On Using the Decision Trees to Identify the Local Extrema in Parallel Global Optimization Algorithm

In the present work, the solving of the multidimensional global optimization problems using decision tree to reveal the attractor regions of the local minima is considered. The objective function of the problem is defined as a “black box”, may be non-differentiable, multi-extremal and computational costly. We assume that the function satisfies the Lipschitz condition with a priory unknown constant. Global search algorithm is applied for the search of global minimum in the problems of such type. It is well known that the solution complexity essentially depends on the presence of multiple local extrema. Within the framework of the global search algorithm, we propose a method for selecting the vicinity of local extrema of the objective function based on analysis of accumulated search information. Conducting such an analysis using machine learning techniques allows making a decision to run a local method, which can speed up the convergence of the algorithm. This suggestion was confirmed by the results of numerical experiments demonstrating the speedup when solving a series of test problems.In the present work, the solving of the multidimensional global optimization problems using decision tree to reveal the attractor regions of the local minima is considered. The objective function of the problem is defined as a “black box”, may be non-differentiable, multi-extremal and computational costly. We assume that the function satisfies the Lipschitz condition with a priory unknown constant. Global search algorithm is applied for the search of global minimum in the problems of such type. It is well known that the solution complexity essentially depends on the presence of multiple local extrema. Within the framework of the global search algorithm, we propose a method for selecting the vicinity of local extrema of the objective function based on analysis of accumulated search information. Conducting such an analysis using machine learning techniques allows making a decision to run a local method, which can speed up the convergence of the algorithm. This suggestion was confirmed by the results of numerical experiments demonstrating the speedup when solving a series of test problems

Poisson-Lie group of pseudodifferential symbols

We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of pseudodifferential symbols of an arbitrary real (or complex) order. We show that the usual (second) Benney, KdV (or GL_n--Adler--Gelfand--Dickey) and KP Poisson structures are naturally realized as restrictions of this Poisson structure to submanifolds of this ``universal'' Poisson--Lie group. Moreover, the reduced (=SL_n) versions of these manifolds (W_n-algebras in physical terminology) can be viewed as subspaces of the quotient (or Poisson reduction) of this Poisson--Lie group by the dressing action of the group of functions. Finally, we define an infinite set of functions in involution on the Poisson--Lie group that give the standard families of Hamiltonians when restricted to the submanifolds mentioned above. The Poisson structure and Hamiltonians on the whole group interpolate between the Poisson structures and Hamiltonians of Benney, KP and KdV flows. We also discuss the geometrical meaning of W_\infty as a limit of Poisson algebras W_\epsilon as \epsilon goes to 0.Comment: 64 pages, no figure

Transverse-momentum ptp_t correlations on (η,ϕ)(\eta,\phi) from mean-ptp_{t} fluctuations in Au-Au collisions at sNN=\sqrt{s_{NN}} = 200 GeV

We present first measurements of the pseudorapidity and azimuth $(\eta,\phi)$ bin-size dependence of event-wise mean transverse momentum $$ fluctuations for Au-Au collisions at $\sqrt{s_{NN}} = 200$ GeV. We invert that dependence to obtain $p_t$ autocorrelations on differences $(\eta_\Delta,\phi_\Delta)$ interpreted to represent velocity/temperature distributions on ($\eta,\phi$). The general form of the autocorrelations suggests that the basic correlation mechanism is parton fragmentation. The autocorrelations vary strongly with collision centrality, which suggests that fragmentation is strongly modified by a dissipative medium in the more central Au-Au collisions relative to peripheral or p-p collisions. \\Comment: 7 pages, 3 figure

Probing dense baryon-rich matter with virtual photons

International audienceAbout 10 μs after the Big Bang, the universe was filled—in addition to photons and leptons—with strong-interaction matter consisting of quarks and gluons, which transitioned to hadrons at temperatures close to kT = 150 MeV and densities several times higher than those found in nuclei. This quantum chromodynamics (QCD) matter can be created in the laboratory as a transient state by colliding heavy ions at relativistic energies. The different phases in which QCD matter may exist depend for example on temperature, pressure or baryochemical potential, and can be probed by studying the emission of electromagnetic radiation. Electron–positron pairs emerge from the decay of virtual photons, which immediately decouple from the strong interaction, and thus provide information about the properties of QCD matter at various stages. Here, we report the observation of virtual photon emission from baryon-rich QCD matter. The spectral distribution of the electron–positron pairs is nearly exponential, providing evidence for a source of temperature in excess of 70 MeV with constituents whose properties have been modified, thus reflecting peculiarities of strong-interaction QCD matter. Its bulk properties are similar to the dense matter formed in the final state of a neutron star merger, as apparent from recent multimessenger observation

Recent progress in neutrino factory and muon collider research within the Muon collaboration

We describe the status of our effort to realize a first neutrino factory and the progress made in understanding the problems associated with the collection and cooling of muons towards that end. We summarize the physics that can be done with neutrino factories as well as with intense cold beams of muons. The physics potential of muon colliders is reviewed, both as Higgs Factories and compact high energy lepton colliders. The status and timescale of our research and development effort is reviewed as well as the latest designs in cooling channels including the promise of ring coolers in achieving longitudinal and transverse cooling simultaneously. We detail the efforts being made to mount an international cooling experiment to demonstrate the ionization cooling of muons