# Multidimensional Persistence and Noise

## Related Articles

- Topological Persistence for Circle-Valued Maps. Burghelea, Dan; Dey, Tamal // Discrete & Computational Geometry;Jul2013, Vol. 50 Issue 1, p69
We study circle-valued maps and consider the persistence of the homology of their fibers. The outcome is a finite collection of computable invariants which answer the basic questions on persistence and in addition encode the topology of the source space and its relevant subspaces. Unlike...

- Splittings of von Neumann rho-invariants of knots. Kim, Se‐Goo; Kim, Taehee // Journal of the London Mathematical Society;Jun2014, Vol. 89 Issue 3, p797
We give a sufficient condition under which the vanishing property of Cochranâ€“Orrâ€“Teichner knot concordance obstructions splits under connected sum. The condition is described in terms of self-annihilating submodules with respect to higher-order Blanchfield linking forms. This...

- Examples of area-minimizing surfaces in the sub-Riemannian Heisenberg group $${\mathbb{H}^1}$$ with low regularity. Ritor�, Manuel // Calculus of Variations & Partial Differential Equations;Feb2009, Vol. 34 Issue 2, p179
We give new examples of entire area-minimizing t-graphs in the sub-Riemannian Heisenberg group $${\mathbb{H}^1}$$ . They are locally Lipschitz in Euclidean sense. Some regular examples have prescribed singular set consisting of either a horizontal line or a finite number of horizontal halflines...

- ON FINITELY LIPSCHITZ SPACE MAPPINGS. SALIMOV, R. R. // Sibirskie Elektronnye Matematicheskie Izvestiia;2011, Vol. 8, p284
It is established that a ring Q-homeomorphism with respect to p-modulus in â„n, n â‰¥ 2; is finitely Lipschitz if n - 1 < p < n and if the mean integral value of Q(x) over infinitesimal balls B(x0, Îµ) is finite everywhere.

- One can hear the corners of a drum. Lu, Zhiqin; Rowlett, Julie M. // Bulletin of the London Mathematical Society;Feb2016, Vol. 48 Issue 1, p85
We prove that the presence or absence of corners is spectrally determined in the following sense: any simply connected planar domain with piecewise smooth Lipschitz boundary and at least one corner cannot be isospectral to any connected planar domain, of any genus, that has smooth boundary....

- On Strongly Extending Modules. ATANI, S. EBRAHIMI; KHORAMDEL, M.; PISH HESARI, S. DOLATI // Kyungpook Mathematical Journal;Jun2014, Vol. 54 Issue 2, p237
The purpose of this paper is to introduce the concept of strongly extending modules which are particular subclass of the class of extending modules, and study some basic properties of this new class of modules. A module M is called strongly extending if each submodule of M is essential in a...

- On staggered indecomposable Virasoro modules. Kytölä, Kalle; Ridout, David // Journal of Mathematical Physics;Dec2009, Vol. 50 Issue 12, p123503
In this article, certain indecomposable Virasoro modules are studied. Specifically, the Virasoro mode L0 is assumed to be nondiagonalizable, possessing Jordan blocks of rank 2. Moreover, the module is further assumed to have a highest weight submodule, the â€œleft module,â€ and that the...

- Classification of 2-dimensional graded normal hypersurfaces with a( R) â‰¤ 6. Watanabe, Kei-ichi // Bulletin of the Brazilian Mathematical Society;Dec2014, Vol. 45 Issue 4, p887
We classify 2-dimensional normal weighted homogeneous hypersurface R = k[ X, Y, Z]/( f) with given a-invariant a( R) â‰¤ 6. We show that for a( R) > 0, the number of 'types' are finite.

- Modular invariants and singularity indices of hyperelliptic fibrations. Liu, Xiaolei // Chinese Annals of Mathematics;Nov2016, Vol. 37 Issue 6, p875
The modular invariants of a family of curves are the degrees of the pullback of the corresponding divisors by the moduli map. The singularity indices were introduced by Xiao (1991) to classify singular fibers of hyperelliptic fibrations and to compute global invariants locally. In semistable...

- Second-Order Optimality Conditions in Minimax Optimization Problems. Dhara, Anulekha; Mehra, Aparna // Journal of Optimization Theory & Applications;Mar2013, Vol. 156 Issue 3, p567
The paper primarily is concerned with the second-order optimality conditions for minimax problems, where the constraints are described by a set inclusion and a finite number of equalities, and where all the functions involved are FrÃ©chet differentiable with locally Lipschitz derivatives. We...