An investigation into inter- and intragenomic variations of graphic genomic signatures

We provide, on an extensive dataset and using several different distances, confirmation of the hypothesis that CGR patterns are preserved along a genomic DNA sequence, and are different for DNA sequences originating from genomes of different species. This finding lends support to the theory that CGRs of genomic sequences can act as graphic genomic signatures. In particular, we compare the CGR patterns of over five hundred different 150,000 bp genomic sequences originating from the genomes of six organisms, each belonging to one of the kingdoms of life: H. sapiens, S. cerevisiae, A. thaliana, P. falciparum, E. coli, and P. furiosus. We also provide preliminary evidence of this method's applicability to closely related species by comparing H. sapiens (chromosome 21) sequences and over one hundred and fifty genomic sequences, also 150,000 bp long, from P. troglodytes (Animalia; chromosome Y), for a total length of more than 101 million basepairs analyzed. We compute pairwise distances between CGRs of these genomic sequences using six different distances, and construct Molecular Distance Maps that visualize all sequences as points in a two-dimensional or three-dimensional space, to simultaneously display their interrelationships. Our analysis confirms that CGR patterns of DNA sequences from the same genome are in general quantitatively similar, while being different for DNA sequences from genomes of different species. Our analysis of the performance of the assessed distances uses three different quality measures and suggests that several distances outperform the Euclidean distance, which has so far been almost exclusively used for such studies. In particular we show that, for this dataset, DSSIM (Structural Dissimilarity Index) and the descriptor distance (introduced here) are best able to classify genomic sequences.Comment: 14 pages, 6 figures, 5 table

A variation of a classical Turán-type extremal problem

AbstractA variation of a classical Turán-type extremal problem (Erdős on Graphs: His Legacy of Unsolved Problems (1998) p. 36) is considered as follows: determine the smallest even integer σ(Kr,s,n) such that every n-term graphic non-increasing sequence π=(d1,d2,…,dn) with term sum σ(π)=d1+d2+⋯+dn≥σ(Kr,s,n) has a realization G containing Kr,s as a subgraph, where Kr,s is a r×s complete bipartite graph. In this paper, we determine σ(Kr,s,n) exactly for every fixed s≥r≥3 when n≥n0(r,s), where m=[(r+s+1)24] andn0(r,s)=m+3s2−2s−6,ifs≤2randsis even,m+3s2+2s−8,ifs≤2randsis odd,m+2s2+(2r−6)s+4r−8,ifs≥2r+1

A design representation model for high-level synthesis

Design tools share and exchange various types of information pertaining to the design. The identification of a uniform design representation to capture this information is essential for the development of a successful design environment. We have done an extensive study on the representation needs of existing database tools in the UCI CADLAB; examples of which are graph compilers for high-level hardware specifications, state schedulers, hardware allocators, and microarchitecture optimizers. The result of this study is the development of a design representation model that will serve as a common internal representation (DDM) for all system and behavioral synthesis tools. DDM thus builds the foundation for a CAD Framework in which design tools can communicate via operating on this common representation. The design information is composed of three separate graph models: the conceptual model, the behavioral model and the structural model. The conceptual model (represented by a Design Entity Graph) captures the overall organization of the design information, such as, versions and configurations. The behavioral model (represented by an Augmented Control/Data Flow Graph) describes the design behavior. The structural model (represented by an Annotated Component Graph) captures the hierarchical data path structure and its geometric information. In this paper, we define the last two graph models. They both capture the actual design data of the application domain. Since VHDL has gained increasing popularity as hardware description language for synthesis, we give numerous examples throughout this report that show how the proposed design representation model can be used to represent VHDL specifications

A representation of the natural numbers by means of cycle-numbers, with consequences in number theory

In this paper we give rules for creating a number triangle T in a manner analogous to that for producing Pascal's arithmetic triangle; but all of its elements belong to {0, 1}, and cycling of its rows is involved in the creation. The method of construction of any one row of T from its preceding rows will be defined, and that, together with starting and boundary conditions, will suffice to define the whole triangle, by sequential continuation. We shall use this triangle in order to define the so-called cycle-numbers, which can be mapped to the natural numbers. T will be called the 'cyclenumber triangle'. First we shall give some theorems about relationships between the cyclenumbers and the natural numbers, and discuss the cycling of patterns within the triangle's rows and diagonals. We then begin a study of figures (i.e. (0,1)- patterns, found on lines, triangles and squares, etc.) within T. In particular, we shall seek relationships which tell us something about the prime numbers. For our later studies, we turn the triangle onto its side and work with a doubly-infinite matrix C. We shall find that a great deal of cycling of figures occurs within T and C, and we exploit this fact whenever we can. The phenomenon of cycling patterns leads us to muse upon a 'music of the integers', indeed a 'symphony of the integers', being played out on the cycle-number triangle or on C. Like Pythagoras and his 'music of the spheres', we may well be the only persons capable of hearing it!

Generating constrained random graphs using multiple edge switches

The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily possible to access all graphs obeying some given con- straints through a classical switching procedure calling on pairs of edges. We therefore propose to get round this issue by generalizing this classical approach through the use of higher-order edge switches. This method, which we denote by "k-edge switching", makes it possible to progres- sively improve the covered portion of a set of constrained graphs, thereby providing an increasing, asymptotically certain confidence on the statistical representativeness of the obtained sample.Comment: 15 page