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The pT-differential non-linear flow modes, v4,22, v5,32, v6,33 and v6,222 for π±, K±, K0S , p + p¯¯¯, Λ + Λ¯¯¯¯ and ϕ-meson have been measured for the first time at sNN−−−√ = 5.02 TeV in Pb-Pb collisions with the ALICE detector at the Large Hadron Collider. The results were obtained with a multi-particle technique, correlating the identified hadrons with reference charged particles from a different pseudorapidity region. These non-linear observables probe the contribution from the second and third order initial spatial anisotropy coefficients to higher flow harmonics. All the characteristic features observed in previous pT-differential anisotropic flow measurements for various particle species are also present in the non-linear flow modes, i.e. increase of magnitude with increasing centrality percentile, mass ordering at low pT and particle type grouping in the intermediate pT range. Hydrodynamical calculations (iEBE-VISHNU) that use different initial conditions and values of shear and bulk viscosity to entropy density ratios are confronted with the data at low transverse momenta. These calculations exhibit a better agreement with the anisotropic flow coefficients than the non-linear flow modes. These observations indicate that non-linear flow modes can provide additional discriminatory power in the study of initial conditions as well as new stringent constraints to hydrodynamical calculations.
Automated deduction in higher-order program calculi, where properties of transformation rules are demanded, or confluence or other equational properties are requested, can often be done by syntactically computing overlaps (critical pairs) of reduction rules and transformation rules. Since higher-order calculi have alpha-equivalence as fundamental equivalence, the reasoning procedure must deal with it. We define ASD1-unification problems, which are higher-order equational unification problems employing variables for atoms, expressions and contexts, with additional distinct-variable constraints, and which have to be solved w.r.t. alpha-equivalence. Our proposal is to extend nominal unification to solve these unification problems. We succeeded in constructing the nominal unification algorithm NomUnifyASC. We show that NomUnifyASC is sound and complete for these problem class, and outputs a set of unifiers with constraints in nondeterministic polynomial time if the final constraints are satisfiable. We also show that solvability of the output constraints can be decided in NEXPTIME, and for a fixed number of context-variables in NP time. For terms without context-variables and atom-variables, NomUnifyASC runs in polynomial time, is unitary, and extends the classical problem by permitting distinct-variable constraints.
1998 ACM Subject Classification F.4.1 Mathematical Logic
A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for expressions, for DAGs, and for garbage-free expressions and determine their complexity. As extension a nominal unification algorithm for higher-order expressions with recursive let and atom-variables is constructed, where we show that it also runs in non-deterministic polynomial time.
In this paper we regard first the situation where parallel channels are disturbed by noise. With the goal of maximal information conservation we deduce the conditions for a transform which "immunizes" the channels against noise influence before the signals are used in later operations. It shows up that the signals have to be decorrelated and normalized by the filter which corresponds for the case of one channel to the classical result of Shannon. Additional simulations for image encoding and decoding show that this constitutes an efficient approach for noise suppression. Furthermore, by a corresponding objective function we deduce the stochastic and deterministic learning rules for a neural network that implements the data orthonormalization. In comparison with other already existing normalization networks our network shows approximately the same in the stochastic case but, by its generic deduction ensures the convergence and enables the use as independent building block in other contexts, e.g. whitening for independent component analysis. Keywords: information conservation, whitening filter, data orthonormalization network, image encoding, noise suppression.
We present a practical algorithm that given an LLL-reduced lattice basis of dimension n, runs in time O(n3(k=6)k=4+n4) and approximates the length of the shortest, non-zero lattice vector to within a factor (k=6)n=(2k). This result is based on reasonable heuristics. Compared to previous practical algorithms the new method reduces the proven approximation factor achievable in a given time to less than its fourthth root. We also present a sieve algorithm inspired by Ajtai, Kumar, Sivakumar [AKS01].
The future heavy-ion experiment CBM (FAIR/GSI, Darmstadt, Germany) will focus on measurement of very rare probes at interaction rates up to 10 MHz with data flow of up to 1 TB/s. The beam will provide free stream of beam particles without bunch structure. That requires full online event reconstruction and selection not only in space, but also in time, so-called 4D event building and selection.
The FLES (First-Level Event Selection) reconstruction and selection package consists of several modules: track finding, track fitting, short-lived particles finding, event building and event selection. A time-slice is reconstructed in parallel between cores within a same CPU, thus minimizing the communication between CPUs. After all tracks are found and fitted in 4D, they are collected into clusters of tracks originated from common primary vertices, which then are fitted, thus identifying 4D interaction points registered within the time-slice. Secondary tracks are associated with primary vertices according to their estimated production time. After that, short-lived particles are found and the full event building process is finished. The last stage of the FLES package is the selection of events according to the requested trigger signatures.
In ultraperipheral collisions (UPCs) of relativistic nuclei without overlap of nuclear densities, the two nuclei are excited by the Lorentz-contracted Coulomb fields of their collision partners. In these UPCs, the typical nuclear excitation energy is below a few tens of MeV, and a small number of nucleons are emitted in electromagnetic dissociation (EMD) of primary nuclei, in contrast to complete nuclear fragmentation in hadronic interactions. The cross sections of emission of given numbers of neutrons in UPCs of 208Pb nuclei at sNN−−−√=5.02 TeV were measured with the neutron zero degree calorimeters (ZDCs) of the ALICE detector at the LHC, exploiting a similar technique to that used in previous studies performed at sNN−−−√=2.76 TeV. In addition, the cross sections for the exclusive emission of one, two, three, four, and five forward neutrons in the EMD, not accompanied by the emission of forward protons, and thus mostly corresponding to the production of 207,206,205,204,203Pb, respectively, were measured for the first time. The predictions from the available models describe the measured cross sections well. These cross sections can be used for evaluating the impact of secondary nuclei on the LHC components, in particular, on superconducting magnets, and also provide useful input for the design of the Future Circular Collider (FCC-hh).
In ultraperipheral collisions (UPCs) of relativistic nuclei without overlap of nuclear densities, the two nuclei are excited by the Lorentz-contracted Coulomb fields of their collision partners. In these UPCs, the typical nuclear excitation energy is below a few tens of MeV, and a small number of nucleons are emitted in electromagnetic dissociation (EMD) of primary nuclei, in contrast to complete nuclear fragmentation in hadronic interactions. The cross sections of emission of given numbers of neutrons in UPCs of 208Pb nuclei at sNN−−−√=5.02 TeV were measured with the neutron zero degree calorimeters (ZDCs) of the ALICE detector at the LHC, exploiting a similar technique to that used in previous studies performed at sNN−−−√=2.76 TeV. In addition, the cross sections for the exclusive emission of one, two, three, four, and five forward neutrons in the EMD, not accompanied by the emission of forward protons, and thus mostly corresponding to the production of 207,206,205,204,203Pb, respectively, were measured for the first time. The predictions from the available models describe the measured cross sections well. These cross sections can be used for evaluating the impact of secondary nuclei on the LHC components, in particular, on superconducting magnets, and also provide useful input for the design of the Future Circular Collider (FCC-hh).
In ultraperipheral collisions (UPCs) of relativistic nuclei without overlap of nuclear densities, the two nuclei are excited by the Lorentz-contracted Coulomb fields of their collision partners. In these UPCs, the typical nuclear excitation energy is below a few tens of MeV, and a small number of nucleons are emitted in electromagnetic dissociation (EMD) of primary nuclei, in contrast to complete nuclear fragmentation in hadronic interactions. The cross sections of emission of given numbers of neutrons in UPCs of 208Pb nuclei at sNN−−−√=5.02 TeV were measured with the neutron zero degree calorimeters (ZDCs) of the ALICE detector at the LHC, exploiting a similar technique to that used in previous studies performed at sNN−−−√=2.76 TeV. In addition, the cross sections for the exclusive emission of one, two, three, four, and five forward neutrons in the EMD, not accompanied by the emission of forward protons, and thus mostly corresponding to the production of 207,206,205,204,203Pb, respectively, were measured for the first time. The predictions from the available models describe the measured cross sections well. These cross sections can be used for evaluating the impact of secondary nuclei on the LHC components, in particular, on superconducting magnets, and also provide useful input for the design of the Future Circular Collider (FCC-hh).
We present the first measurement of event-by-event fluctuations in the kaon sector in Pb-Pb collisions at sNN−−−√= 2.76 TeV with the ALICE detector at the LHC. The robust fluctuation correlator νdyn is used to evaluate the magnitude of fluctuations of the relative yields of neutral and charged kaons, as well as the relative yields of charged kaons, as a function of collision centrality and selected kinematic ranges. While the correlator νdyn[K+,K−] exhibits a scaling approximately in inverse proportion of the charged particle multiplicity, νdyn[K0S,K±] features a significant deviation from such scaling. Within uncertainties, the value of νdyn[K0S,K±] is independent of the selected transverse momentum interval, while it exhibits a pseudorapidity dependence. The results are compared with HIJING, AMPT and EPOS-LHC predictions, and are further discussed in the context of the possible production of disoriented chiral condensates in central Pb-Pb collisions.