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Automation transformed various aspects of our human civilization, revolutionizing industries and streamlining processes. In the domain of scientific inquiry, automated approaches emerged as powerful tools, holding promise for accelerating discovery, enhancing reproducibility, and overcoming the traditional impediments to scientific progress. This article evaluates the scope of automation within scientific practice and assesses recent approaches. Furthermore, it discusses different perspectives to the following questions: Where do the greatest opportunities lie for automation in scientific practice?; What are the current bottlenecks of automating scientific practice?; and What are significant ethical and practical consequences of automating scientific practice? By discussing the motivations behind automated science, analyzing the hurdles encountered, and examining its implications, this article invites researchers, policymakers, and stakeholders to navigate the rapidly evolving frontier of automated scientific practice.

We introduce a new class of anticipative backward stochastic differential equations with a dependence of McKean type on the law of the solution, that we name MKABSDE. We provide existence and uniqueness results in a general framework with relatively general regularity assumptions on the coefficients. We show how such stochastic equations arise within the modern paradigm of derivative pricing where a central counterparty (CCP) requires the members to deposit variation and initial margins to cover their exposure. In the case when the initial margin is proportional to the Conditional Value-at-Risk (CVaR) of the contract price, we apply our general result to define the price as a solution of a MKABSDE. We provide several linear and non-linear simpler approximations, which we solve using different numerical (deterministic and Monte-Carlo) methods.

In this article we design a novel quasi-regression Monte Carlo algorithm in order to approximate the solution of discrete time backward stochastic differential equations (BSDEs), and we analyze the convergence of the proposed method. The algorithm also approximates the solution to the related semi-linear parabolic partial differential equation (PDE) obtained through the well-known Feynman-Kac representation. For the sake of enriching the algorithm with high-order convergence a weighted approximation of the solution is computed and appropriate conditions on the parameters of the method are inferred. With the challenge of tackling problems in high dimensions we propose suitable projections of the solution and efficient parallelizations of the algorithm taking advantage of powerful many-core processors such as graphics processing units (GPUs).

In this paper, we design a novel algorithm based on Least-Squares Monte Carlo (LSMC) in order to approximate the solution of discrete time Backward Stochastic Differential Equations (BSDEs). Our algorithm allows massive parallelization of the computations on many core processors such as graphics processing units (GPUs). Our approach consists of a novel method of stratification which appears to be crucial for large scale parallelization. In this way, we minimize the exposure to the memory requirements due to the storage of simulations. Indeed, we note the lower memory overhead of the method compared with previous works.

In this work we study the numerical approximation of a class of ergodic Backward Stochastic Differential Equations. These equations are formulated in an infinite horizon framework and provide a probabilistic representation for elliptic Partial Differential Equations of ergodic type. In order to build our numerical scheme, we put forward a new representation of the PDE solution by using a classical probabilistic representation of the gradient. Then, based on this representation, we propose a fully implementable numerical scheme using a Picard iteration procedure, a grid space discretization and a Monte-Carlo approximation. Up to a limiting technical condition that guarantees the contraction of the Picard procedure, we obtain an upper bound for the numerical error. We also provide some numerical experiments that show the efficiency of this approach for small dimensions.

We study the restriction of the strong Bruhat order on an arbitrary Coxeter group $W$ to cosets $x W_L^\theta$, where $x$ is an element of $W$ and $W_L^\theta$ the subgroup of fixed points of an automorphism $\theta$ of order at most two of a standard parabolic subgroup $W_L$ of $W$. When $\theta\neq\mathrm{id}$, there is in general more than one element of minimal length in a given coset, and we explain how to relate elements of minimal length. We also show that elements of minimal length in cosets are exactly those elements which are minimal for the restriction of the Bruhat order., Comment: 8 pages, 2 figures. Comments welcome!

We study the effects of irradiating water with 3 MeV protons at high doses by observing the motion of charged polystyrene beads outside the proton beam. By single-particle tracking, we measure a radial velocity of the order of microns per second. Combining electrokinetic theory with simulations of the beam-generated reaction products and their outward diffusion, we find that the bead motion is due to electrophoresis in the electric field induced by the mobility contrast of cations and anions. This work sheds light on the perturbation of biological systems by high-dose radiations and paves the way for the manipulation of colloid or macromolecular dispersions by radiation-induced diffusiophoresis.

In this note, we give a new proof of a result of Matthew Dyer stating that in an arbitrary Coxeter group $W$, every pair $t,t'$ of distinct reflections lie in a unique maximal dihedral reflection subgroup of $W$. Our proof only relies on the combinatorics of words, in particular we do not use root systems at all. As an application, we deduce a new proof of a recent result of Delucchi-Paolini-Salvetti, stating that the poset $[1,c]_T$ of generalized noncrossing partitions in any Coxeter group of rank $3$ is a lattice. We achieve this by showing the more general statement that any interval of length $3$ in the absolute order on an arbitrary Coxeter group is a lattice. This implies that the interval group attached to any interval $[1,w]_T$ where $w$ is an element of an arbitrary Coxeter group with $\ell_T(w)=3$ is a quasi-Garside group., Comment: 5 pages, comments welcome !

The development of Additive Manufacturing (AM) for the fabrication of metallic parts allows structures to be directly manufactured from 3D models. The Electron Beam Melting (EBM) technology is an example of AM technologies that enables the manufacturing of new designs. The process is particularly well suited for the fabrication of lattice structures. Octet-truss lattice structure has been a subject for research in recent years. Besides being lightweighted, the structure could provide solid mechanical properties. However, researchers always encounter the same issue regarding this particular structure. During Finite Element Analysis (FEA) simulation, stress concentration tends to appear at the struts intersection. This is due to the sharp edges, thus provoking the presence of singularities. In this respect, the proposed solution is to integrate fillets at the struts intersection. However, adding fillet entails a mass increase of octet-truss structures. To avoid this mass increase related to these fillets, it is necessary to reduce the size of octet-truss struts. This research work studies the influence of fillets onto the mechanical properties of structures with identical mass. To do so, a set of 15 octet-truss structures are designed with various fillet sizes and strut sizes and compared. Whereas some of them have thick struts and small fillets, others have smaller struts and bigger fillets. The main technical issue in this study remains the design of fillets for octet-truss structures. These latter can indeed be created for up to 12 struts that converge to the same point. Once designed, these octet-truss structures are fabricated by EBM technology and undergo static compression testing. Mechanical properties of each structure are finally determined. Results show that for the same relative density, octet-truss with fillets degrades the mechanical characteristics of the whole structures.

We study two families of lattices whose number of elements are given by the numbers in even (respectively odd) positions in the Fibonacci sequence. The even Fibonacci lattice arises as the lattice of simple elements of a Garside monoid partially ordered by left-divisibility, and the odd Fibonacci lattice is an order ideal in the even one. We give a combinatorial proof of the lattice property, relying on a description of words for the Garside element in terms of Schr\"oder trees, and on a recursive description of the even Fibonacci lattice. This yields an explicit formula to calculate meets and joins in the lattice. As a byproduct we also obtain that the number of words for the Garside element is given by a little Schr\"oder number., Comment: 20 pages, 7 figures. Comments welcome!

We use non-symmetric Cauchy kernel identities to get the law of last passagepercolation models in terms of Demazure characters. The construction is basedon some restrictions of the RSK correspondence that we rephrase in a unifiedway which is compatible with crystal basis theory.

We propose a non-asymptotic convergence analysis of a two-step approach to learn a conditional value-at-risk (VaR) and a conditional expected shortfall (ES) using Rademacher bounds, in a non-parametric setup allowing for heavy-tails on the financial loss. Our approach for the VaR is extended to the problem of learning at once multiple VaRs corresponding to different quantile levels. This results in efficient learning schemes based on neural network quantile and least-squares regressions. An a posteriori Monte Carlo procedure is introduced to estimate distances to the ground-truth VaR and ES. This is illustrated by numerical experiments in a Student-$t$ toy model and a financial case study where the objective is to learn a dynamic initial margin.

Several distinct Garside monoids having torus knot groups as groups of fractions are known. For $n,m\geq 2$ two coprime integers, we introduce a new Garside monoid $\mathcal{M}(n,m)$ having as Garside group the $(n,m)$-torus knot group, thereby generalizing to all torus knot groups a construction that we previously gave for the $(n,n+1)$-torus knot group. As a byproduct, we obtain new Garside structures for the braid groups of a few exceptional complex reflection groups of rank two. Analogous Garside structures are also constructed for a few additional braid groups of exceptional complex reflection groups of rank two which are not isomorphic to torus knot groups, namely for $G_{13}$ and for dihedral Artin groups of even type., Comment: 24 pages, 1 figure. Comments welcome !

We design a novel calibration procedure that is designed to handle the specific characteristics of options on cryptocurrency markets, namely large bid-ask spreads and the possibility of missing or incoherent prices in the considered data sets. We show that this calibration procedure is significantly more robust and accurate than the standard one based on trade and mid-prices., Comment: 36 pages, 39 figures

We provide explicit approximation formulas for VIX futures and options in forward variance models, with particular emphasis on the family of so-called Bergomi models: the one-factor Bergomi model [Bergomi, Smile dynamics II, Risk, 2005], the rough Bergomi model [Bayer, Friz, and Gatheral, Pricing under rough volatility, Quantitative Finance, 16(6):887-904, 2016], and an enhanced version of the rough model that can generate realistic positive skew for VIX smiles -- introduced simultaneously by De Marco [Bachelier World Congress, 2018] and Guyon [Bachelier World Congress, 2018] on the lines of [Bergomi, Smile dynamics III, Risk, 2008], that we refer to as 'mixed rough Bergomi model'. Following the methodology set up in [Gobet and Miri, Weak approximation of averaged diffusion processes. Stochastic Process.\ Appl., 124(1):475-504, 2014], we derive weak approximations for the law of the VIX, leading to option price approximations under the form of explicit combinations of Black-Scholes prices and greeks. As new contributions, we cope with the fractional integration kernel appearing in rough models and treat the case of non-smooth payoffs, so to encompass VIX futures, call and put options. We stress that our approach does not rely on small-time asymptotics nor small-parameter (such as small volatility-of-volatility) asymptotics, and can therefore be applied to any option maturity and a wide range of parameter configurations. Our results are illustrated by several numerical experiments and calibration tests to VIX market data.

Calculations of the cross sections of inelastic electron scattering $(e,e')$ on a nucleus in the multi-keV energy range strongly depend on the description of the screening of the nuclear Coulomb potential as well as on the deformation of the wave functions of the incoming and outgoing electron in the vicinity of the nucleus. These cross sections are evaluated at values lower than $10^{-30}$ cm$^2$ which vary by several orders of magnitude according to the models. Experimental measurements would be required to constrain the models but it is a real challenge to measure such low cross sections. In this study, we demonstrate that inelastic electron scattering is the main nuclear excitation mechanism in a $^{181}$Ta target irradiated with a new intense 10 - 30 keV electron beam produced with a biased laser-plasma. Calculations show that through the detection of conversion electrons, it should be possible to measure the nuclear excitation yields. The effect of electron beam heating and of plasma deposition on the tantalum target are quantified, thus allowing the dimensioning of a possible experimental configuration to study $(e,e')$ processes in this range of energy for the first time.

High power lasers have proven being capable to produce high energy gamma rays, charged particles and neutrons to induce all kinds of nuclear reactions. At ELI, the studies with high power lasers will enter for the first time into new domains of power and intensities.

Several finite complex reflection groups have a braid group which is isomorphic to a torus knot group. The reflection group is obtained from the torus knot group by declaring meridians to have order $k$ for some $k\geq 2$, and meridians are mapped to reflections. We study all possible quotients of torus knot groups obtained by requiring meridians to have finite order. Using the theory of $J$-groups of Achar and Aubert, we show that these groups behave like (in general infinite) complex reflection groups of rank two. The large family of "toric reflection groups" which we obtain includes, among others, all finite complex reflection groups of rank two with a single conjugacy class of reflecting hyperplanes, as well as Coxeter's truncations of the $3$-strand braid group. We classify these toric reflection groups and explain why the corresponding torus knot group can be naturally considered as its braid group. In particular, this yields a new infinite family of reflection-like groups admitting a braid group which is a Garside group. Moreover, we show that a toric reflection group has cyclic center by showing that the quotient by the center is isomorphic to the alternating subgroup of a Coxeter group of rank three. To this end we use the fact that the center of the alternating subgroup of an irreducible, infinite Coxeter group of rank at least three is trivial. Several ingredients of the proofs are purely Coxeter-theoretic, and might be of independent interest., Comment: 24 pages, v2: minor changes, references updated

In this paper we present a series of results that permit to extend in a direct manner uniform deviation inequalities of the empirical process from the independent to the dependent case characterizing the additional error in terms of $\beta-$mixing coefficients associated to the training sample. We then apply these results to some previously obtained inequalities for independent samples associated to the deviation of the least-squared error in nonparametric regression to derive corresponding generalization bounds for regression schemes in which the training sample may not be independent. These results provide a framework to analyze the error associated to regression schemes whose training sample comes from a large class of $\beta-$mixing sequences, including geometrically ergodic Markov samples, using only the independent case. More generally, they permit a meaningful extension of the Vapnik-Chervonenkis and similar theories for independent training samples to this class of $\beta-$mixing samples., Comment: 36 pages