共查询到20条相似文献,搜索用时 15 毫秒
1.
C. S. Güntürk M. Lammers A. M. Powell R. Saab Ö. Yılmaz 《Foundations of Computational Mathematics》2013,13(1):1-36
Quantization of compressed sensing measurements is typically justified by the robust recovery results of Candès, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size δ is used to quantize m measurements y=Φx of a k-sparse signal x∈? N , where Φ satisfies the restricted isometry property, then the approximate recovery x # via ? 1-minimization is within O(δ) of x. The simplest and commonly assumed approach is to quantize each measurement independently. In this paper, we show that if instead an rth-order ΣΔ (Sigma–Delta) quantization scheme with the same output alphabet is used to quantize y, then there is an alternative recovery method via Sobolev dual frames which guarantees a reduced approximation error that is of the order δ(k/m)(r?1/2)α for any 0<α<1, if m? r,α k(logN)1/(1?α). The result holds with high probability on the initial draw of the measurement matrix Φ from the Gaussian distribution, and uniformly for all k-sparse signals x whose magnitudes are suitably bounded away from zero on their support. 相似文献
2.
The infinite horizon risk-sensitive control problem for non-degenerate controlled diffusions is analyzed under a ‘near monotonicity’
condition on the running cost that penalizes large excursions of the process. 相似文献
3.
We demonstrate that for all linear devices and/or sensors, signal requisition and reconstruction is naturally a mathematical frame expansion and reconstruction issue, whereas the measurement is carried out via a sequence generated by the exact physical response function (PRF) of the device, termed sensory frame {h n }. The signal reconstruction, on the other hand, will be carried out using the dual frame $\{\tilde{h}^{a}_{n}\}$ of an estimated sensory frame {h n a }. This consequently results in a one-sided perturbation to a frame expansion, which resides in each and every signal and image reconstruction problem. We show that the stability of such a one-sided frame perturbation exits. Examples of image reconstructions in de-blurring are demonstrated. 相似文献
4.
Isaac Pesenson 《Journal of Geometric Analysis》2009,19(2):390-419
An approximation theory by bandlimited functions (≡ Paley-Wiener functions) on Riemannian manifolds of bounded geometry is
developed. Based on this theory multiscale approximations to smooth functions in Sobolev and Besov spaces on manifolds are
obtained. The results have immediate applications to the filtering, denoising and approximation and compression of functions
on manifolds. There exists applications to problems arising in data dimension reduction, image processing, computer graphics,
visualization and learning theory.
相似文献
5.
Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively applied to Signal Processing,
Statistical Analysis and Mathematical Modeling. We propose an extension of SVD for both the qualitative detection and quantitative
determination of nonlinearity in a time series. The method is to augment the embedding matrix with additional nonlinear columns
derived from the initial embedding vectors and extract the nonlinear relationship using SVD. The paper demonstrates an application
of nonlinear SVD to identify parameters when the signal is generated by a nonlinear transformation. Examples of maps (Logistic
map and Henon map) and flows (Van der Pol oscillator and Duffing oscillator) are used to illustrate the method of nonlinear
SVD to identify parameters. The paper presents the recovery of parameters in the following scenarios: (i) data generated by
maps and flows, (ii) comparison of the method for both noisy and noise-free data, (iii) surrogate data analysis for both the
noisy and noise-free cases. The paper includes two applications of the method: (i) Mathematical Modeling and (ii) Chaotic
Cryptanalysis. 相似文献
6.
First we establish a Carleman estimate for Lotka-Volterra competition-diffusion system of three equations with variable coefficients.
Then the internal observations with two measurements are allowed to obtain the stability result for the inverse problem consisting
of retrieving two smooth diffusion coefficients in the given parabolic system for the dimension n≤3. The proof of the results rely on Carleman estimates and certain energy estimates for parabolic system. 相似文献
7.
Pham Loi Vu 《Acta Appl Math》2010,109(3):789-787
We derive the continual system of nonlinear interaction waves from the compatibility of the transport equation on the whole
line and the equation governing the time-evolution of the eigenfunctions of the transport operator. The transport equation
represents the continual generalization from the n-component system of first-order ordinary differential equations. The continual system describes a nonlinear interaction of
waves. We prove that the continual system can be integrated by the inverse scattering method. The method is based on applying
the results of the inverse scattering problem for the transport equation to finding the solution of the Cauchy initial-value
problem for the continual system. Indeed, the transition operator for the scattering problem admits right and left Volterra
factorizations. The intermediate operator for this problem determines the one-to-one correspondence between the preimages
of a solution of the transport equation. This operator is related to the transition operator and admits not only right and
left Volterra factorizations but also the analytic factorization. By virtue of this fact the potential in the transport equation
is uniquely reconstructed in terms of the solutions of the fundamental equations in inverse problem. 相似文献
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9.
The original version of the article was published in Central European Journal of Mathematics, 2011, 9(4), 915–921, DOI: 10.2478/s11533-011-0029-8.
Unfortunately, the original version of this article contains a mistake: Lemma 2.1 (2) is not true. We correct Lemma 2.2 (2)
and Theorem 1.1 in our paper where this lemma was used. 相似文献
10.
We previously constructed the theory of quantum thermodynamics, which assigns operators to dual variables (for example, pressure and volume or temperature and entropy, i.e., dual pairs of extensive and intensive variables similar to momenta and coordinates in classical mechanics) similarly to the theory of quantum mechanics. Here we show that in both the bosonic and fermionic cases, the quantized entropy introduced as an operator in special Fock spaces containing a new variable, called the statistical spin, depends on some variables that do not affect any physical results and are hence called ghosts. 相似文献
11.
We consider several models of networks of interacting particles and prove the existence of quasi-periodic equilibrium solutions. We assume (1) that the network and the interaction among particles are invariant under a group that satisfies some mild assumptions; (2) that the state of each particle is given by a real number; (3) that the interaction is invariant by adding an integer to the state of all the particles at the same time; (4) that the interaction is ferromagnetic and coercive (it favors local alignment and penalizes large local oscillations); and (5) some technical assumptions on the regularity speed of decay of the interaction with the distance. Note that the assumptions are mainly qualitative, so that they cover many of the models proposed in the literature. We conclude (A) that there are minimizing (ground states) quasi-periodic solutions of every frequency and that they satisfy several geometric properties; (B) if the minimizing solutions do not cover all possible values at a point, there is another equilibrium point which is not a ground state. These results generalize basic results of Aubry–Mather theory (take the network and the group to be ?). In particular, we provide with a generalization of the celebrated criterion of existence of invariant circles if and only iff the Peierls–Nabarro barrier vanishes. 相似文献
12.
A. J. Novak G. Feichtinger G. Leitmann 《Journal of Optimization Theory and Applications》2010,144(3):533-555
The question of how best to prosecute the ‘war on terror’ leads to strategic interaction in an intertemporal setting. We consider
a nonzero sum differential game between a government and a terrorist organisation. Due to the state-separability of the game
we are able to determine Nash and Stackelberg solutions in analytic form. Their comparison as well as the sensitivity analysis
deliver interesting insight into the design of efficient measures to combat terror. 相似文献
13.
Let G(OS)\mathbf{G}(\mathcal{O}_{S}) be an S-arithmetic subgroup of a connected, absolutely almost simple linear algebraic group G over a global function field K. We show that the sum of local ranks of G determines the homological finiteness properties of G(OS)\mathbf{G}(\mathcal{O}_{S}) provided the K-rank of G is 1. This shows that the general upper bound for the finiteness length of G(OS)\mathbf{G}(\mathcal{O}_{S}) established in an earlier paper is sharp in this case. 相似文献
14.
We investigate connections between an important parameter in the theory of Banach spaces called the -norm, and two properties of classes of functions which are essential in Learning Theory – the uniform law of large numbers and the Vapnik–Chervonenkis (VC) dimension. We show that if the -norm of a set of functions is bounded in some sense, then the set satisfies the uniform law of large numbers. Applying this result, we show that if X is a Banach space which has a nontrivial type, then the unit ball of its dual satisfies the uniform law of large numbers. Next, we estimate the -norm of a set of {0,1}-functions in terms of its VC dimension. Finally, we present a `Gelfand number' like estimate of certain classes of functions. We use this estimate to formulate a learning rule, which may be used to approximate functions from the unit balls of several Banach spaces. 相似文献
15.
Obstruction Theory and Coincidences in Positive Codimension 总被引:1,自引:0,他引:1
Daciberg GONCALVES Jerzy JEZIERSKI Peter WONG 《数学学报(英文版)》2006,22(5):1591-1602
Let f, g : X→Y be two maps between closed manifolds with dim X ≥ dim Y = n ≥ 3. We study the primary obstruction on(f, g) to deforming f and g to be coincidence free on the n-th skeleton of X. We give examples for which obstructions to deforming f and g to be coincidence free are detected by on (f, g). 相似文献
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17.
In this paper we investigate the degree and the homotopy theory of Orlicz–Sobolev mappings W
1,P
(M,N) between manifolds, where the Young function P satisfies a divergence condition and forms a slightly larger space than W
1,n
, n=dim M. In particular, we prove that if M and N are compact oriented manifolds without boundary and dim M=dim N=n, then the degree is well defined in W
1,P
(M,N) if and only if the universal cover of N is not a rational homology sphere, and in the case n=4, if and only if N is not homeomorphic to S
4. 相似文献
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19.
We obtain the Peter–Weyl decomposition of the star product and star restriction associated to the Toeplitz calculus on complex
and real symmetric domains, respectively, under the action of the maximal compact subgroup. Both the Berezin and the Berezin–Toeplitz
cases are covered. 相似文献
20.