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Any discrete distribution with support on $\{0,\ldots, d\}$ can be constructed as the distribution of sums of Bernoulli variables. We prove that the class of $d$-dimensional Bernoulli variables $\boldsymbol{X}=(X_1,\ldots, X_d)$ whose sums $\sum_{i=1}^dX_i$ have the same distribution $p$ is a convex polytope $\mathcal{P}(p)$ and we analytically find its extremal points. Our main result is to prove that the Hausdorff measure of the polytopes $\mathcal{P}(p), p\in \mathcal{D}_d,$ is a continuous function $l(p)$ over $\mathcal{D}_d$ and it is the density of a finite measure $\mu_s$ on $\mathcal{D}_d$ that is Hausdorff absolutely continuous. We also prove that the measure $\mu_s$ normalized over the simplex $\mathcal{D}$ belongs to the class of Dirichlet distributions. We observe that the symmetric binomial distribution is the mean of the Dirichlet distribution on $\mathcal{D}$ and that when $d$ increases it converges to the mode.

Many successful methods to learn dynamical systems from data have recently been introduced. Such methods often rely on the availability of the system's full state. However, this underlying hypothesis is rather restrictive as it is typically not confirmed in practice, leaving us with partially observed systems. Utilizing the Mori-Zwanzig (MZ) formalism from statistical physics, we demonstrate that Constant Lag Neural Delay Differential Equations (NDDEs) naturally serve as suitable models for partially observed states. In empirical evaluation, we show that such models outperform existing methods on both synthetic and experimental data.

Let $q$ be a prime power, $\ell$ a prime not dividing $q$, and $e$ the order of $q$ modulo $\ell$. We show that the geometric realisation of the nerve of the transporter category of $e$-split Levi subgroups of a finite reductive group $G$ over $\mathbb{F}_q$ is homotopy equivalent to the classifying space $BG$ up to $\ell$-completion. We suggest a generalisation of this equivalence to the setting of $\mathbb{Z}_\ell$-reflection cosets and establish a related fact involving the associated orbit spaces. We also establish a Dade-like formula for unipotent characters of $\mathbb{Z}_\ell$-spetses inspired by a question of Brou\'e., Comment: 18 pages

The paper revisits a Lyapunov-based feedback control to implement spacecraft orbital transfer maneuvers. The spacecraft equations of motion in the form of Gauss Variational Equations (GVEs) are used. By shaping the Lyapunov function using barrier functions, we demonstrate that state and control constraints during orbital maneuvers can be enforced. Simulation results from orbital maneuvering scenarios are reported. The synergistic use of the reference governor in conjunction with the barrier functions is proposed to ensure convergence to the target orbit (liveness) while satisfying the imposed constraints., Comment: This is the author's original manuscript (pre-print) of the paper AAS 23-292 presented at 33rd AAS/AIAA Space Flight Mechanics Meeting, Austin, Texas, January 15-19 2023, https://www.space-flight.org/docs/2023_winter/33rdSFFM-Full_Program_Abstracts.pdf

We prove that the Parker--Semeraro systems satisfy six of the nine Kessar--Linckelmann--Lynd--Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain that Robinson's ordinary weight conjecture holds for the principal $3$-block of Aut$(G_2(3))$, the principal $5$-blocks of $HN$, $BM$, Aut$(HN)$, $Ly$, the principal $7$-block of $M$, and the principal $p$-blocks of $G_2(p)$ for $p\geq 3 $., Comment: 27 pages, 4 tables

Building on the one-to-one relationship between generalized FGM copulas and multivariate Bernoulli distributions, we prove that the class of multivariate distributions with generalized FGM copulas is a convex polytope. Therefore, we find sharp bounds in this class for many aggregate risk measures, such as value-at-risk, expected shortfall, and entropic risk measure, by enumerating their values on the extremal points of the convex polytope. This is infeasible in high dimensions. We overcome this limitation by considering the aggregation of identically distributed risks with generalized FGM copula specified by a common parameter $p$. In this case, the analogy with the geometrical structure of the class of Bernoulli distribution allows us to provide sharp analytical bounds for convex risk measures., Comment: 30 pages, 1 figure

In the pursuit of advancing natural language processing for the Italian language, we introduce a state-of-the-art Large Language Model (LLM) based on the novel Meta LLaMA-3 model: LLaMAntino-3-ANITA-8B-Inst-DPO-ITA. We fine-tuned the original 8B parameters instruction tuned model using the Supervised Fine-tuning (SFT) technique on the English and Italian language datasets in order to improve the original performance. Consequently, a Dynamic Preference Optimization (DPO) process has been used to align preferences, avoid dangerous and inappropriate answers, and limit biases and prejudices. Our model leverages the efficiency of QLoRA to fine-tune the model on a smaller portion of the original model weights and then adapt the model specifically for the Italian linguistic structure, achieving significant improvements in both performance and computational efficiency. Concurrently, DPO is employed to refine the model's output, ensuring that generated content aligns with quality answers. The synergy between SFT, QLoRA's parameter efficiency and DPO's user-centric optimization results in a robust LLM that excels in a variety of tasks, including but not limited to text completion, zero-shot classification, and contextual understanding. The model has been extensively evaluated over standard benchmarks for the Italian and English languages, showing outstanding results. The model is freely available over the HuggingFace hub and, examples of use can be found in our GitHub repository. https://huggingface.co/swap-uniba/LLaMAntino-3-ANITA-8B-Inst-DPO-ITA

arcjetCV is an open-source Python software designed to automate time-resolved measurements of heatshield material recession and recession rates from arcjet test video footage. This new automated and accessible capability greatly exceeds previous manual extraction methods, enabling rapid and detailed characterization of material recession for any sample with a profile video. arcjetCV automates the video segmentation process using machine learning models, including a one-dimensional (1D) Convolutional Neural Network (CNN) to infer the time-window of interest, a two-dimensional (2D) CNN for image and edge segmentation, and a Local Outlier Factor (LOF) for outlier filtering. A graphical user interface (GUI) simplifies the user experience and an application programming interface (API) allows users to call the core functions from scripts, enabling video batch processing. arcjetCV's capability to measure time-resolved recession in turn enables characterization of non-linear processes (shrinkage, swelling, melt flows, etc.), contributing to higher fidelity validation and improved modeling of heatshield material performance. The source code associated with this article can be found at https://github.com/magnus-haw/arcjetCV.

If $\mathcal{F}$ is a saturated fusion system on a finite $p$-group $S$, we define the Chern subring $Ch(\mathcal{F})$ of $\mathcal{F}$ to be the subring of the mod-$p$ cohomology $H^*(S)$ of $S$ generated by the Chern classes of $\mathcal{F}$-stable representations of $S$. We show that $Ch(\mathcal{F})$ is contained in $H^*(\mathcal{F})$ and apply a result of Green and the first author to describe its spectrum in terms of a certain category of elementary abelian subgroups of $S$. We obtain similar results for various related subrings, including those generated by characteristic classes of $\mathcal{F}$-stable $S$-sets., Comment: 14 pages

Large Language Models represent state-of-the-art linguistic models designed to equip computers with the ability to comprehend natural language. With its exceptional capacity to capture complex contextual relationships, the LLaMA (Large Language Model Meta AI) family represents a novel advancement in the field of natural language processing by releasing foundational models designed to improve the natural language understanding abilities of the transformer architecture thanks to their large amount of trainable parameters (7, 13, and 70 billion parameters). In many natural language understanding tasks, these models obtain the same performances as private company models such as OpenAI Chat-GPT with the advantage to make publicly available weights and code for research and commercial uses. In this work, we investigate the possibility of Language Adaptation for LLaMA models, explicitly focusing on addressing the challenge of Italian Language coverage. Adopting an open science approach, we explore various tuning approaches to ensure a high-quality text generated in Italian suitable for common tasks in this underrepresented language in the original models' datasets. We aim to release effective text generation models with strong linguistic properties for many tasks that seem challenging using multilingual or general-purpose LLMs. By leveraging an open science philosophy, this study contributes to Language Adaptation strategies for the Italian language by introducing the novel LLaMAntino family of Italian LLMs.

The key result of this paper is to find all the joint distributions of random vectors whose sums $S=X_1+\ldots+X_d$ are minimal in convex order in the class of symmetric Bernoulli distributions. The minimal convex sums distributions are known to be strongly negatively dependent. Beyond their interest per se, these results enable us to explore negative dependence within the class of copulas. In fact, there are two classes of copulas that can be built from multivariate symmetric Bernoulli distributions: the extremal mixture copulas, and the FGM copulas. We study the extremal negative dependence structure of the copulas corresponding to symmetric Bernoulli vectors with minimal convex sums and we explicitly find a class of minimal dependence copulas. Our main results stem from the geometric and algebraic representations of multivariate symmetric Bernoulli distributions, which effectively encode several of their statistical properties.

Our aim is to predict how often genic and non-genic promoters fire within a cell. We first review a parsimonious pan-genomic model for genome organization and gene regulation, where transcription rate is determined by proximity in 3D space of promoters to clusters containing appropriate factors and RNA polymerases -- structures variously called transcription factories, hubs, and condensates. This model allows reconciliation of conflicting results indicating that regulatory mammalian networks are both simple (as over-expressing just 4 transcription factors switches cell state) and complex (as genome-wide association studies show phenotypes like cell type are determined by thousands of loci rarely encoding such factors). It also yields simple explanations of how mysterious motifs like quantitative trait loci, enhancers, and silencers work. We then present 3D polymer simulations, and a proximity formula based on our biological model that enables prediction of transcriptional activities of all promoters in three human cell types. This simple fitting-free formula contains just one variable (distance on the genetic map to the nearest active promoter), and we suggest it can be applied to any organism.

Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard Ordinary Differential Equations (ODE), or data-driven approximations such as Neural Ordinary Differential Equations (NODE). To circumvent this issue, latent variables are typically introduced to solve the dynamics of the system in a higher dimensional space and obtain the solution as a projection to the original space. However, this solution lacks physical interpretability. In contrast, Delay Differential Equations (DDEs), and their data-driven approximated counterparts, naturally appear as good candidates to characterize such systems. In this work we revisit the recently proposed Neural DDE by introducing Neural State-Dependent DDE (SDDDE), a general and flexible framework that can model multiple and state- and time-dependent delays. We show that our method is competitive and outperforms other continuous-class models on a wide variety of delayed dynamical systems. Code is available at the repository \href{https://github.com/thibmonsel/Time-and-State-Dependent-Neural-Delay-Differential-Equations}{here}.

TomoSAM has been developed to integrate the cutting-edge Segment Anything Model (SAM) into 3D Slicer, a highly capable software platform used for 3D image processing and visualization. SAM is a promptable deep learning model that is able to identify objects and create image masks in a zero-shot manner, based only on a few user clicks. The synergy between these tools aids in the segmentation of complex 3D datasets from tomography or other imaging techniques, which would otherwise require a laborious manual segmentation process. The source code associated with this article can be found at https://github.com/fsemerar/SlicerTomoSAM

We present Surf-NeRF, a modified implementation of the recently introduced Shadow Neural Radiance Field (S-NeRF) model. This method is able to synthesize novel views from a sparse set of satellite images of a scene, while accounting for the variation in lighting present in the pictures. The trained model can also be used to accurately estimate the surface elevation of the scene, which is often a desirable quantity for satellite observation applications. S-NeRF improves on the standard Neural Radiance Field (NeRF) method by considering the radiance as a function of the albedo and the irradiance. Both these quantities are output by fully connected neural network branches of the model, and the latter is considered as a function of the direct light from the sun and the diffuse color from the sky. The implementations were run on a dataset of satellite images, augmented using a zoom-and-crop technique. A hyperparameter study for NeRF was carried out, leading to intriguing observations on the model's convergence. Finally, both NeRF and S-NeRF were run until 100k epochs in order to fully fit the data and produce their best possible predictions. The code related to this article can be found at https://github.com/fsemerar/surfnerf.

The goal of this paper is to investigate how the marginal and dependence structures of a variety of multivariate L\'evy models affect calibration and pricing. To this aim, we study the approaches of Luciano and Semeraro (2010) and Ballotta and Bonfiglioli (2016) to construct multivariate processes. We explore several calibration methods that can be used to fine-tune the models, and that deal with the observed trade-off between marginal and correlation fit. We carry out a thorough empirical analysis to evaluate the ability of the models to fit market data, price exotic derivatives, and embed a rich dependence structure. By merging theoretical aspects with the results of the empirical test, we provide tools to make suitable decisions about the models and calibration techniques to employ in a real context.

We propose AeroSPEED, a solver based on the Spectral Element Method (SEM) that solves the aeroacoustic Lighthill's wave equation. First, the fluid solution is computed employing a cell centered Finite Volume method. Then, AeroSPEED maps the sound source coming from the flow solution onto the acoustic grid, where finally the Lighthill's wave equation is solved. An ad-hoc projection strategy is adopted to apply the flow source term in the acoustic solver. A model problem with a manufactured solution and the Noise Box test case are used as benchmark for the acoustic problem. We studied the noise generated by the complex flow field around tandem cylinders as a relevant aeroacoustic application. AeroSPEED is an effective and accurate solver for both acoustics and aeroacoustic problems.

Let $\ell$ be a prime. If ${\mathbf G} $ is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from $\ell$, and $\ell$ is a good prime for ${\mathbf G}$, we show that the number of weights of the $\ell$-fusion system of ${\mathbf G}$ is equal to the number of irreducible characters of its Weyl group. The proof relies on the classification of $\ell$-stubborn subgroups in compact Lie groups.

The spread of machine learning (ML) techniques in combination with the availability of high-quality experimental and numerical data boosted in recent years numerous applications in fluid mechanics. Among those, examples of closure models for turbulent flows or data-assimilation based on neural networks (NN) are already numerous. However, it is well known that these techniques are prone to over-fit and necessitate an exceedingly large amount of data, unless enforcing physical constraints. We address those limitations by applying graph neural networks (GNN). This architecture is characterized by a net of nodes that can be easily adapted to unstructured meshes. Moreover, it is known GNN can show remarkable generalization capabilities as compared to standard network models. Here, we demonstrate the use of GNN by interfacing them with a finite elements (FEM) solver for the supervised learning of Reynolds-averaged Navier--Stokes equations. We consider as a test-case the flow past bluff bodies; we train the model using the wake past a cylinder, at different Reynolds numbers 40

We study the active work fluctuations of an active Ornstein-Uhlenbeck particle in the presence of a confining harmonic potential. We tackle the problem analytically both for stationary and generic uncorrelated initial states. Our results show that harmonic confinement can induce singularities in the active work rate function, with linear stretches at large positive and negative active work, at sufficiently large active and harmonic force constants. These singularities originate from big jumps in the displacement and in the active force, occurring at the initial or ending points of trajectories and marking the relevance of boundary terms in this problem., Comment: 6 pages, 3 figures

Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of choosing a risk-neutral measure on convex derivative pricing in incomplete markets. We find analytical bounds for prices of European and American options in the class of all risk-neutral measures, and we also find simulated bounds for given classes of perturbations of the minimal martingale equivalent measure.

Human-robot interaction (HRI) research is progressively addressing multi-party scenarios, where a robot interacts with more than one human user at the same time. Conversely, research is still at an early stage for human-robot collaboration. The use of machine learning techniques to handle such type of collaboration requires data that are less feasible to produce than in a typical HRC setup. This work outlines scenarios of concurrent tasks for non-dyadic HRC applications. Based upon these concepts, this study also proposes an alternative way of gathering data regarding multi-user activity, by collecting data related to single users and merging them in post-processing, to reduce the effort involved in producing recordings of pair settings. To validate this statement, 3D skeleton poses of activity of single users were collected and merged in pairs. After this, such datapoints were used to separately train a long short-term memory (LSTM) network and a variational autoencoder (VAE) composed of spatio-temporal graph convolutional networks (STGCN) to recognise the joint activities of the pairs of people. The results showed that it is possible to make use of data collected in this way for pair HRC settings and get similar performances compared to using training data regarding groups of users recorded under the same settings, relieving from the technical difficulties involved in producing these data. The related code and collected data are publicly available., Comment: This is the accepted manuscript. Please see published version at https://ieeexplore.ieee.org/document/10191782

Surgery for gliomas (intrinsic brain tumors), especially when low-grade, is challenging due to the infiltrative nature of the lesion. Currently, no real-time, intra-operative, label-free and wide-field tool is available to assist and guide the surgeon to find the relevant demarcations for these tumors. While marker-based methods exist for the high-grade glioma case, there is no convenient solution available for the low-grade case; thus, marker-free optical techniques represent an attractive option. Although RGB imaging is a standard tool in surgical microscopes, it does not contain sufficient information for tissue differentiation. We leverage the richer information from hyperspectral imaging (HSI), acquired with a snapscan camera in the 468-787 nm range, coupled to a surgical microscope, to build a deep-learning-based diagnostic tool for cancer resection with potential for intra-operative guidance. However, the main limitation of the HSI snapscan camera is the image acquisition time, limiting its widespread deployment in the operation theater. Here, we investigate the effect of HSI channel reduction and pre-selection to scope the design space for the development of cheaper and faster sensors. Neural networks are used to identify the most important spectral channels for tumor tissue differentiation, optimizing the trade-off between the number of channels and precision to enable real-time intra-surgical application. We evaluate the performance of our method on a clinical dataset that was acquired during surgery on five patients. By demonstrating the possibility to efficiently detect low-grade glioma, these results can lead to better cancer resection demarcations, potentially improving treatment effectiveness and patient outcome., Comment: SPIE Photonics West 2023 conference Optical Biopsy XXI: Toward Real-Time Spectroscopic Imaging and Diagnosis. 18 pages, 11 figures

Transcription is a fundamental cellular process, and the first step of gene expression. In human cells, it depends on the binding to chromatin of various proteins, including RNA polymerases and numerous transcription factors (TFs). Observations indicate that these proteins tend to form macromolecular clusters, known as transcription factories, whose morphology and composition is still debated. While some microscopy experiments have revealed the presence of specialised factories, composed of similar TFs transcribing families of related genes, sequencing experiments suggest instead that mixed clusters may be prevalent, as a panoply of different TFs binds promiscuously the same chromatin region. The mechanisms underlying the formation of specialised or mixed factories remain elusive. With the aim of finding such mechanisms, here we develop a chromatin polymer model mimicking the chromatin binding-unbinding dynamics of different types of complexes of TFs. Surprisingly, both specialised (i.e., demixed) and mixed clusters spontaneously emerge, and which of the two types forms depends mainly on cluster size. The mechanism promoting mixing is the presence of non-specific interactions between chromatin and proteins, which become increasingly important as clusters become larger. This result, that we observe both in simple polymer models and more realistic ones for human chromosomes, reconciles the apparently contrasting experimental results obtained. Additionally, we show how the introduction of different types of TFs strongly affects the emergence of transcriptional networks, providing a pathway to investigate transcriptional changes following gene editing or naturally occurring mutations., Comment: 16 pages, 8 figures

The motion of a Brownian particle in the presence of Coulomb friction and an asymmetric spatial potential was evaluated in this study. The system exhibits a ratchet effect, i.e., an average directed motion even in the absence of an external force, induced by the coupling of non-equilibrium conditions with the spatial asymmetry. Both the average motion and the fluctuations of the Brownian particle were analysed. The stationary velocity shows a non-monotonic behaviour as a function of both the temperature and the viscosity of the bath. The diffusion properties of the particle, which show several time regimes, were also investigated. To highlight the role of non-linear friction in the dynamics, a comparison is presented with a linear model of a Brownian particle driven by a constant external force, which allows for analytical treatment. In particular, the study unveils that the passage times between different temporal regimes are strongly affected by the presence of Coulomb friction., Comment: 6 pages, 5 figures

The paper considers the application of feedback control to orbital transfer maneuvers subject to constraints on the spacecraft thrust and on avoiding the collision with the primary body. Incremental reference governor (IRG) strategies are developed to complement the nominal Lyapunov controller, derived based on Gauss Variational Equations, and enforce the constraints. Simulation results are reported that demonstrate the successful constrained orbital transfer maneuvers with the proposed approach. A Lyapunov function based IRG and a prediction-based IRG are compared. While both implementations successfully enforce the constraints, a prediction-based IRG is shown to result in faster maneuvers., Comment: 17 pages, 14 figures, submitted to Advanced Control for Applications

We employ the diffusing transcription factors model for numerical simulation of chromatin topology conformations and transcriptional processes of human chromatin. Simulations of a short chromatin filament reveal different possible pathways to regulate transcription: it is shown that the transcriptional activity profile can be regulated and controlled by either acting on the chain structural properties, or on external factors, such as the number of transcription factors. Additionally, comparisons between GRO-seq experimental data and large scale numerical simulation of entire chromosomes from the human umbilical vein endothelial cell and the B-lmphocyte GM12878 show that the model provides reliable and statistically significant predictions for transcription across different cell-lines., Comment: 26 pages, 10 figures