VLSI Architectures for the Steerable-Discrete-Cosine-Transform (SDCT)

Since frame resolution of modern video streams is rapidly growing, the need for more complex and efficient video compression methods arises. H.265/HEVC represents the state of the art in video coding standard. Its architecture is however not completely standardized, as many parts are only described at software level to allow the designer to implement new compression techniques. This paper presents an innovative hardware architecture for the Steerable Discrete Cosine Transform (SDCT), which has been recently embedded into the HEVC standard, providing better compression ratios. Such technique exploits directional DCT using basis having different orientation angles, leading to a sparser representation which translates to an improved coding efficiency. The final design is able to work at a frequency of 188 MHZ, reaching a throughput of 3.00 GSample/s. In particular, this architecture supports 8k UltraHigh Definition (UHD) (7680 × 4320) with a frame rate of 60 Hz, which is one of the best resolutions supported by HEVC

Analysis of Genomic and Proteomic Signals Using Signal Processing and Soft Computing Techniques

Bioinformatics is a data rich field which provides unique opportunities to use computational techniques to understand and organize information associated with biomolecules such as DNA, RNA, and Proteins. It involves in-depth study in the areas of genomics and proteomics and requires techniques from computer science,statistics and engineering to identify, model, extract features and to process data for analysis and interpretation of results in a biologically meaningful manner.In engineering methods the signal processing techniques such as transformation,filtering, pattern analysis and soft-computing techniques like multi layer perceptron(MLP) and radial basis function neural network (RBFNN) play vital role to effectively resolve many challenging issues associated with genomics and proteomics. In this dissertation, a sincere attempt has been made to investigate on some challenging problems of bioinformatics by employing some efficient signal and soft computing methods. Some of the specific issues, which have been attempted are protein coding region identification in DNA sequence, hot spot identification in protein, prediction of protein structural class and classification of microarray gene expression data. The dissertation presents some novel methods to measure and to extract features from the genomic sequences using time-frequency analysis and machine intelligence techniques.The problems investigated and the contribution made in the thesis are presented here in a concise manner. The S-transform, a powerful time-frequency representation technique, possesses superior property over the wavelet transform and short time Fourier transform as the exponential function is fixed with respect to time axis while the localizing scalable Gaussian window dilates and translates. The S-transform uses an analysis window whose width is decreasing with frequency providing a frequency dependent resolution. The invertible property of S-transform makes it suitable for time-band filtering application. Gene prediction and protein coding region identification have been always a challenging task in computational biology,especially in eukaryote genomes due to its complex structure. This issue is resolved using a S-transform based time-band filtering approach by localizing the period-3 property present in the DNA sequence which forms the basis for the identification.Similarly, hot spot identification in protein is a burning issue in protein science due to its importance in binding and interaction between proteins. A novel S-transform based time-frequency filtering approach is proposed for efficient identification of the hot spots. Prediction of structural class of protein has been a challenging problem in bioinformatics.A novel feature representation scheme is proposed to efficiently represent the protein, thereby improves the prediction accuracy. The high dimension and low sample size of microarray data lead to curse of dimensionality problem which affects the classification performance.In this dissertation an efficient hybrid feature extraction method is proposed to overcome the dimensionality issue and a RBFNN is introduced to efficiently classify the microarray samples

Using Representation Theorems for Proving Polynomials Non-negative

Proving polynomials non-negative when variables range on a subset of numbers (e.g., [0, +∞)) is often required in many applications (e.g., in the analysis of program termination). Several representations for univariate polynomials P that are non-negative on [0, +∞) have been investigated. They can often be used to characterize the property, thus providing a method for checking it by trying a match of P against the representation. We introduce a new characterization based on viewing polynomials P as vectors, and find the appropriate polynomial basis B in which the non-negativeness of the coordinates [P]B representing P in B witnesses that P is non-negative on [0, +∞). Matching a polynomial against a representation provides a way to transform universal sentences ∀x ∈ [0, +∞) P(x) ≥ 0 into a constraint solving problem which can be solved by using efficient methods. We consider different approaches to solve both kind of problems and provide a quantitative evaluation of performance that points to an early result by P´olya and Szeg¨o’s as an appropriate basis for implementations in most cases.Lucas Alba, S. (2014). Using Representation Theorems for Proving Polynomials Non-negative. En Artificial Intelligence and Symbolic Computation: 12th International Conference, AISC 2014, Seville, Spain, December 11-13, 2014. Proceedings. Springer Verlag (Germany). 21-33. doi:10.1007/978-3-319-13770-4_4S2133Alarcón, B., Gutiérrez, R., Lucas, S., Navarro-Marset, R.: Proving Termination Properties with mu-term. In: Johnson, M., Pavlovic, D. (eds.) AMAST 2010. LNCS, vol. 6486, pp. 201–208. Springer, Heidelberg (2011)Basu, S., Pollack, R., Roy, M.-F.: Algorithms in Real Algebraic Geometry. Springer, Berlin (2006)Bernstein, S.: Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités. Communic. Soc. Math. de Kharkow 13(2), 1–2 (1912)Bernstein, S.: Sur la répresentation des polynômes positifs. Communic. Soc. Math. de Kharkow 14(2), 227–228 (1915)Borralleras, C., Lucas, S., Oliveras, A., Rodríguez, E., Rubio, A.: SAT Modulo Linear Arithmetic for Solving Polynomial Constraints. Journal of Automated Reasoning 48, 107–131 (2012)Boudaoud, F., Caruso, F., Roy, M.-F.: Certificates of Positivity in the Bernstein Basis. Discrete Computational Geometry 39, 639–655 (2008)Choi, M.D., Lam, T.Y., Reznick, B.: Sums of squares of real polynomials. In: Proc. of the Symposium on Pure Mathematics, vol. 4, pp. 103–126. American Mathematical Society (1995)Contejean, E., Marché, C., Tomás, A.-P., Urbain, X.: Mechanically proving termination using polynomial interpretations. Journal of Automated Reasoning 32(4), 315–355 (2006)Hilbert, D.: Über die Darstellung definiter Formen als Summe von Formenquadraten. Mathematische Annalen 32, 342–350 (1888)Hong, H., Jakuš, D.: Testing Positiveness of Polynomials. Journal of Automated Reasoning 21, 23–38 (1998)Karlin, S., Studden, W.J.: Tchebycheff systems: with applications in analysis and statistics. Interscience, New York (1966)Lucas, S.: Polynomials over the reals in proofs of termination: from theory to practice. RAIRO Theoretical Informatics and Applications 39(3), 547–586 (2005)Polya, G., Szegö, G.: Problems and Theorems in Analysis II. Springer (1976)Powers, V., Reznick, B.: Polynomials that are positive on an interval. Transactions of the AMS 352(10), 4677–4692 (2000)Powers, V., Wörmann, T.: An algorithm for sums of squares of real polynomials. Journal of Pure and Applied Algebra 127, 99–104 (1998

Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms

The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient (size poly(n,d,log(1/\epsilon)) for accuracy \epsilon) quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. These circuits are based on efficient circuits for the Clebsch-Gordan transformation. We also present an efficient circuit for a limited version of the Schur transform in which one needs only to project onto different Schur subspaces. This second circuit is based on a generalization of phase estimation to any nonabelian finite group for which there exists a fast quantum Fourier transform.Comment: 4 pages, 3 figure

Efficient Quantum Transforms

Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a generalized Kronecker product is given. Applications include re-development of the networks for computing the Walsh-Hadamard and the quantum Fourier transform. New networks for two wavelet transforms are given. Quantum computation of Fourier transforms for non-Abelian groups is defined. A slightly relaxed definition is shown to simplify the analysis and the networks that computes the transforms. Efficient networks for computing such transforms for a class of metacyclic groups are introduced. A novel network for computing a Fourier transform for a group used in quantum error-correction is also given.Comment: 30 pages, LaTeX2e, 7 figures include