. It reduces the computational load to ∼O(N) number of computations, and thus making the algorithm more attractive and faster than current hierarchical algorithms.

Labeling large scale social media data using budget-driven One-class SVM classification

The social media classification problems draw more and more attention in the past few years. With the rapid development of Internet and the popularity of computers, there is astronomical amount of information in the social network (social media platforms). The datasets are generally large scale and are often corrupted by noise. The presence of noise in training set has strong impact on the performance of supervised learning (classification) techniques. A budget-driven One-class SVM approach is presented in this thesis that is suitable for large scale social media data classification. Our approach is based on an existing online One-class SVM learning algorithm, referred as STOCS (Self-Tuning One-Class SVM) algorithm. To justify our choice, we first analyze the noise-resilient ability of STOCS using synthetic data. The experiments suggest that STOCS is more robust against label noise than several other existing approaches. Next, to handle big data classification problem for social media data, we introduce several budget driven features, which allow the algorithm to be trained within limited time and under limited memory requirement. Besides, the resulting algorithm can be easily adapted to changes in dynamic data with minimal computational cost. Compared with two state-of-the-art approaches, Lib-Linear and kNN, our approach is shown to be competitive with lower requirements of memory and time.

Detection and Classification of Whale Acoustic Signals

This dissertation focuses on two vital challenges in relation to whale acoustic signals: detection and classification.

In detection, we evaluated the influence of the uncertain ocean environment on the spectrogram-based detector, and derived the likelihood ratio of the proposed Short Time Fourier Transform detector. Experimental results showed that the proposed detector outperforms detectors based on the spectrogram. The proposed detector is more sensitive to environmental changes because it includes phase information.

In classification, our focus is on finding a robust and sparse representation of whale vocalizations. Because whale vocalizations can be modeled as polynomial phase signals, we can represent the whale calls by their polynomial phase coefficients. In this dissertation, we used the Weyl transform to capture chirp rate information, and used a two dimensional feature set to represent whale vocalizations globally. Experimental results showed that our Weyl feature set outperforms chirplet coefficients and MFCC (Mel Frequency Cepstral Coefficients) when applied to our collected data.

Since whale vocalizations can be represented by polynomial phase coefficients, it is plausible that the signals lie on a manifold parameterized by these coefficients. We also studied the intrinsic structure of high dimensional whale data by exploiting its geometry. Experimental results showed that nonlinear mappings such as Laplacian Eigenmap and ISOMAP outperform linear mappings such as PCA and MDS, suggesting that the whale acoustic data is nonlinear.

We also explored deep learning algorithms on whale acoustic data. We built each layer as convolutions with either a PCA filter bank (PCANet) or a DCT filter bank (DCTNet). With the DCT filter bank, each layer has different a time-frequency scale representation, and from this, one can extract different physical information. Experimental results showed that our PCANet and DCTNet achieve high classification rate on the whale vocalization data set. The word error rate of the DCTNet feature is similar to the MFSC in speech recognition tasks, suggesting that the convolutional network is able to reveal acoustic content of speech signals.

Degree classification and recent graduates’ ability: Is there any signalling effect?

Research across several countries has shown that degree classification (i.e. the final grade awarded to students successfully completing university) is an important determinant of graduates’ first destination outcome. Graduates leaving university with higher degree classifications have better employment opportunities and a higher likelihood of continuing education relative to those with lower degree classifications. This article investigates whether one of the reasons for this result is that employers and higher education institutions use degree classification as a signalling device for the ability that recent graduates may possess. Given the large number of applicants and the amount of time and resources typically required to assess their skills, employers and higher education institutions may decide to rely on this measure when forming beliefs about recent graduates’ abilities. Using data on two cohorts of recent graduates from a UK university, results suggest that an Upper Second degree classification may have a signalling role.

Second-order cyclostationarity-based detection and classification of LTE SC-FDMA signals for cognitive radio

Cognitive radio (CR) was developed for utilizing the spectrum bands efficiently. Spectrum sensing and awareness represent main tasks of a CR, providing the possibility of exploiting the unused bands. In this thesis, we investigate the detection and classification of Long Term Evolution (LTE) single carrier-frequency division multiple access (SC-FDMA) signals, which are used in uplink LTE, with applications to cognitive radio. We explore the second-order cyclostationarity of the LTE SC-FDMA signals, and apply results obtained for the cyclic autocorrelation function to signal detection and classification (in other words, to spectrum sensing and awareness). The proposed detection and classification algorithms provide a very good performance under various channel conditions, with a short observation time and at low signal-to-noise ratios, with reduced complexity. The validity of the proposed algorithms is verified using signals generated and acquired by laboratory instrumentation, and the experimental results show a good match with computer simulation results.

Detection of mesoscale thermal fronts from 4km data using smoothing techniques: Gradient-based fronts classification and basin scale application

In order to optimize frontal detection in sea surface temperature fields at 4 km resolution, a combined statistical and expert-based approach is applied to test different spatial smoothing of the data prior to the detection process. Fronts are usually detected at 1 km resolution using the histogram-based, single image edge detection (SIED) algorithm developed by Cayula and Cornillon in 1992, with a standard preliminary smoothing using a median filter and a 3 × 3 pixel kernel. Here, detections are performed in three study regions (off Morocco, the Mozambique Channel, and north-western Australia) and across the Indian Ocean basin using the combination of multiple windows (CMW) method developed by Nieto, Demarcq and McClatchie in 2012 which improves on the original Cayula and Cornillon algorithm. Detections at 4 km and 1 km of resolution are compared. Fronts are divided in two intensity classes (“weak” and “strong”) according to their thermal gradient. A preliminary smoothing is applied prior to the detection using different convolutions: three type of filters (median, average and Gaussian) combined with four kernel sizes (3 × 3, 5 × 5, 7 × 7, and 9 × 9 pixels) and three detection window sizes (16 × 16, 24 × 24 and 32 × 32 pixels) to test the effect of these smoothing combinations on reducing the background noise of the data and therefore on improving the frontal detection. The performance of the combinations on 4 km data are evaluated using two criteria: detection efficiency and front length. We find that the optimal combination of preliminary smoothing parameters in enhancing detection efficiency and preserving front length includes a median filter, a 16 × 16 pixel window size, and a 5 × 5 pixel kernel for strong fronts and a 7 × 7 pixel kernel for weak fronts. Results show an improvement in detection performance (from largest to smallest window size) of 71% for strong fronts and 120% for weak fronts. Despite the small window used (16 × 16 pixels), the length of the fronts has been preserved relative to that found with 1 km data. This optimal preliminary smoothing and the CMW detection algorithm on 4 km sea surface temperature data are then used to describe the spatial distribution of the monthly frequencies of occurrence for both strong and weak fronts across the Indian Ocean basin. In general strong fronts are observed in coastal areas whereas weak fronts, with some seasonal exceptions, are mainly located in the open ocean. This study shows that adequate noise reduction done by a preliminary smoothing of the data considerably improves the frontal detection efficiency as well as the global quality of the results. Consequently, the use of 4 km data enables frontal detections similar to 1 km data (using a standard median 3 × 3 convolution) in terms of detectability, length and location. This method, using 4 km data is easily applicable to large regions or at the global scale with far less constraints of data manipulation and processing time relative to 1 km data.