1. Algebraic independence of the two functions ℘(z) and ez. Legendre’s relation η2ω1 − η1ω2 = 2iπ. Proof: integrate ζ(z)dz on a fundamental parallelogram. Application: algebraic independence of the two functions az + bζ(z) and ℘(z). 2. Section § 10.7.2: Morphisms between elliptic curves. The modular invariant. 3. Section § 10.7.3: Endomorphisms of an elliptic curve; complex multiplications. Alg...

Switching between different alternative polyadenylation (APA) sites plays an important role in the fine tuning of gene expression. New technologies for the execution of 3'-end enriched RNA-seq allow genome-wide detection of the genes that exhibit significant APA site switching between different samples. Here, we show that the independence test gives better results than the linear trend test in ...

Fungal cellulases offer advantages of a secreted enzyme complex and relative easiness and economy of producing enzyme. Considerable amount of work has been done on fungal cellulases, especially with resurgence of interest in biomass-ethanol and concept of bio-refineries. Significant information has also been gained on basic biology of organisms producing cellulases, and in process development f...

Multiagent systems (MAS), long studied in artificial intelligence, have recently become popular in mainstream IS research. This resurgence in MAS research can be attributed to two phenomena: the spread of concurrent and distributed computing with the advent of the web; and a deeper integration of computing into organizations and the lives of people, which has led to increasing collaborations am...

A matrix is free, or generic, if its nonzero entries are algebraically independent. Necessary and sufficient combinatorial conditions are presented for a complex free matrix to have a free Moore-Penrose inverse. These conditions extend previously known results for square, nonsingular free matrices. The result used to prove this characterization relates the combinatorial structure of a free matr...

It is well-known that the associated analytic space of an affine variety defined over complex number field is Stein but the converse is not true, that is, an algebraic Stein variety is not necessarily affine. In this talk, we will give sufficient and necessary conditions for an algebraic Stein variety to be affine. One of our results is that a quasi-projective variety Y defined over complex num...

We introduce a growing network model which generates both modular and hierarchical structure in a self-organized way. To this end, we modify the Barabási–Albert model into the one evolving under the principles of division and independence as well as growth and preferential attachment (PA). A newly added vertex chooses one of the modules composed of existing vertices, and attaches edges to verti...

This paper considers the theory of database queries on the complex value data model with external functions. Motivated by concerns regarding query evaluation, we first identify recursive sets of formulas, called embedded allowed, which is a class with desirable properties of ‘‘reasonable” queries. We then show that all embedded allowed calculus (or fix-point) queries are domain independent and ...

We construct several pairwise-incomparable bounds on the projective dimensions of edge ideals. Our bounds use combinatorial properties of the associated graphs. In particular, we draw heavily from the topic of dominating sets. Through Hochster’s Formula, we recover and strengthen existing results on the homological connectivity of graph independence complexes.

Let G be an infinite graph such that the automorphism group of G contains a subgroup K ∼= Z with the property that G/K is finite. We examine the homology of the independence complex Σ(G/I) of G/I for subgroups I of K of full rank, focusing on the case that G is the square, triangular, or hexagonal grid. Specifically, we look for a certain kind of homology cycles that we refer to as “cross-cycle...