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In this paper, we focus on estimating the causal effect of an intervention over time on a dynamical system. To that end, we formally define causal interventions and their effects over time on discrete-time stochastic processes (DSPs). Then, we show under which conditions the equilibrium states of a DSP, both before and after a causal intervention, can be captured by a structural causal model (SCM). With such an equivalence at hand, we provide an explicit mapping from vector autoregressive models (VARs), broadly applied in econometrics, to linear, but potentially cyclic and/or affected by unmeasured confounders, SCMs. The resulting causal VAR framework allows us to perform causal inference over time from observational time series data. Our experiments on synthetic and real-world datasets show that the proposed framework achieves strong performance in terms of observational forecasting while enabling accurate estimation of the causal effect of interventions on dynamical systems. We demonstrate, through a case study, the potential practical questions that can be addressed using the proposed causal VAR framework.

We introduce an innovative approach to enhancing the empirical risk minimization (ERM) process in model training through a refined reweighting scheme of the training data to enhance fairness. This scheme aims to uphold the sufficiency rule in fairness by ensuring that optimal predictors maintain consistency across diverse sub-groups. We employ a bilevel formulation to address this challenge, wherein we explore sample reweighting strategies. Unlike conventional methods that hinge on model size, our formulation bases generalization complexity on the space of sample weights. We discretize the weights to improve training speed. Empirical validation of our method showcases its effectiveness and robustness, revealing a consistent improvement in the balance between prediction performance and fairness metrics across various experiments., Comment: accepted at ECAI 2024

Deferring systems extend supervised Machine Learning (ML) models with the possibility to defer predictions to human experts. However, evaluating the impact of a deferring strategy on system accuracy is still an overlooked area. This paper fills this gap by evaluating deferring systems through a causal lens. We link the potential outcomes framework for causal inference with deferring systems. This allows us to identify the causal impact of the deferring strategy on predictive accuracy. We distinguish two scenarios. In the first one, we can access both the human and the ML model predictions for the deferred instances. In such a case, we can identify the individual causal effects for deferred instances and aggregates of them. In the second scenario, only human predictions are available for the deferred instances. In this case, we can resort to regression discontinuity design to estimate a local causal effect. We empirically evaluate our approach on synthetic and real datasets for seven deferring systems from the literature.

Testing for discrimination consists of deriving a profile, known as the comparator, similar to the profile making the discrimination claim, known as the complainant, and comparing the outcomes of these two profiles. An important aspect for establishing discrimination is evidence, often obtained via discrimination testing tools that implement the complainant-comparator pair. In this work, we revisit the role of the comparator in discrimination testing. We argue for the causal modeling nature of deriving the comparator, and introduce a two-kinds classification for the comparator: the ceteris paribus (CP), and mutatis mutandis (MM) comparators. The CP comparator is the standard one among discrimination testing, representing an idealized comparison as it aims for having a complainant-comparator pair that only differs on membership to the protected attribute. As an alternative to it, we define the MM comparator, which requires that the comparator represents what would have been of the complainant without the effects of the protected attribute on the non-protected attributes. The complainant-comparator pair, in that case, may also be dissimilar in terms of all attributes. We illustrate these two comparators and their impact on discrimination testing using a real illustrative example. Importantly, we position generative models and, overall, machine learning methods as useful tools for constructing the MM comparator and, in turn, achieving more complex and realistic comparisons when testing for discrimination.

We study the potential of the axion, $a$, of Quantum Chromodynamics, in the two-flavor color superconducting phase of cold and dense quark matter. We adopt a Nambu-Jona-Lasinio-like model. Our interaction contains two terms, one preserving and one breaking the $U(1)_A$ symmetry: the latter is responsible of the coupling of axions to quarks. We introduce two quark condensates, $h_L$ and $h_R$, describing condensation for left-handed and right-handed quarks respectively; we then study the loci of the minima of the thermodynamic potential, $\Omega$, in the $(h_L,h_R)$ plane, noticing how the instanton-induced interaction favors condensation in the scalar channel when the $\theta-$angle, $\theta=a/f_a$, vanishes. Increasing $\theta$ we find a phase transition where the scalar condensate rotates into a pseudo-scalar one. We present an analytical result for the topological susceptibility, $\chi$, in the superconductive phase, which stands both at zero and at finite temperature. Finally, we compute the axion mass and its self-coupling. In particular, the axion mass $m_a$ is related to the full topological susceptibility via $\chi=m_a^2 f_a^2$, hence our result for $\chi$ gives an analytical result for $m_a$ in the superconductive phase of high-density Quantum Chromodynamics., Comment: Few references added, few typos corrected, upgraded Fig.3 and Fig.6. Version accepted for publication on Physical Review D

Many of the most sensitive physics experiments searching for rare events, like neutrinoless double beta ($0\nu\beta\beta$) decay and dark matter interactions, rely on cryogenic macro-calorimeters operating at the mK-scale. Located underground at the Gran Sasso National Laboratory (LNGS), in central Italy, CUORE (Cryogenic Underground Observatory for Rare Events) is one of the leading experiments for the search of $0\nu\beta\beta$ decay, implementing the low-temperature calorimetric technology. We present a novel multi-detector analysis to correlate environmental phenomena with the low-frequency noise of low-temperature calorimeters. Indeed, the correlation of marine and seismic data with data from a pair of CUORE detectors indicates that cryogenic detectors are sensitive not only to intense vibrations generated by earthquakes, but also to the much fainter vibrations induced by marine microseisms in the Mediterranean Sea due to the motion of sea waves. Proving that cryogenic macro-calorimeters are sensitive to such environmental sources of noise opens the possibility of studying their impact on the detectors physics-case sensitivity. Moreover, this study could pave the road for technology developments dedicated to the mitigation of the noise induced by marine microseisms, from which the entire community of cryogenic calorimeters can benefit.

This study investigates the evolution and dissociation dynamics of $c\bar{c}$ and $b\bar{b}$ pairs within the pre-equilibrium, gluon-dominated stage of high energy nuclear collisions. An attractive potential made of a perturbative Coulomb-like term and of a confining term is used to simulate the attractive strong force in the pairs. Besides, we implement the interaction of the pairs with the evolving Glasma fields by virtue of the Wong equations. The interaction with the classical color fields dominates the dynamics, causing an increase in pair separation and subsequent dissociation. The observed finite probability of dissociation for these states reveals the intricate interplay between QCD dynamics and the suppression of $c\bar{c}$ and $b\bar{b}$ states during the pre-equilibrium stage. The research highlights differences between $c\bar{c}$ and $b\bar{b}$ pairs, revealing the role of quark flavor in the dissociation process. Dissociation spectra analysis indicates a peak shift towards higher momentum, reflecting a slight energy gain by the pairs. This investigation provides valuable insights into the complex dynamics of $c\bar{c}$ and $b\bar{b}$ pairs in the Glasma, which may help in better interpretation of experimental results on further integration with subsequent phases of the created matter., Comment: 10 pages, 8 figures

Planets in binary systems are a fascinating and yet poorly understood phenomenon. Since there are only a few known large-separation systems in which both components host planets, characterizing them is a key target for planetary science. In this paper, we aim to carry out an exhaustive analysis of the interesting XO-2 system, where one component appears to be a system with only one planet, while the other has at least three planets. Over the last 9 years, we have collected 39 spectra of XO-2N and 106 spectra of XO-2S with the High Accuracy Radial velocity Planet Searcher for the Northern emisphere (HARPS-N) in the framework of the Global Architecture of Planetary Systems project, from which we derived precise radial velocity and activity indicator measurements. Additional spectroscopic data from the High Resolution Echelle Spectrometer and from the High Dispersion Spectrograph, and the older HARPS-N data presented in previous papers, have also been used to increase the total time span. We also used photometric data from TESS to search for potential transits that have not been detected yet. For our analysis, we mainly used PyORBIT, an advanced Python tool for the Bayesian analysis of RVs, activity indicators, and light curves. We found evidence for an additional long-period planet around XO-2S and characterized the activity cycle likely responsible for the long-term RV trend noticed for XO-2N. The new candidate is an example of a Jovian analog with $m\sin i \sim 3.7$ M$_J$, $a \sim 5.5$ au, and $e = 0.09$. We also analyzed the stability and detection limits to get some hints about the possible presence of additional planets. Our results show that the planetary system of XO-2S is at least one order of magnitude more massive than that of XO-2N. The implications of these findings for the interpretation of the previously known abundance difference between components are also discussed.

Perception occurs when two individuals interpret the same information differently. Despite being a known phenomenon with implications for bias in decision-making, as individual experience determines interpretation, perception remains largely overlooked in machine learning (ML) research. Modern decision flows, whether partially or fully automated, involve human experts interacting with ML applications. How might we then, e.g., account for two experts that interpret differently a deferred instance or an explanation from a ML model? To account for perception, we first need to formulate it. In this work, we define perception under causal reasoning using structural causal models (SCM). Our framework formalizes individual experience as additional causal knowledge that comes with and is used by a human expert (read, decision maker). We present two kinds of causal perception, unfaithful and inconsistent, based on the SCM properties of faithfulness and consistency. Further, we motivate the importance of perception within fairness problems. We illustrate our framework through a series of decision flow examples involving ML applications and human experts., Comment: arXiv admin note: text overlap with arXiv:2305.09535 by other authors

With the increasing deployment of machine learning models in many socially sensitive tasks, there is a growing demand for reliable and trustworthy predictions. One way to accomplish these requirements is to allow a model to abstain from making a prediction when there is a high risk of making an error. This requires adding a selection mechanism to the model, which selects those examples for which the model will provide a prediction. The selective classification framework aims to design a mechanism that balances the fraction of rejected predictions (i.e., the proportion of examples for which the model does not make a prediction) versus the improvement in predictive performance on the selected predictions. Multiple selective classification frameworks exist, most of which rely on deep neural network architectures. However, the empirical evaluation of the existing approaches is still limited to partial comparisons among methods and settings, providing practitioners with little insight into their relative merits. We fill this gap by benchmarking 18 baselines on a diverse set of 44 datasets that includes both image and tabular data. Moreover, there is a mix of binary and multiclass tasks. We evaluate these approaches using several criteria, including selective error rate, empirical coverage, distribution of rejected instance's classes, and performance on out-of-distribution instances. The results indicate that there is not a single clear winner among the surveyed baselines, and the best method depends on the users' objectives., Comment: Published in The Journal of Data centric Machine Learning Research (DMLR), Vol 1, (17):1-58 (2024)

Decision Trees are accessible, interpretable, and well-performing classification models. A plethora of variants with increasing expressiveness has been proposed in the last forty years. We contrast the two families of univariate DTs, whose split functions partition data through axis-parallel hyperplanes, and multivariate DTs, whose splits instead partition data through oblique hyperplanes. The latter include the former, hence multivariate DTs are in principle more powerful. Surprisingly enough, however, univariate DTs consistently show comparable performances in the literature. We analyze the reasons behind this, both with synthetic and real-world benchmark datasets. Our research questions test whether the pre-processing phase of removing correlation among features in datasets has an impact on the relative performances of univariate vs multivariate DTs. We find that existing benchmark datasets are likely biased towards favoring univariate DTs.

We investigate the thermodynamic geometry of the quark-meson model at finite temperature, $T$, and quark number chemical potential, $\mu$. We extend previous works by the inclusion of fluctuations exploiting the functional renormalization group approach. We use recent developments to recast the flow equation into the form of an advection-diffusion equation. We adopt the local potential approximation for the effective average action. We focus on the thermodynamic curvature, $R$, in the $(\mu,T)$ plane, in proximity of the chiral crossover, up to the critical point of the phase diagram. We find that the inclusion of fluctuations results in a smoother behavior of $R$ near the chiral crossover. Moreover, for small $\mu$, $R$ remains negative, signaling the fact that bosonic fluctuations reduce the capability of the system to completely overcome the fermionic statistical repulsion of the quarks. We investigate in more detail the small $\mu$ region by analyzing a system in which we artificially lower the pion mass, thus approaching the chiral limit in which the crossover is actually a second order phase transition. On the other hand, as $\mu$ is increased and the critical point is approached, we find that $R$ is enhanced and a sign change occurs, in agreement with mean field studies. Hence, we completely support the picture that $R$ is sensitive to a crossover and a phase transition, and provides information about the effective behavior of the system at the phase transition., Comment: 12 pages, 6 figures

Current Total Skin Electron Therapy (TSET) Stanford technique for cutaneous lymphoma, established in the 70's, involves a unique irradiation setup, i.e. patient's position and beam arrangement, for all patients with ensuing great variability in dose distribution and difficult dose optimization. A Geant4-based simulation has been developed to explore the possibility of personalizing the dose to each patient's anatomy. To achieve this optimization of the treatment method, this project enrolls different aspects of the clinical and computational techniques: starting with the knowledge of the experimental parameters involving TSET practice, passing through an innovative approach to model the patient's anatomy, a precise description of the electron beam and a validated configuration of the physics models handling the interactions of the electrons and of secondary particles. The Geant4-based simulation models the patient as a tessellated solid derived from the optical scan of her/his body, realistically reproduces the irradiation environment in detail and calculates the energy deposition corresponding to each facet of the patient's scanned surface. The resulting three-dimensional dose distribution constitutes the basis for the personalization of the medical treatement as appropriate to each patient's specific characteristics., Comment: Presented at the 2022 IEEE Nuclear Science Symposium

The importance of achieving fairness in machine learning models cannot be overstated. Recent research has pointed out that fairness should be examined from a causal perspective, and several fairness notions based on the on Pearl's causal framework have been proposed. In this paper, we construct a reweighting scheme of datasets to address causal fairness. Our approach aims at mitigating bias by considering the causal relationships among variables and incorporating them into the reweighting process. The proposed method adopts two neural networks, whose structures are intentionally used to reflect the structures of a causal graph and of an interventional graph. The two neural networks can approximate the causal model of the data, and the causal model of interventions. Furthermore, reweighting guided by a discriminator is applied to achieve various fairness notions. Experiments on real-world datasets show that our method can achieve causal fairness on the data while remaining close to the original data for downstream tasks., Comment: To be published in the proceedings of 2023 IEEE International Conference on Big Data (IEEE BigData 2023)

Explaining opaque Machine Learning (ML) models is an increasingly relevant problem. Current explanation in AI (XAI) methods suffer several shortcomings, among others an insufficient incorporation of background knowledge, and a lack of abstraction and interactivity with the user. We propose REASONX, an explanation method based on Constraint Logic Programming (CLP). REASONX can provide declarative, interactive explanations for decision trees, which can be the ML models under analysis or global/local surrogate models of any black-box model. Users can express background or common sense knowledge using linear constraints and MILP optimization over features of factual and contrastive instances, and interact with the answer constraints at different levels of abstraction through constraint projection. We present here the architecture of REASONX, which consists of a Python layer, closer to the user, and a CLP layer. REASONX's core execution engine is a Prolog meta-program with declarative semantics in terms of logic theories., Comment: European Conference on Logics in Artificial Intelligence (JELIA 2023)

In eXplainable Artificial Intelligence (XAI), several counterfactual explainers have been proposed, each focusing on some desirable properties of counterfactual instances: minimality, actionability, stability, diversity, plausibility, discriminative power. We propose an ensemble of counterfactual explainers that boosts weak explainers, which provide only a subset of such properties, to a powerful method covering all of them. The ensemble runs weak explainers on a sample of instances and of features, and it combines their results by exploiting a diversity-driven selection function. The method is model-agnostic and, through a wrapping approach based on autoencoders, it is also data-agnostic.

We investigate the role of the initial screening order (ISO) in candidate screening tasks, such as employee hiring and academic admissions, in which a screener is tasked with selecting $k$ candidates from a candidate pool. The ISO refers to the order in which the screener searches the candidate pool. Today, it is common for the ISO to be the product of an information access system, such as an online platform or a database query. The ISO has been largely overlooked in the literature, despite its potential impact on the optimality and fairness of the chosen $k$ candidates, especially under a human screener. We define two problem formulations describing the search behavior of the screener under the ISO: the best-$k$, where the screener selects the $k$ best candidates; and the good-$k$, where the screener selects the $k$ first good-enough candidates. To study the impact of the ISO, we introduce a human-like screener and compare it to its algorithmic counterpart, where the human-like screener is conceived to be inconsistent over time due to fatigue. In particular, our analysis shows that the ISO, under a human-like screener solving for the good-$k$ problem, hinders individual fairness despite meeting group level fairness, and hampers the optimality of the selected $k$ candidates. This is due to position bias, where a candidate's evaluation is affected by its position within the ISO. We report extensive simulated experiments exploring the parameters of the best-$k$ and good-$k$ problems for the algorithmic and human-like screeners. The simulation framework is flexible enough to account for multiple screening settings, being an alternative to running real-world candidate screening procedures. This work is motivated by a real-world candidate screening problem studied in collaboration with an European company.

I propose a novel argument to point identify economically interpretable intertemporal treatment effects in dynamic regression discontinuity designs (RDDs). Specifically, I develop a dynamic potential outcomes model and specialize two assumptions of the difference-in-differences literature, the no anticipation and common trends restrictions, to point identify cutoff-specific impulse responses. The estimand associated with each target parameter can be expressed as the sum of two static RDD outcome contrasts, thereby allowing for estimation via standard local polynomial tools. I leverage a limited path independence assumption to reduce the dimensionality of the problem.

We study the impact of the Glasma fields, used to describe the very early stage of heavy-ion collisions, on the transport of hard probes, namely heavy quarks and jets. We perform numerical simulations of the strong classical fields using techniques from real-time lattice gauge theory. The resulting fields are used as background for the classical transport of ensembles of particles, described by Wong's equations. For this purpose, we develop a numerical solver for the transport of the probes, based on colored particle-in-cell methods. We focus on the dynamics of heavy quarks and jets in the classical colored fields. To quantify the effect of the Glasma, we extract the momentum broadening of hard probes and evaluate the anisotropy transfer from the Glasma to the probes. Lastly, we evaluate the heavy quark $\kappa$ and jet $\hat{q}$ transport coefficients in the Glasma, which turn out to be large and exhibit a peak, irrespective of the particle initialization., Comment: 7 pages, 2 figures, proceedings for the 11th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions (Hard Probes 2023)

We study the isotropization and thermalization of heavy quarks in a non-Markovian medium in high energy nuclear collisions. In particular, we analyze the case of a non-stationary medium with a noise whose time-correlator decays as a power law (heavy tailed noise). We assume the correlations decay with an exponent $\beta-1$, $0\leq\beta<1$; we treat $\beta$ as a free parameter. We analyze the effect of memory on the thermalization and isotropization of heavy quarks in the medium via a generalized Langevin equation. In general, we find that memory slows down the dynamics of heavy quarks; moreover, thermalization and isotropization happen on the same time scale once a realistic initialization is considered. We also find that while the effect on charm quarks can be relevant, beauty quarks are hardly affected by memory in the quark-gluon plasma phase. Finally, we comment on the effect of memory on the estimate of $D_s$ of charm and beauty.

Many high-performing machine learning models are not interpretable. As they are increasingly used in decision scenarios that can critically affect individuals, it is necessary to develop tools to better understand their outputs. Popular explanation methods include contrastive explanations. However, they suffer several shortcomings, among others an insufficient incorporation of background knowledge, and a lack of interactivity. While (dialogue-like) interactivity is important to better communicate an explanation, background knowledge has the potential to significantly improve their quality, e.g., by adapting the explanation to the needs of the end-user. To close this gap, we present REASONX, an explanation tool based on Constraint Logic Programming (CLP). REASONX provides interactive contrastive explanations that can be augmented by background knowledge, and allows to operate under a setting of under-specified information, leading to increased flexibility in the provided explanations. REASONX computes factual and constrative decision rules, as well as closest constrative examples. It provides explanations for decision trees, which can be the ML models under analysis, or global/local surrogate models of any ML model. While the core part of REASONX is built on CLP, we also provide a program layer that allows to compute the explanations via Python, making the tool accessible to a wider audience. We illustrate the capability of REASONX on a synthetic data set, and on a a well-developed example in the credit domain. In both cases, we can show how REASONX can be flexibly used and tailored to the needs of the user., Comment: The 1st World Conference on eXplainable Artificial Intelligence (xAI 2023)

We study the potential of the Quantum Chromodynamics axion in hot and/or dense quark matter, within a Nambu-Jona-Lasinio-like model that includes the coupling of the axion to quarks. Differently from previous studies, we implement local electrical neutrality and $\beta-$equilibrium, which are relevant for the description of the quark matter in the core of compact stellar objects. Firstly we compute the effects of the chiral crossover on the axion mass and self-coupling. We find that the low energy properties of axion are very sensitive to the phase transition of Quantum Chromodynamics, in particular, when the bulk quark matter is close to criticality. Then, for the first time in the literature we compute the axion potential at finite quark chemical potential and study the axion domain walls in bulk quark matter. We find that the energy barrier between two adjacent vacuum states decrease in the chirally restored phase: this results in a lower surface tension of the walls. Finally, we comment on the possibility of production of walls in dense quark matter., Comment: 10 pages, 7 figures

Liberalism-oriented political philosophy reasons that all individuals should be treated equally independently of their protected characteristics. Related work in machine learning has translated the concept of \emph{equal treatment} into terms of \emph{equal outcome} and measured it as \emph{demographic parity} (also called \emph{statistical parity}). Our analysis reveals that the two concepts of equal outcome and equal treatment diverge; therefore, demographic parity does not faithfully represent the notion of \emph{equal treatment}. We propose a new formalization for equal treatment by (i) considering the influence of feature values on predictions, such as computed by Shapley values decomposing predictions across its features, (ii) defining distributions of explanations, and (iii) comparing explanation distributions between populations with different protected characteristics. We show the theoretical properties of our notion of equal treatment and devise a classifier two-sample test based on the AUC of an equal treatment inspector. We study our formalization of equal treatment on synthetic and natural data. We release \texttt{explanationspace}, an open-source Python package with methods and tutorials.

We explore the impact of strong classical color fields, which occur in the earliest stages of heavy-ion collisions and are known as the Glasma, on the classical transport of hard probes, namely heavy quarks and jets. To achieve this, we simulate SU(3) color fields using classical real-time lattice gauge theory and couple them to an ensemble of test particles whose dynamics are described by Wong's equations. We provide an overview of how classical color algebras are constructed and introduce a method to generate random classical SU(3) color charges. We extensively test our numerical particle solver in the limits of infinitely massive heavy quarks and ultra-relativistic light-like jets and obtain excellent quantitative agreement with previous studies. Going towards realistic masses and initial moment, we extract longitudinal and transverse momentum broadening for heavy quarks and jets. The resulting accumulated momenta and the anisotropy of these dynamical hard probes exhibit deviations from limiting scenarios, showing that the full dynamics have a significant effect., Comment: 30 pages, 15 figures; v2 added references, fixed typos v3 published in PRD

In uses of pre-trained machine learning models, it is a known issue that the target population in which the model is being deployed may not have been reflected in the source population with which the model was trained. This can result in a biased model when deployed, leading to a reduction in model performance. One risk is that, as the population changes, certain demographic groups will be under-served or otherwise disadvantaged by the model, even as they become more represented in the target population. The field of domain adaptation proposes techniques for a situation where label data for the target population does not exist, but some information about the target distribution does exist. In this paper we contribute to the domain adaptation literature by introducing domain-adaptive decision trees (DADT). We focus on decision trees given their growing popularity due to their interpretability and performance relative to other more complex models. With DADT we aim to improve the accuracy of models trained in a source domain (or training data) that differs from the target domain (or test data). We propose an in-processing step that adjusts the information gain split criterion with outside information corresponding to the distribution of the target population. We demonstrate DADT on real data and find that it improves accuracy over a standard decision tree when testing in a shifted target population. We also study the change in fairness under demographic parity and equal opportunity. Results show an improvement in fairness with the use of DADT., Comment: *Both authors contributed equally to this work. Accepted at FAccT '23

We present counterfactual situation testing (CST), a causal data mining framework for detecting discrimination in classifiers. CST aims to answer in an actionable and meaningful way the intuitive question "what would have been the model outcome had the individual, or complainant, been of a different protected status?" It extends the legally-grounded situation testing of Thanh et al. (2011) by operationalizing the notion of fairness given the difference using counterfactual reasoning. For any complainant, we find and compare similar protected and non-protected instances in the dataset used by the classifier to construct a control and test group, where a difference between the decision outcomes of the two groups implies potential individual discrimination. Unlike situation testing, which builds both groups around the complainant, we build the test group on the complainant's counterfactual generated using causal knowledge. The counterfactual is intended to reflect how the protected attribute when changed affects the seemingly neutral attributes used by the classifier, which is taken for granted in many frameworks for discrimination. Under CST, we compare similar individuals within each group but dissimilar individuals across both groups due to the possible difference between the complainant and its counterfactual. Evaluating our framework on two classification scenarios, we show that it uncovers a greater number of cases than situation testing, even when the classifier satisfies the counterfactual fairness condition of Kusner et al. (2017).

By shutting down frequency carriers, the power consumed by a base station can be considerably reduced. However, this typically comes with traffic performance degradation, as the congestion on the remaining active carriers is increased. We leverage a hysteresis carrier shutdown policy that attempts to keep the average traffic load on each sector within a certain min/max threshold pair. We propose a closed-loop Bayesian method optimizing such thresholds on a sector basis and aiming at minimizing the power consumed by the power amplifiers while maintaining the probability that KPI's are acceptable above a certain value. We tested our approach in a live customer 4G network. The power consumption at the base station was reduced by 11% and the selected KPI's met the predefined targets.

We study the evolution of the angular momentum of the heavy quarks in the very early stage of high energy nuclear collisions, in which the background is made of evolving Glasma fields. Given the novelty of the problem, we limit ourselves to the use of toy heavy quarks with a large, unphysical mass, in order to implement the kinetic equations for the angular momentum in the non-relativistic limit. We find that as a consequence of the anisotropy of the background fields, angular momentum fluctuations are also anisotropic: we understand this in simple terms relating the fluctuations of the angular momentum, $L$, to those of linear momentum. While orbital angular momentum diffuses and develops substantial fluctuations and anisotropies, the spin does not. Hence, we can identify the fluctuations of $L$ with those of the total angular momentum $J=L + S$. Therefore, our study suggests that the total angular momentum of the heavy quarks in the early stage of high energy nuclear collisions will present anisotropic fluctuations., Comment: 10 pages, 6 figures