Classifiers for centrality determination in proton-nucleus and nucleus-nucleus collisions

Centrality, as a geometrical property of the collision, is crucial for the physical interpretation of nucleus-nucleus and proton-nucleus experimental data. However, it cannot be directly accessed in event-by-event data analysis. Common methods for centrality estimation in A-A and p-A collisions usually rely on a single detector (either on the signal in zero-degree calorimeters or on the multiplicity in some semi-central rapidity range). In the present work, we made an attempt to develop an approach for centrality determination that is based on machine-learning techniques and utilizes information from several detector subsystems simultaneously. Different event classifiers are suggested and evaluated for their selectivity power in terms of the number of nucleons-participants and the impact parameter of the collision. Finer centrality resolution may allow to reduce impact from so-called volume fluctuations on physical observables being studied in heavy-ion experiments like ALICE at the LHC and fixed target experiment NA61/SHINE on SPS.Comment: To be published in proceedings of the "XIIth Quark Confinement and the Hadron Spectrum" conference (Thessaloniki, 2016

Weights for relative motives; relation with mixed complexes of sheaves

The main goal of this paper is to define the so-called Chow weight structure for the category of Beilinson motives over any 'reasonable' base scheme $S$ (this is the version of Voevodsky's motives over $S$ defined by Cisinski and Deglise). We also study the functoriality properties of the Chow weight structure (they are very similar to the well-known functoriality of weights for mixed complexes of sheaves). As shown in a preceding paper, the Chow weight structure automatically yields an exact conservative weight complex functor (with values in $K^b(Chow(S))$). Here $Chow(S)$ is the heart of the Chow weight structure; it is 'generated' by motives of regular schemes that are projective over $S$. Besides, Grothendiek's group of $S$-motives is isomorphic to $K_0(Chow(S))$; we also define a certain 'motivic Euler characteristic' for $S$-schemes. We obtain (Chow)-weight spectral sequences and filtrations for any cohomology of motives; we discuss their relation to Beilinson's 'integral part' of motivic cohomology and to weights of mixed complexes of sheaves. For the study of the latter we introduce a new formalism of relative weight structures.Comment: a few minor corrections mad

On Constructive Axiomatic Method

In this last version of the paper one may find a critical overview of some recent philosophical literature on Axiomatic Method and Genetic Method.Comment: 25 pages, no figure

Spectral synthesis in de Branges spaces

We solve completely the spectral synthesis problem for reproducing kernels in the de Branges spaces $\mathcal{H}(E)$. Namely, we describe the de Branges spaces $\mathcal{H}(E)$ such that all $M$-bases of reproducing kernels (i.e., complete and minimal systems $\{k_\lambda\}_{\lambda\in\Lambda}$ with complete biorthogonal $\{g_\lambda\}_{\lambda\in\Lambda}$) are strong $M$-bases (i.e., every mixed system $\{k_\lambda\}_{\lambda\in\Lambda\setminus\tilde \Lambda} \cup\{g_\lambda\}_{\lambda\in \tilde \Lambda}$ is also complete). Surprisingly this property takes place only for two essentially different classes of de Branges spaces: spaces with finite spectral measure and spaces which are isomorphic to Fock-type spaces of entire functions. The first class goes back to de Branges himself, the second class appeared in a recent work of A. Borichev and Yu. Lyubarskii. Moreover, we are able to give a complete characterisation of this second class in terms of the spectral data for $\mathcal{H}(E)$. In addition, we obtain some results about possible codimension of mixed systems for a fixed de Branges space $\mathcal{H}(E)$, and prove that any minimal system of reproducing kernels in $\mathcal{H}(E)$ is contained in an exact system of reproducing kernels.Comment: 38 pages. Shortened text with streamlined proofs. This version is accepted for publication in "Geometric and Functional Analysis

On the strong difference in reactivity of acyclic and cyclic diazodiketones with thioketones: experimental results and quantum-chemical interpretation

The 1,3-dipolar cycloaddition of acyclic 2-diazo-1,3-dicarbonyl compounds (DDC) and thioketones preferably occurs with Z,Econformers and leads to the formation of transient thiocarbonyl ylides in two stages. The thermodynamically favorable further transformation of C=S ylides bearing at least one acyl group is identified as the 1,5-electrocyclization into 1,3-oxathioles. However, in the case of diazomalonates, the dominating process is 1,3-cyclization into thiiranes followed by their spontaneous desulfurization yielding the corresponding alkenes. Finally, carbocyclic diazodiketones are much less reactive under similar conditions due to the locked cyclic structure and are unfavorable for the 1,3-dipolar cycloaddition due to the Z,Z-conformation of the diazo molecule. This structure results in high, positive values of the Gibbs free energy change for the first stage of the cycloaddition process.A. V. I. thanks the Saint Petersburg State University for financial support of his stay at the University of Łódź with Prof. G. Mloston (order 1831/1; 02.06.2011). A. S. M. acknowledges the Saint Petersburg State University for financial support in the form of a postdoctoral fellowship (No. 12.50.1562.2013). G. M. acknowledges support by the National Science Center (PLCracow) within the Grant Maestro–3 (Dec–2012/06/A/ST5/ 00219). The calculations were performed with the assistance of the Saint Petersburg State University Computer Center and the Chemistry Department of Saint Petersburg State University