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Let $X=(X_1,\ldots,X_p)$ be a $p$-variate random vector and $F$ a fixed finite set. In a number of applications, mainly in genetics, it turns out that $X_i\in F$ for each $i=1,\ldots,p$. Despite the latter fact, to obtain a knockoff $\widetilde{X}$ (in the sense of \cite{CFJL18}), $X$ is usually modeled as an absolutely continuous random vector. While comprehensible from the point of view of applications, this approximate procedure does not make sense theoretically, since $X$ is supported by the finite set $F^p$. In this paper, explicit formulae for the joint distribution of $(X,\widetilde{X})$ are provided when $P(X\in F^p)=1$ and $X$ is exchangeable or partially exchangeable. In fact, when $X_i\in F$ for all $i$, there seem to be various reasons for assuming $X$ exchangeable or partially exchangeable. The robustness of $\widetilde{X}$, with respect to the de Finetti's measure $\pi$ of $X$, is investigated as well. Let $\mathcal{L}_\pi(\widetilde{X}\mid X=x)$ denote the conditional distribution of $\widetilde{X}$, given $X=x$, when the de Finetti's measure is $\pi$. It is shown that $$\norm{\mathcal{L}_{\pi_1}(\widetilde{X}\mid X=x)-\mathcal{L}_{\pi_2}(\widetilde{X}\mid X=x)}\le c(x)\,\norm{\pi_1-\pi_2}$$ where $\norm{\cdot}$ is total variation distance and $c(x)$ a suitable constant. Finally, a numerical experiment is performed. Overall, the knockoffs of this paper outperform the alternatives (i.e., the knockoffs obtained by giving $X$ an absolutely continuous distribution) as regards the false discovery rate but are slightly weaker in terms of power., Comment: submitted paper. 24 pages. 5 figures

In this paper, we compare the effectiveness of a two-stage control strategy for the energy management system (EMS) of a grid-connected microgrid under uncertain solar irradiance and load demand using a real-world dataset from an island in Southeast Asia (SEA). The first stage computes a day-ahead commitment for power profile exchanged with the main grid, while the second stage focuses on real-time controls to minimize the system operating cost. Given the challenges in accurately forecasting solar irradiance for a long time horizon, scenario-based stochastic programming (SP) is considered for the first stage. For the second stage, as the most recent weather conditions can be used, several methodologies to handle the uncertainties are investigated, including: (1) the rule-based method historically deployed on EMS, (2) model predictive controller (MPC) using either an explicit forecast or scenario-based stochastic forecast, and (3) Deep Reinforcement Learning (DRL) computing its own implicit forecast through a distribution of costs. Performances of these methodologies are compared in terms of precision with a reference control assuming perfect forecast -- i.e. representing the minimal achievable operation cost in theory. Obtained results show that MPC with a stochastic forecast outperforms MPC with a simple deterministic prediction. This suggests that using an explicit forecast, even within a short time window, is challenging. Using weather conditions can, however, be more efficient, as demonstrated by DRL (with implicit forecast), outperforming MPC with stochastic forecast by 1.3\%., Comment: Published in Sustainable Energy, Grids and Networks 2024

Among the key contributions of Vitamin-V (2023-2025 Horizon Europe project), we develop a complete RISC-V open-source software stack for cloud services with comparable performance to the cloud-dominant x86 counterpart. In this paper, we detail the software suites and applications ported plus the three cloud setups under evaluation., Comment: RISC-V Summit Europe 2024, 24-28 June 2024

Deep learning, particularly Convolutional Neural Networks (CNNs), has gained significant attention for its effectiveness in computer vision, especially in agricultural tasks. Recent advancements in instance segmentation have improved image classification accuracy. In this work, we introduce a comprehensive dataset for training neural networks to detect weeds and soy plants through instance segmentation. Our dataset covers various stages of soy growth, offering a chronological perspective on weed invasion's impact, with 1,000 meticulously annotated images. We also provide 6 state of the art models, trained in this dataset, that can understand and detect soy and weed in every stage of the plantation process. By using this dataset for weed and soy segmentation, we achieved a segmentation average precision of 79.1% and an average recall of 69.2% across all plant classes, with the YOLOv8X model. Moreover, the YOLOv8M model attained 78.7% mean average precision (mAp-50) in caruru weed segmentation, 69.7% in grassy weed segmentation, and 90.1% in soy plant segmentation., Comment: 11th IEEE International Conference on Cybernetics and Intelligent Systems (CIS)

Parikh-collinear morphisms have the property that all the Parikh vectors of the images of letters are collinear, i.e., the associated adjacency matrix has rank 1. In the conference DLT-WORDS 2023 we showed that fixed points of Parikh-collinear morphisms are automatic. We also showed that the abelian complexity function of a binary fixed point of such a morphism is automatic under some assumptions. In this note, we fully generalize the latter result. Namely, we show that the abelian complexity function of a fixed point of an arbitrary, possibly erasing, Parikh-collinear morphism is automatic. Furthermore, a deterministic finite automaton with output generating this abelian complexity function is provided by an effective procedure. To that end, we discuss the constant of recognizability of a morphism and the related cutting set., Comment: 18 pages, 2 figures, long version of [M. Rigo, M. Stipulanti, M. A. Whiteland, Automaticity and Parikh-collinear morphisms. In: Combinatorics on Words. Lecture Notes in Comput. Sci., vol. 13899, pp. 247-260. Springer, 2023]

Semiconductor moir\'e systems, characterized by their periodic spatial light emission, unveil a new paradigm of active metasurfaces. Here, we show that ferroelectric moir\'e domains formed in a twisted hexagonal boron nitride (t-hBN) substrate can modulate light emission from an adjacent semiconductor MoSe$_2$ monolayer, enhancing its functionality as an active metasurface. The electrostatic potential at the surface of the t-hBN substrate provides a simple way to confine excitons in the MoSe$_2$ monolayer. The excitons confined within the domains and at the domain walls are spectrally separated due to a pronounced Stark shift. Moreover, the patterned light emission can be dynamically controlled by electrically gating the ferroelectric domains, introducing a novel functionality beyond conventional semiconductor moir\'e systems. Our findings chart an exciting pathway for integrating nanometer-scale moir\'e ferroelectric domains with various optically active functional layers, paving the way for advanced nanophotonic applications.

A Multiverse can arise from landscapes without de Sitter minima. It can be populated during a period of eternal inflation without trans-Planckian field excursions and without flat potentials. This Multiverse can explain the values of the cosmological constant and of the weak scale. In the process of proving these statements we derive a few simple, but counter-intuitive results. We show that it is easy to write models of eternal inflation compatible with the distance and refined de Sitter conjectures. Secondly, tunneling transitions that move fields from a lower-energy vacuum to a higher-energy vacuum and generate baby Universes are possible, and occur during eternal inflation. Finally, we relax the assumption of no de Sitter minima and show that this more standard Multiverse can be populated by Coleman-De Luccia transitions in about 100 $e$-folds of inflation., Comment: 16 pages + references, 8 figures; updates in agreement with published version

Let $\alpha_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the predictive distributions of a sequence $(X_1,X_2,\ldots)$ of $p$-dimensional random vectors. Suppose $$\alpha_n= \mathcal{N} _p (M_n,Q_n)$$ where $M_n=\frac{1}{n}\sum_{i=1}^nX_i$ and $Q_n=\frac{1}{n}\sum_{i=1}^n(X_i-M_n)(X_i-M_n)^t$. Then, there is a random probability measure $\alpha$ on the Borel subsets of $\mathbb{R}^p$ such that $\lVert\alpha_n-\alpha\rVert\overset{a.s.}\longrightarrow 0$ where $\lVert\cdot\rVert$ is total variation distance. An explicit expression for $\alpha$ is provided and the convergence rate of $\lVert\alpha_n-\alpha\rVert$ is shown to be arbitrarily close to $n^{-1/2}$. Moreover, it is still true that $\lVert\alpha_n-\alpha\rVert\overset{a.s.}\longrightarrow 0$ even if $\alpha_n=\mathcal{L}(M_n,Q_n)$ where $\mathcal{L}$ belongs to a class of distributions much larger than the normal. The predictives $\alpha_n$ are useful in various frameworks, including Bayesian predictive inference and predictive resampling. Finally, the asymptotic behavior of copula-based predictive distributions (introduced in [13]) is investigated and a numerical experiment is performed.

We have introduced a q-deformation, i.e., a polynomial in q with natural coefficients, of the binomial coefficient of two finite words u and v counting the number of occurrences of v as a subword of u. In this paper, we examine the q-deformation of Parikh matrices as introduced by E\u{g}ecio\u{g}lu in 2004. Many classical results concerning Parikh matrices generalize to this new framework: Our first important observation is that the elements of such a matrix are in fact q-deformations of binomial coefficients of words. We also study their inverses and as an application, we obtain new identities about q-binomials. For a finite word z and for the sequence $(p_n)_{n\ge 0}$ of prefixes of an infinite word, we show that the polynomial sequence $\binom{p_n}{z}_q$ converges to a formal series. We present links with additive number theory and k-regular sequences. In the case of a periodic word $u^\omega$, we generalize a result of Salomaa: the sequence $\binom{u^n}{z}_q$ satisfies a linear recurrence relation with polynomial coefficients. Related to the theory of integer partition, we describe the growth and the zero set of the coefficients of the series associated with $u^\omega$. Finally, we show that the minors of a q-Parikh matrix are polynomials with natural coefficients and consider a generalization of Cauchy's inequality. We also compare q-Parikh matrices associated with an arbitrary word with those associated with a canonical word $12\cdots k$ made of pairwise distinct symbols., Comment: 26 pages, submitted

Gaussian binomial coefficients are q-analogues of the binomial coefficients of integers. On the other hand, binomial coefficients have been extended to finite words, i.e., elements of the finitely generated free monoids. In this paper we bring together these two notions by introducing q-analogues of binomial coefficients of words. We study their basic properties, e.g., by extending classical formulas such as the q-Vandermonde and Manvel's et al. identities to our setting. As a consequence, we get information about the structure of the considered words: these q-deformations of binomial coefficients of words contain much richer information than the original coefficients. From an algebraic perspective, we introduce a q-shuffle and a family q-infiltration products for non-commutative formal power series. Finally, we apply our results to generalize a theorem of Eilenberg characterizing so-called p-group languages. We show that a language is of this type if and only if it is a Boolean combination of specific languages defined through q-binomial coefficients seen as polynomials over $\mathbb{F}_p$., Comment: 33 pages, submitted

Generalized quantum impurity models -- which feature a few localized and strongly-correlated degrees of freedom coupled to itinerant conduction electrons -- describe diverse physical systems, from magnetic moments in metals to nanoelectronics quantum devices such as quantum dots or single-molecule transistors. Correlated materials can also be understood as self-consistent impurity models through dynamical mean field theory. Accurate simulation of such models is challenging, especially at low temperatures, due to many-body effects from electronic interactions, resulting in strong renormalization. In particular, the interplay between local impurity complexity and Kondo physics is highly nontrivial. A common approach, which we further develop in this work, is to consider instead a simpler effective impurity model that still captures the low-energy physics of interest. The mapping from bare to effective model is typically done perturbatively, but even this can be difficult for complex systems, and the resulting effective model parameters can anyway be quite inaccurate. Here we develop a non-perturbative, unsupervised machine learning approach to systematically obtain low-energy effective impurity-type models, based on the renormalization group framework. The method is shown to be general and flexible, as well as accurate and systematically improvable. We benchmark the method against exact results for the Anderson impurity model, and provide an outlook for more complex models beyond the reach of existing methods., Comment: 28 pages, 8 figures

We extend the methods used by V. Ferenczi and Ch. Rosendal to obtain the `third dichotomy' in the program of classification of Banach spaces up to subspaces, in order to prove that a Banach space E with an admissible system of blocks with admissible set A, contains an infinite dimensional subspace with a basis which is either A-tight or A-minimal. In this setting we obtain, in particular, dichotomies regarding subsequences of a basis, and as a corollary, we show that every normalized basic sequence has a subsequence which either satisfies a tightness property or is spreading. Other dichotomies between notions of minimality and tightness are demonstrated, and the Ferenczi-Godefroy interpretation of tightness in terms of Baire category is extended to this new context., Comment: 42 pages

Let $(\Omega,\mathcal{F})$ be a standard Borel space and $\mathcal{P}(\mathcal{F})$ the collection of all probability measures on $\mathcal{F}$. Let $E\subset\Omega\times\Omega$ be a measurable equivalence relation, that is, $E\in\mathcal{F}\otimes\mathcal{F}$ and the relation on $\Omega$ defined as $x\sim y$ $\Leftrightarrow$ $(x,y)\in E$ is reflexive, symmetric and transitive. It is shown that there are two $\sigma$-fields $\mathcal{G}_0$ and $\mathcal{G}_1$ on $\Omega$ such that, for all $\mu,\,\nu\in\mathcal{P}(\mathcal{F})$, $$\inf_{P\in\Gamma(\mu,\nu)}(1-P(E))=\norm{\mu-\nu}_{\mathcal{G}_1}\quad\text{and}\quad\min_{P\in\Gamma(\mu,\nu_0)}(1-P(E))=\norm{\mu-\nu}_{\mathcal{G}_0}.$$ Here, $\nu_0\in\mathcal{P}(\mathcal{F})$ is a suitable probability measure satisfying $\nu_0=\nu$ on $\mathcal{G}_0$. Moreover, $\mathcal{G}_0\subset\mathcal{F}$ while $\mathcal{G}_1\subset\widehat{\mathcal{F}}$, where $\widehat{\mathcal{F}}$ is the universally measurable $\sigma$-field with respect to $\mathcal{F}$. However, for all $\mu,\,\nu\in\mathcal{P}(\mathcal{F})$, there is a $\sigma$-field $\mathcal{G}(\mu,\nu)\subset\mathcal{F}$ such that $$\inf_{P\in\Gamma(\mu,\nu)}(1-P(E))=\norm{\mu-\nu}_{\mathcal{G}(\mu,\nu)}.$$, Comment: 11 pages

In recent years, the field of legged robotics has seen growing interest in enhancing the capabilities of these robots through the integration of articulated robotic arms. However, achieving successful loco-manipulation, especially involving interaction with heavy objects, is far from straightforward, as object manipulation can introduce substantial disturbances that impact the robot's locomotion. This paper presents a novel framework for legged loco-manipulation that considers whole-body coordination through a hierarchical optimization-based control framework. First, an online manipulation planner computes the manipulation forces and manipulated object task-based reference trajectory. Then, pose optimization aligns the robot's trajectory with kinematic constraints. The resultant robot reference trajectory is executed via a linear MPC controller incorporating the desired manipulation forces into its prediction model. Our approach has been validated in simulation and hardware experiments, highlighting the necessity of whole-body optimization compared to the baseline locomotion MPC when interacting with heavy objects. Experimental results with Unitree Aliengo, equipped with a custom-made robotic arm, showcase its ability to lift and carry an 8kg payload and manipulate doors., Comment: 7 pages, 7 figures

The recent LHCb determination of the direct CP asymmetries in the decays $D^0 \to K^+ K^-, \pi^+ \pi^-$ hints at a sizeable breaking of two approximate symmetries of the SM: CP and U-spin. We aim at explaining the data with BSM physics and use the framework of flavorful $Z^\prime$ models. Interestingly, experimental and theoretical constraints very much narrow down the shape of viable models: Viable, anomaly-free models are electron- and muon-phobic and feature a light $Z^\prime$ of 10-20 GeV coupling only to right-handed fermions. The $Z^\prime$ can be searched for in low mass dijets or at the LHC as well as dark photon searches. A light $Z^\prime$ of $\sim$ 3 GeV or $\sim$ 5-7 GeV can moreover resolve the longstanding discrepancy in the $J/\psi, \psi^\prime$ branching ratios with pion form factors from fits to $e^+ e^- \to \pi^+ \pi^-$ data, and simultaneously explain the charm CP asymmetries. Smoking gun signatures for this scenario are $\Upsilon$ and charmonium decays into pions, taus or invisbles., Comment: 2 pages, 4 figures

Rare decays mediated by $b \to s \nu \bar \nu$ transitions have been reported by the Belle II experiment. The branching ratio of the decay $B^+ \to K^+ \nu \bar \nu$ is found to be enhanced with respect to the standard model value. If taken at face value, the implications are profound: either lepton flavor universality is violated at the (multi)-TeV-scale, or light new physics is involved. This holds in general if $\mathcal{B}(B^+ \to K^+ \nu \bar \nu)$ exceeds $1.2 \cdot 10^{-5} \, (1.3 \cdot 10^{-5})$ at $1 \sigma$ ($2 \sigma$), which tightens with a decreasing upper limit on $\mathcal{B}(B \to K^*\nu \bar \nu)$, that is in reach of the Belle II experiment. In view of the strong constraints on electron-muon universality violation in $|\Delta b|=|\Delta s|=1$ processes, viable explanations are heavy, $(5-10)$-TeV tree-level new physics mediators that couple only to tau-flavors, or lepton flavor violating ones. In addition, couplings of similar size to both left- and right-handed quarks are generically required, implying non-minimal BSM sectors which are carefully balanced against flavor constraints. The decay $B_s^0 \to \text{invisibles}$ can shed light on whether new physics is light or heavy. In the former case, branching ratios can be as large as $10^{-5}$., Comment: 7 pages, 3 figures. v2: References and clarifications to Eqs.(3),(21),(22), and the model sections added, upper limit Bs to nothing corrected. v3: Discussion on b--> s tau tau couplings improved (new Fig. 3), minor corrections and references added

Moir\'e superlattices formed by vertically stacking van der Waals layers host a rich variety of correlated electronic phases and function as novel photonic materials. The moir\'e potential of the superlattice, however, is fixed by the interlayer coupling of the stacked functional layers (e.g. graphene) and dependent on carrier types (e.g. electrons or holes) and valleys (e.g. {\Gamma} vs. K). In contrast, twisted hexagonal boron nitride (hBN) layers are predicted to impose a periodic electrostatic potential that may be used to engineer the properties of an adjacent functional thin layer. Here, we show that this potential is described by a simple theory of electric polarization originating from the interfacial charge redistribution, validated by its dependence on supercell sizes and distance from the twisted interfaces. We demonstrate that the potential depth and profile can be further controlled by assembling a double moir\'e structure. When the twist angles are similar at the two interfaces, the potential is deepened by adding the potential from the two twisted interfaces, reaching ~ 400 meV. When the twist angles are dissimilar at the two interfaces, multi-level polarization states are observed. As an example of controlling a functional layer, we demonstrate how the electrostatic potential from a twisted hBN substrate impedes exciton diffusion in a semiconductor monolayer. These findings suggest exciting opportunities for engineering properties of an adjacent functional layer using the surface potential of a twisted hBN substrate.

Higgs coupling deviations from Standard Model predictions contain information about two scales of Nature: that of new physics responsible for the deviation, and the scale where new bosons must appear. The two can coincide, but they do not have to. The scale of new bosons can be calculated by going beyond an effective field theory description of the coupling deviation. We compute model-independent upper bounds on the scale of new bosons for deviations in Higgs to $WW$ and $ZZ$ couplings, finding that any measured deviation at present or future colliders requires the existence of new bosons within experimental reach. This has potentially interesting implications for naturalness., Comment: 41 pages + references, 14 figures. v2: JHEP version

Vitamin-V is a 2023-2025 Horizon Europe project that aims to develop a complete RISC-V open-source software stack for cloud services with comparable performance to the cloud-dominant x86 counterpart and a powerful virtual execution environment for software development, validation, verification, and test that considers the relevant RISC-V ISA extensions for cloud deployment., Comment: Paper accepted and presented at the RISC-V Summit Europe, Barcelona, 5-9th June 2023. arXiv admin note: substantial text overlap with arXiv:2305.01983

We describe cosmological solutions of the holographic dilaton with the aim of exploring alternatives to the commonly studied thermal Randall-Sundrum phase transition. It is well known that the thermal transition is typically strongly first order, with the requirement of a perturbative 5D gravity theory obstructing completion of the transition. This thermal transition corresponds to nucleation of an infrared brane through the surface of an AdS-Schwarzschild horizon. The approach we study instead invokes an early epoch in which the cosmology is fully 5-dimensional, with highly relativistic brane motion, and with Rindler horizons obscuring the infrared brane at early times. Our approach corresponds, via AdS/CFT, to a non-equilibrium approach to the conformal phase transition. We comment on a class of initial conditions that generically leads to completion of the phase transition without sacrificing perturbativity of the 5D theory., Comment: 43 pages, 9 figures

This study investigates how to schedule nanosatellite tasks more efficiently using Graph Neural Networks (GNNs). In the Offline Nanosatellite Task Scheduling (ONTS) problem, the goal is to find the optimal schedule for tasks to be carried out in orbit while taking into account Quality-of-Service (QoS) considerations such as priority, minimum and maximum activation events, execution time-frames, periods, and execution windows, as well as constraints on the satellite's power resources and the complexity of energy harvesting and management. The ONTS problem has been approached using conventional mathematical formulations and exact methods, but their applicability to challenging cases of the problem is limited. This study examines the use of GNNs in this context, which has been effectively applied to optimization problems such as the traveling salesman, scheduling, and facility placement problems. More specifically, we investigate whether GNNs can learn the complex structure of the ONTS problem with respect to feasibility and optimality of candidate solutions. Furthermore, we evaluate using GNN-based heuristic solutions to provide better solutions (w.r.t. the objective value) to the ONTS problem and reduce the optimization cost. Our experiments show that GNNs are not only able to learn feasibility and optimality for instances of the ONTS problem, but they can generalize to harder instances than those seen during training. Furthermore, the GNN-based heuristics improved the expected objective value of the best solution found under the time limit in 45%, and reduced the expected time to find a feasible solution in 35%, when compared to the SCIP (Solving Constraint Integer Programs) solver in its off-the-shelf configuration