Pathways to quiescence: SHARDS view on the star formation histories of massive quiescent galaxies at 1.0 < z < 1.5

We present star formation histories (SFHs) for a sample of 104 massive (stellar mass M > 10^10 M_⊙) quiescent galaxies (MQGs) at z = 1.0–1.5 from the analysis of spectrophotometric data from the Survey for High-z Absorption Red and Dead Sources (SHARDS) and HST/WFC3 G102 and G141 surveys of the GOODS-North field, jointly with broad-band observations from ultraviolet (UV) to far-infrared (far-IR). The sample is constructed on the basis of rest-frame UVJ colours and specific star formation rates (sSFRs = SFR/Mass). The spectral energy distributions (SEDs) of each galaxy are compared to models assuming a delayed exponentially declining SFH. A Monte Carlo algorithm characterizes the degeneracies, which we are able to break taking advantage of the SHARDS data resolution, by measuring indices such as MgUV and D4000. The population of MQGs shows a duality in their properties. The sample is dominated (85 per cent) by galaxies with young mass-weighted ages, t_M t_M < 2 Gyr, short star formation time-scales, 〈τ〉 ∼ 60–200 Myr, and masses log(M/M_⊙) ∼ 10.5. There is an older population (15 per cent) with t_M t_M = 2–4 Gyr, longer star formation time-scales, 〈τ〉∼ 400 Myr, and larger masses, log(M/M_⊙) ∼ 10.7. The SFHs of our MQGs are consistent with the slope and the location of the main sequence of star-forming galaxies at z > 1.0, when our galaxies were 0.5–1.0 Gyr old. According to these SFHs, all the MQGs experienced a luminous infrared galaxy phase that lasts for ∼500 Myr, and half of them an ultraluminous infrared galaxy phase for ∼100 Myr. We find that the MQG population is almost assembled at z ∼ 1, and continues evolving passively with few additions to the population.

LR property of non-well-formed scales

This article studies generated scales having exactly three different step sizes within the language of algebraic combinatorics on words. These scales and their corresponding step-patterns are called non well formed. We prove that they can be naturally inserted in the Christoffel tree of well-formed words. Our primary focus in this study is on the left- and right-Lyndon factorization of these words. We will characterize the non-well-formed words for which both factorizations coincide. We say that these words satisfy the LR property and show that the LR property is satisfied exactly for half of the non-well-formed words. These are symmetrically distributed in the extended Christoffel tree. Moreover, we find a surprising connection between the LR property and the Christoffel duality. Finally, we prove that there are infinitely many Christoffel–Lyndon words among the set of non-well-formed words and thus there are infinitely many generated scales having as step-pattern a Christoffel–Lyndon word.

Emotional Theory of Rationality

In recent decades, it has been definitely established the existence of a close relationship between the emotional phenomena and rational processes, but we still do not have a unified definition, or effective models to describe any of them well. To advance our understanding of the mechanisms governing the behavior of living beings we must integrate multiple theories, experiments and models from both fields. In this paper we propose a new theoretical framework that allows integrating and understanding, from a functional point of view, the emotion-cognition duality. Our reasoning, based on evolutionary principles, add to the definition and understanding of emotion, justifying its origin, explaining its mission and dynamics, and linking it to higher cognitive processes, mainly with attention, cognition, decision-making and consciousness. According to our theory, emotions are the mechanism for brain function optimization, besides being the contingency and stimuli prioritization system. As a result of this approach, we have developed a dynamic systems-level model capable of providing plausible explanations for some psychological and behavioral phenomena, and establish a new framework for scientific definition of some fundamental psychological terms.