The term ‘Multidimensional Scaling’ or MDS is used in two essentially different ways in statistics (de Leeuw & Heiser 1980a). MDS in the wide sense refers to any technique that produces a multidimensional geometric representation of data, where quantitative or qualitative relationships in the data are made to correspond with geometric relationships in the representation. MDS in the narrow sense...

We study open B-model representing D-branes on 2-cycles of local Calabi–Yau geometries. To this end we work out a reduction technique linking D-branes partition functions and multi-matrix models in the case of conifold geometries so that the matrix potential is related to the complex moduli of the conifold. We study the geometric engineering of the multi-matrix models and focus on two-matrix mo...

With the deconstruction technique, the geometric information of a torus can be encoded in a sequence of orbifolds. By studying the Matrix Theory on these orbifolds as quiver mechanics, we present a formulation that (de)constructs the torus of generic shape on which Matrix Theory is “compactified”. The continuum limit of the quiver mechanics gives rise to a (1+2)dimensional SYM. A hidden (fourth...

In many real-world applications data exhibits non-stationarity, i.e., its distribution changes over time. One approach to handling non-stationarity is to remove or minimize it before attempting to analyze the data. In the context of brain computer interface (BCI) data analysis this is sometimes achieved using stationary subspace analysis (SSA). The classic SSA method finds a matrix that project...

Model systems in which fluid particles move in a disordered matrix of immobile obstacles have been found to be a reasonable representation of a colloidal fluid confined in a disordered porous medium. For systems consisting of hard-sphere particles, the obstacle matrix partitions the space available to the fluid particles into voids of finite volume (“traps”) and a percolating void that extends ...

We present a geometric approach for the analysis of dynamic scenes containing multiple rigidly moving objects seen in two perspective views. Our approach exploits the algebraic and geometric properties of the so-called multibody epipolar constraint and its associated multibody fundamental matrix, which are natural generalizations of the epipolar constraint and of the fundamental matrix to multi...

In this paper, we use the algebra methods, the properties of the r-circulant matrix and the geometric circulant matrix to study the upper and lower bound estimate problems for the spectral norms of a geometric circulant matrix involving the generalized k-Horadam numbers, and we obtain some sharp estimations for them. We can also give a new estimation for the norms of a r-circulant matrix involv...

In this paper, we set up a geometric framework for solving sparse matrix problems. We introduce geometric sparseness, a notion which applies to several well-known families of sparse matrix. Two algorithms are presented for solving geometrically-sparse matrix problems. These algorithms are inspired by techniques in classical algebraic topology, and involve the construction of a simplicial comple...

We use production matrices to count several classes of geometric graphs. present novel for non-crossing partitions, connected graphs, and k -angulations, which provide another, simple elegant, way counting the number such objects. Counting graphs is then equivalent calculating powers a matrix. Applying technique Riordan Arrays these matrices, we establish new formulas numbers as well combinator...