Ruyer and Simondon on Technological Inventiveness and Form Outlasting its Medium

A summary is provided of Ruyer's important contribution, also a reversal from some conclusions held in his secondary doctoral dissertation, about the limits inherent in technological progress, and an attempt is made to show the coherence of this position to Ruyer's metaphysics. Simondon's response is also presented, and subsequently analyzed especially as it culminates in a concept of concretizations. As Simondon indicated, and with a displacement in Ruyer's limitating framework on unconditional growth, we end up searching for what represents the category of the ultimate for those two philosophers of the cyberworld

The Emperor's New Science, or Jerry Coyne on the Incompatibility of Science and Religion

Review Article on Jerry A. Coyne, Faith versus Fact: Why Science and Religion are Incompatible

Improving QED-Tutrix by Automating the Generation of Proofs

The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects. QED-Tutrix is an intelligent tutor for geometry offering an interface to help high school students in the resolution of demonstration problems. It focuses on specific goals: 1) to allow the student to freely explore the problem and its figure, 2) to accept proofs elements in any order, 3) to handle a variety of proofs, which can be customized by the teacher, and 4) to be able to help the student at any step of the resolution of the problem, if the need arises. The software is also independent from the intervention of the teacher. QED-Tutrix offers an interesting approach to geometry education, but is currently crippled by the lengthiness of the process of implementing new problems, a task that must still be done manually. Therefore, one of the main focuses of the QED-Tutrix' research team is to ease the implementation of new problems, by automating the tedious step of finding all possible proofs for a given problem. This automation must follow fundamental constraints in order to create problems compatible with QED-Tutrix: 1) readability of the proofs, 2) accessibility at a high school level, and 3) possibility for the teacher to modify the parameters defining the "acceptability" of a proof. We present in this paper the result of our preliminary exploration of possible avenues for this task. Automated theorem proving in geometry is a widely studied subject, and various provers exist. However, our constraints are quite specific and some adaptation would be required to use an existing prover. We have therefore implemented a prototype of automated prover to suit our needs. The future goal is to compare performances and usability in our specific use-case between the existing provers and our implementation.Comment: In Proceedings ThEdu'17, arXiv:1803.0072

Ruyer, la pensée de l’espace et la métaphore fondatrice de la connaissance

I present first the challenge for epistemology when it faces the dilemma between rationalism and empiricism, followed by a presentation of the ideas introduced by Ruyer in order to ask if they can be articulated to the "third way" in epistemology. I explore the consequences of Ruyer's inversion of our understanding of space which can be looked upon as psychic. I consider Ruyer's refusal to locate in pure immanence the scheme of eupraxic resolution of successful aggregates–as living forms–in our experience. I then highlight the major principles of Gaston Bachelard's and Michel Serres's respective epistemologies, and in a lesser measure those of Bergon and Deleuze as well, in order to underscore Ruyer's refusal to limit philosophy to what science allows one to say, but also in order to finally situate the verticalism of his position

Extended I-Love relations for slowly rotating neutron stars

Observations of gravitational waves from inspiralling neutron star binaries---such as GW170817---can be used to constrain the nuclear equation of state by placing bounds on stellar tidal deformability. For slowly rotating neutron stars, the response to a weak quadrupolar tidal field is characterized by four internal-structure-dependent constants called "Love numbers." The tidal Love numbers $k_2^\text{el}$ and $k_2^\text{mag}$ measure the tides raised by the gravitoelectric and gravitomagnetic components of the applied field, and the rotational-tidal Love numbers $\mathfrak{f}^\text{o}$ and $\mathfrak{k}^\text{o}$ measure those raised by couplings between the applied field and the neutron star spin. In this work we compute these four Love numbers for perfect fluid neutron stars with realistic equations of state. We discover (nearly) equation-of-state independent relations between the rotational-tidal Love numbers and the moment of inertia, thereby extending the scope of I-Love-Q universality. We find that similar relations hold among the tidal and rotational-tidal Love numbers. These relations extend the applications of I-Love universality in gravitational-wave astronomy. As our findings differ from those reported in the literature, we derive general formulas for the rotational-tidal Love numbers in post-Newtonian theory and confirm numerically that they agree with our general-relativistic computations in the weak-field limit.Comment: 31 pages, 6 figures, 9 tables; v2: updated to match published versio

Theoretical properties of Bayesian Student-tt linear regression

Student-$t$ linear regression is a commonly used alternative to the normal model in Bayesian analysis when one wants to gain robustness against outliers. The assumption of heavy-tailed error distribution makes the model more adapted to a potential presence of outliers by assigning higher probabilities to extreme values. Even though the Student-$t$ model is often used in practice, not a lot is known about its theoretical properties. In this paper, we aim to fill some gaps by providing analyses in two different asymptotic scenarios. In the first one, outliers are considered to be further and further away from the bulk of the data. The analysis allows to characterize the limiting posterior distribution, a distribution in which a trace of the outliers is present, making the approach partially robust. The impact of the trace is seen to increase with the degrees of freedom of the Student-$t$ distribution assumed. The second asymptotic scenario is one where the sample size increases and the normal model is the true generating process to be able to compare the efficiency of the robust estimator to the ordinary-least-squares one when the latter is the benchmark. The asymptotic efficiency is comparable, in the sense that the variance of the robust estimator is inflated but only by a factor, and this factor converges to 1 as the degrees of freedom increase. The trade-off between robustness and efficiency controlled through the degrees of freedom is thus precisely characterized (at least asymptotically)

An asymptotic Peskun ordering and its application to lifted samplers

A Peskun ordering between two samplers, implying a dominance of one over the other, is known among the Markov chain Monte Carlo community for being a remarkably strong result, but it is also known for being one that is notably difficult to establish. Indeed, one has to prove that the probability to reach a state $\mathbf{y}$ from a state $\mathbf{x}$, using a sampler, is greater than or equal to the probability using the other sampler, and this must hold for all pairs $(\mathbf{x}, \mathbf{y})$ such that $\mathbf{x} \neq \mathbf{y}$. We provide in this paper a weaker version that does not require an inequality between the probabilities for all these states: essentially, the dominance holds asymptotically, as a varying parameter grows without bound, as long as the states for which the probabilities are greater than or equal to belong to a mass-concentrating set. The weak ordering turns out to be useful to compare lifted samplers for partially-ordered discrete state-spaces with their Metropolis--Hastings counterparts. An analysis in great generality yields a qualitative conclusion: they asymptotically perform better in certain situations (and we are able to identify them), but not necessarily in others (and the reasons why are made clear). A thorough study in a specific context of graphical-model simulation is also conducted

Robust heavy-tailed versions of generalized linear models with applications in actuarial science

Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amount in insurance. A flaw of GLMs is that they are not robust against outliers (i.e., against erroneous or extreme data points). A difference in trends in the bulk of the data and the outliers thus yields skewed inference and prediction. Cantoni and Ronchetti (2001) proposed a robust frequentist approach which is now the most commonly applied. It consists in an estimator which is derived from a modification of the derivative of the log-likelihood. We propose an approach which is modelling-based and thus fundamentally different. It allows for an understanding and interpretation of the modelling, and it can be applied for both frequentist and Bayesian statistical analyses. We show that the approach possesses appealing theoretical and empirical properties. In particular, we show through a simulation study that it offers an advantage in terms of estimation performance