23,167 research outputs found
Norms as a function of p are linearly independent in finite dimensions
We show that there are no non-trivial linear dependencies among p-norms of
vectors in finite dimensions that hold for all p. The proof is by complex
analytic continuation.Comment: 1 page, 1 figure. Proof simplified thanks to the refere
Blind Multilinear Identification
We discuss a technique that allows blind recovery of signals or blind
identification of mixtures in instances where such recovery or identification
were previously thought to be impossible: (i) closely located or highly
correlated sources in antenna array processing, (ii) highly correlated
spreading codes in CDMA radio communication, (iii) nearly dependent spectra in
fluorescent spectroscopy. This has important implications --- in the case of
antenna array processing, it allows for joint localization and extraction of
multiple sources from the measurement of a noisy mixture recorded on multiple
sensors in an entirely deterministic manner. In the case of CDMA, it allows the
possibility of having a number of users larger than the spreading gain. In the
case of fluorescent spectroscopy, it allows for detection of nearly identical
chemical constituents. The proposed technique involves the solution of a
bounded coherence low-rank multilinear approximation problem. We show that
bounded coherence allows us to establish existence and uniqueness of the
recovered solution. We will provide some statistical motivation for the
approximation problem and discuss greedy approximation bounds. To provide the
theoretical underpinnings for this technique, we develop a corresponding theory
of sparse separable decompositions of functions, including notions of rank and
nuclear norm that specialize to the usual ones for matrices and operators but
apply to also hypermatrices and tensors.Comment: 20 pages, to appear in IEEE Transactions on Information Theor
Computation of vector sublattices and minimal lattice-subspaces of R^k. Applications in finance
In this article we perform a computational study of Polyrakis algorithms
presented in [12,13]. These algorithms are used for the determination of the
vector sublattice and the minimal lattice-subspace generated by a finite set of
positive vectors of R^k. The study demonstrates that our findings can be very
useful in the field of Economics, especially in completion by options of
security markets and portfolio insurance.Comment: 22 page
Range convergence monotonicity for vector measures and range monotonicity of the mass
We prove that the range of sequence of vector measures converging widely
satisfies a weak lower semicontinuity property, that the convergence of the
range implies the strict convergence (convergence of the total variation) and
that the strict convergence implies the range convergence for strictly convex
norms. In dimension 2 and for Euclidean spaces of any dimensions, we prove that
the total variation of a vector measure is monotone with respect to the range.Comment: 28 page
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