Miracle-dz/UniFAR-FTUs huggingface dataset:
L G ] 7 O ct 2 01 9 Neural network integral representations with the ReLU activation function

We derive a formula for neural network integral representations on the sphere with the ReLU activation function under the finite L1 norm (with respect to Lebesgue measure on the sphere) assumption on the outer weights. In one dimensional case, we further solve via a closed-form formula all possible such representations. Additionally, in this case our formula allows one to explicitly solve the least L1 norm neural network representation for a given function.
Sensitivity of the Cherenkov Telescope Array to a dark matter signal from the Galactic centre

We provide an updated assessment of the power of the Cherenkov Telescope Array (CTA) to search for thermally produced dark matter at the TeV scale, via the associated gamma-ray signal from pair-annihilating dark matter particles in the region around the Galactic centre. We find that CTA will open a new window of discovery potential, significantly extending the range of robustly testable models given a standard cuspy profile of the dark matter density distribution. Importantly, even for a cored profile, the projected sensitivity of CTA will be sufficient to probe various well-motivated models of thermally produced dark matter at the TeV scale. This is due to CTA’s unprecedented sensitivity, angular and energy resolutions, and the planned observational strategy. The survey of the inner Galaxy will cover a much larger region than corresponding previous observational campaigns with imaging atmospheric Cherenkov telescopes. CTA will map with unprecedented precision the large-scale diffuse emission in high-energy gamma rays, constituting a background for dark matter searches for which we adopt state-of-the-art models based on current data. Throughout our analysis, we use up-to-date event reconstruction Monte Carlo tools developed by the CTA consortium, and pay special attention to quantifying the level of instrumental systematic uncertainties, as well as background template systematic errors, required to probe thermally produced dark matter at these energies.
Combination antiretroviral therapy and the risk of myocardial infarction.

BACKGROUND It remains controversial whether exposure to combination antiretroviral treatment increases the risk of myocardial infarction. METHODS In this prospective observational study, we enrolled 23,468 patients from 11 previously established cohorts from December 1999 to April 2001 and collected follow-up data until February 2002. Data were collected on infection with the human immunodeficiency virus and on risk factors for and the incidence of myocardial infarction. Relative rates were calculated with Poisson regression models. Combination antiretroviral therapy was defined as any combination regimen of antiretroviral drugs that included a protease inhibitor or a nonnucleoside reverse transcriptase inhibitor. RESULTS Over a period of 36,199 person-years, 126 patients had a myocardial infarction. The incidence of myocardial infarction increased with longer exposure to combination antiretroviral therapy (adjusted relative rate per year of exposure, 1.26 [95 percent confidence interval, 1.12 to 1.41]; P<0.001). Other factors significantly associated with myocardial infarction were older age, current or former smoking, previous cardiovascular disease, and male sex, but not a family history of coronary heart disease. A higher total serum cholesterol level, a higher triglyceride level, and the presence of diabetes were also associated with an increased incidence of myocardial infarction. CONCLUSIONS Combination antiretroviral therapy was independently associated with a 26 percent relative increase in the rate of myocardial infarction per year of exposure during the first four to six years of use. However, the absolute risk of myocardial infarction was low and must be balanced against the marked benefits from antiretroviral treatment.
Evaluation of Emotional Responses to Television Advertising through Neuromarketing

Since the last century, we have witnessed a steady evolution of advertising techniques in an effort to adapt to the new social context in the market. As a strategic resource, Neuroscience brings a new perspective by allowing you to explore those difficult or verbally unconscious motives behind consumer behaviours. The present work aims to discover the relationship between the emotions induced in audiovisual advertising messages and their impact on the memory of the subjects. To achieve this goal, an experiment was carried out with eight audiovisual advertising messages (six representatives of the basic emotions: joy, surprise, anger, disgust, fear and sadness, and two rational ones that show the technical specifications of the product). Neuromarketing techniques such as the electrical activity of the heart (ECG) and the electrodermal activity (EDA) of the subjects are used, on one hand; and, on the other, a conventional research technique, a questionnaire applied to the subjects that participated in the research. The results show variations in the measures performed in the commercials corresponding to joy, surprise and anger, while for both, remembrance of the message transmitted and activity of the advertiser, the commercial with the best results has been the one regarding sadness, advertisement that has also been considered the most attractive for participating subjects. RESUMEN Desde el siglo pasado hemos presenciado una evolución constante de las técnicas de comunicación publicitarias en un intento de adaptación a las nuevas realidades sociales del mercado. Como recurso estratégico, la Neurociencia aporta una nueva perspectiva al permitir explorar aquellos motivos difíciles de verbalizar o inconscientes que hay detrás de los comportamientos de los consumidores. El presente trabajo tiene como objetivo descubrir la relación entre las emociones inducidas en los mensajes publicitarios audiovisuales y su impacto en el recuerdo de los sujetos. Para alcanzar este objetivo se ha realizado un experimento con ocho mensajes publicitarios audiovisuales (seis representativos de seis emociones básicas: alegría, sorpresa, ira, asco, miedo y tristeza; y dos racionales) en el que se han utilizado, por un lado, técnicas de Neuromarketing como son la actividad eléctrica cardíaca (ECG) y la actividad eléctrica de la dermis (AED) de los sujetos; y, por otro, una técnica de investigación convencional, un cuestionario aplicado a los sujetos que han participado en la investigación. Los resultados ponen de manifiesto variaciones en las medidas realizadas en los mensajes correspondientes a la alegría, la sorpresa y la ira, mientras que, tanto para el recuerdo sugerido del mensaje trasmitido como para la actividad del anunciante, el anuncio con mejores resultados ha sido el de la tristeza, anuncio que también ha sido considerado el más atractivo para los sujetos participantes.
Quantum Lower Bounds by Sample-to-Query Lifting

We propose a quantum sample-to-query lifting theorem. It reveals a quadratic relation between quantum sample and query complexities regarding quantum property testing, which is optimal and saturated by quantum state discrimination. Based on it, we provide a new method for proving lower bounds on quantum query algorithms from an information theory perspective. Using this method, we prove the following new results: 1. A matching lower bound $\widetilde \Omega(\beta)$ for quantum Gibbs sampling at inverse temperature $\beta$, showing that the quantum Gibbs sampler by Gily\'en, Su, Low, and Wiebe (2019) is optimal. 2. A new lower bound $\widetilde \Omega(1/\sqrt{\Delta})$ for the entanglement entropy problem with gap $\Delta$, which was recently studied by She and Yuen (2023). In addition, we also provide unified proofs for some known lower bounds that have been proven previously via different techniques, including those for phase/amplitude estimation and Hamiltonian simulation.
Statistical Estimation Under Distribution Shift: Wasserstein Perturbations and Minimax Theory

Distribution shifts are a serious concern in modern statistical learning as they can systematically change the properties of the data away from the truth. We focus on Wasserstein distribution shifts, where every data point may undergo a slight perturbation, as opposed to the Huber contamination model where a fraction of observations are outliers. We consider perturbations that are either independent or coordinated joint shifts across data points. We analyze several important statistical problems, including location estimation, linear regression, and non-parametric density estimation. Under a squared loss for mean estimation and prediction error in linear regression, we find the exact minimax risk, a least favorable perturbation, and show that the sample mean and least squares estimators are respectively optimal. For other problems, we provide nearly optimal estimators and precise finite-sample bounds. We also introduce several tools for bounding the minimax risk under general distribution shifts, not just for Wasserstein perturbations, such as a smoothing technique for location families, and generalizations of classical tools including least favorable sequences of priors, the modulus of continuity, as well as Le Cam's, Fano's, and Assouad's methods.
Lie-algebraic classical simulations for variational quantum computing

Classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity, and in the development of quantum technologies. Compared to other techniques for efficient classical simulations, methods relying on the Lie-algebraic structure of quantum dynamics have received relatively little attention. At their core, these simulations leverage the underlying Lie algebra - and the associated Lie group - of a dynamical process. As such, rather than keeping track of the individual entries of large matrices, one instead keeps track of how its algebraic decomposition changes during the evolution. When the dimension of the algebra is small (e.g., growing at most polynomially in the system size), one can leverage efficient simulation techniques. In this work, we review the basis for such methods, presenting a framework that we call"$\mathfrak{g}$-sim", and showcase their efficient implementation in several paradigmatic variational quantum computing tasks. Specifically, we perform Lie-algebraic simulations to train and optimize parametrized quantum circuits, design enhanced parameter initialization strategies, solve tasks of quantum circuit synthesis, and train a quantum-phase classifier.
Pointwise localization and sharp weighted bounds for Rubio de Francia square functions

Let $H_\omega f$ be the Fourier restriction of $f\in L^2(\mathbb{R})$ to an interval $\omega\subset \mathbb{R}$. If $\Omega$ is an arbitrary collection of pairwise disjoint intervals, the square function of $\{H_\omega f: \omega \in \Omega\}$ is termed the Rubio de Francia square function $T^\Omega$. This article proves a pointwise bound for $T^\Omega f$ by a sparse operator involving local $L^2$-averages. A pointwise bound for the smooth version of $T^\Omega$ by a sparse square function is also proved. These pointwise localization principles lead to quantified $L^p(w)$, $p>2$ and weak $L^p(w)$, $p\geq 2$ norm inequalities for $T^\Omega$. In particular, the obtained weak $L^p(w)$ norm bounds are new for $p\geq 2$ and sharp for $p>2$. The proofs rely on sparse bounds for abstract balayages of Carleson sequences, local orthogonality and very elementary time-frequency analysis techniques. The paper also contains two results related to the outstanding conjecture that $T^\Omega$ is bounded on $L^2(w)$ if and only if $w\in A_1$. The conjecture is verified for radially decreasing even $A_1$ weights, and in full generality for the Walsh group analogue of $T^\Omega$.
Dimensionless parameter of structural ordering and excess entropy of metallic and tellurite glasses

Using a notion on the excess entropy of glass with respect to the counterpart crystal, we introduce a simple dimensionless order parameter $\xi$, which changes from $\xi \rightarrow 0$ to $\xi \rightarrow 1$. The former case corresponds to a strongly disordered liquid-like structure while the latter situation describes a highly ordered crystal-like glass. This approach is applied to 13 metallic and 2 tellurite glasses. We found that $\xi$ is strongly sensitive to structural state and/or chemical composition. It can be also used for a comparison of the order in glasses belonging to different classes and appear to represent a new way of structural analysis.
Hierarchical Federated Learning in Wireless Networks: Pruning Tackles Bandwidth Scarcity and System Heterogeneity

While a practical wireless network has many tiers where end users do not directly communicate with the central server, the users' devices have limited computation and battery powers, and the serving base station (BS) has a fixed bandwidth. Owing to these practical constraints and system models, this paper leverages model pruning and proposes a pruning-enabled hierarchical federated learning (PHFL) in heterogeneous networks (HetNets). We first derive an upper bound of the convergence rate that clearly demonstrates the impact of the model pruning and wireless communications between the clients and the associated BS. Then we jointly optimize the model pruning ratio, central processing unit (CPU) frequency and transmission power of the clients in order to minimize the controllable terms of the convergence bound under strict delay and energy constraints. However, since the original problem is not convex, we perform successive convex approximation (SCA) and jointly optimize the parameters for the relaxed convex problem. Through extensive simulation, we validate the effectiveness of our proposed PHFL algorithm in terms of test accuracy, wall clock time, energy consumption and bandwidth requirement.
Uncertainty Analysis for Accurate Ground Truth Trajectories with Robotic Total Stations

In the context of robotics, accurate ground truth positioning is essential for the development of Simultaneous Localization and Mapping (SLAM) and control algorithms. Robotic Total Stations (RTSs) provide accurate and precise reference positions in different types of outdoor environments, especially when compared to the limited accuracy of Global Navigation Satellite System (GNSS) in cluttered areas. Three RTSs give the possibility to obtain the six-Degrees Of Freedom (DOF) reference pose of a robotic platform. However, the uncertainty of every pose is rarely computed for trajectory evaluation. As evaluation algorithms are getting increasingly precise, it becomes crucial to take into account this uncertainty. We propose a method to compute this six-DOF uncertainty from the fusion of three RTSs based on Monte Carlo (MC) methods. This solution relies on point-to-point minimization to propagate the noise of RTSs on the pose of the robotic platform. Five main noise sources are identified to model this uncertainty: noise inherent to the instrument, tilt noise, atmospheric factors, time synchronization noise, and extrinsic calibration noise. Based on extensive experimental work, we compare the impact of each noise source on the prism uncertainty and the final estimated pose. Tested on more than 50 km of trajectories, our comparison highlighted the importance of the calibration noise and the measurement distance, which should be ideally under 75 m. Moreover, it has been noted that the uncertainty on the pose of the robot is not prominently affected by one particular noise source, compared to the others.
Excited bound states and their role in dark matter production

We explore the impact of highly excited bound states on the evolution of number densities of new physics particles, specifically dark matter, in the early Universe. Focusing on dipole transitions within perturbative, unbroken gauge theories, we develop an efficient method for including around a million bound state formation and bound-to-bound transition processes. This enables us to examine partial-wave unitarity and accurately describe the freeze-out dynamics down to very low temperatures. In the non-Abelian case, we find that highly excited states can prevent the particles from freezing out, supporting a continuous depletion in the regime consistent with perturbativity and unitarity. We apply our formalism to a simplified dark matter model featuring a colored and electrically charged $t$-channel mediator. Our focus is on the regime of superWIMP production which is commonly characterized by a mediator freeze-out followed by its late decay into dark matter. In contrast, we find that excited states render mediator depletion efficient all the way until its decay, introducing a dependence of the dark matter density on the mediator lifetime as a novel feature. The impact of bound states on the viable dark matter mass can amount to an order of magnitude, relaxing constraints from Lyman-$\alpha$ observations.
Eigenvalue bounds for Schrödinger operators with complex potentials. II

Laptev and Safronov conjectured that any non-positive eigenvalue of a Schrodinger operator −Δ+Vin L2(Rν) with complex potential has absolute value at most a constant times ∥V∥(γ+ν/2)/γγ+ν/2 for 0<γ≤ν/2 in dimension ν≥2. We prove this conjecture for radial potentials if 0<γ<ν/2 and we 'almost disprove' it for general potentials if 1/2<γ<ν/2. In addition, we prove various bounds that hold, in particular, for positive eigenvalues.
Characterization of differences in immune responses during bolus and continuous infusion endotoxin challenges using mathematical modelling.

Endotoxin administration is commonly used to study the inflammatory response, and though traditionally given as a bolus injection, it can be administered as a continuous infusion over multiple hours. Several studies hypothesize that the latter better represents the prolonged and pronounced inflammation observed in conditions like sepsis. Yet very few experimental studies have administered endotoxin using both strategies, leaving significant gaps in determining the underlying mechanisms responsible for their differing immune responses. We used mathematical modelling to analyse cytokine data from two studies administering a 2 ng kg-1 dose of endotoxin, one as a bolus and the other as a continuous infusion over 4 h. Using our model, we simulated the dynamics of mean and subject-specific cytokine responses as well as the response to long-term endotoxin administration. Cytokine measurements revealed that the bolus injection led to significantly higher peaks for interleukin (IL)-8, while IL-10 reaches higher peaks during continuous administration. Moreover, the peak timing of all measured cytokines occurred later with continuous infusion. We identified three model parameters that significantly differed between the two administration methods. Monocyte activation of IL-10 was greater during the continuous infusion, while tumour necrosis factor α $ {\alpha} $ and IL-8 recovery rates were faster for the bolus injection. This suggests that a continuous infusion elicits a stronger, longer-lasting systemic reaction through increased stimulation of monocyte anti-inflammatory mediator production and decreased recovery of pro-inflammatory catalysts. Furthermore, the continuous infusion model exhibited prolonged inflammation with recurrent peaks resolving within 2 days during long-term (20-32 h) endotoxin administration.
Correlation of the tokamak H-mode density limit with ballooning stability at the separatrix

We show for JET and ASDEX Upgrade, based on Thomson-scattering measurements, a clear correlation of the density limit of the tokamak H-mode high-confinement regime with the approach to the ideal ballooning instability threshold at the periphery of the plasma. It is shown that the MHD ballooning parameter at the separatrix position αsep increases about linearly with the separatrix density normalized to Greenwald density, ne,sep/nGW for a wide range of discharge parameters in both devices. The observed operational space is found to reach at maximum ne,sep/nGW≈0.4–0.5 at values for αsep≈2–2.5, in the range of theoretical predictions for ballooning instability. This work supports the hypothesis that the H-mode density limit may be set by ballooning stability at the separatrix.
Towards a Learning Theory of Causation

We pose causal inference as the problem of learning to classify probability distributions. In particular, we assume access to a collection {(Si, li)}i=1, where each Si is a sample drawn from the probability distribution ofXi×Yi, and li is a binary label indicating whether “Xi → Yi” or “Xi ← Yi”. Given these data, we build a causal inference rule in two steps. First, we featurize each Si using the kernel mean embedding associated with some characteristic kernel. Second, we train a binary classifier on such embeddings to distinguish between causal directions. We present generalization bounds showing the statistical consistency and learning rates of the proposed approach, and provide a simple implementation that achieves state-of-the-art cause-effect inference. Furthermore, we extend our ideas to infer causal relationships between more than two variables.
STARLIKENESS AND SCHWARZIAN DERIVATIVES OF HIGHER ORDER OF ANALYTIC FUNCTIONS

In this paper we apply the third-order diﬀerential subordination results to normalized analytic functions in the open unit disk. We obtain appropriate classes of admissible functions and ﬁnd some suf-ﬁcient conditions of functions to be starlike associated with Tamanoi’s Schwarzian derivative of third order. Several interesting examples are also discussed.
Generic stability, randomizations, and NIP formulas

We prove a number of results relating the concepts of Keisler measures, generic stability, randomizations, and NIP formulas. Among other things, we do the following: (1) We introduce the notion of a Keisler-Morley measure, which plays the role of a Morley sequence for a Keisler measure. We prove that if $\mu$ is fim over $M$, then for any Keisler-Morley measure $\lambda$ in $\mu$ over $M$ and any formula $\varphi(x,b)$, $\lim_{i \to \infty} \lambda(\varphi(x_i,b)) = \mu(\varphi(x,b))$. We also show that any measure satisfying this conclusion must be fam. (2) We study the map, defined by Ben Yaacov, taking a definable measure $\mu$ to a type $r_\mu$ in the randomization. We prove that this map commutes with Morley products, and that if $\mu$ is fim then $r_\mu$ is generically stable. (3) We characterize when generically stable types are closed under Morley products by means of a variation of ict-patterns. Moreover, we show that NTP$_2$ theories satisfy this property. (4) We prove that if a local measure admits a suitably tame global extension, then it has finite packing numbers with respect to any definable family. We also characterize NIP formulas via the existence of tame extensions for local measures.