For an equivariant Morse stratification which contains a unique open stratum, we introduce the notion of equivariant antiperfection, which means the difference of the equivariant Morse series and the equivariant Poincaré series achieves the maximal possible value (instead of the minimal possible value 0 in the equivariantly perfect case). We also introduce a weaker condition of local equivarian...

Morse theory inspired several robust and well grounded tools in discrete function analysis, geometric modeling and visualization. Such techniques need to adapt the original differential concepts of Morse theory in a discrete setting, generally using either piecewise–linear (PL) approximations or Forman’s combinatorial formulation. The former carries the intuition behind Morse critical sets, whi...

We suggest a coarse-grained model for DPD simulations of polypeptides in solutions. The model mimics hydrogen bonding that stabilizes α-helical and β-structures using dissociable Morse bonds between quasiparticles representing the peptide groups amenable to hydrogen bonding. We demonstrate the capabilities of the model by simulating transitions between coil-like, globular, α-helical, and β-hair...

A variant of a new empirical method, enables one fo express a collinear triaromic potential energy surface as a Family of Morse curves along “natural” bond order coordinates orthogonal to the reaction coordinate. The procedure depends on a single adjustable parameter which is related to the barrier-s height. Because an analytical expression for the number of vibrational states of a Morse oscill...

Reeb graphs provide a method to combinatorially describe the shape of a manifold endowed with a Morse function. One question deserving attention is whether Reeb graphs are robust against function perturbations. Focusing on 1-dimensional manifolds, we define an editing distance between Reeb graphs of curves, in terms of the cost necessary to transform one graph into another through editing moves...

In this paper we prove Morse type inequalities for the contractible 1-periodic solutions of time dependent Hamiltonian differential equations on those compact symplectic manifolds M for which the symplectic form and the first Chern class of the tangent bundle vanish over q ( M ) . The proof is based on a version of infinite dimensional Morse theory which is due to Floer. The key point is an ind...

A bst r ac t This paper is focused on the study of perfect discrete Morse functions on a 2-simplicial complex. These are those discrete Morse functions such that the number of critical i-simplices coincides with the i-th Betti number of the complex. In particular, we establish conditions under which a 2-complex admits a perfect discrete Morse function and conversely, we get topological properti...

We present a new approach to Morse and Novikov theories, based on the deRham Federer theory of currents, using the finite volume flow technique of Harvey and Lawson [HL]. In the Morse case, we construct a noncompact analogue of the Morse complex, relating a Morse function to the cohomology with compact forward supports of the manifold. This complex is then used in Novikov theory, to obtain a ge...

With improvements in sensor technology and simulation methods, datasets are growing in size, calling for the investigation of efficient and scalable tools for their analysis. Topological methods, able to extract essential features from data, are a prime candidate for the development of such tools. Here, we examine an approach based on discrete Morse theory and compare it to the well-known water...

A code is presented for fast, easy and efficient communication over channels that allow only two signal types: a single sound (e.g. a knock), or no sound (i.e. silence). This is a true binary code while Morse code is a ternary code and does not work in such situations. Thus the presented code is more universal than Morse and can be used in much more situations. Additionally it is very tolerant ...