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We present a combination of two quick guides aimed at summarizing relevant information about the CompOSE nuclear equation of state repository. The first is aimed at nuclear physicists and describes how to provide standard equation of state tables. The second quick guide is meant for users and describes the basic procedures to obtain customized tables with equation of state data. Several examples are included to help providers and users to understand and benefit from the CompOSE database. 

The effect of isospin-dependent nuclear forces on the inner crust of neutron stars is modeled within the framework of Quantum Molecular Dynamics (QMD). To successfully control the density dependence of the symmetry energy of neutron-star matter below nuclear saturation density, a mixed vector-isovector potential is introduced. This approach is inspired by the baryon density and isospin density-dependent repulsive Skyrme force of asymmetric nuclear matter. In isospin-asymmetric nuclear matter, the system shows nucleation, as nucleons are arranged into shapes resembling nuclear pasta. The dependence of clusterization in the system on the isospin properties is also explored by calculating two-point correlation functions. We show that, as compared to previous results that did not involve such mixed interaction terms, the energy symmetry slope L is successfully controlled by varying the corresponding coupling strength. Nevertheless, the effect of changing the slope of the nuclear symmetry energy L on the crust-core transition density does not seem significant. To the knowledge of the authors, this is the first implementation of such a coupling in a QMD model for isospin asymmetric matter, which is relevant to the inner crust of neutron and proto-neutron stars. 

In this conference proceeding, we review important theoretical developments related to the production of strangeness in astrophysics. This includes its effects in supernova explosions, neutron stars, and compact-star mergers. We also discuss in detail how the presence of net strangeness affects the deconfinement to quark matter, expected to take place at large densities and/or temperatures. We conclude that a complete description of dense matter containing hyperons and strange quarks is fundamental for the understanding of modern high-energy astrophysics. 

In this work, we discuss the deconfinement phase transition to quark matter in hot/dense matter. We examine the effect that different charge fractions, isospin fractions, net strangeness, and chemical equilibrium with respect to leptons have on the position of the coexistence line between different phases. In particular, we investigate how different sets of conditions that describe matter in neutron stars and their mergers, or matter created in heavy-ion collisions affect the position of the critical end point, namely where the first-order phase transition becomes a crossover. We also present an introduction to the topic of critical points, including a review of recent advances concerning QCD critical points.