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The diagonal of tropical matroid varieties and cycle intersections
diagonal of tropical matroid varieties cycle intersections
2011/2/21
We define an intersection product of tropical cycles on matroid varieties (via cutting out the diagonal) and show that it is well-behaved. In particular, this enables us to intersect cycles on moduli ...
Aspectual Principle, Benford's Law and Russell's Paradox
Aspectual Principle Benford's Law Russell's paradox
2011/2/28
In the present article Benford's law and Russell's paradox are explained by means of Aspectual Principle.
On intersection of two embedded spheres in 3-space
intersection two embedded spheres 3-space
2011/1/18
We find necessary and sufficient conditions on sequences x = x1, x2, . . . , xn, y = y1, y2, ..., yn of positive integers, for existence of embeddings f, g : S2 → R3 such that S2 − g−1(S2)...
Polynomial invariants of graphs on surfaces
Graphs on surfaces ribbon graphs matroids Krushkal polynomial
2011/2/25
For a graph embedded into a surface, we relate many combinatorial parameters of the cycle matroid of the graph and the bond matroid of the dual graph with the topological parameters of the embedding. ...
Given a right eigenvector x and a left eigenvector y associated with the same eigen-
value of a matrix A, there is a Hermitian positive definite matrix H for which y = Hx. The matrix H defines an inn...
The differences between natural and artificial life. Towards a definition of life
differences natural artificial life definition of life
2010/12/28
It is high time to openly and without finalism define the dangerous but needed term‘purposeful information’, whose quantity is an Eigen information value. Using the term ‘biological information’ in it...
The measure of Jensen-Fisher divergence between probability distributions is introduced and its theoretical grounds set up.
Among all electromagnetic theories which (a) are derivable from a Lagrangian, (b) satisfy the
dominant energy condition, and (c) in the weak eld limit coincide with classical linear electromagnetics...
Compression-induced failure of electro-active polymeric thin films
actuators electroactive polymers (EAP) compression
2011/1/19
The insurgence of compression induces wrinkling in actuation devices based on EAPs thin films leading to a sudden decrease of performances up to fail-ure.
The contact homology of Legendrian knots with maximal Thurston-Bennequin invariant
contact homology of Legendrian knots maximal Thurston-Bennequin invariant
2011/2/25
We show that there exists a Legendrian knot with maximal Thurston-Bennequin invariant whose contact homology is trivial. We also provide another Legendrian knot which has the same knot type and classi...
The standard model of online prediction deals with serial processing of inputs by a single
processor.
The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of...
In [3] we have introduced the notion of covering projection on a general topos E. These are locally constant objects with an additional property.
An integral presentation for the scalar products of nested Bethe vectors for the quantum integrable models associated with the quantum affine algebra Uq(bgl3) is given.This result is obtained in the f...
We prove an algebraic formula, conjectured by M. Kontsevich, for com-puting the monodromy of the vanishing cycles of a regular function on a smooth complex algebraic variety.