Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Why Daubechies Wavelets Are So Successful, Solymar Ayala Cortez, Laxman Bokati, Aaron Velasco, Vladik Kreinovich
Why Daubechies Wavelets Are So Successful, Solymar Ayala Cortez, Laxman Bokati, Aaron Velasco, Vladik Kreinovich
Departmental Technical Reports (CS)
In many applications, including analysis of seismic signals, Daubechies wavelets perform much better than other families of wavelets. In this paper, we provide a possible theoretical explanation for the empirical success of Daubechies wavelets. Specifically, we show that these wavelets are optimal with respect to any optimality criterion that satisfies the natural properties of scale- and shift-invariance.
Many Known Quantum Algorithms Are Optimal: Symmetry-Based Proofs, Vladik Kreinovich, Oscar Galindo, Olga Kosheleva
Many Known Quantum Algorithms Are Optimal: Symmetry-Based Proofs, Vladik Kreinovich, Oscar Galindo, Olga Kosheleva
Departmental Technical Reports (CS)
Many quantum algorithms have been proposed which are drastically more efficient that the best of the non-quantum algorithms for solving the same problems. A natural question is: are these quantum algorithms already optimal -- in some reasonable sense -- or they can be further improved? In this paper, we review recent results showing that many known quantum algorithms are actually optimal. Several of these results are based on appropriate invariances (symmetries).
Why Kappa Regression?, Julio C. Urenda, Orsolya Csiszár, József Dombi, György Eigner, Olga Kosheleva, Vladik Kreinovich
Why Kappa Regression?, Julio C. Urenda, Orsolya Csiszár, József Dombi, György Eigner, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
A recent book provide examples that a new class of probability distributions and membership functions -- called kappa-regression distributions and membership functions -- leads to better data processing results than using previously known classes. In this paper, we provide a theoretical explanation for this empirical success -- namely, we show that these distributions are the only ones that satisfy reasonable invariance requirements.