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This paper studies sparse covariance operator estimation for nonstationary Gaussian processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covariance operator estimator that adaptively thresholds the sample covariance function using an estimate of the variance components. Building on recent results from empirical process theory, we derive an operator norm bound on the estimation error in terms of the sparsity level of the covariance and the expected supremum of the normalized process. Our theory and numerical simulations demonstrate the advantage of adaptive threshold estimators over universal threshold and sample covariance estimators in nonstationary settings., Comment: 38 pages, 5 figures

Centaurs, distinguished by their volatile-rich compositions, play a pivotal role in understanding the formation and evolution of the early solar system, as they represent remnants of the primordial material that populated the outer regions. Stellar occultations offer a means to investigate their physical properties, including shape, rotational state, or the potential presence of satellites and rings. This work aims to conduct a detailed study of the centaur (54598) Bienor through stellar occultations and rotational light curves from photometric data collected during recent years. We successfully predicted three stellar occultations by Bienor, which were observed from Japan, Eastern Europe, and the USA. In addition, we organized observational campaigns from Spain to obtain rotational light curves. At the same time, we develop software to generate synthetic light curves from three-dimensional shape models, enabling us to validate the outcomes through computer simulations. We resolve Bienor's projected ellipse for December 26, 2022, determine a prograde sense of rotation, and confirm an asymmetric rotational light curve. We also retrieve the axes of its triaxial ellipsoid shape as a = (127 $\pm$ 5) km, b = (55 $\pm$ 4) km, and c = (45 $\pm$ 4) km. Moreover, we refine the rotation period to 9.1736 $\pm$ 0.0002 hours and determine a geometric albedo of (6.5 $\pm$ 0.5) %, higher than previously determined by other methods. Finally, by comparing our findings with previous results and simulated rotational light curves, we analyze whether an irregular or contact-binary shape, the presence of an additional element such as a satellite, or significant albedo variations on Bienor's surface, may be present.

This is a concise mathematical introduction to Monte Carlo methods, a rich family of algorithms with far-reaching applications in science and engineering. Monte Carlo methods are an exciting subject for mathematical statisticians and computational and applied mathematicians: the design and analysis of modern algorithms are rooted in a broad mathematical toolbox that includes ergodic theory of Markov chains, Hamiltonian dynamical systems, transport maps, stochastic differential equations, information theory, optimization, Riemannian geometry, and gradient flows, among many others. These lecture notes celebrate the breadth of mathematical ideas that have led to tangible advancements in Monte Carlo methods and their applications. To accommodate a diverse audience, the level of mathematical rigor varies from chapter to chapter, giving only an intuitive treatment to the most technically demanding subjects. The aim is not to be comprehensive or encyclopedic, but rather to illustrate some key principles in the design and analysis of Monte Carlo methods through a carefully-crafted choice of topics that emphasizes timeless over timely ideas. Algorithms are presented in a way that is conducive to conceptual understanding and mathematical analysis -- clarity and intuition are favored over state-of-the-art implementations that are harder to comprehend or rely on ad-hoc heuristics. To help readers navigate the expansive landscape of Monte Carlo methods, each algorithm is accompanied by a summary of its pros and cons, and by a discussion of the type of problems for which they are most useful. The presentation is self-contained, and therefore adequate for self-guided learning or as a teaching resource. Each chapter contains a section with bibliographic remarks that will be useful for those interested in conducting research on Monte Carlo methods and their applications., Comment: 150 pages, 21 figures

Recent discoveries of Earth-sized planets transiting nearby M dwarfs have made it possible to characterize the atmospheres of terrestrial planets via follow-up spectroscopic observations. However, the number of such planets receiving low insolation is still small, limiting our ability to understand the diversity of the atmospheric composition and climates of temperate terrestrial planets. We report the discovery of an Earth-sized planet transiting the nearby (12 pc) inactive M3.0 dwarf Gliese 12 (TOI-6251) with an orbital period ($P_{\rm{orb}}$) of 12.76 days. The planet, Gliese 12b, was initially identified as a candidate with an ambiguous $P_{\rm{orb}}$ from TESS data. We confirmed the transit signal and $P_{\rm{orb}}$ using ground-based photometry with MuSCAT2 and MuSCAT3, and validated the planetary nature of the signal using high-resolution images from Gemini/NIRI and Keck/NIRC2 as well as radial velocity (RV) measurements from the InfraRed Doppler instrument on the Subaru 8.2 m telescope and from CARMENES on the CAHA 3.5 m telescope. X-ray observations with XMM-Newton showed the host star is inactive, with an X-ray-to-bolometric luminosity ratio of $\log L_{\rm X}/L_{\rm bol} \approx -5.7$. Joint analysis of the light curves and RV measurements revealed that Gliese 12b has a radius of 0.96 $\pm$ 0.05 $R_\oplus$, a 3$\sigma$ mass upper limit of 3.9 $M_\oplus$, and an equilibrium temperature of 315 $\pm$ 6 K assuming zero albedo. The transmission spectroscopy metric (TSM) value of Gliese 12b is close to the TSM values of the TRAPPIST-1 planets, adding Gliese 12b to the small list of potentially terrestrial, temperate planets amenable to atmospheric characterization with JWST., Comment: 29 pages (20 pages in main body), 13 figures (10 figures in main body). Equal contributions from M. K. and A. F.. Accepted for Publication in ApJL at 2024 March 21

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'

Modern data-driven surrogate models for weather forecasting provide accurate short-term predictions but inaccurate and nonphysical long-term forecasts. This paper investigates online weather prediction using machine learning surrogates supplemented with partial and noisy observations. We empirically demonstrate and theoretically justify that, despite the long-time instability of the surrogates and the sparsity of the observations, filtering estimates can remain accurate in the long-time horizon. As a case study, we integrate FourCastNet, a state-of-the-art weather surrogate model, within a variational data assimilation framework using partial, noisy ERA5 data. Our results show that filtering estimates remain accurate over a year-long assimilation window and provide effective initial conditions for forecasting tasks, including extreme event prediction.

Transformers are crucial for reliable and efficient power system operations, particularly in supporting the integration of renewable energy. Effective monitoring of transformer health is critical to maintain grid stability and performance. Thermal insulation ageing is a key transformer failure mode, which is generally tracked by monitoring the hotspot temperature (HST). However, HST measurement is complex, costly, and often estimated from indirect measurements. Existing HST models focus on space-agnostic thermal models, providing worst-case HST estimates. This article introduces a spatio-temporal model for transformer winding temperature and ageing estimation, which leverages physics-based partial differential equations (PDEs) with data-driven Neural Networks (NN) in a Physics Informed Neural Networks (PINNs) configuration to improve prediction accuracy and acquire spatio-temporal resolution. The computational accuracy of the PINN model is improved through the implementation of the Residual-Based Attention (PINN-RBA) scheme that accelerates the PINN model convergence. The PINN-RBA model is benchmarked against self-adaptive attention schemes and classical vanilla PINN configurations. For the first time, PINN based oil temperature predictions are used to estimate spatio-temporal transformer winding temperature values, validated through PDE numerical solution and fiber optic sensor measurements. Furthermore, the spatio-temporal transformer ageing model is inferred, which supports transformer health management decision-making. Results are validated with a distribution transformer operating on a floating photovoltaic power plant., Comment: 23 pages, 18 figures

Aligning Large Language Models (LLMs) with human values and preferences is essential for making them helpful and safe. However, building efficient tools to perform alignment can be challenging, especially for the largest and most competent LLMs which often contain tens or hundreds of billions of parameters. We create NeMo-Aligner, a toolkit for model alignment that can efficiently scale to a thousand GPUs for training the largest open-source LLMs such as Nemotron 4 340B and Llama 3.1 405B. NeMo-Aligner comes with highly optimized and scalable implementations for major paradigms of model alignment such as: Reinforcement Learning from Human Feedback (RLHF), Direct Preference Optimization (DPO), SteerLM, and Self-Play Fine-Tuning (SPIN). Additionally, our toolkit supports running most of the alignment techniques in a Parameter Efficient Fine-Tuning (PEFT) setting. NeMo-Aligner is designed for extensibility, allowing support for other alignment techniques with minimal effort. It is open-sourced with Apache 2.0 License and we invite community contributions at https://github.com/NVIDIA/NeMo-Aligner, Comment: 16 pages, 4 figures, Accepted to COLM 2024

During the first Gyr of their life, exoplanet atmospheres suffer from different atmospheric escape phenomena that can strongly affect the shape and morphology of the exoplanet itself. These processes can be studied with Ly$\alpha$, H$\alpha$ and/or He I triplet observations. We present high-resolution spectroscopy observations from CARMENES and GIARPS checking for He I and H$\alpha$ signals in 20 exoplanetary atmospheres: V1298Tau c, K2-100b, HD63433b, HD63433c, HD73583b, HD73583c, K2-77b, TOI-2076b, TOI-2048b, HD235088b, TOI-1807b, TOI-1136d, TOI-1268b, TOI-1683b, TOI-2018b, MASCARA-2b, WASP-189b, TOI-2046b, TOI-1431b, and HAT-P-57b. We report two new high-resolution spectroscopy He I detections for TOI-1268b and TOI-2018b, and an H$\alpha$ detection for TOI-1136d. The MOPYS (Measuring Out-flows in Planets orbiting Young Stars) project aims to understand the evaporating phenomena and test their predictions from the current observations. We compiled a list of 70 exoplanets with He I and/or H$\alpha$ observations, from this work and the literature, and we considered the He I and H$\alpha$ results as proxy for atmospheric escape. Our principal results are that 0.1-1Gyr-old planets do not exhibit more He I or H$\alpha$ detections than older planets, and evaporation signals are more frequent for planets orbiting $\sim$1-3Gyr-old stars. We provide new constrains to the cosmic shoreline, the empirical division between rocky planets and planets with atmosphere, by using the evaporation detections and explore the capabilities of a new dimensionless parameter, $R_{\rm He}/R_{\rm Hill}$, to explain the He I triplet detections. Furthermore, we present a statistically significant upper boundary for the He I triplet detections in the $T_{\rm eq}$ vs $\rho_{\rm p}$ parameter space. Planets located above that boundary are unlikely to show He I absorption signals., Comment: Accepted in A&A. 64 pages, many figures. Supplementary material in Zenodo

Low-dimensional quantum magnets are a versatile materials platform for studying the emergent many-body physics and collective excitations that can arise even in systems with only short-range interactions. Understanding their low-temperature structure and spin Hamiltonian is key to explaining their magnetic properties, including unconventional quantum phases, phase transitions, and excited states. We study the metal-organic coordination compound (C$_5$H$_9$NH$_3$)$_2$CuBr$_4$ and its deuterated counterpart, which upon its discovery was identified as a candidate two-leg quantum ($S = 1/2$) spin ladder in the strong-leg coupling regime. By growing large single crystals and probing them with both bulk and microscopic techniques, we deduce that two previously unknown structural phase transitions take place between 136 K and 113 K. The low-temperature structure has a monoclinic unit cell giving rise to two inequivalent spin ladders. We further confirm the absence of long-range magnetic order down to 30 mK and discuss the implications of this two-ladder structure for the magnetic properties of (C$_5$H$_9$NH$_3$)$_2$CuBr$_4$.

Due to the pseudo-scalar nature of the axion-like particle (ALP), the CP- conserving production of two Higgs bosons via the ALP necessarily involves an additional Z or $\gamma$ boson. We examine the existing constraints from di-Higgs searches at Run 2 of the LHC and find that, despite the presence of extra objects in the final state, these searches are sensitive to a combination of ALP couplings to gluons and three-bosons in the TeV scale range. Additionally, we propose a specialized search strategy incorporating an energetic leptonic Z boson. This refined ALP-induced production process would allow for the identification of the h h $\rightarrow$ 4 b-jet final state and could potentially probe the TeV scale using data from Run 2 of the LHC. This production process can also occur through a coupling between the top quark and the ALP. We translate the current constraints on di-Higgs production into new limits on the ALP-top coupling., Comment: 19 pages, 9 figures

We report the first detection in the interstellar medium of $N$-cyanomethanimine (H$_2$CNCN), the stable dimer of HCN of highest energy, and the most complex organic molecule identified in space containing the prebiotically relevant NCN backbone. We have identified a plethora of $a$-type rotational transitions with 3 $\leq J_\text{up} \leq$ 11 and $K_\text{a} \leq$ 2 that belong to this species towards the Galactic Center G+0.693-0.027 molecular cloud, the only interstellar source showing the three cyanomethanimine isomers (including the $Z$- and $E$- isomers of $C$-cyanomethanimine, HNCHCN). We have derived a total column density for H$_2$CNCN of (2.9$\, \pm \,$0.1)$\times$10$^{12}$ cm$^{-2}$, which translates into a total molecular abundance with respect to H$_2$ of (2.1$\, \pm \,$0.3)$\times$10$^{-11}$. We have also revisited the previous detection of $E$- and $Z$-HNCHCN, and found a total $C/N$-cyanomethanimine abundance ratio of 31.8$\, \pm \,$1.8 and a $Z/E$-HNCHCN ratio of 4.5$\, \pm \,$0.2. While the latter can be explained on the basis of thermodynamic equilibrium, chemical kinetics are more likely responsible for the observed $C/N$-cyanomethanimine abundance ratio, where the gas-phase reaction between methanimine (CH$_2$NH) and the cyanogen radical (CN) arises as the primary formation route., Comment: 22 pages, 8 figures, 3 tables, 2 appendix - Accepted for publication in The Astrophysical Journal

We present the first detection in space of thionylimide (HNSO) toward the Galactic Center molecular cloud G+0.693-0.027, thanks to the superb sensitivity of an ultradeep molecular line survey carried out with the Yebes 40$\,$m and IRAM 30$\,$m telescopes. This molecule is the first species detected in the interstellar medium containing, simultaneously, N, S and O. We have identified numerous $K$$_a$ = 0, 1 and 2 transitions belonging to HNSO covering from $J$$_{\rm up}$ = 2 to $J$$_{\rm up}$ = 10, including several completely unblended features. We derive a molecular column density of $N$ = (8 $\pm$ 1)$\times$10$^{13}$ cm$^{-2}$, yielding a fractional abundance relative to H$_2$ of $\sim$6$\times$10$^{-10}$, which is about $\sim$37 and $\sim$4.8 times less abundant than SO and SO2, respectively. Although there are still many unknowns in the interstellar chemistry of NSO-bearing molecules, we propose that HNSO is likely formed through the reaction of the NSO radical and atomic H on the surface of icy grains, with alternative routes also deserving exploration. Finally, HNSO appears as a promising link between N- , S- and O- interstellar chemistry and its discovery paves the route to the detection of a new family of molecules in space., Comment: Forthcoming paper in The Astrophysical Journal Letters (in press)

In this paper we describe how to compute a Saito basis of a cusp, a plane curve with only one Puiseux pair. Moreover, the 1-forms of the Saito basis that we compute are characterized in terms of their divisorial orders associated to the "cuspidal" divisor of the minimal reduction of singularities of the cusp. We also introduce a new family of analytic invariants for plane curves computed in terms of Saito bases.

Hyperspectral (HS) imaging presents itself as a non-contact, non-ionizing and non-invasive technique, proven to be suitable for medical diagnosis. However, the volume of information contained in these images makes difficult providing the surgeon with information about the boundaries in real-time. To that end, High-Performance-Computing (HPC) platforms become necessary. This paper presents a comparison between the performances provided by five different HPC platforms while processing a spatial-spectral approach to classify HS images, assessing their main benefits and drawbacks. To provide a complete study, two different medical applications, with two different requirements, have been analyzed. The first application consists of HS images taken from neurosurgical operations; the second one presents HS images taken from dermatological interventions. While the main constraint for neurosurgical applications is the processing time, in other environments, as the dermatological one, other requirements can be considered. In that sense, energy efficiency is becoming a major challenge, since this kind of applications are usually developed as hand-held devices, thus depending on the battery capacity. These requirements have been considered to choose the target platforms: on the one hand, three of the most powerful Graphic Processing Units (GPUs) available in the market; and, on the other hand, a low-power GPU and a manycore architecture, both specifically thought for being used in battery-dependent environments., Comment: 18 pages, 7 figues

In this work, we present the technical details of the discussion presented in [J.J. Relancio, L.Santamar\'ia-Sanz (2024) arXiv:2403.18772], where we establish the basis of quantum theories of the free massive scalar, the massive fermionic, and the electromagnetic fields, in a doubly special relativity scenario. This construction is based on a geometrical interpretation of the kinematics of these kind of theories. In order to describe the modified actions, we find that a higher (indeed infinite) derivative field theory is needed, from which the deformed kinematics can be read. From our construction we are able to restrict the possible models of doubly special relativity to particular bases that preserve linear Lorentz invariance. We quantize the theories and also obtain a deformed version of the Maxwell equations. We analyze the electromagnetic vector potential either for an electric point-like source and a magnetic dipole. We observe that the electric and magnetic fields do not diverge at the origin for some models described with an anti de Sitter space but do for the de Sitter one in both problems., Comment: 15 pages, 5 figures

Recommender systems can be helpful for individuals to make well-informed decisions in complex financial markets. While many studies have focused on predicting stock prices, even advanced models fall short of accurately forecasting them. Additionally, previous studies indicate that individual investors often disregard established investment theories, favoring their personal preferences instead. This presents a challenge for stock recommendation systems, which must not only provide strong investment performance but also respect these individual preferences. To create effective stock recommender systems, three critical elements must be incorporated: 1) individual preferences, 2) portfolio diversification, and 3) the temporal dynamics of the first two. In response, we propose a new model, Portfolio Temporal Graph Network Recommender, PfoTGNRec, which can handle time-varying collaborative signals and incorporates diversification-enhancing sampling. On real-world individual trading data, our approach demonstrates superior performance compared to state-of-the-art baselines, including cutting-edge dynamic embedding models and existing stock recommendation models. Indeed, we show that PfoTGNRec is an effective solution that can balance customer preferences with the need to suggest portfolios with high Return-on-Investment. The source code and data are available at https://anonymous.4open.science/r/ICAIF2024-E23E.

Dimensionality reduction represents a critical preprocessing step in order to increase the efficiency and the performance of many hyperspectral imaging algorithms. However, dimensionality reduction algorithms, such as the Principal Component Analysis (PCA), suffer from their computationally demanding nature, becoming advisable for their implementation onto high-performance computer architectures for applications under strict latency constraints. This work presents the implementation of the PCA algorithm onto two different high-performance devices, namely, an NVIDIA Graphics Processing Unit (GPU) and a Kalray manycore, uncovering a highly valuable set of tips and tricks in order to take full advantage of the inherent parallelism of these high-performance computing platforms, and hence, reducing the time that is required to process a given hyperspectral image. Moreover, the achieved results obtained with different hyperspectral images have been compared with the ones that were obtained with a field programmable gate array (FPGA)-based implementation of the PCA algorithm that has been recently published, providing, for the first time in the literature, a comprehensive analysis in order to highlight the pros and cons of each option., Comment: 30 pages, 10 figures

Non-local quantum field theories could be a solution to the inconsistencies arising when quantizing gravity. Doubly special relativity is regarded as a low-energy limit of a quantum gravity theory with testable predictions. We present a new formulation of quantum field theories in doubly special relativity with non-local behavior. Our construction restricts the models to those showing linear Lorentz invariance. The deformed Klein--Gordon, Dirac, and electromagnetic Lagrangians are derived. The deformed Maxwell equations and the electric potential of a point charge are discussed., Comment: 5 pages, 1 figure

Zero-noise extrapolation (ZNE) stands as the most widespread quantum error mitigation technique in order to aim the recovery of noise-free expectation values of observables of interest by means of Noisy Intermediate-Scale Quantum (NISQ) machines. Recently, Otten and Gray proposed a multidimensional generalization of polynomial ZNE for systems where there is not a tunable global noise source [Phys. Rev. A \textbf{99,} 012338 (2019)]. Specifically, the authors refer to multiqubit systems where each of the qubits experiences several noise processes with different rates, i.e. a non-identically distributed noise model. The authors proposed a hypersurface method for mitigating such noise, which is technically correct. While effective, the proposed method presents an unbearable experiment repetition overhead, making it impractical, at least from the perspective of quantum computing. In this comment, we show that the traditional extrapolation techniques can be applied for such non-identically distributed noise setting consisted of many different noise sources, implying that the measurement overhead is reduced considerably. For doing so, we clarify what it is meant by a tunable global noise source in the context of ZNE, concept that we consider important to be clarified for a correct understanding about how and why these methods work., Comment: 5 pages, 1 figure; comment on arXiv:1806.07860

Over the last two decades, augmented reality (AR) has led to the rapid development of new interfaces in various fields of social and technological application domains. One such domain is medicine, and to a higher extent surgery, where these visualization techniques help to improve the effectiveness of preoperative and intraoperative procedures. Following this trend, this paper presents SLIMBRAIN, a real-time acquisition and processing AR system suitable to classify and display brain tumor tissue from hyperspectral (HS) information. This system captures and processes HS images at 14 frames per second (FPS) during the course of a tumor resection operation to detect and delimit cancer tissue at the same time the neurosurgeon operates. The result is represented in an AR visualization where the classification results are overlapped with the RGB point cloud captured by a LiDAR camera. This representation allows natural navigation of the scene at the same time it is captured and processed, improving the visualization and hence effectiveness of the HS technology to delimit tumors. The whole system has been verified in real brain tumor resection operations., Comment: 14 pages, 19 figues

We develop Polaris, the first safety-focused LLM constellation for real-time patient-AI healthcare conversations. Unlike prior LLM works in healthcare focusing on tasks like question answering, our work specifically focuses on long multi-turn voice conversations. Our one-trillion parameter constellation system is composed of several multibillion parameter LLMs as co-operative agents: a stateful primary agent that focuses on driving an engaging conversation and several specialist support agents focused on healthcare tasks performed by nurses to increase safety and reduce hallucinations. We develop a sophisticated training protocol for iterative co-training of the agents that optimize for diverse objectives. We train our models on proprietary data, clinical care plans, healthcare regulatory documents, medical manuals, and other medical reasoning documents. We align our models to speak like medical professionals, using organic healthcare conversations and simulated ones between patient actors and experienced nurses. This allows our system to express unique capabilities such as rapport building, trust building, empathy and bedside manner. Finally, we present the first comprehensive clinician evaluation of an LLM system for healthcare. We recruited over 1100 U.S. licensed nurses and over 130 U.S. licensed physicians to perform end-to-end conversational evaluations of our system by posing as patients and rating the system on several measures. We demonstrate Polaris performs on par with human nurses on aggregate across dimensions such as medical safety, clinical readiness, conversational quality, and bedside manner. Additionally, we conduct a challenging task-based evaluation of the individual specialist support agents, where we demonstrate our LLM agents significantly outperform a much larger general-purpose LLM (GPT-4) as well as from its own medium-size class (LLaMA-2 70B).

In this paper we give full classification of the axially symmetric one phase minimizers of the Alt-Phillips free boundary problem in dimensions 3, 4, and 5. To accomplish this, we establish a stability inequality that extends the one for the Alt-Caffarelli problem.

We present two alternative methods for optimizing minimum energy conical intersection (MECI) molecular geometries without knowledge of the derivative coupling (DC). These methods are based on the utilization of Lagrange multipliers: i) one method uses an approximate calculation of the DC, while the other ii) do not require the DC. Both methods use the fact that information of the DC is contained in the Hessian of the squared energy difference. Tests done on a set of small molecular systems, in comparison with other methods, show the ability of the proposed methods to optimize MECIs. Finally, we apply the methods to the furimamide molecule, to optimize and characterize its S$_1$ /S$_2$ MECI, and to optimizing the S$_0$ /S$_1$ MECI of the silver trimer.

The push-forward operation enables one to redistribute a probability measure through a deterministic map. It plays a key role in statistics and optimization: many learning problems (notably from optimal transport, generative modeling, and algorithmic fairness) include constraints or penalties framed as push-forward conditions on the model. However, the literature lacks general theoretical insights on the (non)convexity of such constraints and its consequences on the associated learning problems. This paper aims at filling this gap. In a first part, we provide a range of sufficient and necessary conditions for the (non)convexity of two sets of functions: the maps transporting one probability measure to another; the maps inducing equal output distributions across distinct probability measures. This highlights that for most probability measures, these push-forward constraints are not convex. In a second time, we show how this result implies critical limitations on the design of convex optimization problems for learning generative models or group-fair predictors. This work will hopefully help researchers and practitioners have a better understanding of the critical impact of push-forward conditions onto convexity.

In this short review we present the key definitions, ideas and techniques involved in the study of symmetry resolved entanglement measures, with a focus on the symmetry resolved entanglement entropy. In order to be able to define such entanglement measures, it is essential that the theory under study possess an internal symmetry. Then, symmetry resolved entanglement measures quantify the contribution to a particular entanglement measure that can be associated to a chosen symmetry sector. Our review focuses on conformal (gapless/massless/critical) and integrable (gapped/massive) quantum field theories, where the leading computational technique employs symmetry fields known as (composite) branch point twist fields., Comment: 32 pages, 1 figure. v2 includes additional references

The fast dynamics of molecular polaritonics is scrutinized theoretically through the implementation of two-dimensional spectroscopy protocols. We derive conceptually simple and computationally efficient formulas to calculate two-dimensional spectra for molecules, each of them modeled as a system of two electronic states including vibrational relaxation, immersed in an optical cavity, thus coupled to quantized radiation. Cavity photon losses and molecular relaxation are incorporated into the Hamiltonian dynamics to form an open quantum system that is solved through a master equation. In the collective case, the relaxation dynamics into dark states reveals to be the crucial factor to explain the asymmetries in both the diagonal and cross peaks of two-dimensional spectra for long waiting times between excitation and detection, a feature shown by recent experiments. Our theoretical method provides a deeper insight in those processes that yield relevant signals in multidimensional molecular spectroscopy., Comment: 15 pages, 11 figures