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This paper presents the spherical lower dimensional representation for daily medium voltage load profiles, based on principal component analysis. The objective is to unify and simplify the tasks for (i) clustering visualisation, (ii) outlier detection and (iii) generative profile modelling under one concept. The lower dimensional projection of standardised load profiles unveils a latent distribution in a three-dimensional sphere. This spherical structure allows us to detect outliers by fitting probability distribution models in the spherical coordinate system, identifying measurements that deviate from the spherical shape. The same latent distribution exhibits an arc shape, suggesting an underlying order among load profiles. We develop a principal curve technique to uncover this order based on similarity, offering new advantages over conventional clustering techniques. This finding reveals that energy consumption in a wide region can be seen as a continuously changing process. Furthermore, we combined the principal curve with a von Mises-Fisher distribution to create a model capable of generating profiles with continuous mixtures between clusters. The presence of the spherical distribution is validated with data from four municipalities in the Netherlands. The uncovered spherical structure implies the possibility of employing new mathematical tools from directional statistics and differential geometry for load profile modelling.

We study the evolution of eccentric, equatorial extreme-mass-ratio inspirals (EMRIs) immersed in the accretion disks of active galactic nuclei. We find that single gravitational-wave observations from these systems could provide measurements with ~ 10 % relative precision of, simultaneously, the disk viscosity and mass accretion rate of the central supermassive black hole. This is possible when the EMRI transitions, within the observation time, from supersonic to subsonic motion relative to the disk gas, for eccentricities e > ~ 0.025-0.1. The estimate of the accretion rate would assist in the identification of the EMRI's host galaxy, or the observation of a direct electromagnetic counterpart, improving the chances of using these sources as cosmological sirens. Our work highlights the rich phenomenology of binary evolution in astrophysical environments and the need to improve the modelling and analysis of these systems for future gravitational-wave astronomy., Comment: 12 pages + 3 pages in Appendix, 8 figures

Deformations of spacelike hypersurfaces in space-time play an important role in discussions of general covariance and slicing independence in gravitational theories. In a canonical formulation, they provide the geometrical meaning of gauge transformations generated by the diffeomorphism and Hamiltonian constraints. However, it has been known for some time that the relationship between hypersurface deformations and general covariance is not a kinematical equivalence but holds only on the solution space of the constraints and requires their gauge equations and equations of motion to be used. The off-shell behavior of hypersurface deformations on their own, without imposing constraint and gauge equations, is therefore different from space-time diffeomorphisms. Its complete understanding is important for potential quantizations or modifications of general relativity in canonical form and of compatible space-time geometries that may be implied by them. Here, a geometrical analysis of hypersurface deformations is performed, allowing for a dependence of hypersurface deformation generators (the lapse function and the shift vector) on the phase-space degrees of freedom given by the geometry of an embedded spacelike hypersurface. The result is compared in detail with Poisson brackets of the gravitational constraints. As a new implication of physical relevance, covariance conditions are obtained for theories of emergent modified gravity without symmetry restrictions., Comment: 45 pages, 2 figures

Emergent modified gravity is a post-Einsteinian gravitational theory where spacetime geometry is not fundamental but rather emerges from the gravitational degrees of freedom in a non-trivial way. The specific relationship between geometry and these degrees of freedom is unique for each theory, but it is not predetermined. Instead, it is derived from constraints and equations of motion, relying on key aspects of the canonical formulation of gravity, such as structure functions in Poisson brackets of constraints and covariance conditions. As shown in previous work, these new theories allow for two types of scalar matter coupling: (1) minimal coupling, where the matter equations of motion mirror the Klein-Gordon equation on a curved emergent spacetime, and (2) nonminimal coupling, where the equations deviate from the Klein-Gordon form but still respect covariance. Observable features, such as the quasinormal mode spectrum, can help distinguish between different couplings based on how well their predictions match the data. In this work, the spectra of scalar quasinormal modes for both minimal and nonminimal couplings are derived using the third-order WKB approximation. Significant differences are found between the two cases. Notably, the nonminimal coupling allows for vanishing real and imaginary frequency components, and even opposite-sign values for the imaginary part at sufficiently small mass scales, pointing to potential new physical implications. Finally, the high-frequency QNM spectra in emergent modified gravity is identical to the classical result, up to an overall constant, suggesting that the horizon area spectrum remains equispaced., Comment: 47 pages, 16 figures

Extreme-Mass-Ratio Inspirals (EMRIs) are one of the key targets for future space-based gravitational wave detectors, such as LISA. The scientific potential of these sources can only be fully realized with fast and accurate waveform models. In this work, we extend the \textsc{FastEMRIWaveform} (\texttt{FEW}) framework by providing fully relativistic waveforms at adiabatic order for circular, equatorial orbits in Kerr spacetime, for mass ratios up to $10^{-3}$. We study the importance of including relativistic corrections in the waveform for both vacuum and non-vacuum environments. For EMRIs in vacuum, we find that non-relativistic waveforms can result in $\sim 35\%$ error in the predicted source's horizon redshift. By developing relativistic non-vacuum EMRI waveforms, we demonstrate significant improvements in detecting environmental effects. Our analysis shows that incorporating relativistic corrections enhances constraints on accretion disks, modeled through power-law torques, and improves the constraints on disk parameters (error $\sim6\%$), representing a significant improvement from previous estimates. We also estimated the evidence for models in a scenario where ignoring the accretion disk causes bias in parameter estimation (PE) and report a $\log_{10}$ Bayes factor of $1.1$ in favor of the accretion disk model. Additionally, in a fully relativistic setup, we estimate the parameters of superradiant scalar clouds with high accuracy, achieving errors below $5\%$ for the scalar cloud's mass and below $0.5\%$ for the ultralight field's mass. These results demonstrate that incorporating relativistic effects greatly enhances the accuracy and reliability of waveform predictions, essential for PE and model selection., Comment: 22 pages, 13 figures

Dealing with boundary conditions in Smoothed Particle Hydrodynamics (SPH) poses significant difficulties, indeed being one of the SPHERIC Grand Challenges. In particular, wall boundary conditions have been pivotal in SPH model development since it evolved from astrophysics to more generic fluid dynamics simulations. Despite considerable attention from researchers and numerous publications dedicated to formulating and assessing wall boundary conditions, few of them have addressed the crucial aspect of energy conservation. This work introduces a novel boundary condition designed with energy conservation as a primary consideration, effectively extending the unconditional stability of SPH to problems involving wall boundary conditions. The result is formulated within the framework of the Boundary Integrals technique. The proposal is tested on a number of cases: normal impact against a wall, adiabatic oscillations of a piston, dam break, and the water landing of a spacecraft., Comment: 35 pages, 25 figures. SPH solver released as free software (see https://gitlab.com/sanguinariojoe/aquagpusph). Accepted for publication on "Computers & Fluids"

Our current understanding is that an environment - mainly consisting of gas or stars - is required to bring massive black hole binaries (MBHBs) with total redshifted mass $M_z\sim[10^{4},10^7]~{\rm M}_\odot$ to the LISA band from parsec separation. Even in the gravitational wave (GW) dominated final inspiral, realistic environments can non-negligibly speed up or slow down the binary evolution, or leave residual, measurable eccentricity in the LISA band. Despite this fact, most of the literature does not consider environmental effects or orbital eccentricity in modelling GWs from near-equal mass MBHBs. Considering either a circular MBHB embedded in a circumbinary disc or a vacuum eccentric binary, we explore if ignoring either secular gas effects (migration and accretion) or eccentric corrections to the GW waveform can mimic a failure of General Relativity (GR). We use inspiral-only aligned-spin 3.5 post-Newtonian waveforms, a complete LISA response model, and Bayesian inference to perform a parameterized test of GR. For a four-year LISA observation of an MBHB with $M_z=10^{5}~{\rm M}_\odot$, primary-to-secondary mass ratio $q=8$, and component BHs' dimensionless spins $\chi_{1,2}=0.9$ at redshift $z=1$, even a moderate gas-disc imprint (Eddington ratio ${\rm f}_{\rm Edd}\sim0.1$) or low initial eccentricity ($e_0\sim10^{-2.5}$) causes a false violation of GR in several PN orders. However, correctly modelling either effect can mitigate systematics while avoiding significant biases in vacuum circular systems. The adoption of LISA makes it urgent to consider gas imprints and eccentricity in waveform models to ensure accurate inference for MBHBs., Comment: 11 pages, 8 figures. Accepted by MNRAS

This work tackles the critical challenge of mitigating "hardware noise" in deep analog neural networks, a major obstacle in advancing analog signal processing devices. We propose a comprehensive, hardware-agnostic solution to address both correlated and uncorrelated noise affecting the activation layers of deep neural models. The novelty of our approach lies in its ability to demystify the "black box" nature of noise-resilient networks by revealing the underlying mechanisms that reduce sensitivity to noise. In doing so, we introduce a new explainable regularization framework that harnesses these mechanisms to significantly enhance noise robustness in deep neural architectures.

The ringdown phase following a binary black hole coalescence is a powerful tool for measuring properties of the remnant black hole. Future gravitational wave detectors will increase the precision of these measurements and may be sensitive to the environment surrounding the black hole. This work examines how environments affect the ringdown from a binary coalescence. Our analysis shows that for astrophysical parameters and sensitivity of planned detectors, the ringdown signal is indistinguishable from its vacuum counterpart, suggesting that ringdown-only analyses can reliably extract the (redshifted) mass and spin of the remnant black hole. These conclusions include models with spectral instabilities, suggesting that these are not relevant from an observational viewpoint. Deviations from inspiral-only estimates could then enhance the characterisation of environmental effects present during the coalescence., Comment: 5 pages, 3 figures

Accurate assessment of Parkinsonian tremor is vital for monitoring disease progression and evaluating treatment efficacy. We introduce a pixel-based deep learning model designed to analyse postural tremor in Parkinson's disease (PD) from video data, overcoming the limitations of traditional pose estimation techniques. Trained on 2,742 assessments from five specialised movement disorder centres across two continents, the model demonstrated robust concordance with clinical evaluations. It effectively predicted treatment effects for levodopa and deep brain stimulation (DBS), detected lateral asymmetry of symptoms, and differentiated between different tremor severities. Feature space analysis revealed a non-linear, structured distribution of tremor severity, with low-severity scores occupying a larger portion of the feature space. The model also effectively identified outlier videos, suggesting its potential for adaptive learning and quality control in clinical settings. Our approach offers a scalable and objective method for tremor scoring, with potential integration into other MDS-UPDRS motor assessments, including bradykinesia and gait. The system's adaptability and performance underscore its promise for high-frequency, longitudinal monitoring of PD symptoms, complementing clinical expertise and enhancing decision-making in patient management. Future work will extend this pixel-based methodology to other cardinal symptoms of PD, aiming to develop a comprehensive, multi-symptom model for automated Parkinson's disease severity assessment.

Cosmic microwave background (CMB) temperature and polarization observations indicate that in the best-fit $\Lambda$ Cold Dark Matter model of the Universe, the local geometry is consistent with at most a small amount of positive or negative curvature, i.e., $\vert\Omega_K\vert\ll1$. However, whether the geometry is flat ($E^3$), positively curved ($S^3$) or negatively curved ($H^3$), there are many possible topologies. Among the topologies of $S^3$ geometry, the lens spaces $L(p,q)$, where $p$ and $q$ ($p>1$ and $0

Deep Reinforcement Learning (DRL) presents a promising avenue for optimizing Energy Storage Systems (ESSs) dispatch in distribution networks. This paper introduces RL-ADN, an innovative open-source library specifically designed for solving the optimal ESSs dispatch in active distribution networks. RL-ADN offers unparalleled flexibility in modeling distribution networks, and ESSs, accommodating a wide range of research goals. A standout feature of RL-ADN is its data augmentation module, based on Gaussian Mixture Model and Copula (GMC) functions, which elevates the performance ceiling of DRL agents. Additionally, RL-ADN incorporates the Laurent power flow solver, significantly reducing the computational burden of power flow calculations during training without sacrificing accuracy. The effectiveness of RL-ADN is demonstrated using in different sizes of distribution networks, showing marked performance improvements in the adaptability of DRL algorithms for ESS dispatch tasks. This enhancement is particularly beneficial from the increased diversity of training scenarios. Furthermore, RL-ADN achieves a tenfold increase in computational efficiency during training, making it highly suitable for large-scale network applications. The library sets a new benchmark in DRL-based ESSs dispatch in distribution networks and it is poised to advance DRL applications in distribution network operations significantly. RL-ADN is available at: https://github.com/ShengrenHou/RL-ADN and https://github.com/distributionnetworksTUDelft/RL-ADN.

We present the abundances of magnesium (Mg) and silicon (Si) for 314 dwarf stars with spectral types in the interval K7.0-M5.5 (Teff range ~4200-3050 K) observed with the CARMENES high-resolution spectrograph at the 3.5 m telescope at the Calar Alto Observatory. Our analysis employs the BT-Settl model atmospheres, the radiative transfer code Turbospectrum, and a state-of-the-art selection of atomic and molecular data. These Mg and Si abundances are critical for understanding both the chemical evolution and assembly of the Milky Way and the formation and composition of rocky planets. Our chemical abundances show a line-to-line scatter at the level of 0.1 dex for all studied spectral types. The typical error bar of our chemical abundance measurements is +- 0.11 dex (Mg) and +- 0.16 dex (Si) for all spectral types based on the comparison of the results obtained for stellar components of multiple systems. The derived abundances are consistent with the galactic evolution trends and observed chemical abundance distribution of earlier FGK-type stars in the solar neighbourhood. Besides, our analysis provides compatible abundances for stars in multiple systems. In addition, we studied the abundances of different galactic stellar populations. In this paper, we also explore the relation of the Mg and Si abundances of stars with and without known planets., Comment: 11 Pages, 5 figures. Accepted for publication in A&A

The search for atmospheric biosignatures in Earth-like exoplanets is one of the most pressing challenges in observational astrobiology. Detecting biogenic gases in terrestrial planets requires high resolution and long integration times. In this work, we developed and tested a machine-learning general methodology, intended to classify transmission spectra with low Signal-to-Noise Ratio according to their potential to contain biosignatures. For that purpose, we trained a set of models capable of classifying noisy transmission spectra, as having methane, ozone, and/or water (multilabel classification), or simply as being interesting for follow-up observations (binary classification). The models were trained with $\sim\, 10^6$ synthetic spectra of planets similar to TRAPPIST-1 e, which were generated with the package MultiREx, especially developed for this work. The trained algorithms correctly classified test planets with transmission spectra having SNR $<$ 6 and containing methane and/or ozone at mixing ratios similar to those of modern and Proterozoic Earth. Tests on realistic synthetic spectra based on the current Earth\'s atmosphere show at least one of our models would classify as likely having biosignatures and using only one transit, most of the inhabited terrestrial planets observed with the JWST/NIRSpec PRISM around M-dwarfs located at distances similar or smaller than that of TRAPPIST-1 e. The implication of this result for the designing of observing programs and future surveys is enormous since machine-assisted strategies similar to those presented here could significantly optimize the usage of JWST resources for biosignature searching, while maximizing the chances of a real discovery after dedicated follow-up observations of promising candidates., Comment: 21 pages, under review in MNRAS, 18 figures, MultiREx package available at https://github.com/D4san/MultiREx-public

Protecting data in memory from attackers continues to be a concern in computing systems. CHERI is a promising approach to achieve such protection, by providing and enforcing fine-grained memory protection directly in the hardware. Creating trust for the entire system stack, however, requires a gap-free verification of CHERI's hardware-based protection mechanisms. Existing verification methods for CHERI target the abstract ISA model rather than the underlying hardware implementation. Fully ensuring the CHERI security guarantees for a concrete RTL implementation is a challenge in previous flows and demands high manual efforts. This paper presents VeriCHERI, a novel approach to security verification. It is conceptionally different from previous works in that it does not require any ISA specification. Instead of checking compliance with a golden ISA model, we check against well-established global security objectives of confidentiality and integrity. Fully covering these objectives, VeriCHERI uses as few as four unbounded properties to exhaustively prove or disprove any vulnerability. We demonstrate the effectiveness and scalability of VeriCHERI on a RISC-V based processor implementing a CHERI variant., Comment: Accepted for publication at the 43rd International Conference on Computer-Aided Design (ICCAD `24), Oct 27-31, 2024, New Jersey, USA

Causal diamonds are known to have thermal behavior that can be probed by finite-lifetime observers equipped with energy-scaled detectors. This thermality can be attributed to the time evolution of observers within the causal diamond, governed by one of the conformal quantum mechanics (CQM) symmetry generators: the noncompact hyperbolic operator $S$. In this paper, we show that the unbounded nature of $S$ endows it with a quantum instability, which is a generalization of a similar property exhibited by the inverted harmonic oscillator potential. Our analysis is semiclassical, including a detailed phase-space study of the classical dynamics of $S$ and its dual operator $R$, and a general semiclassical framework yielding basic instability and thermality properties that play a crucial role in the quantum behavior of the theory. For an observer with a finite lifetime $\mathcal{T}$, the detected temperature $T_D = 2 \hbar/(\pi \mathcal{T})$ is associated with a Lyapunov exponent $\lambda_L = \pi T_D/\hbar$, which is half the upper saturation bound of the information scrambling rate., Comment: 29 pages, 4 figures

An observer with a finite lifetime $\mathcal{T}$ perceives the Minkowski vacuum as a thermal state at temperature $T_D = 2 \hbar/(\pi \mathcal{T})$, as a result of being constrained to a double-coned-shaped region known as a causal diamond. In this paper, we explore the emergence of thermality in causal diamonds due to the role played by the symmetries of conformal quantum mechanics (CQM) as a (0+1)-dimensional conformal field theory, within the de Alfaro-Fubini-Furlan model and generalizations. In this context, the hyperbolic operator $S$ of the SO(2,1) symmetry of CQM is the generator of the time evolution of a diamond observer, and its dynamical behavior leads to the predicted thermal nature. Our approach is based on a comprehensive framework of path-integral representations of the CQM generators in canonical and microcanonical forms, supplemented by semiclassical arguments. The properties of the operator $S$ are studied with emphasis on an operator duality with the corresponding elliptic operator $R$, using a representation in terms of an effective scale-invariant inverse square potential combined with inverted and ordinary harmonic oscillator potentials., Comment: 38 pages, 2 figures

We introduce the concept of emergent electric field. This is distinguished from the fundamental one in that the emergent electric field directly appears in observations through the Lorentz force, while the latter enters the phase space as the canonical momentum of the electromagnetic field. In Hamiltonian classical electromagnetism this concept naturally appears after introducing the topological $\theta$ term. Furthermore, we show that in the spherically symmetric model the concept of emergent electric field allows us to formulate a modified theory of electromagnetism that is otherwise impossible. The relation between the fundamental and the emergent electric fields is derived from the imposition of general covariance of the electromagnetic strength tensor, which is a nontrivial task in the canonical formulation the modified theory is based on. We couple this theory to emergent modified gravity, where a similar distinction between spacetime and gravity is made such that the spacetime, which defines the observable geometry, is an emergent field composed of the fundamental gravitational field. In this more encompassing emergent field theory coupling gravity and electromagnetism, we show that the spherically symmetric model contains a nonsingular black hole solution where not only modified gravity but also modified electromagnetism is crucial for a robust singularity resolution and to avoid the existence of (super)extermal black holes., Comment: 38 pages, 3 new figures and 2 new tables added, new reference added, typos corrected

New covariant theories of emergent modified gravity exist not only in spherically symmetric models, as previously found, but also in polarized Gowdy systems that have a local propagating degree of freedom. Several explicit versions are derived here, depending on various modification functions. These models do not have instabilities from higher time derivatives, and a large subset is compatible with gravitational waves and minimally coupled massless matter fields travelling at the same speed. Interpreted as models of loop quantum gravity, covariant Hamiltonian constraints derived from the covariance conditions found in polarized Gowdy systems are more restricted than those in spherical symmetry, requiring new forms of holonomy modifications with an anisotropy dependence that has not been considered before. Assuming homogeneous space, the models provide access to the full anisotropy parameters of modified Bianchi I dynamics, in which case different fates of the classical singularity are realized depending on the specific class of modifications., Comment: 55 pages, two figures

The $Reflection$ $Calculus$ ($\mathcal{\mathbf{RC}}$) is the fragment of the polymodal logic $\mathcal{\mathbf{GLP}}$ in the language $L^+$ whose formulas are built up from $\top$ and propositional variables using conjunction and diamond modalities. $\mathcal{\mathbf{RC}}$ is complete with respect to the arithmetical interpretation that associates modalities with reflection principles and has various applications in proof theory, specifically ordinal analysis. We present ${\sf TRC}$, a tree rewriting system that is adequate and complete with respect to $\mathcal{\mathbf{RC}}$, designed to simulate $\mathcal{\mathbf{RC}}$ derivations. ${\sf TRC}$ is based on a given correspondence between formulas of $L^{+}$ and modal trees ${\sf Tree}^{\Diamond}$. Modal trees are presented as an inductive type allowing precise positioning and transformations which give rise to the formal definition of rewriting rules and facilitates formalization in proof assistants. Furthermore, we provide a rewrite normalization theorem for systematic rule application. The normalization of the rewriting process enhances proof search efficiency and facilitates implementation. By providing ${\sf TRC}$ as an efficient provability tool for $\mathcal{\mathbf{RC}}$, we aim to help on the study of various aspects of the logic such as the subformula property and rule admissibility.

Emergent modified gravity provides a covariant, effective framework for obtaining spherically symmetric black hole solutions in models of loop quantum gravity with scale-dependent holonomy modifications. Exact solutions for vacuum black holes in the presence of a cosmological constant are derived here and analyzed in four different gauges, explicitly related to one another by standard coordinate transformations. The global structure is obtained by gluing space-time regions corresponding to the gauge choices, reconstructing a non-singular wormhole space-time for an arbitrary scale-dependent holonomy parameter. This outcome demonstrates the robustness of black-hole models with covariant holonomy modifications under quantization ambiguities. Compared with previous constructions, full covariance of the resulting space-time models as derived here implies subtle new effects and leads to a novel understanding of the parameters in holonomy modifications, distinguishing a constant holonomy length from a possibly scale-dependent function that may change coefficients of holonomy terms. New physical results are obtained for instance in the context of a non-trivial zero-mass limit of holonomy-modified space-times. The existence of a consistent effective space-time structure implies various novel aspects of a net gravitational stress-energy and related thermodynamical properties., Comment: 84+2 pages, 7 figures (all at the end of the draft); comments welcome

The standard cosmological model, which assumes statistical isotropy and parity invariance, predicts the absence of correlations between even-parity and odd-parity observables of the cosmic microwave background (CMB). Contrary to these predictions, large-angle CMB temperature anomalies generically involve correlations between even-$\ell$ and odd-$\ell$ angular power spectrum $C_\ell$, while recent analyses of CMB polarization have revealed non-zero equal-$\ell$ $EB$ correlations. These findings challenge the conventional understanding, suggesting deviations from statistical isotropy, violations of parity, or both. Cosmic topology, which involves changing only the boundary conditions of space relative to standard cosmology, offers a compelling framework to potentially account for such parity-violating observations. Topology inherently breaks statistical isotropy, and can also break homogeneity and parity, providing a natural paradigm for explaining observations of parity-breaking observables without the need to add parity violation to the underlying microphysics. Our investigation delves into the harmonic space implications of topology for CMB correlations, using as an illustrative example $EB$ correlations generated by tensor perturbations under both parity-preserving and parity-violating scenarios. Consequently, these findings not only challenge the foundational assumptions of the standard cosmological model but also open new avenues for exploring the topological structure of the Universe through CMB observations., Comment: 20 pages, 4 figures. v2: version published in JCAP

Polyhedral semantics is a recently introduced branch of spatial modal logic, in which modal formulas are interpreted as piecewise linear subsets of an Euclidean space. Polyhedral semantics for the basic modal language has already been well investigated. However, for many practical applications of polyhedral semantics, it is advantageous to enrich the basic modal language with a reachability modality. Recently, a language with an Until-like spatial modality has been introduced, with demonstrated applicability to the analysis of 3D meshes via model checking. In this paper, we exhibit an axiom system for this logic, and show that it is complete with respect to polyhedral semantics. The proof consists of two major steps: First, we show that this logic, which is built over Grzegorczyk's system $\mathsf{Grz}$, has the finite model property. Subsequently, we show that every formula satisfied in a finite poset is also satisfied in a polyhedral model, thereby establishing polyhedral completeness., Comment: 17 pages, 1 figure, Advances in Modal Logics Conference

Artificially intelligent agents are increasingly being integrated into human decision-making: from large language model (LLM) assistants to autonomous vehicles. These systems often optimize their individual objective, leading to conflicts, particularly in general-sum games where naive reinforcement learning agents empirically converge to Pareto-suboptimal Nash equilibria. To address this issue, opponent shaping has emerged as a paradigm for finding socially beneficial equilibria in general-sum games. In this work, we introduce Advantage Alignment, a family of algorithms derived from first principles that perform opponent shaping efficiently and intuitively. We achieve this by aligning the advantages of interacting agents, increasing the probability of mutually beneficial actions when their interaction has been positive. We prove that existing opponent shaping methods implicitly perform Advantage Alignment. Compared to these methods, Advantage Alignment simplifies the mathematical formulation of opponent shaping, reduces the computational burden and extends to continuous action domains. We demonstrate the effectiveness of our algorithms across a range of social dilemmas, achieving state-of-the-art cooperation and robustness against exploitation., Comment: 25 Pages, 8 figures

The Hessian map is the rational map that sends a homogeneous polynomial to the determinant of its Hessian matrix. We prove that the Hessian map is birational on its image for ternary forms of degree $d\ge 4$, $d\neq 5$, by considering the action of the orthogonal group. In a previous paper we proved the analogous result for binary forms, with more geometric techniques., Comment: by Ciro Ciliberto, Giorgio Ottaviani, with an appendix by Jerson Caro, Juanita Duque-Rosero

Optimizing discrete black-box functions is key in several domains, e.g. protein engineering and drug design. Due to the lack of gradient information and the need for sample efficiency, Bayesian optimization is an ideal candidate for these tasks. Several methods for high-dimensional continuous and categorical Bayesian optimization have been proposed recently. However, our survey of the field reveals highly heterogeneous experimental set-ups across methods and technical barriers for the replicability and application of published algorithms to real-world tasks. To address these issues, we develop a unified framework to test a vast array of high-dimensional Bayesian optimization methods and a collection of standardized black-box functions representing real-world application domains in chemistry and biology. These two components of the benchmark are each supported by flexible, scalable, and easily extendable software libraries (poli and poli-baselines), allowing practitioners to readily incorporate new optimization objectives or discrete optimizers. Project website: https://machinelearninglifescience.github.io/hdbo_benchmark, Comment: Accepted at the Datasets and Benchmarks track of NeurIPS 2024

Data visualization via dimensionality reduction is an important tool in exploratory data analysis. However, when the data are noisy, many existing methods fail to capture the underlying structure of the data. The method called Empirical Intrinsic Geometry (EIG) was previously proposed for performing dimensionality reduction on high dimensional dynamical processes while theoretically eliminating all noise. However, implementing EIG in practice requires the construction of high-dimensional histograms, which suffer from the curse of dimensionality. Here we propose a new data visualization method called Functional Information Geometry (FIG) for dynamical processes that adapts the EIG framework while using approaches from functional data analysis to mitigate the curse of dimensionality. We experimentally demonstrate that the resulting method outperforms a variant of EIG designed for visualization in terms of capturing the true structure, hyperparameter robustness, and computational speed. We then use our method to visualize EEG brain measurements of sleep activity.

The student-optimal stable mechanism (DA), the most popular mechanism in school choice, is the only one that is both stable and strategy-proof. However, when DA is implemented, a student can change the schools of others without changing her own. We show that this drawback is limited: a student cannot change her classmates without modifying her school. We refer to this new property as {\it{local non-bossiness}} and use it to provide a new characterization of DA that does not rely on stability. Furthermore, we show that local non-bossiness plays a crucial role in providing incentives to be truthful when students have preferences over their colleagues. As long as students first consider the school to which they are assigned and then their classmates, DA induces the only stable and strategy-proof mechanism. There is limited room to expand this preference domain without compromising the existence of a stable and strategy-proof mechanism.

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'

Stationary, asymptotically flat, black hole solutions of the vacuum field equations of General Relativity belong to the Kerr family. But how does one approach this state, dynamically? Linearized fluctuations decay at late times, at fixed spatial position, as a Price power law for generic initial conditions. However, little attention was paid to forced and nonlinear spacetimes, where matter and nonlinearities play a role. We uncover a new, source-driven tail governing waves generated by pointlike matter and nonlinearities, which can dominate over Price's decay., Comment: 13 pages, to appear in Physical Review D Letters

In various real-world scenarios, interactions among agents often resemble the dynamics of general-sum games, where each agent strives to optimize its own utility. Despite the ubiquitous relevance of such settings, decentralized machine learning algorithms have struggled to find equilibria that maximize individual utility while preserving social welfare. In this paper we introduce Learning with Opponent Q-Learning Awareness (LOQA), a novel, decentralized reinforcement learning algorithm tailored to optimizing an agent's individual utility while fostering cooperation among adversaries in partially competitive environments. LOQA assumes the opponent samples actions proportionally to their action-value function Q. Experimental results demonstrate the effectiveness of LOQA at achieving state-of-the-art performance in benchmark scenarios such as the Iterated Prisoner's Dilemma and the Coin Game. LOQA achieves these outcomes with a significantly reduced computational footprint, making it a promising approach for practical multi-agent applications., Comment: accepted to ICLR but still not in proceedings https://openreview.net/forum?id=FDQF6A1s6M

To optimize efficiently over discrete data and with only few available target observations is a challenge in Bayesian optimization. We propose a continuous relaxation of the objective function and show that inference and optimization can be computationally tractable. We consider in particular the optimization domain where very few observations and strict budgets exist; motivated by optimizing protein sequences for expensive to evaluate bio-chemical properties. The advantages of our approach are two-fold: the problem is treated in the continuous setting, and available prior knowledge over sequences can be incorporated directly. More specifically, we utilize available and learned distributions over the problem domain for a weighting of the Hellinger distance which yields a covariance function. We show that the resulting acquisition function can be optimized with both continuous or discrete optimization algorithms and empirically assess our method on two bio-chemical sequence optimization tasks.