The conformal metric structure of Geometrothermodynamics

We present a thorough analysis on the invariance of the most widely used metrics in the Geometrothermodynamics (GTD) programme. We centre our attention in the invariance of the curvature of the space of equilibrium states under a change of fundamental representation. Assuming that the systems under consideration can be described by a fundamental relation which is a homogeneous function of a definite order, we demonstrate that such invariance is only compatible with total Legendre transformations in the present form of the programme. We give the explicit form of a metric which is invariant under total Legendre transformations and whose induced metric produces a curvature which is independent of the fundamental representation. Finally, we study a generic system with two degrees of freedom and whose fundamental relation is homogeneous of order one.Comment: Accepted in Journal of Mathematical Physic

Variational Principle underlying Scale Invariant Social Systems

MaxEnt's variational principle, in conjunction with Shannon's logarithmic information measure, yields only exponential functional forms in straightforward fashion. In this communication we show how to overcome this limitation via the incorporation, into the variational process, of suitable dynamical information. As a consequence, we are able to formulate a somewhat generalized Shannonian Maximum Entropy approach which provides a unifying "thermodynamic-like" explanation for the scale-invariant phenomena observed in social contexts, as city-population distributions. We confirm the MaxEnt predictions by means of numerical experiments with random walkers, and compare them with some empirical data

Estimating Time-Varying Effective Connectivity in High-Dimensional fMRI Data Using Regime-Switching Factor Models

Recent studies on analyzing dynamic brain connectivity rely on sliding-window analysis or time-varying coefficient models which are unable to capture both smooth and abrupt changes simultaneously. Emerging evidence suggests state-related changes in brain connectivity where dependence structure alternates between a finite number of latent states or regimes. Another challenge is inference of full-brain networks with large number of nodes. We employ a Markov-switching dynamic factor model in which the state-driven time-varying connectivity regimes of high-dimensional fMRI data are characterized by lower-dimensional common latent factors, following a regime-switching process. It enables a reliable, data-adaptive estimation of change-points of connectivity regimes and the massive dependencies associated with each regime. We consider the switching VAR to quantity the dynamic effective connectivity. We propose a three-step estimation procedure: (1) extracting the factors using principal component analysis (PCA) and (2) identifying dynamic connectivity states using the factor-based switching vector autoregressive (VAR) models in a state-space formulation using Kalman filter and expectation-maximization (EM) algorithm, and (3) constructing the high-dimensional connectivity metrics for each state based on subspace estimates. Simulation results show that our proposed estimator outperforms the K-means clustering of time-windowed coefficients, providing more accurate estimation of regime dynamics and connectivity metrics in high-dimensional settings. Applications to analyzing resting-state fMRI data identify dynamic changes in brain states during rest, and reveal distinct directed connectivity patterns and modular organization in resting-state networks across different states.Comment: 21 page

Set-Based Concurrent Engineering Model for Automotive Electronic/Software Systems Development

Organised by: Cranfield UniversityThis paper is presenting a proposal of a novel approach to automotive electronic/software systems development. It is based on the combination of Set-Based Concurrent Engineering, a Toyota approach to product development, with the standard V-Model of software development. Automotive industry currently faces the problem of growing complexity of electronic/software systems. This issue is especially visible at the level of integration of these systems which is difficult and error-prone. The presented conceptual proposal is to establish better processes that could handle the electronic/software systems design and development in a more integrated and consistent manner.Mori Seiki – The Machine Tool Compan

Cosmography and constraints on the equation of state of the Universe in various parametrizations

We use cosmography to present constraints on the kinematics of the Universe, without postulating any underlying theoretical model. To this end, we use a Monte Carlo Markov Chain analysis to perform comparisons to the supernova Ia Union 2 compilation, combined with the Hubble Space Telescope measurements of the Hubble constant, and the Hubble parameter datasets. We introduce a sixth order cosmographic parameter and show that it does not enlarge considerably the posterior distribution when comparing to the fifth order results. We also propose a way to construct viable parameter variables to be used as alternatives of the redshift $z$. These can overcome both the problems of divergence and lack of accuracy associated with the use of $z$. Moreover, we show that it is possible to improve the numerical fits by re-parameterizing the cosmological distances. In addition, we constrain the equation of state of the Universe as a whole by the use of cosmography. Thus, we derive expressions which can be directly used to fit the equation of state and the pressure derivatives up to fourth order. To this end, it is necessary to depart from a pure cosmographic analysis and to assume the Friedmann equations as valid. All our results are consistent with the $\Lambda$CDM model, although alternative fluid models, with nearly constant pressure and no cosmological constant, match the results accurately as well.Comment: 23 pages. 1 reference added. Minor correction

El Triásico del sector de Mansilla (Demanda Suroriental-LaRioja)

[ES] Sobre un zócalo paleozoico fuertemente plegado y erosionado se depositan discordantes series atribuibles al Triásico, en general de poco espesor y que en detalle tienen importantes variaciones de facies y potencia. Se reconocen los tres litotipos clásicos, Buntsandstein, Muschelkalk y Keuper. El Buntsandstein suele comenzar por un conglomerado de poco espesor, a veces brechoide, cuya textura, composición litológica y espesor está regulada por el paleorrelieve infrayacente, constituido por una «penillanura» con valles encajados que se rellenan por aportes con gran influencia local. Sobre estos rellenos se encuentra una serie de materiales detríticos que constituyen una grosera alternancia de areniscas y lutitas, con marcado carácter continental, donde predominan los depósitos fluviales, tanto de canal como de llanura de inundación, siendo asimismo patentes los procesos edáficos. Los últimos metros de este litotipo marcan un tránsito gradual al Muschelkalk, apreciándose en ellos una progresiva influencia marina. El Muschelkalk, de poco espesor (máximo 20 mil presenta muchas variaciones de potencia y distribución, llegando incluso a faltar. Las facies más frecuentes corresponden a depósitos carbonáticos con predominio de dolomías con abundantes estructuras algares, deformaciones y brechas atribuibles a la existencia de evaporitas, así como señales de emersión. En conjunto estos depósitos corresponden a un medio mareal carbonatado. Finalmente el Keuper, también de poco espesor (30-40 m. máximo), está formado por lutitas versicolores con sales dispersas que sólo localmente son abundantes. A techo se encuentran dolomías brechoides (carniolas) en contacto impreciso y a veces mecanizado. Por el momento no existen datos bioestratigráficos detallados de esta zona y las referencias bibliográficas, en base a faunas encontradas en el Muschelkalk, no aportan mayor precisión. Los minerales pesados, mayoritariamente turmalina, zircón y óxidos de titanio, revelan en los tramos basales del Buntsandstein una neta influencia del propio Paleozoico de la Sierra de la Demanda como área fuente, pasándose en la vertical a mezcla con aportes de otras áreas fuente más alejadas, caracterizado por la abundancia de micas y variaciones en la morfología de las turmalinas. El alto contenido en turmalina permite comparar estas series con las del Buntsandstein de áreas próximas, excluyendo provisionalmen. te la presencia en la base de facies saxonienses, con diferentes espectros mineralógicos.[EN] Triassic materials outcropping southeast of Sierra de la Demanda are basically represented by germanic type facies: Buntsandstein, Muschelkalk and Keuper. Buntsandstein facies are clastics, towards the bottom predominate conglomerates, occasionally brecciated. This facies lie unconformably over lower paleozoic sediments strongly folded. Unconformity shows areas where scour surfaces predominate here interpreted as ancient valleys. Facies distribution over the unconformity plane are mainly controlled by the pre-existing relief, also controlling its thickness and here interpreted as fluvial deposits. Muschelkalk facies is characterized by the occurrence of algal limestones and tidal associated deposits. Evaporites appear to-wards the top of the stratigraphical sections studied and are primarity composed of fine interbedded clastic with gypsum and associated salts. Heavy minerals occurring in the Buntsandstein facies are basically tourmaline, zircon and titanium oxides. Lacking of palaeontological data, hig tourmaline content suggests that this deposits are comparable to Buntsandstein matehais outcropping in nearly areas. Mineralogical content of the facies here studied suggests the possibility of considering this deposits as Buntsandstein, non existing the typical mineralogical facies characterizing the Saxonian, Permian in age.Este trabajo ha sido financiado por la CAICYT y C.S.I.C., proyecto número 452. 691Peer reviewe