We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for such operators and hence deduce that these operators have a bounded functional calculus. In particular, we deduce a Kato square root type estimate.

A large literature on multitasking bottlenecks suggests that people cannot generally make decisions or select responses in two different tasks at the same time. However, these tasks have all involved retrieving preinstructed responses, rather than spontaneously choosing actions based on anticipated hedonic consequences. To assess whether the same bottlenecks encompasses voluntary choices, a gam...

Contents 1. Introduction 1 1.1. Braid monodromy invariants 3 1.2. The degree doubling process 6 1.3. Degree doubling for symplectic Lefschetz pencils 9 2. Stably quasiholomorphic coverings 10 2.1. Quasiholomorphic coverings and braided curves 10 2.2. Stably quasiholomorphic coverings 11 2.3. Proof of Proposition 1 18 3. The degree doubling formula for braid monodromies 21 3.

This paper explains the implications of a mathematical theory (by the same authors) of holes in fractals and their relation to dimension for measurements. The novelty of our approach is to consider the fractal measure on a set rather than just the support of that measure. This should take into account in a more precise way the distribution of data points in measured sets, such as the distributi...

The purpose of this paper is to prove some classical estimates for fractional derivatives of functions defined on a Coifman-Weiss space of homogeneous type. In particular the Product Rule and Chain Rule estimates in [KP] and [CW]. The fractional calculus of M. Riesz was extended to these spaces in [GSV]. Our main tools are fractional difference quotients and the square fractional derivative of ...

In spite of its massively parallel architecture [1], the human brain is fundamentally limited if required to perform two tasks at the same time [2, 3]. This limitation can be studied with the psychological refractory period (PRP) paradigm, where two stimuli that require speeded responses occur in close succession [4]. Interference generally takes the form of a delay in the time to respond to th...

We establish that there are bounded Jordan domains Ω ⊂ R (n ≥ 2) that do not carry a (nontrivial) doubling measure with respect to the Euclidean distance. More generally, it is shown that every nonempty metric space (X, d) without isolated points has an open and dense subset A such that (A, d) does not carry a doubling measure.

2014 A simple mechanical system consisting of a bouncing ball subject to repeated impacts with a vibrating table is studied in the period doubling regime. Two control parameters (the table’s forcing frequency and amplitude) are varied to discover the curves in parameter space that separate periodic orbits. Experimental results for the period doubling boundaries agree with calculations from a si...

Let μ be a Radon measure on R, which may be non doubling. The only condition that μ must satisfy is the size condition μ(B(x, r)) ≤ C r, for some fixed 0 < n ≤ d. Recently, the author introduced spaces of type BMO(μ) and H(μ) with properties similar to ones of the classical spaces BMO and H defined for doubling measures. These new spaces proved to be useful to study the L(μ) boundedness of Cald...