Related papers: Efficient formulas for efficiency correction of cu…
We derive formulas for the efficiency correction of cumulants with many efficiency bins. The derivation of the formulas is simpler than the previously suggested method, but the numerical cost is drastically reduced from the naive method.…
In this note we discuss subtleties associated with the efficiency corrections for measurements of off-diagonal cumulants and factorial moments for a situation when one deals with overlapping sets of particles, such as correlations between…
In this note we extend previous work on efficiency corrections for cumulant measurements [1,2]. We will discuss the limitations of the methods presented in these papers. Specifically we will consider multiplicity dependent efficiencies as…
In this brief note we derive and present the formulas necessary to correct measurements of cumulants for detection efficiency. In particular we consider the case where the efficiency may depend on the phase-space, such as transverse…
We propose a simplified procedure for the experimental application of the efficiency correction on higher order cumulants in heavy-ion collisions. By using the track-by-track efficiency, we can eliminate possible bias arising from the…
We derive analytic formulas to reconstruct particle-averaged quantities from experimental results that suffer from the efficiency loss of particle measurements. These formulas are derived under the assumption that the probabilities of…
We perform a systematic study on the effect of non-uniform track efficiency correction in higher-order cumulant analysis in heavy-ion collisions. Through analytical derivation, we find that the true values of cumulants can be successfully…
The formulae for correlators K2 and K3 of a given particle observable (e.g. energy or transverse momentum) accounting for the track reconstruction efficiency are presented. Similar to the case of an ideal detector, the correlators can be…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
We provide a unified description of efficiency correction and error estimation for moments of conserved quantifies in heavy-ion collisions. Moments and cumulants are expressed in terms of the factorial moments, which can be easily corrected…
Shape dependence of higher order correlations introduces complication in direct determination of these quantities. For this reason theoretical and observational progress has been restricted in calculating one point distribution functions…
There exists a wide variety of efficiency methods for natural language processing (NLP) tasks, such as pruning, distillation, dynamic inference, quantization, etc. We can consider an efficiency method as an operator applied on a model.…
We propose a general procedure for the detector-response correction (including efficiency correction) of higher order cumulants observed by the event-by-event analysis in heavy-ion collisions. This method makes use of the moments of the…
We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate…
The concept of efficiency plays a prominent role in the formal solution of decision problems that involve incomparable alternatives. This paper develops necessary and sufficient conditions for the efficient points in a sum of sets of…
Composition methodologies in the current literature are mainly to promote estimation efficiency via direct composition, either, of initial estimators or of objective functions. In this paper, composite estimation is investigated for both…
In this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the $d^\text{th}$ order cumulant can be presented in the form of an $d$-dimensional tensor, the algorithm is presented…
We construct product formulas for exponentials of commutators and explore their applications. First, we directly construct a third-order product formula with six exponentials by solving polynomial equations obtained using the operator…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
We propose a method to remove the contributions of pileup events from higher-order cumulants and moments of event-by-event particle distributions. Assuming that the pileup events are given by the superposition of two independent…