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Numerical, Monte Carlo simulations of Lattice QCD have been enjoying greatsuccess in the investigation of the properties of quarks and gluons.However, this standard approach is not applicable at non-zero quark densitybecause of the notorious ``sign problem'': the weight of each configurationin the partition sum no longer is always positive, which prevents its interpretationas a Monte Carlo sampling probability.Thus, information is noisy and limited to small systems.An ubiquitous measurement step consists of taking the trace of a function ofthe Dirac matrix. Stochastic estimators are used, often at significant computing cost.We want to take advantage of recentdevelopments in Numerical Analysis on this topic.Moreover, improved observables, ''mode numbers'' originally proposed by M. Luscher,can provide more sensitive probes of the properties of QCD.Two applications look promising and important: A. Improving the determination of critical points in the QCD phase diagram.B. Extending the Taylor expansion of the QCD pressure at non-zero quark density.The necessary large-scale simulations will be conducted in collaboration withProf. Massimo D'Elia at the University of Pisa.