Memory-centric VDF Graph Transformations for Practical FPGA Implementation

Realising memory intensive applications such as image and video processing on FPGA requires creation of complex, multi-level memory hierarchies to achieve real-time performance; however commerical High Level Synthesis tools are unable to automatically derive such structures and hence are unable to meet the demanding bandwidth and capacity constraints of these applications. Current approaches to solving this problem can only derive either single-level memory structures or very deep, highly inefficient hierarchies, leading in either case to one or more of high implementation cost and low performance. This paper presents an enhancement to an existing MC-HLS synthesis approach which solves this problem; it exploits and eliminates data duplication at multiple levels levels of the generated hierarchy, leading to a reduction in the number of levels and ultimately higher performance, lower cost implementations. When applied to synthesis of C-based Motion Estimation, Matrix Multiplication and Sobel Edge Detection applications, this enables reductions in Block RAM and Look Up Table (LUT) cost of up to 25%, whilst simultaneously increasing throughput.

Wavelet entropy of Doppler ultrasound blood velocity flow waveforms distinguishes nitric oxide-modulated states

Wavelet entropy assesses the degree of order or disorder in signals and presents this complex information in a simple metric. Relative wavelet entropy assesses the similarity between the spectral distributions of two signals, again in a simple metric. Wavelet entropy is therefore potentially a very attractive tool for waveform analysis. The ability of this method to track the effects of pharmacologic modulation of vascular function on Doppler blood velocity waveforms was assessed. Waveforms were captured from ophthalmic arteries of 10 healthy subjects at baseline, after the administration of glyceryl trinitrate (GTN) and after two doses of N(G)-nitro-L-arginine-methyl ester (L-NAME) to produce vasodilation and vasoconstriction, respectively. Wavelet entropy had a tendency to decrease from baseline in response to GTN, but significantly increased after the administration of L-NAME (mean: 1.60 ± 0.07 after 0.25 mg/kg and 1.72 ± 0.13 after 0.5 mg/kg vs. 1.50 ± 0.10 at baseline, p < 0.05). Relative wavelet entropy had a spectral distribution from increasing doses of L-NAME comparable to baseline, 0.07 ± 0.04 and 0.08 ± 0.03, respectively, whereas GTN had the most dissimilar spectral distribution compared with baseline (0.17 ± 0.08, p = 0.002). Wavelet entropy can detect subtle changes in Doppler blood velocity waveform structure in response to nitric-oxide-mediated changes in arteriolar smooth muscle tone.

A generalization of the Hoffman-Lovász upper bound on the independence number of a regular graph

A family of quadratic programming problems whose optimal values are upper bounds on the independence number of a graph is introduced. Among this family, the quadratic programming problem which gives the best upper bound is identified. Also the proof that the upper bound introduced by Hoffman and Lovász for regular graphs is a particular case of this family is given. In addition, some new results characterizing the class of graphs for which the independence number attains the optimal value of the above best upper bound are given. Finally a polynomial-time algorithm for approximating the size of the maximum independent set of an arbitrary graph is described and the computational experiments carried out on 36 DIMACS clique benchmark instances are reported.

Contributions to the theory of maximum entropy estimation for ill-posed models

As técnicas estatísticas são fundamentais em ciência e a análise de regressão linear é, quiçá, uma das metodologias mais usadas. É bem conhecido da literatura que, sob determinadas condições, a regressão linear é uma ferramenta estatística poderosíssima. Infelizmente, na prática, algumas dessas condições raramente são satisfeitas e os modelos de regressão tornam-se mal-postos, inviabilizando, assim, a aplicação dos tradicionais métodos de estimação. Este trabalho apresenta algumas contribuições para a teoria de máxima entropia na estimação de modelos mal-postos, em particular na estimação de modelos de regressão linear com pequenas amostras, afetados por colinearidade e outliers. A investigação é desenvolvida em três vertentes, nomeadamente na estimação de eficiência técnica com fronteiras de produção condicionadas a estados contingentes, na estimação do parâmetro ridge em regressão ridge e, por último, em novos desenvolvimentos na estimação com máxima entropia. Na estimação de eficiência técnica com fronteiras de produção condicionadas a estados contingentes, o trabalho desenvolvido evidencia um melhor desempenho dos estimadores de máxima entropia em relação ao estimador de máxima verosimilhança. Este bom desempenho é notório em modelos com poucas observações por estado e em modelos com um grande número de estados, os quais são comummente afetados por colinearidade. Espera-se que a utilização de estimadores de máxima entropia contribua para o tão desejado aumento de trabalho empírico com estas fronteiras de produção. Em regressão ridge o maior desafio é a estimação do parâmetro ridge. Embora existam inúmeros procedimentos disponíveis na literatura, a verdade é que não existe nenhum que supere todos os outros. Neste trabalho é proposto um novo estimador do parâmetro ridge, que combina a análise do traço ridge e a estimação com máxima entropia. Os resultados obtidos nos estudos de simulação sugerem que este novo estimador é um dos melhores procedimentos existentes na literatura para a estimação do parâmetro ridge. O estimador de máxima entropia de Leuven é baseado no método dos mínimos quadrados, na entropia de Shannon e em conceitos da eletrodinâmica quântica. Este estimador suplanta a principal crítica apontada ao estimador de máxima entropia generalizada, uma vez que prescinde dos suportes para os parâmetros e erros do modelo de regressão. Neste trabalho são apresentadas novas contribuições para a teoria de máxima entropia na estimação de modelos mal-postos, tendo por base o estimador de máxima entropia de Leuven, a teoria da informação e a regressão robusta. Os estimadores desenvolvidos revelam um bom desempenho em modelos de regressão linear com pequenas amostras, afetados por colinearidade e outliers. Por último, são apresentados alguns códigos computacionais para estimação com máxima entropia, contribuindo, deste modo, para um aumento dos escassos recursos computacionais atualmente disponíveis.

Necessary and sufficient conditions for a Hamiltonian graph

A graph is singular if the zero eigenvalue is in the spectrum of its 0-1 adjacency matrix A. If an eigenvector belonging to the zero eigenspace of A has no zero entries, then the singular graph is said to be a core graph. A ( k,t)-regular set is a subset of the vertices inducing a k -regular subgraph such that every vertex not in the subset has t neighbours in it. We consider the case when k=t which relates to the eigenvalue zero under certain conditions. We show that if a regular graph has a ( k,k )-regular set, then it is a core graph. By considering the walk matrix we develop an algorithm to extract ( k,k )-regular sets and formulate a necessary and sufficient condition for a graph to be Hamiltonian.

Spectra of graphs obtained by a generalization of the join graph operation

Taking a Fiedler’s result on the spectrum of a matrix formed from two symmetric matrices as a motivation, a more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs (regular in the case of adjacency spectra and arbitrary in the case of Laplacian spectra). Some additional consequences are explored, namely regarding the largest eigenvalue and algebraic connectivity.

Generate disaggregated soil allocation data using a Minimum Cross Entropy Model

Montado ecosystem in the Alentejo Region, south of Portugal, has enormous agro-ecological and economics heterogeneities. A definition of homogeneous sub-units among this heterogeneous ecosystem was made, but for them is disposal only partial statistical information about soil allocation agro-forestry activities. The paper proposal is to recover the unknown soil allocation at each homogeneous sub-unit, disaggregating a complete data set for the Montado ecosystem area using incomplete information at sub-units level. The methodological framework is based on a Generalized Maximum Entropy approach, which is developed in thee steps concerning the specification of a r order Markov process, the estimates of aggregate transition probabilities and the disaggregation data to recover the unknown soil allocation at each homogeneous sub-units. The results quality is evaluated using the predicted absolute deviation (PAD) and the "Disagegation Information Gain" (DIG) and shows very acceptable estimation errors.

Combined disaggregation of agricultural land uses, livestock numbers and crops' production: an entropy approach

This paper presents several combined agricultural data disaggregation models in order to recover the farms' land uses, the livestock numbers and main crops' productions. The proposed approach estimates incomplete information at disaggregated level through entropy, using an information prior, and generating information for a combined calculation use of data in the estimation of other variables. The models were applied to the region of Algarve, to some rural pilot areas (Salir-Ameixial-Cachopo and Alcoutim) for livestock data, since this data in some Algarve's inland areas is needed for a European forest fire prevention project, and to the agrarian zones in a more complex framework. The results are promising. They were validated, in cross reference to real data, having proven to be valid and reliable. The total error was small and a considerable level of information heterogeneity was recovered. The total error was about 27,9% for the counties' land uses and 21% for the agrarian zones, and for the livestock it was also acceptable. The level of heterogeneity recovered was always higher than 50%, revealing some improvements regarding previous studies.

Gene Network Inference using Machine Learning and Graph Algorithms on Big Biomedical Data

Thesis (Master's)--University of Washington, 2016-03

Power law and entropy analysis of catastrophic phenomena

Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, tsunamis, floods and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties has separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the statistical distributions of the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data sets are better approximated by two PLs instead of a single one. We plot the PL parameters, corresponding to several events, and observe an interesting pattern in the charts, where the lines that connect each pair of points defining the double PLs are almost parallel to each other. A complementary data analysis is performed by means of the computation of the entropy. The results reveal relationships hidden in the data that may trigger a future comprehensive explanation of this type of phenomena.

Entropy analysis of integer and fractional dynamical systems

This paper investigates the adoption of entropy for analyzing the dynamics of a multiple independent particles system. Several entropy definitions and types of particle dynamics with integer and fractional behavior are studied. The results reveal the adequacy of the entropy concept in the analysis of complex dynamical systems.

A Fractional Perspective to the Bond Graph Modelling of World Economies

Inspired in dynamic systems theory and Brewer’s contributions to apply it to economics, this paper establishes a bond graph model. Two main variables, a set of inter-connectivities based on nodes and links (bonds) and a fractional order dynamical perspective, prove to be a good macro-economic representation of countries’ potential performance in nowadays globalization. The estimations based on time series for 50 countries throughout the last 50 decades confirm the accuracy of the model and the importance of scale for economic performance.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

Graph usage in financial reports: Evidence from Portuguese listed companies

When assessing investment options, investors focus on the graphs of annual reports, despite lack of auditing. If poorly constructed, graphs distort perceptions and lead to inaccurate decisions. This study examines graph usage in all the companies listed on Euronext Lisbon in 2013. The findings suggest that graphs are common in the annual reports of Portuguese companies and that, while there is no evidence of Selectivity Distortion, both Measurement and Orientation Distortions are pervasive. The study recommends the auditing of financial graphs, and urges preparers and users of annual reports to be wary of the possibility of graph distortion.