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Jump-Sparse and Sparse Recovery Using Potts Functionals

Martin Storath, Andreas Weinmann, Laurent Demaret
2014 IEEE Transactions on Signal Processing  
We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals.  ...  We then propose a new optimization method for these functionals which is based on dynamic programming and the alternating direction method of multipliers (ADMM).  ...  Theorem 2 . 2 There are linear operators A and data b in L p , 1 ≤ p < ∞, such that the continuous time inverse Potts problem with respect to A and b does not have a minimizer.  ... 
doi:10.1109/tsp.2014.2329263 fatcat:uncc7tdwzbeipdsmdvdvqwue7e

Page 3402 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
A.] (RS-SART; Saratov) Inverse spectral problems for singular non-selfadjoint differential operators with discontinuities in an interior point.  ...  For this inverse problem the authors prove a uniqueness theorem, obtain a procedure for constructing the solution and provide necessary and sufficient conditions for the solvability of the inverse problem  ... 

On the structure of the degrees of relative provability

Uri Andrews, Mingzhong Cai, David Diamondstone, Steffen Lempp, Joseph S. Miller
2015 Israel Journal of Mathematics  
Our work continues and greatly expands the second author's paper on this topic by answering a number of open questions from that paper, comparing three different notions of a jump operator and studying  ...  jump inversion as well as the corresponding high/low hierarchies, investigating the structure of true Π 0 1 -statements as a substructure, and connecting the degrees of provability to escape and domination  ...  Other natural questions concern jump inversion. We proved a number of jump inversion theorems, including the analog of the Friedberg jump inversion theorem for this structure.  ... 
doi:10.1007/s11856-015-1182-8 fatcat:umzkztj7djganfrwdzghrzmsty

Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials

Liubov Efremova, Gerhard Freiling
2013 Open Mathematics  
AbstractWe consider Sturm-Liouville differential operators on a finite interval with discontinuous potentials having one jump.  ...  As the main result we obtain a procedure of recovering the location of the discontinuity and the height of the jump.  ...  Introduction This paper is devoted to the numerical solution of the inverse spectral problem for Sturm-Liouville differential operators with discontinuous potentials on a finite interval.  ... 
doi:10.2478/s11533-013-0301-1 fatcat:27m4jcc435b2fhhfpcibs3fqd4

The jump inversion theorem for $Q\sb{2n+1}$-degrees

Ilias G. Kastanas
1984 Proceedings of the American Mathematical Society  
Assuming projective determinacy we extend Friedberg's Jump Inversion theorem to Ç2/i+i"degrees, after noticing that it fails for A'2"+(-degrees. 0. Preliminaries.  ...  The set Cm is made up of A'm-degrees (a A'm-degree is a set ol reals that is an equivalence class for the equivalence relation a =a", ß ö a E A'm(/T and ß E A'm(a)).  ...  The answer is yes [6] : Jump Inversion theorem for A1,-degrees. // b > 0' then there exists an a such that a' = a V 0' = b.  ... 
doi:10.1090/s0002-9939-1984-0728361-5 fatcat:4ochg54n4jdrvk72kr52ecd3em

Linear inverse problems for Markov processes and their regularisation [article]

Umut Çetin
2016 arXiv   pre-print
We study the solutions of the inverse problem g(z)=∫ f(y) P_T(z,dy) for a given g, where (P_t(·,·))_t ≥ 0 is the transition function of a given Markov process, X, and T is a fixed deterministic time, which  ...  to 1, and J is a suitably constructed jump process.  ...  Note that the inverse problem given by g = Kf , where K is a non-negative operator on a Hilbert space with norm less than 1, can be recast in the form of (1.1).  ... 
arXiv:1608.04918v2 fatcat:bcskhpeux5hbdfdd34j52rntly

Stability properties of a crack inverse problem in half space [article]

Darko Volkov, Yulong Jiang
2021 arXiv   pre-print
The highlight of this paper is showing a stability result for this inverse problem.  ...  We show in this paper a Lipschitz stability result for a crack inverse problem in half space. The direct problem is a Laplace equation with zero Neumann condition on the top boundary.  ...  Since the injective operator A m 0 is compact, its inverse is unbounded, so a non-zero lower bound for A m 0 h 0 L 2 (V ) has to be considered rather than a lower bound for h 0 H 1 0 (R) .  ... 
arXiv:2009.14747v2 fatcat:nqdcdcdk2jcwdpdckz2ywtokci

Jump inversions inside effectively closed sets and applications to randomness

George Barmpalias, Rod Downey, Keng Meng Ng
2011 Journal of Symbolic Logic (JSL)  
We study inversions of the jump operator on classes, combined with certain basis theorems.  ...  These jump inversions have implications for the study of the jump operator on the random degrees—for various notions of randomness.  ...  By the Shoenfield jump Inversion theorem [Sho59] , the range of the jump operator on the ∆ 0 2 sets is the class of Σ 0 2 degrees above 0 .  ... 
doi:10.2178/jsl/1305810761 fatcat:icmx4pqznvdqrj4cg23wkknz2m

Fractional normal inverse Gaussian diffusion

A. Kumar, Mark M. Meerschaert, P. Vellaisamy
2011 Statistics and Probability Letters  
Similarly, we show that the NIG process, a Brownian motion subordinated to an inverse Gaussian process, is the limit of a random walk with uncorrelated jumps separated by i.i.d. waiting times.  ...  This paper shows how the FNIG process emerges naturally as the limit of a random walk with correlated jumps separated by i.i.d. waiting times.  ...  A. Kumar was supported by a research fellowship from the Council of Scientific and Industrial Research (CSIR), India.  ... 
doi:10.1016/j.spl.2010.10.007 fatcat:cnl46zvjsbdwvp6pvu3qjaczyq

A Galois connection between Turing jumps and limits [article]

Vasco Brattka
2018 arXiv   pre-print
As a monad of this pair of adjoint operations we obtain a problem that characterizes the low functions and dually to this another problem that characterizes the functions that are computable relative to  ...  Limit computable functions can be characterized by Turing jumps on the input side or limits on the output side.  ...  As another non-uniform side result of the limit inversion theorem (Theorem 31) we obtain a classical result from computability theory, the Friedberg jump inversion theorem [21] .  ... 
arXiv:1802.01355v2 fatcat:fqh5g37tfvdrtovyfxgxjpdgui

Entropy production and fluctuations in a Maxwell's refrigerator with squeezing

G. Manzano
2018 The European Physical Journal Special Topics  
Clarifying the impact of quantumness in the operation and properties of thermal machines represents a major challenge.  ...  We study the validity of the transient entropy production fluctuation theorem in the model with and without squeezing as well as its decomposition into adiabatic and non-adiabatic contributions.  ...  ACKNOWLEDGEMENTS It is a pleasure to thank Juan M. R. Parrondo for useful comments and discussions. G. M. acknowledge funding from MINECO (Grants No. FIS2014-52486-R, No.  ... 
doi:10.1140/epjst/e2018-00093-9 fatcat:q7epdsjwpvepxlfwuo4sdzsxau

Stability estimates for the fault inverse problem [article]

Faouzi Triki, Darko Volkov
2018 arXiv   pre-print
We study in this paper stability estimates for the fault inverse problem. In this problem, faults are assumed to be planar open surfaces in a half space elastic medium with known Lamé coefficients.  ...  A traction free condition is imposed on the boundary of the half space. Displacement fields present jumps across faults, called slips, while traction derivatives are continuous.  ...  Theorem 2.2 asserts that this mapping is injective, so an inverse operator can be defined. It is well known, however, that such an operator M is compact, therefore its inverse is unbounded.  ... 
arXiv:1807.06896v1 fatcat:6ejja7646ndlxocy2xbwozdzgu

Toeplitz Operators on H 2 Spaces

Allen Devinatz
1964 Transactions of the American Mathematical Society  
The problem of invertibility for I2., also using the ideas of [6], was solved in 1960 by H. Widom and announced by him, in part, in [13].  ...  We have solved this problem by showing that the problem of invertibility of a general Toeplitz operator can be reduced to the problem of invertibility of a special type of Toeplitz operator and that, in  ...  We shall list these below and refer to [7] for the proofs. Theorem B. Let w be a non-negative function on X summable with respect to dp.  ... 
doi:10.2307/1994297 fatcat:mdshh5c4o5hqdbn5m3tbovvt7a

Toeplitz operators on $H\sp{2}$ spaces

Allen Devinatz
1964 Transactions of the American Mathematical Society  
The problem of invertibility for I2., also using the ideas of [6], was solved in 1960 by H. Widom and announced by him, in part, in [13].  ...  We have solved this problem by showing that the problem of invertibility of a general Toeplitz operator can be reduced to the problem of invertibility of a special type of Toeplitz operator and that, in  ...  We shall list these below and refer to [7] for the proofs. Theorem B. Let w be a non-negative function on X summable with respect to dp.  ... 
doi:10.1090/s0002-9947-1964-0163174-9 fatcat:22jtguv74fbhfjosiqrexwymau

Fractional diffusion equation with distributed-order material derivative. Stochastic foundations [article]

Marcin Magdziarz, Marek Teuerle
2015 arXiv   pre-print
Then we introduce a Levy walk process of distributed-order type to establish our main result, which is the scaling limit of the considered process.  ...  It appears that the probability density function of the scaling limit process fulfills, in a weak sense, the fractional diffusion equation with material derivative of distributed-order type.  ...  Acknowledgements This research was partially supported by NCN Maestro grant no. 2012/06/A/ST1/00258. References  ... 
arXiv:1510.00315v1 fatcat:4rzaw7rplnhejbtynynsgs72du
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