Marriages of Mathematics and Physics: A Challenge for Biology

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences

From physics to biology by extending criticality and symmetry breakings

Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different role in this discipline, when compared to those in current physics. By this comparison, we stress that symmetries must be understood in relation to conservation and stability properties, as represented in the theories. We posit that the dynamics of biological organisms, in their various levels of organization, are not just processes, but permanent (extended, in our terminology) critical transitions and, thus, symmetry changes. Within the limits of a relative structural stability (or interval of viability), variability is at the core of these transitions

Astroinformatics of galaxies and quasars: a new general method for photometric redshifts estimation

With the availability of the huge amounts of data produced by current and future large multi-band photometric surveys, photometric redshifts have become a crucial tool for extragalactic astronomy and cosmology. In this paper we present a novel method, called Weak Gated Experts (WGE), which allows to derive photometric redshifts through a combination of data mining techniques. \noindent The WGE, like many other machine learning techniques, is based on the exploitation of a spectroscopic knowledge base composed by sources for which a spectroscopic value of the redshift is available. This method achieves a variance \sigma^2(\Delta z)=2.3x10^{-4} (\sigma^2(\Delta z) =0.08), where \Delta z = z_{phot} - z_{spec}) for the reconstruction of the photometric redshifts for the optical galaxies from the SDSS and for the optical quasars respectively, while the Root Mean Square (RMS) of the \Delta z variable distributions for the two experiments is respectively equal to 0.021 and 0.35. The WGE provides also a mechanism for the estimation of the accuracy of each photometric redshift. We also present and discuss the catalogs obtained for the optical SDSS galaxies, for the optical candidate quasars extracted from the DR7 SDSS photometric dataset {The sample of SDSS sources on which the accuracy of the reconstruction has been assessed is composed of bright sources, for a subset of which spectroscopic redshifts have been measured.}, and for optical SDSS candidate quasars observed by GALEX in the UV range. The WGE method exploits the new technological paradigm provided by the Virtual Observatory and the emerging field of Astroinformatics.Comment: 36 pages, 22 figures and 8 table

Astroinformatics, data mining and the future of astronomical research

Astronomy, as many other scientific disciplines, is facing a true data deluge which is bound to change both the praxis and the methodology of every day research work. The emerging field of astroinformatics, while on the one end appears crucial to face the technological challenges, on the other is opening new exciting perspectives for new astronomical discoveries through the implementation of advanced data mining procedures. The complexity of astronomical data and the variety of scientific problems, however, call for innovative algorithms and methods as well as for an extreme usage of ICT technologies.Comment: To appear in the Proceedings of the 2-nd International Conference on Frontiers on diagnostic technologie

No entailing laws, but enablement in the evolution of the biosphere

Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phenotypes, niches, ecosystems. We wish to argue that the evolution of life marks the end of a physics world view of law entailed dynamics. Our considerations depend upon discussing the variability of the very "contexts of life": the interactions between organisms, biological niches and ecosystems. These are ever changing, intrinsically indeterminate and even unprestatable: we do not know ahead of time the "niches" which constitute the boundary conditions on selection. More generally, by the mathematical unprestatability of the "phase space" (space of possibilities), no laws of motion can be formulated for evolution. We call this radical emergence, from life to life. The purpose of this paper is the integration of variation and diversity in a sound conceptual frame and situate unpredictability at a novel theoretical level, that of the very phase space. Our argument will be carried on in close comparisons with physics and the mathematical constructions of phase spaces in that discipline. The role of (theoretical) symmetries as invariant preserving transformations will allow us to understand the nature of physical phase spaces and to stress the differences required for a sound biological theoretizing. In this frame, we discuss the novel notion of "enablement". This will restrict causal analyses to differential cases (a difference that causes a difference). Mutations or other causal differences will allow us to stress that "non conservation principles" are at the core of evolution, in contrast to physical dynamics, largely based on conservation principles as symmetries. Critical transitions, the main locus of symmetry changes in physics, will be discussed, and lead to "extended criticality" as a conceptual frame for a better understanding of the living state of matter

Automated physical classification in the SDSS DR10. A catalogue of candidate Quasars

We discuss whether modern machine learning methods can be used to characterize the physical nature of the large number of objects sampled by the modern multi-band digital surveys. In particular, we applied the MLPQNA (Multi Layer Perceptron with Quasi Newton Algorithm) method to the optical data of the Sloan Digital Sky Survey - Data Release 10, investigating whether photometric data alone suffice to disentangle different classes of objects as they are defined in the SDSS spectroscopic classification. We discuss three groups of classification problems: (i) the simultaneous classification of galaxies, quasars and stars; (ii) the separation of stars from quasars; (iii) the separation of galaxies with normal spectral energy distribution from those with peculiar spectra, such as starburst or starforming galaxies and AGN. While confirming the difficulty of disentangling AGN from normal galaxies on a photometric basis only, MLPQNA proved to be quite effective in the three-class separation. In disentangling quasars from stars and galaxies, our method achieved an overall efficiency of 91.31% and a QSO class purity of ~95%. The resulting catalogue of candidate quasars/AGNs consists of ~3.6 million objects, of which about half a million are also flagged as robust candidates, and will be made available on CDS VizieR facility.Comment: Accepted for publication by MNRAS, 13 pages, 6 figure

Data-Rich Astronomy: Mining Sky Surveys with PhotoRApToR

In the last decade a new generation of telescopes and sensors has allowed the production of a very large amount of data and astronomy has become a data-rich science. New automatic methods largely based on machine learning are needed to cope with such data tsunami. We present some results in the fields of photometric redshifts and galaxy classification, obtained using the MLPQNA algorithm available in the DAMEWARE (Data Mining and Web Application Resource) for the SDSS galaxies (DR9 and DR10). We present PhotoRApToR (Photometric Research Application To Redshift): a Java based desktop application capable to solve regression and classification problems and specialized for photo-z estimation.Comment: proceedings of the IAU Symposium, Vol. 306, Cambridge University Pres

Stellar formation rates in galaxies using Machine Learning models

Global Stellar Formation Rates or SFRs are crucial to constrain theories of galaxy formation and evolution. SFR's are usually estimated via spectroscopic observations which require too much previous telescope time and therefore cannot match the needs of modern precision cosmology. We therefore propose a novel method to estimate SFRs for large samples of galaxies using a variety of supervised ML models.Comment: ESANN 2018 - Proceedings, ISBN-13 978287587048

Science, Problem Solving and Bibliometrics

Proceedings, Wim Blockmans et al. (eds), Portland Press, 2014International audienceThe head of a prestigious scientific institution recently said, by paraphrasing a famous quotation: "we solve problems that are posed, not that we pose". This view totally misses the history and role of human knowledge construction and prepares wrong ways for evaluating it.Science is not problem solving, it is theory building. Any relevant, difficult problem requires the construction of a new theoretical frame to deal with the problem in an original and effective way. Moreover, problems follow from the proposal of a theory. Animals continually solve problems that are posed to them by events. We, the humans, by language, in our communicating community, we looked at the Moon, at the Stars, which pose no problem, and invented Myths and Theories, and derived from them countless problems. We also looked at inert matter, a stone, some sand on a Greek beach, and proposed the atomistic theory. Science originated by these attempts to organize the world by concepts and theories. Later, it was radically renewed by looking again at planets, but from a different perspective: from the point of view of the Sun, on the grounds of a different metaphysics, which lead to a theoretical revolution. It was also renewed by looking at two falling stones in an original way and at physical trajectories as inertial, at the infinite limit of a non-existing frictionless movement..