We consider the equations of state for systems of particles with exclusion statistics in a harmonic well. Paradygmatic examples are noninteracting particles obeying ideal fractional exclusion statistics placed in (i) a harmonic well on a line, and (ii) a harmonic well in the Lowest Landau Level (LLL) of an exterior magnetic field. We show their identity with (i) the Calogero model and (ii) anyo...

Lattice reduction algorithms behave much better in practice than their theoretical analysis predicts, with respect to both output quality and runtime. In this paper we present a probabilistic analysis that proves an average-case bound for the length of the first basis vector of an LLL reduced basis which reflects LLL experiments much better. Additionally, we use the same method to generate aver...

• PTH levels determined using assays for iPTH and PTH(1-84) correlate closely. However, iPTH assays vary in their detection of C-terminal PTH fragments and values may differ between assays (Level lll evidence). PTH(1–84) assays that measure the full length polypeptide are reported to be more directly comparable. (Level lll evidence) For comparison of PTH values in multicentre clinical trials, t...

BACKGROUND Our study aimed to compare the efficacy of seal-wing paclitaxel-eluting balloon catheters (PEB) with iopromide-coated PEB and everolimus-eluting stents (EES) for treating bare metal stent restenosis (BMS-ISR). METHODS We enrolled 64 patients with 69 BMS-ISR. The control group comprised patients from the iopromide-PEB and EES arms of a previous TIS study. The primary end-point was 1...

In this paper, we consider the open problem of the complexity of the LLL algorithm in the case when the approximation parameter t of the algorithm has its extreme value 1. This case is of interest because the output is then the strongest Lovász–reduced basis. Experiments reported by Lagarias and Odlyzko [LO83] seem to show that the algorithm remain polynomial in average. However no bound better...

Stochastic stability is a popular solution concept for stochastic learning dynamics in games. However, a critical limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steadystate behavior. We address this limitation for the first time and develop a framework for the comparative analysis of stochastic learning dynamics with di...

• Two Simple Applications of the LLL • Packet Routing In this lecture, we prove the general form of the Lovász Local Lemma, and see two applications of the lemma: hypergraph coloring and finding satisfying assignments for Boolean CNF formulas. We then begin studying packet routing, another area in which we will apply the lemma. In the last lecture, we proved the symmetric form of the Lovász Loc...

We show that, within mean-field theory, the density profile of a rapidly rotating harmonically trapped Bose-Einstein condensate is of the Thomas-Fermi form as long as the number of vortices is much larger than unity. Two forms of the condensate wave function are explored: (i) the lowest Landau level (LLL) wave function with a regular lattice of vortices multiplied by a slowly varying envelope f...

Entangled states of rotating, trapped ultracold bosons form a very promising scenario for quantum metrology. In order to employ such states for metrology, it is vital to understand their detailed form and the enhanced accuracy with which they could measure phase, in this case generated through rotation. In this work, we study the rotation of ultracold bosons in an asymmetric trapping potential ...

The Interaction Network Ontology (INO) has been demonstrated to be valuable in providing a structured ontological vocabulary for literature mining of gene-gene interactions from biomedical literature. Our analysis of the Learning Logic in Language (LLL) challenge and vaccine datasets showed that many interactions are signaled with 2 or more interaction keywords used in combination. In this pape...