It is known that rational approximations of elementary analytic functions (exp, log, trigonometric, and hyperbolic functions, their inverse functions) are computable in the weak complexity class TC0. We show how to formalize construction basic properties these corresponding theory bounded arithmetic, VTC0.

Understanding the strength and slip behaviour of tectonic faults is a central problem in earthquake physics and seismichazard assessment1–8. Many major faults, including the San Andreas Fault, are weak compared with the surrounding rock, but the cause of this weakness is debated1. Previous measurements of the frictional strength of San Andreas Fault rocks are too high to explain the observed we...

Hard processes at the TeV scale exhibit enhanced (double log) EW corrections even for inclusive observables, leading to violation of the Bloch-Nordsieck theorem. This effect, previously related to the non abelian nature of free EW charges in the initial state (ee, ep, pp ...), is here investigated for fermion initiated hard processes and to all orders in EW couplings. We find that the effect is...

We present a framework that yields a variety of weighted and vector-valued estimates for maximally modulated Calderón-Zygmund singular (and maximal singular) integrals from a single a priori weak type unweighted estimate for the maximal modulations of such operators. We discuss two approaches, one based on the good-λ method of Coifman and Fefferman [CF] and an alternative method employing the s...

Logs contain valuable information about the runtime behaviors of software systems. Thus, practitioners rely on logs for various tasks such as debugging, system comprehension, and anomaly detection. However, are difficult to analyze due their unstructured nature large size. In this paper, we propose a novel approach called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http:...

A (k, ε)-non-malleable extractor is a function nmExt : {0, 1}×{0, 1} → {0, 1} that takes two inputs, a weak source X ∼ {0, 1} of min-entropy k and an independent uniform seed s ∈ {0, 1}, and outputs a bit nmExt(X, s) that is ε-close to uniform, even given the seed s and the value nmExt(X, s′) for an adversarially chosen seed s′ 6= s. Dodis and Wichs (STOC 2009) showed the existence of (k, ε)-no...

Let T be a set of n triangles in three-dimensional space, let s be a line segment, and let t be a triangle, both disjoint from T . We consider the visibility map of s with respect to T , i.e., the portions of T that are visible from s. The visibility map of t is defined analogously. We look at two different notions of visibility: strong (complete) visibility, and weak (partial) visibility. The ...

Dutton (1993) presents a further HEAPSORT variant called WEAK-HEAPSORT, which also contains a new data structure for priority queues. The sorting algorithm and the underlying data structure are analyzed showing that WEAK-HEAPSORT is the best HEAPSORT variant and that it has a lot of nice properties. It is shown that the worst case number of comparisons is ndlog ne 2 ne + n dlog ne n log n+ 0:1n...

Radio networks (RN) are distributed systems (ad hoc networks) consisting in n ≥ 2 radio stations. Assuming the number n unknown, two distinct models of RN without collision detection (no-CD) are addressed: the model with weak no-CD RN and the one with strong no-CD RN. We design and analyze two distributed leader election protocols, each one running in each of the above two (no-CD RN) models, re...