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Foundation models (FMs), large deep learning models pre-trained on vast, unlabeled datasets, exhibit powerful capabilities in understanding complex patterns and generating sophisticated outputs. However, they often struggle to adapt to specific tasks. Reinforcement learning (RL), which allows agents to learn through interaction and feedback, offers a compelling solution. Integrating RL with FMs enables these models to achieve desired outcomes and excel at particular tasks. Additionally, RL can be enhanced by leveraging the reasoning and generalization capabilities of FMs. This synergy is revolutionizing various fields, including robotics. FMs, rich in knowledge and generalization, provide robots with valuable information, while RL facilitates learning and adaptation through real-world interactions. This survey paper comprehensively explores this exciting intersection, examining how these paradigms can be integrated to advance robotic intelligence. We analyze the use of foundation models as action planners, the development of robotics-specific foundation models, and the mutual benefits of combining FMs with RL. Furthermore, we present a taxonomy of integration approaches, including large language models, vision-language models, diffusion models, and transformer-based RL models. We also explore how RL can utilize world representations learned from FMs to enhance robotic task execution. Our survey aims to synthesize current research and highlight key challenges in robotic reasoning and control, particularly in the context of integrating FMs and RL--two rapidly evolving technologies. By doing so, we seek to spark future research and emphasize critical areas that require further investigation to enhance robotics. We provide an updated collection of papers based on our taxonomy, accessible on our open-source project website at: https://github.com/clmoro/Robotics-RL-FMs-Integration., Comment: Submitted for publication to the Special Issue on Foundation Models and Neural-Symbolic AI for Robotics in The International Journal of Robotics Research (IJRR)

Recently introduced by some of the authors, the in-context identification paradigm aims at estimating, offline and based on synthetic data, a meta-model that describes the behavior of a whole class of systems. Once trained, this meta-model is fed with an observed input/output sequence (context) generated by a real system to predict its behavior in a zero-shot learning fashion. In this paper, we enhance the original meta-modeling framework through three key innovations: by formulating the learning task within a probabilistic framework; by managing non-contiguous context and query windows; and by adopting recurrent patching to effectively handle long context sequences. The efficacy of these modifications is demonstrated through a numerical example focusing on the Wiener-Hammerstein system class, highlighting the model's enhanced performance and scalability.

The landscape of Deep Learning has experienced a major shift with the pervasive adoption of Transformer-based architectures, particularly in Natural Language Processing (NLP). Novel avenues for physical applications, such as solving Partial Differential Equations and Image Vision, have been explored. However, in challenging domains like robotics, where high non-linearity poses significant challenges, Transformer-based applications are scarce. While Transformers have been used to provide robots with knowledge about high-level tasks, few efforts have been made to perform system identification. This paper proposes a novel methodology to learn a meta-dynamical model of a high-dimensional physical system, such as the Franka robotic arm, using a Transformer-based architecture without prior knowledge of the system's physical parameters. The objective is to predict quantities of interest (end-effector pose and joint positions) given the torque signals for each joint. This prediction can be useful as a component for Deep Model Predictive Control frameworks in robotics. The meta-model establishes the correlation between torques and positions and predicts the output for the complete trajectory. This work provides empirical evidence of the efficacy of the in-context learning paradigm, suggesting future improvements in learning the dynamics of robotic systems without explicit knowledge of physical parameters. Code, videos, and supplementary materials can be found at project website. See https://sites.google.com/view/robomorph/

The Euclid mission will measure cosmological parameters with unprecedented precision. To distinguish between cosmological models, it is essential to generate realistic mock observables from cosmological simulations that were run in both the standard $\Lambda$-cold-dark-matter ($\Lambda$CDM) paradigm and in many non-standard models beyond $\Lambda$CDM. We present the scientific results from a suite of cosmological N-body simulations using non-standard models including dynamical dark energy, k-essence, interacting dark energy, modified gravity, massive neutrinos, and primordial non-Gaussianities. We investigate how these models affect the large-scale-structure formation and evolution in addition to providing synthetic observables that can be used to test and constrain these models with Euclid data. We developed a custom pipeline based on the Rockstar halo finder and the nbodykit large-scale structure toolkit to analyse the particle output of non-standard simulations and generate mock observables such as halo and void catalogues, mass density fields, and power spectra in a consistent way. We compare these observables with those from the standard $\Lambda$CDM model and quantify the deviations. We find that non-standard cosmological models can leave significant imprints on the synthetic observables that we have generated. Our results demonstrate that non-standard cosmological N-body simulations provide valuable insights into the physics of dark energy and dark matter, which is essential to maximising the scientific return of Euclid., Comment: 22 pages, 7 figures

Given any $\varepsilon>0$ we prove that every sufficiently large $n$-vertex $3$-graph $H$ where every pair of vertices is contained in at least $(1/3+\varepsilon)n$ edges contains a copy of $C_{10}$, i.e.\ the tight cycle on $10$ vertices. In fact we obtain the same conclusion for every cycle $C_\ell$ with $\ell\geq 19$., Comment: 5 pages

Cell-penetrating peptides (CPPs) are powerful vectors for the intracellular delivery of a diverse array of therapeutic molecules. Despite their potential, the rational design of CPPs remains a challenging task that often requires extensive experimental efforts and iterations. In this study, we introduce an innovative approach for the de novo design of CPPs, leveraging the strengths of machine learning (ML) and optimization algorithms. Our strategy, named LightCPPgen, integrates a LightGBM-based predictive model with a genetic algorithm (GA), enabling the systematic generation and optimization of CPP sequences. At the core of our methodology is the development of an accurate, efficient, and interpretable predictive model, which utilizes 20 explainable features to shed light on the critical factors influencing CPP translocation capacity. The CPP predictive model works synergistically with an optimization algorithm, which is tuned to enhance computational efficiency while maintaining optimization performance. The GA solutions specifically target the candidate sequences' penetrability score, while trying to maximize similarity with the original non-penetrating peptide in order to retain its original biological and physicochemical properties. By prioritizing the synthesis of only the most promising CPP candidates, LightCPPgen can drastically reduce the time and cost associated with wet lab experiments. In summary, our research makes a substantial contribution to the field of CPP design, offering a robust framework that combines ML and optimization techniques to facilitate the rational design of penetrating peptides, by enhancing the explainability and interpretability of the design process.

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

With a specific emphasis on control design objectives, achieving accurate system modeling with limited complexity is crucial in parametric system identification. The recently introduced deep structured state-space models (SSM), which feature linear dynamical blocks as key constituent components, offer high predictive performance. However, the learned representations often suffer from excessively large model orders, which render them unsuitable for control design purposes. The current paper addresses this challenge by means of system-theoretic model order reduction techniques that target the linear dynamical blocks of SSMs. We introduce two regularization terms which can be incorporated into the training loss for improved model order reduction. In particular, we consider modal $\ell_1$ and Hankel nuclear norm regularization to promote sparsity, allowing one to retain only the relevant states without sacrificing accuracy. The presented regularizers lead to advantages in terms of parsimonious representations and faster inference resulting from the reduced order models. The effectiveness of the proposed methodology is demonstrated using real-world ground vibration data from an aircraft.

This paper addresses the challenge of overfitting in the learning of dynamical systems by introducing a novel approach for the generation of synthetic data, aimed at enhancing model generalization and robustness in scenarios characterized by data scarcity. Central to the proposed methodology is the concept of knowledge transfer from systems within the same class. Specifically, synthetic data is generated through a pre-trained meta-model that describes a broad class of systems to which the system of interest is assumed to belong. Training data serves a dual purpose: firstly, as input to the pre-trained meta model to discern the system's dynamics, enabling the prediction of its behavior and thereby generating synthetic output sequences for new input sequences; secondly, in conjunction with synthetic data, to define the loss function used for model estimation. A validation dataset is used to tune a scalar hyper-parameter balancing the relative importance of training and synthetic data in the definition of the loss function. The same validation set can be also used for other purposes, such as early stopping during the training, fundamental to avoid overfitting in case of small-size training datasets. The efficacy of the approach is shown through a numerical example that highlights the advantages of integrating synthetic data into the system identification process.

Satellites equipped with optical sensors capture high-resolution imagery, providing valuable insights into various environmental phenomena. In recent years, there has been a surge of research focused on addressing some challenges in remote sensing, ranging from water detection in diverse landscapes to the segmentation of mountainous and terrains. Ongoing investigations goals to enhance the precision and efficiency of satellite imagery analysis. Especially, there is a growing emphasis on developing methodologies for accurate water body detection, snow and clouds, important for environmental monitoring, resource management, and disaster response. Within this context, this paper focus on the cloud segmentation from remote sensing imagery. Accurate remote sensing data analysis can be challenging due to the presence of clouds in optical sensor-based applications. The quality of resulting products such as applications and research is directly impacted by cloud detection, which plays a key role in the remote sensing data processing pipeline. This paper examines seven cutting-edge semantic segmentation and detection algorithms applied to clouds identification, conducting a benchmark analysis to evaluate their architectural approaches and identify the most performing ones. To increase the model's adaptability, critical elements including the type of imagery and the amount of spectral bands used during training are analyzed. Additionally, this research tries to produce machine learning algorithms that can perform cloud segmentation using only a few spectral bands, including RGB and RGBN-IR combinations. The model's flexibility for a variety of applications and user scenarios is assessed by using imagery from Sentinel-2 and Landsat-8 as datasets. This benchmark can be reproduced using the material from this github link: https://github.com/toelt-llc/cloud_segmentation_comparative., Comment: Submitted to Expert Systems and Applications. Under license CC-BY-NC-ND

In-context system identification aims at constructing meta-models to describe classes of systems, differently from traditional approaches that model single systems. This paradigm facilitates the leveraging of knowledge acquired from observing the behaviour of different, yet related dynamics. This paper discusses the role of meta-model adaptation. Through numerical examples, we demonstrate how meta-model adaptation can enhance predictive performance in three realistic scenarios: tailoring the meta-model to describe a specific system rather than a class; extending the meta-model to capture the behaviour of systems beyond the initial training class; and recalibrating the model for new prediction tasks. Results highlight the effectiveness of meta-model adaptation to achieve a more robust and versatile meta-learning framework for system identification.

State estimation has a pivotal role in several applications, including but not limited to advanced control design. Especially when dealing with nonlinear systems state estimation is a nontrivial task, often entailing approximations and challenging fine-tuning phases. In this work, we propose to overcome these challenges by formulating an in-context state-estimation problem, enabling us to learn a state estimator for a class of (nonlinear) systems abstracting from particular instances of the state seen during training. To this end, we extend an in-context learning framework recently proposed for system identification, showing via a benchmark numerical example that this approach allows us to (i) use training data directly for the design of the state estimator, (ii) not requiring extensive fine-tuning procedures, while (iii) achieving superior performance compared to state-of-the-art benchmarks.

Common regularization algorithms for linear regression, such as LASSO and Ridge regression, rely on a regularization hyperparameter that balances the tradeoff between minimizing the fitting error and the norm of the learned model coefficients. As this hyperparameter is scalar, it can be easily selected via random or grid search optimizing a cross-validation criterion. However, using a scalar hyperparameter limits the algorithm's flexibility and potential for better generalization. In this paper, we address the problem of linear regression with l2-regularization, where a different regularization hyperparameter is associated with each input variable. We optimize these hyperparameters using a gradient-based approach, wherein the gradient of a cross-validation criterion with respect to the regularization hyperparameters is computed analytically through matrix differential calculus. Additionally, we introduce two strategies tailored for sparse model learning problems aiming at reducing the risk of overfitting to the validation data. Numerical examples demonstrate that our multi-hyperparameter regularization approach outperforms LASSO, Ridge, and Elastic Net regression. Moreover, the analytical computation of the gradient proves to be more efficient in terms of computational time compared to automatic differentiation, especially when handling a large number of input variables. Application to the identification of over-parameterized Linear Parameter-Varying models is also presented.

We investigate the approximations needed to efficiently predict the large-scale clustering of matter and dark matter halos in beyond-$\Lambda$CDM scenarios. We examine the normal branch of the Dvali-Gabadadze-Porrati model, the Hu-Sawicki $f(R)$ model, a slowly evolving dark energy, an interacting dark energy model and massive neutrinos. For each, we test approximations for the perturbative kernel calculations, including the omission of screening terms and the use of perturbative kernels based on the Einstein-de Sitter universe; we explore different infrared-resummation schemes, tracer bias models and a linear treatment of massive neutrinos; we employ two models for redshift space distortions, the Taruya-Nishimishi-Saito prescription and the Effective Field Theory of Large-Scale Structure. This work further provides a preliminary validation of the codes being considered by Euclid for the spectroscopic clustering probe in beyond-$\Lambda$CDM scenarios. We calculate and compare the $\chi^2$ statistic to assess the different modelling choices. This is done by fitting the spectroscopic clustering predictions to measurements from numerical simulations and perturbation theory-based mock data. We compare the behaviour of this statistic in the beyond-$\Lambda$CDM cases, as a function of the maximum scale included in the fit, to the baseline $\Lambda$CDM case. We find that the Einstein-de Sitter approximation without screening is surprisingly accurate for all cases when comparing to the halo clustering monopole and quadrupole obtained from simulations. Our results suggest that the inclusion of multiple redshift bins, higher-order multipoles, higher-order clustering statistics (such as the bispectrum) and photometric probes such as weak lensing, will be essential to extract information on massive neutrinos, modified gravity and dark energy., Comment: 29 pages, 10 figures, 4 tables, 3 appendices. Journal accepted version

In this paper, we address the Sim2Real gap in the field of vision-based tactile sensors for classifying object surfaces. We train a Diffusion Model to bridge this gap using a relatively small dataset of real-world images randomly collected from unlabeled everyday objects via the DIGIT sensor. Subsequently, we employ a simulator to generate images by uniformly sampling the surface of objects from the YCB Model Set. These simulated images are then translated into the real domain using the Diffusion Model and automatically labeled to train a classifier. During this training, we further align features of the two domains using an adversarial procedure. Our evaluation is conducted on a dataset of tactile images obtained from a set of ten 3D printed YCB objects. The results reveal a total accuracy of 81.9%, a significant improvement compared to the 34.7% achieved by the classifier trained solely on simulated images. This demonstrates the effectiveness of our approach. We further validate our approach using the classifier on a 6D object pose estimation task from tactile data., Comment: 6 pages, accepted to ICRA 2024

A simplicial complex $H$ consists of a pair of sets $(V,E)$ where $V$ is a set of vertices and $E\subseteq\mathscr{P}(V)$ is a collection of subsets of $V$ closed under taking subsets. Given a simplicial complex $F$ and $n\in \mathbb N$, the extremal number $\text{ex}(n,F)$ is the maximum number of edges that a simplicial complex on $n$ vertices can have without containing a copy of $F$. We initiate the systematic study of extremal numbers in this context by asymptotically determining the extremal numbers of several natural simplicial complexes. In particular, we asymptotically determine the extremal number of a simplicial complex for which the extremal example has more than one incomplete layer., Comment: 22 pages

This work systematically investigates the oxidation of extra virgin olive oil (EVOO) under accelerated storage conditions with UV absorption and total fluorescence spectroscopy. With the large amount of data collected, it proposes a method to monitor the oil's quality based on machine learning applied to highly-aggregated data. EVOO is a high-quality vegetable oil that has earned worldwide reputation for its numerous health benefits and excellent taste. Despite its outstanding quality, EVOO degrades over time owing to oxidation, which can affect both its health qualities and flavour. Therefore, it is highly relevant to quantify the effects of oxidation on EVOO and develop methods to assess it that can be easily implemented under field conditions, rather than in specialized laboratories. The following study demonstrates that fluorescence spectroscopy has the capability to monitor the effect of oxidation and assess the quality of EVOO, even when the data are highly aggregated. It shows that complex laboratory equipment is not necessary to exploit fluorescence spectroscopy using the proposed method and that cost-effective solutions, which can be used in-field by non-scientists, could provide an easily-accessible assessment of the quality of EVOO.

The calibration and training of a neural network is a complex and time-consuming procedure that requires significant computational resources to achieve satisfactory results. Key obstacles are a large number of hyperparameters to select and the onset of overfitting in the face of a small amount of data. In this framework, we propose an innovative training strategy for feed-forward architectures - called split-boost - that improves performance and automatically includes a regularizing behaviour without modeling it explicitly. Such a novel approach ultimately allows us to avoid explicitly modeling the regularization term, decreasing the total number of hyperparameters and speeding up the tuning phase. The proposed strategy is tested on a real-world (anonymized) dataset within a benchmark medical insurance design problem.

We present a direct data-driven approach to synthesize robust control invariant (RCI) sets and their associated gain-scheduled feedback control laws for linear parameter-varying (LPV) systems subjected to bounded disturbances. A data-set consisting of a single state-input-scheduling trajectory is gathered from the system, which is directly utilized to compute polytopic RCI set and controllers by solving a semidefinite program. The proposed method does not require an intermediate LPV model identification step. Through a numerical example, we show that the proposed approach can generate RCI sets with a relatively small number of data samples when the data satisfies certain excitation conditions., Comment: 6 pages, 3 figures. Accepted for publication, IEEE Control System Letters (LCSS) 2023

Is it possible to understand the intricacies of a dynamical system not solely from its input/output pattern, but also by observing the behavior of other systems within the same class? This central question drives the study presented in this paper. In response to this query, we introduce a novel paradigm for system identification, addressing two primary tasks: one-step-ahead prediction and multi-step simulation. Unlike conventional methods, we do not directly estimate a model for the specific system. Instead, we learn a meta model that represents a class of dynamical systems. This meta model is trained on a potentially infinite stream of synthetic data, generated by simulators whose settings are randomly extracted from a probability distribution. When provided with a context from a new system-specifically, an input/output sequence-the meta model implicitly discerns its dynamics, enabling predictions of its behavior. The proposed approach harnesses the power of Transformers, renowned for their \emph{in-context learning} capabilities. For one-step prediction, a GPT-like decoder-only architecture is utilized, whereas the simulation problem employs an encoder-decoder structure. Initial experimental results affirmatively answer our foundational question, opening doors to fresh research avenues in system identification.

The problem of fitting concentric ellipses is a vital problem in image processing, pattern recognition, and astronomy. Several methods have been developed but all address very special cases. In this paper, this problem has been investigated under a more general setting, and two estimators for estimating the parameters have been proposed. Since both estimators are obtained iterative fashion, several numerical schemes are investigated and the best initial guess is determined. Furthermore, the constraint Cram\'{e} Rao lower bound for this problem is derived and it is compared with the variance of each estimator. Finally, our theory is assessed and validated by a series of numerical experiments on both real and synthetic data., Comment: it has a serious mistake that needs major revision and it could take several months to fix

Let $k\geq 3$. Given a $k$-uniform hypergraph $H$, the minimum codegree $\delta(H)$ is the largest $d\in\mathbb{N}$ such that every $(k-1)$-set of $V(H)$ is contained in at least $d$ edges. Given a $k$-uniform hypergraph $F$, the codegree Tur\'an density $\gamma(F)$ of $F$ is the smallest $\gamma \in [0,1]$ such that every $k$-uniform hypergraph on $n$ vertices with $\delta(H)\geq (\gamma + o(1))n$ contains a copy of $F$. Similarly as other variants of the hypergraph Tur\'an problem, determining the codegree Tur\'an density of a hypergraph is in general notoriously difficult and only few results are known. In this work, we show that for every $\varepsilon>0$, there is a $k$-uniform hypergraph $F$ with $0<\gamma(F)<\varepsilon$. This is in contrast to the classical Tur\'an density, which cannot take any value in the interval $(0,k!/k^k)$ due to a fundamental result by Erd\H{o}s., Comment: 12 pages

Given graphs $F$ and $G$, a perfect $F$-tiling in $G$ is a collection of vertex-disjoint copies of $F$ in $G$ that together cover all the vertices in $G$. The study of the minimum degree threshold forcing a perfect $F$-tiling in a graph $G$ has a long history, culminating in the K\"uhn--Osthus theorem [Combinatorica 2009] which resolves this problem, up to an additive constant, for all graphs $F$. In this paper we initiate the study of the analogous question for edge-ordered graphs. In particular, we characterize for which edge-ordered graphs $F$ this problem is well-defined. We also apply the absorbing method to asymptotically determine the minimum degree threshold for forcing a perfect $P$-tiling in an edge-ordered graph, where $P$ is any fixed monotone path., Comment: 29 pages. We have made a number of updates to the paper, particularly in the concluding remarks section

Effective quantification of uncertainty is an essential and still missing step towards a greater adoption of deep-learning approaches in different applications, including mission-critical ones. In particular, investigations on the predictive uncertainty of deep-learning models describing non-linear dynamical systems are very limited to date. This paper is aimed at filling this gap and presents preliminary results on uncertainty quantification for system identification with neural state-space models. We frame the learning problem in a Bayesian probabilistic setting and obtain posterior distributions for the neural network's weights and outputs through approximate inference techniques. Based on the posterior, we construct credible intervals on the outputs and define a surprise index which can effectively diagnose usage of the model in a potentially dangerous out-of-distribution regime, where predictions cannot be trusted.

Black-box optimization refers to the optimization problem whose objective function and/or constraint sets are either unknown, inaccessible, or non-existent. In many applications, especially with the involvement of humans, the only way to access the optimization problem is through performing physical experiments with the available outcomes being the preference of one candidate with respect to one or many others. Accordingly, the algorithm so-called Active Preference Learning has been developed to exploit this specific information in constructing a surrogate function based on standard radial basis functions, and then forming an easy-to-solve acquisition function which repetitively suggests new decision vectors to search for the optimal solution. Based on this idea, our approach aims to extend the algorithm in such a way that can exploit further information effectively, which can be obtained in reality such as: 5-point Likert type scale for the outcomes of the preference query (i.e., the preference can be described in not only "this is better than that" but also "this is much better than that" level), or multiple outcomes for a single preference query with possible additive information on how certain the outcomes are. The validation of the proposed algorithm is done through some standard benchmark functions, showing a promising improvement with respect to the state-of-the-art algorithm.

In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs of objects; (2) are always able to pick the best preferred object. In many situations, they may be instead choosing out of a set with more than two elements and, because of lack of information and/or incomparability (objects with contradictory characteristics), they may not able to select a single most preferred object. To address these situations, we need a choice-model which allows an individual to express a set-valued choice. Choice functions provide such a mathematical framework. We propose a Gaussian Process model to learn choice functions from choice-data. The proposed model assumes a multiple utility representation of a choice function based on the concept of Pareto rationalization, and derives a strategy to learn both the number and the values of these latent multiple utilities. Simulation experiments demonstrate that the proposed model outperforms the state-of-the-art methods.

In this paper, we address the problem of estimating the in-hand 6D pose of an object in contact with multiple vision-based tactile sensors. We reason on the possible spatial configurations of the sensors along the object surface. Specifically, we filter contact hypotheses using geometric reasoning and a Convolutional Neural Network (CNN), trained on simulated object-agnostic images, to promote those that better comply with the actual tactile images from the sensors. We use the selected sensors configurations to optimize over the space of 6D poses using a Gradient Descent-based approach. We finally rank the obtained poses by penalizing those that are in collision with the sensors. We carry out experiments in simulation using the DIGIT vision-based sensor with several objects, from the standard YCB model set. The results demonstrate that our approach estimates object poses that are compatible with actual object-sensor contacts in $87.5\%$ of cases while reaching an average positional error in the order of $2$ centimeters. Our analysis also includes qualitative results of experiments with a real DIGIT sensor., Comment: Accepted for publication at 2023 IEEE International Conference on Robotics and Automation (ICRA)

Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled discrete distributions, is even harder. Existing approaches to address these problems have shortcomings: they are biased, heuristic, work only for some distributions, and/or cannot be applied to all information-theoretic metrics. Here, we propose a fast, semi-analytical estimator for sparsely sampled distributions that is efficient, precise, and general. Its derivation is grounded in probabilistic considerations and uses a hierarchical Bayesian approach to extract as much information as possible from the few observations available. Our approach provides estimates of the Shannon entropy with precision at least comparable to the state of the art, and most often better. It can also be used to obtain accurate estimates of any other information-theoretic metric, including the notoriously challenging Kullback-Leibler divergence. Here, again, our approach performs consistently better than existing estimators., Comment: 10 pages, 5 figures

In 2003, Bohman, Frieze, and Martin initiated the study of randomly perturbed graphs and digraphs. For digraphs, they showed that for every $\alpha>0$, there exists a constant $C$ such that for every $n$-vertex digraph of minimum semi-degree at least $\alpha n$, if one adds $Cn$ random edges then asymptotically almost surely the resulting digraph contains a consistently oriented Hamilton cycle. We generalize their result, showing that the hypothesis of this theorem actually asymptotically almost surely ensures the existence of every orientation of a cycle of every possible length, simultaneously. Moreover, we prove that we can relax the minimum semi-degree condition to a minimum total degree condition when considering orientations of a cycle that do not contain a large number of vertices of indegree $1$. Our proofs make use of a variant of an absorbing method of Montgomery., Comment: 24 pages, 7 figures. Author accepted manuscript, to appear in Combinatorics, Probability and Computing

Given $\alpha>0$ and an integer $\ell\geq5$, we prove that every sufficiently large $3$-uniform hypergraph $H$ on $n$ vertices in which every two vertices are contained in at least $\alpha n$ edges contains a copy of $C_\ell^{-}$, a tight cycle on $\ell$ vertices minus one edge. This improves a previous result by Balogh, Clemen, and Lidick\'y., Comment: 6 pages, 1 figure

We develop a pipeline to set new constraints on scale-independent modified gravity, from the galaxy power spectrum in redshift space of BOSS DR12. The latter is modelled using the effective field theory of large-scale structure up to 1-loop order in perturbation theory. We test our pipeline on synthetic and simulated data, to assess systematic biases on the inferred cosmological parameters due to marginalization and theoretical errors, and we apply it to the normal branch of the DGP model with a $\Lambda$CDM background. When applied to synthetic data and cosmological simulations, we observe biased posteriors due to the strong degeneracy between the nDGP parameter $\Omega_{\rm rc}$ and the primordial amplitude of fluctuations $A_s$. Fixing the latter to the Planck central value, we obtain a posterior distribution with $\Omega_{\rm rc}\lesssim 0.65$ at 95$\%$ C.L., under the assumption of a flat prior on $\log_{10} \Omega_{\rm rc}$. This upper bound, however, depends strongly on the prior on $\Omega_{\rm rc}$. To alleviate this effect, we provide an upper bound based on the Bayes factor between the nDGP model and $\Lambda$CDM model, which gives $\Omega_{\rm rc}\lesssim 0.2$ at 95$\%$ C.L.., Comment: 33 pages, 10 figures

We show that $k$-uniform hypergraphs on $n$ vertices whose codegree is at least $(2/3 + o(1))n$ can be decomposed into tight cycles, subject to the trivial divisibility conditions. As a corollary, we show those graphs contain tight Euler tours as well. In passing, we also investigate decompositions into tight paths. In addition, we also prove an alternative condition for building absorbers for edge-decompositions of arbitrary $k$-uniform hypergraphs, which should be of independent interest., Comment: v3: including referee comments. Accepted to JCTB

Should Primordial Black Holes (PBHs) exist in nature, they would inevitably accrete baryonic matter in their vicinity. In turn, the consequent emission of high-energy radiation could affect the thermal history of the universe to an extent that can be probed with a number of cosmological observables such as the Cosmic Microwave Background (CMB) anisotropies. However, our understanding of the accretion and radiation emission processes in the context of PBHs is still in its infancy, and very large theoretical uncertainties affect the resulting constraints on the PBH abundance. Building on state-of-the-art literature, in this work we take a step towards the development of a more realistic picture of PBH accretion by accounting for the contribution of outflows. Specifically, we derive CMB-driven constraints on the PBH abundance for various accretion geometries, ionization models and mass distributions in absence and in presence of mechanical feedback and non-thermal emissions due to the outflows. As a result, we show that the presence of such outflows introduces an additional layer of uncertainty that needs to be taken into account when quoting cosmological constraints on the PBH abundance, with important consequences in particular in the LIGO-Virgo-KAGRA observational window., Comment: 34 pages, 8 figures

An increasing number of nonspecialist robotic users demand easy-to-use machines. In the context of visual servoing, the removal of explicit image processing is becoming a trend, allowing an easy application of this technique. This work presents a deep learning approach for solving the perception problem within the visual servoing scheme. An artificial neural network is trained using the supervision coming from the knowledge of the controller and the visual features motion model. In this way, it is possible to give a geometrical interpretation to the estimated visual features, which can be used in the analytical law of the visual servoing. The approach keeps perception and control decoupled, conferring flexibility and interpretability on the whole framework. Simulated and real experiments with a robotic manipulator validate our approach., Comment: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2022

This paper presents an algorithm for direct continuous-time (CT) identification of linear switched state-space (LSS) models. The key idea for direct CT identification is based on an integral architecture consisting of an LSS model followed by an integral block. This architecture is used to approximate the continuous-time state map of a switched system. A properly constructed objective criterion is proposed based on the integral architecture in order to estimate the unknown parameters and signals of the LSS model. A coordinate descent algorithm is employed to optimize this objective, which alternates between computing the unknown model matrices, switching sequence and estimating the state variables. The effectiveness of the proposed algorithm is shown via a simulation case study., Comment: Preprint submitted to IFAC World Congress 2023

Let $R(G)$ be the two-colour Ramsey number of a graph $G$. In this note, we prove that for any non-decreasing function $n \leq f(n) \leq R(K_n)$, there exists a sequence of connected graphs $(G_n)_{n\in\mathbb N}$, with $|V(G_n)| = n$ for all $n \geq 1$, such that $R(G_n) = \Theta(f(n))$. In contrast, we also show that an analogous statement does not hold for hypergraphs of uniformity at least $5$. We also use our techniques to answer a question posed by DeBiasio about the existence of sequences of graphs whose $2$-colour Ramsey number is linear whereas their $3$-colour Ramsey number has superlinear growth., Comment: Accepted to The Electronic Journal of Combinatorics