Kiam Heong Kwa

Core words and Parikh matrices

Parikh matrices have been widely investigated due to their applicability in arithmetizing words by numbers. This paper introduces the core of a binary word, which captures the essential part of a word from the perspective of its Parikh matrix. Additionally, the stronger notion of core M-unambiguity is introduced and the characterization of core M-unambiguous binary words is obtained. Finally, a generalization of the core of a binary word and some of its interesting properties are investigated.

Additive maps of rank r tensors and symmetric tensors

Abstract Let and be fields and let n be a positive integer. Let and be linear spaces over such that and let and be linear spaces over . Let be the tensor product of and and let be the subspace of symmetric tensors of . In this paper, we show that a map satisfies for all rank r tensors if and only if is additive. Here r is a fixed integer such that and with , or with and . Examples showing the indispensability of assumption in our results are included.

A note on classical adjoint commuting linear maps of tensor products of matrices

Let be the algebra of matrices over a field with at least three elements. Inspired by linear preserver problems related to quantum information science, we characterize classical adjoint commuting linear maps, i.e. linear maps such that with , that preserve decomposable tensors of . Some examples are given to distinguish the study of classical adjoint commuting linear maps of tensor products of matrices from those found in the study of classical adjoint commuting linear maps on matrix spaces.

LINEAR SPACES AND PRESERVERS OF BOUNDED RANK-TWO PER-SYMMETRIC TRIANGULAR MATRICES

Let F be a field and m,n be integers m,n > 3. Let SMn(F) and STn(F) denote the linear space of n × n per-symmetric matrices over F and the linear space of n × n per-symmetric triangular matrices over F, respectively. In this note, the structure of spaces of bounded rank-two matrices of STn(F) is determined. Using this structural result, a classification of bounded rank-two linear preservers : STn(F) ! SMm(F), with F of characteristic not two, is obtained. As a corollary, a complete description of bounded rank-two linear preservers between per-symmetric triangular matrix spaces over a field of characteristic not two is addressed.

Commuting maps on rank k triangular matrices

ABSTRACT Let be an integer and let be a field with . Let be the ring of upper triangular matrices over with centre . Fixing an integer , we prove that an additive map satisfies for all rank k matrices if and only if there exist an additive map , and in which when or k<n such that for all . Here, is the matrix whose th entry is one and zeros elsewhere.

Classical adjoint commuting and determinant preserving linear maps on Kronecker products of Hermitian matrices

ABSTRACT Let be a linear map on the Kronecker product of spaces of Hermitian matrices of size . (If d=1, we identify with .) We establish a condition under which if and only if for all . Then for , we apply this fact to characterize maps such that with some mild conditions.

Predicting new drug indications from network analysis

This work adapts centrality measures commonly used in social network analysis to identify drugs with better positions in drug-side effect network and drug-indication network for the purpose of drug repositioning. Our basic hypothesis is that drugs having similar phenotypic profiles such as side effects may also share similar therapeutic properties based on related mechanism of action and vice versa. The networks were constructed from Side Effect Resource (SIDER) 4.1 which contains 1430 unique drugs with side effects and 1437 unique drugs with indications. Within the giant components of these networks, drugs were ranked based on their centrality scores whereby 18 prominent drugs from the drug-side effect network and 15 prominent drugs from the drug-indication network were identified. Indications and side effects of prominent drugs were deduced from the profiles of their neighbors in the networks and compared to existing clinical studies while an optimum threshold of similarity among drugs was sought for. The threshold can then be utilized for predicting indications and side effects of all drugs. Similarities of drugs were measured by the extent to which they share phenotypic profiles and neighbors. To improve the likelihood of accurate predictions, only profiles such as side effects of common or very common frequencies were considered. In summary, our work is an attempt to offer an alternative approach to drug repositioning using centrality measures commonly used for analyzing social networks.

Differential geometric analysis of radiation--particle interaction

On the basis of the Lorentz equations of motion, the orbit of a charge driven by a generic EM field with planar symmetry is formulated and analyzed within the framework of a Lorentzian geometry with a curvature whose order of magnitude is parametrized by the radiation intensity and frequency. This reformulation leads to (i) a demonstration of the integrability of the particle motion in a plane-wave field as a result of the vanishing of the curvature, (ii) a manifestation of the parametric dependence of the dynamical response of the particle orbit to the EM field on the impulse factor in terms of local stability and the occurrence of parametric resonance, and (iii) a mathematically precise meaning to the ponderomotive oscillation center of the charge executing oscillatory motion in a sufficiently low impulsive EM field, which is subsequently used to raise (iv) a discussion of the domain of applicability of the ponderomotive approximation.

Perfect Clar structures and 3-homogeneous simplicial complexes

Abstract In this paper we discuss the notion of a Clar structure on a 3-homogeneous simplicial complex, in particular on a triangulated surface. Such structures arise in theoretical chemistry, from where they also have received the name. We discuss various aspects of Clar structures, particularly existence of Clar structures on (closed compact) surfaces of general genus, and a possible variation of the definition using a splitting. We give an interpretation of Clar structures in terms of (mod 2) two step homology groups, which establishes the relationship of these structures with certain standard calculations in algebraic topology.