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In applications of Bayesian procedures, even when the prior law is carefully specified, it may be delicate to elicit the prior hyperparameters so that it is often tempting to fix them from the data, usually by their maximum likelihood estimates (MMLE), obtaining a so-called empirical Bayes posterior distribution. Although questionable, this is a common practice; but theoretical properties seem mostly only available on a case-by-case basis. In this paper we provide general properties for parametric models. First, we study the limit behavior of the MMLE and prove results in quite general settings, while also conceptualizing the frequentist context as an unexplored case of maximum likelihood estimation under model misspecification. We cover both identifiable models, illustrating applications to sparse regression, and non-identifiable models - specifically, overfitted mixture models. Finally, we prove higher order merging results. In regular cases, the empirical Bayes posterior is shown to be a fast approximation to the Bayesian posterior distribution of the researcher who, within the given class of priors, has the most information about the true model's parameters. This is a faster approximation than classic Bernstein-von Mises results. Given the class of priors, our work provides formal contents to common beliefs on this popular practice.

This paper introduces a novel compact mixed integer linear programming (MILP) formulation and a discretization discovery-based solution approach for the Vehicle Routing Problem with Time Windows (VRPTW). We aim to solve the optimization problem efficiently by constraining the linear programming (LP) solutions to use only flows corresponding to time and capacity-feasible routes that are locally elementary (prohibiting cycles of customers localized in space). We employ a discretization discovery algorithm to refine the LP relaxation iteratively. This iterative process alternates between two steps: (1) increasing time/capacity/elementarity enforcement to increase the LP objective, albeit at the expense of increased complexity (more variables and constraints), and (2) decreasing enforcement without decreasing the LP objective to reduce complexity. This iterative approach ensures we produce an LP relaxation that closely approximates the optimal MILP objective with minimal complexity, facilitating an efficient solution via an off-the-shelf MILP solver. The effectiveness of our method is demonstrated through empirical evaluations on classical VRPTW instances. We showcase the efficiency of solving the final MILP and multiple iterations of LP relaxations, highlighting the decreased integrality gap of the final LP relaxation. We believe that our approach holds promise for addressing a wide range of routing problems within and beyond the VRPTW domain.

We have performed classical molecular dynamics simulations of 3 keV Ar + $(\mathrm{C}_{24}\mathrm{H}_{12})_n(\mathrm{C}_{60})_{m}$ collisions where $(n,m)=(3,2), (1,4), (9,4)$ and $(2,11)$. The simulated mass spectra of covalently bound reaction products reproduce the main features of the corresponding experimental results reported by Domaracka et al., PCCP, 2018, 20, 15052. The present results support their conclusion that molecular growth is mainly driven by knockout where individual atoms are promptly removed in Rutherford type scattering processes. The so formed highly reactive fragments may then bind with neighboring molecules in the clusters producing a rich variety of growth products extending up to sizes containing several hundreds of atoms, and here we show examples of such structures. In addition, knocked out atoms may be absorbed such that e.g. hydrogenated coronene and fullerene molecules are formed., Comment: 7 pages, 7 figures

Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient propagators in constraint programming (such as the weighted circuit constraint). However, the conventional process of deriving Lagrangian multipliers (e.g., using subgradient methods) is often computationally intensive, limiting its practicality for large-scale or time-sensitive problems. To address this challenge, we propose an innovative unsupervised learning approach that harnesses the capabilities of graph neural networks to exploit the problem structure, aiming to generate accurate Lagrangian multipliers efficiently. We apply this technique to the well-known Held-Karp Lagrangian relaxation for the travelling salesman problem. The core idea is to predict accurate Lagrangian multipliers and to employ them as a warm start for generating Held-Karp relaxation bounds. These bounds are subsequently utilized to enhance the filtering process carried out by branch-and-bound algorithms. In contrast to much of the existing literature, which primarily focuses on finding feasible solutions, our approach operates on the dual side, demonstrating that learning can also accelerate the proof of optimality. We conduct experiments across various distributions of the metric travelling salesman problem, considering instances with up to 200 cities. The results illustrate that our approach can improve the filtering level of the weighted circuit global constraint, reduce the optimality gap by a factor two for unsolved instances up to a timeout, and reduce the execution time for solved instances by 10%.

This work studies nonparametric Bayesian estimation of the intensity function of an inhomogeneous Poisson point process in the important case where the intensity depends on covariates, based on the observation of a single realisation of the point pattern over a large area. It is shown how the presence of covariates allows to borrow information from far away locations in the observation window, enabling consistent inference in the growing domain asymptotics. In particular, optimal posterior contraction rates under both global and point-wise loss functions are derived. The rates in global loss are obtained under conditions on the prior distribution resembling those in the well established theory of Bayesian nonparametrics, here combined with concentration inequalities for functionals of stationary processes to control certain random covariate-dependent loss functions appearing in the analysis. The local rates are derived with an ad-hoc study that builds on recent advances in the theory of P\'olya tree priors, extended to the present multivariate setting with a novel construction that makes use of the random geometry induced by the covariates., Comment: 55 pages

Due to uncertainty in demand, sometimes management may delay their planning of shifts later in the horizon when they have more information. We consider a novel dynamic and flexible system for scheduling personnel for work shifts planned at the last minute called 'on-call' shifts. The flexibility in the system allows employees to freely select or reject shifts offered to them. Senior employees may also replace or bump junior employees from the current schedule if no other shift of their choice is available provided certain conditions are met. The operator seeks to quickly assign all available shifts to employees while ensuring minimum total bumps. We develop several easy-to-implement policy approximations as well as deep reinforcement learning-based policies to efficiently operate the system. A comparison of all the developed policies is made using real data from our industrial partner. We identify the best policies under different settings and significantly improve upon the current practices.

Organising an AI challenge does not end with the final event. The long-lasting impact also needs to be organised. This chapter covers the various activities after the challenge is formally finished. The target audience of different post-challenge activities is identified. The various outputs of the challenge are listed with the means to collect them. The main part of the chapter is a template for a typical post-challenge paper, including possible graphs as well as advice on how to turn the challenge into a long-lasting benchmark., Comment: 5th chapter of book "AI Competitions and Benchmarks: the science behind the contests" see: https://sites.google.com/chalearn.org/book/home

The reconstruction of charged particle trajectories is a crucial challenge of particle physics experiments as it directly impacts particle reconstruction and physics performances. To reconstruct these trajectories, different reconstruction algorithms are used sequentially. Each of these algorithms uses many configuration parameters that must be fine-tuned to properly account for the detector/experimental setup, the available CPU budget and the desired physics performance. Examples of such parameters are cut values limiting the algorithm's search space, approximations accounting for complex phenomenons, or parameters controlling algorithm performance. Until now, these parameters had to be optimised by human experts, which is inefficient and raises issues for the long-term maintainability of such algorithms. Previous experience using machine learning for particle reconstruction (such as the TrackML challenge) has shown that they can be easily adapted to different experiments by learning directly from the data. We propose to bring the same approach to the classic track reconstruction algorithms by connecting them to an agent-driven optimiser, allowing us to find the best input parameters using an iterative tuning approach. We have so far demonstrated this method on different track reconstruction algorithms within A Common Tracking Software (ACTS) framework using the Open Data Detector (ODD). These algorithms include the trajectory seed reconstruction and selection, the particle vertex reconstruction and the generation of simplified material maps used for trajectory reconstruction., Comment: 6 pages, 2 figures, Talk presented at the 21st International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2022)

The reconstruction of particle trajectories is a key challenge of particle physics experiments, as it directly impacts particle identification and physics performances while also representing one of the main CPU consumers of many high-energy physics experiments. As the luminosity of particle colliders increases, this reconstruction will become more challenging and resource-intensive. New algorithms are thus needed to address these challenges efficiently. One potential step of track reconstruction is ambiguity resolution. In this step, performed at the end of the tracking chain, we select which tracks candidates should be kept and which must be discarded. The speed of this algorithm is directly driven by the number of track candidates, which can be reduced at the cost of some physics performance. Since this problem is fundamentally an issue of comparison and classification, we propose to use a machine learning-based approach to the Ambiguity Resolution. Using a shared-hits-based clustering algorithm, we can efficiently determine which candidates belong to the same truth particle. Afterwards, we can apply a Neural Network (NN) to compare those tracks and decide which ones are duplicates and which ones should be kept. This approach is implemented within A Common Tracking Software (ACTS) framework and tested on the Open Data Detector (ODD), a realistic virtual detector similar to a future ATLAS one. This new approach was shown to be 15 times faster than the default ACTS algorithm while removing 32 times more duplicates down to less than one duplicated track per event., Comment: 8 pages, 3 figures, 1 table, Talk presented at the 26th International Conference on Computing in High Energy & Nuclear Physics (CHEP 2023)

The proliferation of Internet of Things (IoT) devices has intensified the demand for energyefficient solutions supporting ondevice and distributed learning applications. This re search presents a circumscribed comparative analysis of radioenabled ultralow power IoT devices, specifically focusing on their suitability for computationheavy use cases. Our analysis centers on middleend IoT devices that serve as a vital interface between the Electronics and Machine Learn ing communities. The evaluation encompasses a diverse range of IoT hardware equipped with inte grated radios. We established functional datasheetbased criteria completed with accessibility and communitywise criteria to study and offer valuable insights into each selected node's performance tradeoffs, strengths, and weaknesses. This study provides crucial guidance for TinyML practitioners seeking to make informed device selections for their applications.

Many real-world scenarios involve solving bi-level optimization problems in which there is an outer discrete optimization problem, and an inner problem involving expensive or black-box computation. This arises in space-time dependent variants of the Traveling Salesman Problem, such as when planning space missions that visit multiple astronomical objects. Planning these missions presents significant challenges due to the constant relative motion of the objects involved. There is an outer combinatorial problem of finding the optimal order to visit the objects and an inner optimization problem that requires finding the optimal departure time and trajectory to travel between each pair of objects. The constant motion of the objects complicates the inner problem, making it computationally expensive. This paper introduces a novel framework utilizing decision diagrams (DDs) and a DD-based branch-and-bound technique, Peel-and-Bound, to achieve exact solutions for such bi-level optimization problems, assuming sufficient inner problem optimizer quality. The framework leverages problem-specific knowledge to expedite search processes and minimize the number of expensive evaluations required. As a case study, we apply this framework to the Asteroid Routing Problem (ARP), a benchmark problem in global trajectory optimization. Experimental results demonstrate the framework's scalability and ability to generate robust heuristic solutions for ARP instances. Many of these solutions are exact, contingent on the assumed quality of the inner problem's optimizer., Comment: 40 pages, 10 figures, 8 tables

We present new high-spectral resolution observations (R = $\lambda/\Delta\lambda$ = 7000) of the filamentary nebula surrounding NGC 1275, the central galaxy of the Perseus cluster. These observations have been obtained with SITELLE, an imaging Fourier transform spectrometer installed on the Canada-France-Hawai Telescope (CFHT) with a field of view of $11\text{ arcmin }\times 11 \text{ arcmin}$ encapsulating the entire filamentary structure of ionised gas despite its large size of $80 \text{ kpc}\times50 \text{ kpc}$. Here, we present renewed flux, velocity and velocity dispersion maps that show in great detail the kinematics of the optical nebula at \sii$\lambda6716$, \sii$\lambda6731$, \nii$\lambda6584$, H$\alpha$(6563\AA), and \nii$\lambda6548$. These maps reveal the existence of a bright flattened disk-shaped structure in the core extending to r $\sim 10$ kpc and dominated by a chaotic velocity field. This structure is located in the wake of X-ray cavities and characterised by a high mean velocity dispersion of $134$ km/s. The disk-shaped structure is surrounded by an extended array of filaments spread out to $r\sim 50$ kpc that are 10 times fainter in flux, remarkably quiescent and has a uniform mean velocity dispersion of $44$ km/s. This stability is puzzling given that the cluster core exhibits several energetic phenomena. Based on these results, we argue that there are two mechanisms to form multiphase gas in clusters of galaxies: a first triggered in the wake of X-ray cavities leading to more turbulent multiphase gas and a second, distinct mechanism, that is gentle and leads to large-scale multiphase gas spread throughout the core.

The nucleus of comet 67P/Churyumov-Gerasimenko exhibits a broad spectral reflectance feature around 3.2 $\mu$m, which is omnipresent in all spectra of the surface, and whose attribution has remained elusive since its discovery. Based on laboratory experiments, we have shown that most of this absorption feature is due to ammonium (NH4+) salts mixed with the dark surface material. The depth of the band is compatible with semi-volatile ammonium salts being a major reservoir of nitrogen in the comet, which could dominate over refractory organic matter and volatile species. These salts may thus represent the long-sought reservoir of nitrogen in comets, possibly bringing their nitrogen-to-carbon ratio in agreement with the solar value. Moreover, the reflectance spectra of several asteroids are compatible with the presence of NH4+ salts at their surfaces. The presence of such salts, and other NH4+-bearing compounds on asteroids, comets, and possibly in proto-stellar environments, suggests that NH4+ may be a tracer of the incorporation and transformation of nitrogen in ices, minerals and organics, at different phases of the formation of the Solar System.

We consider the asymptotic properties of Approximate Bayesian Computation (ABC) for the realistic case of summary statistics with heterogeneous rates of convergence. We allow some statistics to converge faster than the ABC tolerance, other statistics to converge slower, and cover the case where some statistics do not converge at all. We give conditions for the ABC posterior to converge, and provide an explicit representation of the shape of the ABC posterior distribution in our general setting; in particular, we show how the shape of the posterior depends on the number of slow statistics. We then quantify the gain brought by the local linear post-processing step.

We verify the transcendental part of a conjecture of Campana predicting that the rational points on the weakly-special non-special simply-connected smooth projective threefolds constructed by Bogomolov-Tschinkel are not dense. To prove our result, we establish fundamental properties of moduli spaces of orbifold maps. The crux of the argument relies on a dimension bound for such moduli spaces which relies on a recently established extension of Kobayashi-Ochiai's finiteness theorem to the more general setting of Campana's orbifold pairs., Comment: Minor improvements

We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors with independent coordinates having ordinary smooth densities, we derive an inversion inequality relating the $L^1$-Wasserstein distance between two distributions of the signal to the $L^1$-distance between the corresponding mixture densities of the observations. This smoothing inequality outperforms existing inversion inequalities. As an application of the inversion inequality to the Bayesian framework, we consider $1$-Wasserstein deconvolution with Laplace noise in dimension one using a Dirichlet process mixture of normal densities as a prior measure on the mixing distribution (or distribution of the signal). We construct an adaptive approximation of the sampling density by convolving the Laplace density with a well-chosen mixture of normal densities and show that the posterior measure concentrates around the sampling density at a nearly minimax rate, up to a log-factor, in the $L^1$-distance. The same posterior law is also shown to automatically adapt to the unknown Sobolev regularity of the mixing density, thus leading to a new Bayesian adaptive estimation procedure for mixing distributions with regular densities under the $L^1$-Wasserstein metric. We illustrate utility of the inversion inequality also in a frequentist setting by showing that an appropriate isotone approximation of the classical kernel deconvolution estimator attains the minimax rate of convergence for $1$-Wasserstein deconvolution in any dimension $d\geq 1$, when only a tail condition is required on the latent mixing density and we derive sharp lower bounds for these problems, Comment: arXiv admin note: text overlap with arXiv:2111.06846

A new method is proposed to predict the topological properties of one-dimensional periodic structures in wave physics, including quantum mechanics. From Bloch waves, a unique complex valued function is constructed, exhibiting poles and zeros. The sequence of poles and zeros of this function is a topological invariant that can be linked to the Berry-Zak phase. Since the characterization of the topological properties is done in the complex plane, it can easily be extended to the case of non-hermitian systems. The sequence of poles and zeros allows to predict topological phase transitions., Comment: 18 pages, 15 figures