As with most computer science problems, representation of the data is the key to ecient and eective solutions. Piecewise linear representation has been used for the representation of the data. This representation has been used by various researchers to support clustering, classication, indexing and association rule mining of time series data. A variety of algorithms have been proposed to obtain...

Despite the lack of direct evidence, it is generally believed that top-down signals are mediated by the abundant feedback connections from higher- to lower-order sensory areas. Here we provide direct evidence for a top-down mechanism. We stained the visual cortex of the ferret with a voltage-sensitive dye and presented a short-duration contrast square. This elicited an initial feedforward and l...

Let M= ( A B C 0 ) be a complex square matrix where A is square. When BCB = 0, rank(BC) = rank(B) and the group inverse of ( BAB 0 CB 0 ) exists, the group inverse of M exists if and only if rank(BC + A ( BAB ) π BA) = rank(B). In this case, a representation of M in terms of the group inverse and Moore-Penrose inverse of its subblocks is given. Let A be a real matrix. The sign pattern of A is a...

‎for a set of non-negative integers~$l$‎, ‎the $l$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $a_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|a_u cap a_v|in l$‎. ‎the bipartite $l$-intersection number is defined similarly when the conditions are considered only for the ver...

A touching triangle graph (TTG) representation of a planar graph is a planar drawing Γ of the graph, where each vertex is represented as a triangle and each edge e is represented as a side contact of the triangles that correspond to the end vertices of e. We call Γ a proper TTG representation if Γ determines a tiling of a triangle, where each tile corresponds to a distinct vertex of the input g...

The paper presents a new ECG-dedicated noise removal technique. The proposed algorithm makes use of the local bandwidth variability of cardiac electrical representation. Background activities of any origin (muscle, mains interference etc.) are measured in specified regions of the time-frequency plane. Outside of these regions, where normally the cardiac representation components are expected, w...

We connect the algebraic geometry and representation theory associated to Freudenthal's magic square. We give unified geometric descriptions of several classes of orbit closures, describing their hyperplane sections and desingularizations, and interpreting them in terms of composition algebras. In particular, we show how a class of invariant quartic polynomials can be viewed as generalizations ...

Inspired by Lomonaco–Kauffman paper on quantum knots and knot mosaics we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. We introduce codes for mirror-curves treated as knot or link diagrams placed in rectangular square grid, suitable for software implementations and discuss possible applications of mirror-curves.

This note is concerned with the generalization of the continuous shearlet transform to higher dimensions. Quite recently, a first approach has been derived in [4]. We present an alternative version which deviates from [4] mainly by a different generalization of the shear component. It turns out that the resulting integral transform is again associated with a square-integrable group representation.