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The astronomy, astroparticle and particle physics communities are brought together through the ESCAPE (European Science Cluster of Astronomy and Particle Physics ESFRI research infrastructures) project to create a cluster focused on common issues in data-driven research. Among the ESCAPE work packages, the OSSR (ESCAPE Open-source Scientific Software and Service Repository) is a curated, long-term, open-access repository that makes it possible for scientists to exchange software and services and promote open science. It has been developed on top of a Zenodo community, connected to other services. A Python library, the eOSSR, has been developed to take care of the interactivity between Zenodo, services and OSSR users, allowing an automated handling of the OSSR records. In this work, we present the eOSSR, its main functionalities and how it's been used in the ESCAPE context to ease the publication of scientific software, analysis, and datasets by researchers

In the upcoming decades, the KM3NeT detectors will produce valuable data that can be used in various scientific contexts from astro- and particle physics to environmental and Earth and Sea science. Based on the Open Science policy established by the KM3NeT Collaboration, several efforts to offer science-ready data, foster common analysis approaches and publish open source software are currently pursued. In this contribution, ongoing projects focusing on the exchange of high-level data and simulation derivatives, production of particle event simulations and establishment of an integrated computing environment supporting an open-science focused workflow will be discussed.

The KM3NeT neutrino detectors are currently under construction at two locations in the Mediterranean Sea, aiming to detect the Cherenkov light generated by high-energy relativistic charged particles in sea water. The KM3NeT collaboration will produce scientific data valuable both for the astrophysics and neutrino physics communities as well as for the Earth and Sea science community. An Open Science Portal and infrastructure are under development to provide public access to open KM3NeT data, software and services. In this contribution, the current architecture, interfaces and usage examples are presented., Comment: 4 pages, to appear in the proceedings of Astronomical Data Analysis Software and Systems XXX published by ASP

The KM3NeT research infrastructure is currently under construction at two locations in the Mediterranean Sea. The KM3NeT/ORCA water-Cherenkov neutrino detector off the French coast will instrument several megatons of seawater with photosensors. Its main objective is the determination of the neutrino mass ordering. This work aims at demonstrating the general applicability of deep convolutional neural networks to neutrino telescopes, using simulated datasets for the KM3NeT/ORCA detector as an example. To this end, the networks are employed to achieve reconstruction and classification tasks that constitute an alternative to the analysis pipeline presented for KM3NeT/ORCA in the KM3NeT Letter of Intent. They are used to infer event reconstruction estimates for the energy, the direction, and the interaction point of incident neutrinos. The spatial distribution of Cherenkov light generated by charged particles induced in neutrino interactions is classified as shower- or track-like, and the main background processes associated with the detection of atmospheric neutrinos are recognized. Performance comparisons to machine-learning classification and maximum-likelihood reconstruction algorithms previously developed for KM3NeT/ORCA are provided. It is shown that this application of deep convolutional neural networks to simulated datasets for a large-volume neutrino telescope yields competitive reconstruction results and performance improvements with respect to classical approaches.

The gSeaGen code is a GENIE-based application developed to efficiently generate high statistics samples of events, induced by neutrino interactions, detectable in a neutrino telescope. The gSeaGen code is able to generate events induced by all neutrino flavours, considering topological differences between track-type and shower-like events. Neutrino interactions are simulated taking into account the density and the composition of the media surrounding the detector. The main features of gSeaGen are presented together with some examples of its application within the KM3NeT project., Comment: 45 pages, 10 figures

It is pointed out that the derivative of the energy density functional does not provide a valid local electronegativity measure, in spite of its appealing property of becoming constant for ground-state equilibrium systems., Comment: unpublished sec.VI of arXiv:1107.4249v3 made into a separate paper

The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide a proper tool for the determination of the characters of stationary points under constraints. As an illustration, a finite-dimensional example is considered that has previously been used as an illustration for other stationary-point analysis methods., Comment: 18 pages; new sections and references added

It is shown that the ground-state energy as a functional solely of the electron density is determined by the asymptotic value of the derivative of the degree-one homogeneous extension of the universal density functional F[n] at the given electron number. This has the consequence that its derivative cannot be properly determined. Carrying out the derivative of E[n[N,v]] with respect to v(r) leads to a paradox, which is resolved by the non-differentiability of E[n] if one follows traditional wisdom regarding the non-invertibility of the linear response function. However, considering the derivative of v[n[v]] through the one-electron case shows that this paradox has a more elementary origin, namely, an unaccounted restriction of the v(r) domain., Comment: 11 pages

The traditional approach to establishing a local measure of chemical hardness, by defining a local hardness concept through the derivative of the chemical potential with respect to the electron density, has been found to have limited chemical applicability, and has proved to be an unfeasible approach in principle. Here, we propose a new approach via a unique local energy concept. This local energy is shown to emerge from the Hamilton-Jacobi kind of construction of Schrodinger's quantum mechanics. It then leads to the concepts of a local chemical potential, i.e. negative of local electronegativity, and a local hardness just as the chemical potential and hardness are obtained from the energy, namely via differentiations with respect to the number of electrons. The emerging local hardness adds corrections to a recently proposed local hardness expression that has been found to be a good local measure of hardness for a series of atomic and molecular systems. These corrections become relevant for molecules with a large number of electrons. It is pointed out further that the definition of local softness that yields it as the Fukui function times the softness is not well-established, explaining recent observations of failure of this local softness concept as a proper local reactivity index for hard systems., Comment: 22 pages; finalized version

Finding a proper local measure of chemical hardness has been a long-standing aim of density functional theory. The traditional approach to defining a local hardness index, by the derivative of the chemical potential with respect to the electron density subject to the constraint of a fixed external potential, has raised several questions, and its chemical applicability has proved to be limited. Here, we point out that the only actual possibility to obtain a local hardness measure in the traditional approach emerges if the external potential constraint is dropped; consequently, utilizing the ambiguity of a restricted chemical potential derivative is not an option to gain alternative definitions of local hardness. At the same time, however, the arising local hardness concept turns out to be fatally undermined by its inherent connection with the asymptotic value of the second derivative of the universal density functional. The only other local hardness concept one may deduce from the traditional definition is the one that gives a constant value, the global hardness itself, throughout an electron system in its ground state. Consequently, the traditional approach is in principle incapable of delivering a local hardness indicator. The parallel case of defining a local version of the chemical potential itself is also outlined, arriving at a similar conclusion. Namely, the only local chemical potential concept that can be gained from a definition dE[n]/dn(r)|v is the one that gives a constant, mu itself, for electron systems in their ground state., Comment: 29 pages, to appear in Theor. Chem. Acc

With the use of a second derivative test based on constrained second derivatives, a proof is given that excited states in nonrelativistic quantum mechanics are saddle points of the energy expectation value, and is shown, further, how to determine their Morse index., Comment: 15 pages; determination of Morse index added

In the stability analysis of an equilibrium, given by a stationary point of a functional F[n] (free energy functional, e.g.), the second derivative of F[n] plays the essential role. If the system in equilibrium is subject to the conservation constraint of some extensive property (e.g. volume, material, or energy conservation), the Euler equation determining the stationary point corresponding to the equilibrium alters according to the method of Lagrange multipliers. Here, the question as to how the effects of constraints can be taken into account in a stability analysis based on second functional derivatives is examined. It is shown that the concept of constrained second derivatives incorporates all the effects due to constraints; therefore constrained second derivatives provide the proper tool for the stability analysis of equilibria under constraints. For a physically important type of constraints, it is demonstrated how the presented theory works. Further, the rigorous derivation of a recently obtained stability condition for a special case of equilibrium of ultrathin-film binary mixtures is given, presenting a guide for similar analyses. [For details on constrained derivatives, see also math-ph/0603027, physics/0603129, physics/0701145.], Comment: 40 pages; presentation of Secs.II and IV made much clearer (both divided into two subsections), Appendix added

Following a recent work [Gal, Phys. Rev. A 64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree-Fock equations, the Hartree-Fock-Kohn-Sham equations, is presented, completing an integrated view of quantum mechanical theories, in which the Kohn-Sham equations, the Hartree-Fock-Kohn-Sham equations and the ground-state Schrodinger equation formally stem from a common ground: density-functional theory, through its Euler equation for the ground-state density. Along similar lines, the Kohn-Sham formulation of the Hartree-Fock approach is also considered. Further, it is pointed out that the exchange energy of density-functional theory built from the Kohn-Sham orbitals can be given by degree-two homogeneous N-particle density functionals (N=1,2,...), forming a sequence of degree-two homogeneous exchange-energy density functionals, the first element of which is minus the classical Coulomb-repulsion energy functional., Comment: 19 pages; original manuscript from 2001 (v1) revised for publication, with presentation substantially improved, some errors corrected, plus an additional summarizing figure (Appendix B) included

Analysing an application in liquid film dynamics, a guide for obtaining the corresponding constrained functional derivatives for constraints coupling the functional variables is given. The use of constrained derivatives makes the proper account for constraints possible in time-dependent, nonequilibrium physical theories, with physical equations not emerging as Euler-Lagrange equations, which is especially relevant with respect to the dynamics of complex liquids., Comment: 12 pages; with further cases of coupling added, extended opening discussion of constrained derivative, and some notation changed

Analytical formulae for functional differentiation under simultaneous K-conservation constraints, with K the integral of some function of the functional variable, are derived, making the proper account for the simultaneous conservation of normalization and statistical averages, e.g., possible in functional differentiation in nonvariationally built physical theories, which gets particular relevance for nonequilibrium, time-dependent theories., Comment: final version, published in J Phys A; 14 pages; with (34)-(35) and a note after (10) added (to v3)

The mathematics of K-conserving functional differentiation, with K being the integral of some invertible function of the functional variable, is clarified. The most general form for constrained functional derivatives is derived from the requirement that two functionals that are equal over a restricted domain have equal derivatives over that domain. It is shown that the K-conserving derivative formula is the one that yields no effect of K-conservation on the differentiation of K-independent functionals, which gives the basis for its generalization for multiple constraints. Connections with the derivative with respect to the shape of the functional variable and with the shape-conserving derivative, together with their use in the density-functional theory of many-electron systems, are discussed. Yielding an intuitive interpretation of K-conserving functional derivatives, it is also shown that K-conserving derivatives emerge as directional derivatives along K-conserving paths, which is achieved via a generalization of the Gateaux derivative for that kind of paths. These results constitute the background for the practical application of K-conserving differentiation., Comment: final version, published in J Math Chem; with an Appendix with the proof of (17) added, and some errata to [1] inserted