As the name suggests, Curve Shortening is a gradientflow for the length functional on the space of immersed curves in the surfaceM. One can therefore try to use Curve Shortening to prove existence of geodesics by variational methods. In my talk at S’Agarro I observed that geodesics always are curves without self-tangencies, and recalled that the space of such curves has many different connected...

‎A universal schema for diagonalization was popularized by N.S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fi...

Strain-Counterstrain (SCS) intervention has been claimed to elicit immediate and sustained reductions in tenderness at digitally tender points (DTPs), however, there is little experimental evidence to support this. Twenty-eight volunteer participants with low back pain--LBP (17 females and 11 males with mean [SD] age of 39.2 [11.1] and Oswestry disability index of 15.7 [8.6]) participated in th...

In this paper, we apply standard decomposition approaches to the problem of finding local correlations in multi-modal and high-dimensional grasping data, particularly to correlate the local shape of cup-like objects to their associated local grasp configurations. We compare the capability of several decomposition methods to establish these task-relevant, inter-modal correlations and indicate ho...

The assessment of acupuncture-induced effects on brain function is crucial. Ultrasound-assisted brain function monitoring and bioelectrical methods as well as near infrared spectroscopic procedures and functional magnetic resonance investigations form the basis for the latest scientific examination methods for acupuncture research. The laserneedle acupuncture, which was examined scientifically ...

This paper deals with Hamiltonians of the form H = −∇ + v(r), with v(r) periodic along the z direction, v(x, y, z + b) = v(x, y, z). The wavefunctions of H are the well known Bloch functions ψn,λ(r), with the fundamental property ψn,λ(x, y, z + b) = λψn,λ(x, y, z) and ∂zψn,λ(x, y, z + b) = λ∂zψn,λ(x, y, z). We give the generic analytic structure (i.e. the Riemann surface) of ψn,λ(r) and their c...

Federal law mandates the removal of personal bankruptcies from credit reports after 10 years. The removal’s effect is market efficiency in reverse. The short-term effect is a spurious boost in apparent creditworthiness, especially for the more creditworthy bankrupts, delivering a substantial increase in both credit scores and the number and aggregate limit of bank cards. The longer-term effect ...

This paper offers an alternative approach to the existence of sunspot equilibria. The economy has a single perishable good and fiat money within an overlapping generations framework with two possible extraneous events. The analysis uses the dynamic adjustment of market prices during voluntary trade to establish paths of current spot prices whose limit points are rational expectations equilibria...