In this paper we are interested in generalizing Keller-type eigenvalue estimates for the non-selfadjoint Schrödinger operator to Dirac operator, imposing some suitable rigidity conditions on matricial structure of potential, without necessarily requiring smallness its norm.

The structural rigidity property, a generalization of Laman's theorem which characterizes rigid bar frameworks in 2D, is generally considered a good heuristic to detect rigidities in a geometric constraint satisfaction problem (GCSP). The gap between rigidity and structural rigidity essentially resides in the fact that structural rigidity is not a geometric property. In this article, we propose...

OBJECTIVE (1) To determine the brain connectivity pattern associated with clinical rigidity scores in Parkinson's disease (PD) and (2) to determine the relation between clinically assessed rigidity and quantitative metrics of motor performance. BACKGROUND Rigidity, the resistance to passive movement, is exacerbated in PD by asking the subject to move the contralateral limb, implying that rigi...

Cell migration is a complex process requiring density and rigidity sensing of the microenvironment to adapt cell migratory speed through focal adhesion and actin cytoskeleton regulation. ICAP-1 (also known as ITGB1BP1), a β1 integrin partner, is essential for ensuring integrin activation cycle and focal adhesion formation. We show that ICAP-1 is monoubiquitylated by Smurf1, preventing ICAP-1 bi...

As an extension of a classical tree-partition problem, we consider decompositions of graphs into edge-disjoint (rooted-)trees with an additional matroid constraint. Specifically, suppose we are given a graph G = (V,E), a multiset R = {r1, . . . , rt} of vertices in V , and a matroid M on R. We prove a necessary and sufficient condition for G to be decomposed into t edge-disjoint subgraphs G1 = ...

We study the sporadic Forbush effects of the galactic cosmic ray intensity using neutron monitors and muon telescopes experimental data and the theoretical modeling developed based on the Parker’s transport equation for a non stationary case. We found that a hard rigidity spectrum in the minimum phase of the Forbush effects of GCR intensity determined by neutron monitors experimental data is re...

The choice of the most suitable orthodontic wire for each stage of treatment requires estimation of the forces generated. In theory, the selection of wire sequences should initially utilize a lower flexural rigidity; thus clinicians use smaller round cross-sectional dimension wires to generate lighter forces during the preliminary alignment stage. This assessment is true for conventional alloys...

It is a long open problem to combinatorially characterize the 3D bar-joint rigidity of graphs. The problem is at the intersection of combinatorics and algebraic geometry, and crops up in practical algorithmic applications ranging from mechanical computer aided design to molecular modeling. The problem is equivalent to combinatorially determining the generic rank of the 3D bar-joint rigidity mat...

The localization of wireless sensor networks is an important problem where the location of wireless sensors is determined using the distance between sensors. Trilateration is a geometric technique used to find location of points in 2D using distances. Using geometry, one can find the location of a point uniquely in 2D given its distance to three other points in 2D. The problem of finding the tr...