• #### Deep Learning Interviews: Hundreds of fully solved job interview questions from a wide range of key topics in AIver. 2

The second edition of Deep Learning Interviews is home to hundreds of fully-solved problems, from a wide range of key topics in AI. It is designed to both rehearse interview or exam specific topics and provide machine learning MSc / PhD. students, and those awaiting an interview a well-organized overview of the field. The problems it poses are tough enough to cut your teeth on and to dramatically improve your skills-but they're framed within thought-provoking questions and engaging stories. That is what makes the volume so specifically valuable to students and job seekers: it provides them with the ability to speak confidently and quickly on any relevant topic, to answer technical questions clearly and correctly, and to fully understand the purpose and meaning of interview questions and answers. Those are powerful, indispensable advantages to have when walking into the interview room. The book's contents is a large inventory of numerous topics relevant to DL job interviews and graduate level exams. That places this work at the forefront of the growing trend in science to teach a core set of practical mathematical and computational skills. It is widely accepted that the training of every computer scientist must include the fundamental theorems of ML, and AI appears in the curriculum of nearly every university. This volume is designed as an excellent reference for graduates of such programs.
Deep learningProgrammingMachine learningField...
• #### Rethinking Channel Dimensions for Efficient Model Designver. 3

Designing an efficient model within the limited computational cost is challenging. We argue the accuracy of a lightweight model has been further limited by the design convention: a stage-wise configuration of the channel dimensions, which looks like a piecewise linear function of the network stage. In this paper, we study an effective channel dimension configuration towards better performance than the convention. To this end, we empirically study how to design a single layer properly by analyzing the rank of the output feature. We then investigate the channel configuration of a model by searching network architectures concerning the channel configuration under the computational cost restriction. Based on the investigation, we propose a simple yet effective channel configuration that can be parameterized by the layer index. As a result, our proposed model following the channel parameterization achieves remarkable performance on ImageNet classification and transfer learning tasks including COCO object detection, COCO instance segmentation, and fine-grained classifications. Code and ImageNet pretrained models are available at https://github.com/clovaai/rexnet.
• #### Implementation and Optimization of the PTOLEMY Transverse Drift Electromagnetic Filterver. 2

The PTOLEMY transverse drift filter is a new concept to enable precision analysis of the energy spectrum of electrons near the tritium beta-decay endpoint. This paper details the implementation and optimization methods for successful operation of the filter. We present the first demonstrator that produces the required magnetic field properties with an iron return-flux magnet. Two methods for the setting of filter electrode voltages are detailed. The challenges of low-energy electron transport in cases of low field are discussed, such as the growth of the cyclotron radius with decreasing magnetic field, which puts a ceiling on filter performance relative to fixed filter dimensions. Additionally, low pitch angle trajectories are dominated by motion parallel to the magnetic field lines and introduce non-adiabatic conditions and curvature drift. To minimize these effects and maximize electron acceptance into the filter, we present a three-potential-well design to simultaneously drain the parallel and transverse kinetic energies throughout the length of the filter. These optimizations are shown, in simulation, to achieve low-energy electron transport from a 1 T iron core (or 3 T superconducting) starting field with initial kinetic energy of 18.6 keV drained to <10 eV (<1 eV) in about 80 cm. This result for low field operation paves the way for the first demonstrator of the PTOLEMY spectrometer for measurement of electrons near the tritium endpoint to be constructed at the Gran Sasso National Laboratary (LNGS) in Italy.
PTOLEMY experimentCyclotronOptimizationCurvatureCurvature driftCharged particleTransverse momentumPitch angleSpectrometersProgramming...
• #### Magnetic Field Evolution in Neutron Star Crusts: Beyond the Hall Effectver. 2

Neutron stars host the strongest magnetic fields that we know of in the Universe. Their magnetic fields are the main means of generating their radiation, either magnetospheric or through the crust. Moreover, the evolution of the magnetic field has been intimately related to explosive events of magnetars, which host strong magnetic fields, and their persistent thermal emission. The evolution of the magnetic field in the crusts of neutron stars has been described within the framework of the Hall effect and Ohmic dissipation. Yet, this description is limited by the fact that the Maxwell stresses exerted on the crusts of strongly magnetised neutron stars may lead to failure and temperature variations. In the former case, a failed crust does not completely fulfil the necessary conditions for the Hall effect. In the latter, the variations of temperature are strongly related to the magnetic field evolution. Finally, sharp gradients of the star's temperature may activate battery terms and alter the magnetic field structure, especially in weakly magnetised neutron stars. In this review, we discuss the recent progress made on these effects. We argue that these phenomena are likely to provide novel insight into our understanding of neutron stars and their observable properties.
Neutron starHall effectNeutron star crustMagnetarStrong magnetic fieldMagnetic field strengthStarMagnetic energyLattice (order)Hall drift...
• #### A Simple Proof of Bohr's Inequality

The classical inequality of Bohr concerning Taylor coeficients of bounded holomorphic functions on the unit disk, has proved to be of significance in answering in the negative the conjecture that if the non-unital von Neumann inequality held for a Banach algebra then it was necessarily an operator algebra. Here we provide a rather short and easy proof of the inequality.
Von Neumann's inequalityHolomorphic functionOperator algebraBlaschke productDisk algebraConvex combinationUniform algebraFree groupConvex hullAlgebra...
• #### Trees, graphs and aggregates: a categorical perspective on combinatorial surface topology, geometry, and algebra

Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via topology, geometry and algebra. In particular, the inclusion of trees into graphs and the dissection of graphs into aggregates yield a concise formalism for cyclic and modular operads as well as their polycyclic and surface type generalizations. The latter occur prominently in two-dimensional topological field theory and in string topology. The categorical viewpoint allows us to use left Kan extensions of Feynman operations as an efficient computational tool. The computations involve the study of certain categories of structured graphs which are expected to be of independent interest.
GraphMorphismIsomorphismAutomorphismSubcategoryTwo-point correlation functionMutationSpanning treeComma categoryPropagator...
• #### Lie groups and Lie algebras

These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT in 2020/2021.
SubgroupManifoldIsomorphismRoot systemNilpotentIrreducible representationHomomorphismVector spaceCohomologyLie subgroup...
• #### Causal-net categoryver. 2

A causal-net is a finite acyclic directed graph. In this paper, we introduce a category, denoted as $\mathbf{Cau}$, whose objects are causal-nets and morphisms are functors of path categories of causal-nets. It is called causal-net category and in fact the Kleisli category of the "free category on a causal-net" monad. We study several composition-closed classes of morphisms in $\mathbf{Cau}$, which characterize interesting causal-net relations, such as coarse-graining, contraction, immersion-minor, topological minor, etc., and prove several useful decomposition theorems. In addition, we show that the notions of a coloring and a minor can be understood as a special kind of minimal-quotient and sub-quotient in $\mathbf{Cau}$, respectively. Base on these results, we conclude that $\mathbf{Cau}$ is a natural setting for studying causal-nets, and the theory of $\mathbf{Cau}$ should shed new light on the category-theoretic understanding of graph theory.
MorphismCoarse grainingEmbeddingGraph theoryGraphDirected graphEdge contractionDirect edgeEmpty Lattice ApproximationPartially ordered set...
• #### Topological data analysis and clustering

Clustering is one of the most common tasks of Machine Learning. In this paper we examine how ideas from topology can be used to improve clustering techniques.
Persistent homologyMarketMachine learningManifoldPrincipal componentBig dataDBSCANPythonUniform distributionHomomorphism...
• #### Polytope: Practical Memory Access Control for C++ Applicationsver. 2

Designing and implementing secure software is inarguably more important than ever. However, despite years of research into privilege separating programs, it remains difficult to actually do so and such efforts can take years of labor-intensive engineering to reach fruition. At the same time, new intra-process isolation primitives make strong data isolation and privilege separation more attractive from a performance perspective. Yet, substituting intra-process security boundaries for time-tested process boundaries opens the door to subtle but devastating privilege leaks. In this work, we present Polytope, a language extension to C++ that aims to make efficient privilege separation accessible to a wider audience of developers. Polytope defines a policy language encoded as C++11 attributes that separate code and data into distinct program partitions. A modified Clang front-end embeds source-level policy as metadata nodes in the LLVM IR. An LLVM pass interprets embedded policy and instruments an IR with code to enforce the source-level policy using Intel MPK. A run-time support library manages partitions, protection keys, dynamic memory operations, and indirect call target privileges. An evaluation demonstrates that Polytope provides equivalent protection to prior systems with a low annotation burden and comparable performance overhead. Polytope also renders privilege leaks that contradict intended policy impossible to express.
ProgrammingSecuritySoftwarePolytopeEngineeringArchitectureEmbeddingApplication programming interfaceNatriumOperating system...
• #### Breaking baryon-cosmology degeneracy with the electron density power spectrum

Uncertain feedback processes in galaxies affect the distribution of matter, currently limiting the power of weak lensing surveys. If we can identify cosmological statistics that are robust against these uncertainties, or constrain these effects by other means, then we can enhance the power of current and upcoming observations from weak lensing surveys such as DES, Euclid, the Rubin Observatory, and the Roman Space Telescope. In this work, we investigate the potential of the electron density auto-power spectrum as a robust probe of cosmology and baryonic feedback. We use a suite of (magneto-)hydrodynamic simulations from the CAMELS project and perform an idealized analysis to forecast statistical uncertainties on a limited set of cosmological and physically-motivated astrophysical parameters. We find that the electron number density auto-correlation, measurable through either kinematic Sunyaev-Zel'dovich observations or through Fast Radio Burst dispersion measures, provides tight constraints on $\Omega_{m}$ and the mean baryon fraction in intermediate-mass halos, $\bar{f}_{\mathrm{bar}}$. By obtaining an empirical measure for the associated systematic uncertainties, we find these constraints to be largely robust to differences in baryonic feedback models implemented in hydrodynamic simulations. We further discuss the main caveats associated with our analysis, and point out possible directions for future work.
Cosmology and Astrophysics with MachinE Learning SimulationsBaryonic feedbackIllustrisTNG simulationFast Radio BurstsCosmic varianceCosmologyAGN feedbackWeak lensingDispersion measureGalaxy...
• #### Separating polynomial $\chi$-boundedness from $\chi$-boundedness

Extending the idea from the recent paper by Carbonero, Hompe, Moore, and Spirkl, for every function $f\colon\mathbb{N}\to\mathbb{N}$ we construct a $\chi$-bounded hereditary class of graphs $\mathcal{C}$ with the property that for every integer $n\ge 2$ there is a graph in $\mathcal{C}$ with clique number at most $n$ and chromatic number at least $f(n)$. In particular, this proves that there are hereditary classes of graphs that are $\chi$-bounded but not polynomially $\chi$-bounded.
• #### Shape Dependence of Holographic R\'enyi Entropy in General Dimensionsver. 2

We present a holographic method for computing the response of R\'enyi entropies in conformal field theories to small shape deformations around a flat (or spherical) entangling surface. Our strategy employs the stress tensor one-point function in a deformed hyperboloid background and relates it to the coefficient in the two-point function of the displacement operator. We obtain explicit numerical results for $d=3,\dots,6$ spacetime dimensions, and also evaluate analytically the limits where the R\'enyi index approaches 1 and 0 in general dimensions. We use our results to extend the work of 1602.08493 and disprove a set of conjectures in the literature regarding the relations between the R\'enyi shape dependence and the conformal weight of the twist operator. We also extend our analysis beyond leading order in derivatives in the bulk theory by studying Gauss-Bonnet gravity.
Conformal field theoryExpectation ValueEntropyGeneral relativityExtrinsic curvatureQuantum field theoryPath integralAnti de Sitter spaceHorizonEntanglement...
• #### The Weak Gravity Conjecture: A Review

The Weak Gravity Conjecture holds that in a theory of quantum gravity, any gauge force must mediate interactions stronger than gravity for some particles. This statement has surprisingly deep and extensive connections to many different areas of physics and mathematics. Several variations on the basic conjecture have been proposed, including statements that are much stronger but are nonetheless satisfied by all known consistent quantum gravity theories. We review these related conjectures and the evidence for their validity in the string theory landscape. We also review a variety of arguments for these conjectures, which tend to fall into two categories: qualitative arguments which claim the conjecture is plausible based on general principles, and quantitative arguments for various special cases or analogues of the conjecture. We also outline the implications of these conjectures for particle physics, cosmology, general relativity, and mathematics. Finally, we highlight important directions for future research.
Black holeAxionGauge fieldQuantum gravityInstantonCharged particleLattice (order)Gauge coupling constantGlobal symmetryHorizon...
• #### On the Energy Dependence of Galactic Cosmic Ray Anisotropies in the Very Local Interstellar Medium

We report on the energy dependence of galactic cosmic rays (GCRs) in the very local interstellar medium (VLISM) as measured by the Low Energy Charged Particle (LECP) instrument on the Voyager 1 (V1) spacecraft. The LECP instrument includes a dual-ended solid state detector particle telescope mechanically scanning through 360 deg across eight equally-spaced angular sectors. As reported previously, LECP measurements showed a dramatic increase in GCR intensities for all sectors of the >=211 MeV count rate (CH31) at the V1 heliopause (HP) crossing in 2012, however, since then the count rate data have demonstrated systematic episodes of intensity decrease for particles around 90{\deg} pitch angle. To shed light on the energy dependence of these GCR anisotropies over a wide range of energies, we use V1 LECP count rate and pulse height analyzer (PHA) data from >=211 MeV channel together with lower energy LECP channels. Our analysis shows that while GCR anisotropies are present over a wide range of energies, there is a decreasing trend in the amplitude of second-order anisotropy with increasing energy during anisotropy episodes. A stronger pitch-angle scattering at the higher velocities is argued as a potential cause for this energy dependence. A possible cause for this velocity dependence arising from weak rigidity dependence of the scattering mean free path and resulting velocity-dominated scattering rate is discussed. This interpretation is consistent with a recently reported lack of corresponding GCR electron anisotropies.
Galactic cosmic raysAnisotropyInterstellar mediumCosmic rays anisotropyHeliopausePitch angleIntensityTelescopesVoyager 1Charged particle...
• #### The size-luminosity relation of lensed galaxies at $z=6-9$ in the Hubble Frontier Fields

We measure the size-luminosity relation of photometrically-selected galaxies within the redshift range $z\sim6-9$, using galaxies lensed by six foreground Hubble Frontier Fields (HFF) clusters. The power afforded by strong gravitational lensing allows us to observe fainter and smaller galaxies than in blank fields. We select our sample of galaxies and obtain their properties, e.g., redshift, magnitude, from the photometrically-derived ASTRODEEP catalogues. The intrinsic size is measured with the Lenstruction software, and completeness maps are created as a function of size and luminosity via the GLACiAR2 software. We perform a Bayesian analysis to estimate the intrinsic and incompleteness-corrected size-luminosity distribution, with parameterization $r_e \propto L^\beta$. We find slopes of $\beta\sim0.48\pm0.08$ at $z\sim6-7$ and $\beta\sim0.68\pm0.14$ at $z\sim8.5$, adopting the Bradac lens model. The slope derived by lensed galaxies is steeper than that obtained in blank fields and is consistent with other independent determinations of the size-luminosity relation from the HFF dataset. We also investigate the systematic uncertainties correlated with the choice of lens models, finding that the slopes of size-luminosity relations derived from different models are consistent with each other, i.e. the modeling errors are not a significant source of uncertainty in the size-luminosity relation.
LuminosityGalaxyHubble Frontier FieldsCompletenessGravitational lens galaxySoftwareLuminosity functionHubble Space TelescopeStrong gravitational lensingSystematic error...
• #### The Magnetic Field versus Density relation in Star-Forming Molecular Clouds

We study the magnetic field to density ($B-\rho$) relation in turbulent molecular clouds with dynamically important magnetic fields using nonideal three-dimensional magnetohydrodynamic simulations. Our simulations show that there is a distinguishable break density $\rho_{\rm T}$ between the relatively flat low density regime and a power-law regime at higher densities. We present an analytic theory for $\rho_{\rm T}$ based on the interplay of the magnetic field, turbulence, and gravity. The break density $\rho_{\rm T}$ scales with the strength of the initial Alfv\'en Mach number $\mathcal{M}_{\rm A0}$ for sub-Alfv\'enic ( $\mathcal{M}_{\rm A0}<1$) and trans-Alfv\'enic ($\mathcal{M}_{\rm A0} \sim 1$) clouds. We fit the variation of $\rho_{\rm T}$ for model clouds as a function of $\mathcal{M}_{\rm A0}$, set by different values of initial sonic Mach number $\mathcal{M_{\rm 0}}$ and the initial ratio of gas pressure to magnetic pressure $\beta_{\rm 0}$. This implies that $\rho_{\rm T}$, which denotes the transition in mass-to-flux ratio from the subcritical to supercritical regime, is set by the initial turbulent compression of the molecular cloud.
TurbulenceMolecular cloudMach numberAmbipolar diffusionStar formationMagnetic pressureMagnetic field strengthOrientationStrong magnetic fieldRam pressure...
• #### A stable and causal model of magnetohydrodynamics

We formulate the theory of first-order dissipative magnetohydrodynamics in an arbitrary hydrodynamic frame under the assumption of parity-invariance and discrete charge symmetry. We study the mode spectrum of Alfv\'en and magnetosonic waves as well as the spectrum of gapped excitations and derive constraints on the transport coefficients such that generic equilibrium states with constant magnetic fields are stable and causal under linearised perturbations. We solve these constraints for a specific equation of state and show that there exists a large family of hydrodynamic frames that renders the linear fluctuations stable and causal. This theory does not require introducing new dynamical degrees of freedom and therefore is a promising and simpler alternative to M\"{u}ller-Israel-Stewart-type theories. Together with a detailed analysis of transport, entropy production and Kubo formulae, the theory presented here is well suited for studying dissipative effects in various contexts ranging from heavy-ion collisions to astrophysics.
CausalityMagnetohydrodynamicsTransport coefficientEntropyKubo formulaDegree of freedomPartition functionHeavy ion collisionWeak field limitRelativistic hydrodynamics...
• #### Modelling astrophysical fluids with particles

Computational fluid dynamics is a crucial tool to theoretically explore the cosmos. In the last decade, we have seen a substantial methodological diversification with a number of cross-fertilizations between originally different methods. Here we focus on recent developments related to the Smoothed Particle Hydrodynamics (SPH) method. We briefly summarize recent technical improvements in the SPH-approach itself, including smoothing kernels, gradient calculations and dissipation steering. These elements have been implemented in the Newtonian high-accuracy SPH code MAGMA2 and we demonstrate its performance in a number of challenging benchmark tests. Taking it one step further, we have used these new ingredients also in the first particle-based, general-relativistic fluid dynamics code that solves the full set of Einstein equations, SPHINCS_BSSN. We present the basic ideas and equations and demonstrate the code performance at examples of relativistic neutron stars that are evolved self-consistently together with the spacetime.
Smoothed-particle hydrodynamicsDissipationNeutron starEntropyStarInstabilityRelativistic hydrodynamicsSPH codeEngineeringTolman-Oppenheimer-Volkoff...
• #### A universe field theory for JT gravity

We present a field theory description for the non-perturbative splitting and joining of baby universes in Euclidean Jackiw-Teitelboim (JT) gravity. We show how the gravitational path integral, defined as a sum over topologies, can be reproduced from the perturbative expansion of a Kodaira-Spencer (KS) field theory for the complex structure deformations of the spectral curve. We use that the Schwinger-Dyson equations for the KS theory can be mapped to the topological recursion relations. We refer to this dual description of JT gravity as a `universe field theory'. By introducing non-compact D-branes in the target space geometry, we can probe non-perturbative aspects of JT gravity. The relevant operators are obtained through a modification of the JT path integral with Neumann boundary conditions. The KS/JT identification suggests that the ensemble average for JT gravity can be understood in terms of a more standard open/closed duality in topological string theory.
Path integralBranch pointTwo-point correlation functionField theoryPartition functionRiemann surfaceTopological stringsRandom matrix theoryLaplace transformVirasoro constraint...
• #### The critical O(N) CFT: Methods and conformal data

The critical $O(N)$ CFT in spacetime dimensions $2< d <4$ is one of the most important examples of a conformal field theory, with the Ising CFT at $N=1$, $2 \leq d < 4$, as a notable special case. Apart from numerous physical applications, it serves frequently as a concrete testing ground for new approaches and techniques based on conformal symmetry. In the perturbative limits - the $4-\varepsilon$ expansion, the large $N$ expansion and the $2+\tilde\epsilon$ expansion - a lot of conformal data have been computed over the years. In this report, we give an overview of the critical $O(N)$ CFT, including some methods to study it, and present a large collection of conformal data. The data, extracted from the literature and supplemented by many additional computations of order $\varepsilon$ anomalous dimensions, is made available through an ancillary data file.
Conformal field theoryAnomalous dimensionOPE coefficientsScaling dimensionCritical exponentConformal BootstrapGlobal symmetryCentral chargeOperator product expansionConformal symmetry...
• #### Optical Properties of Peaked Spectrum Radio Sourcesver. 2

In this work, we study the optical properties of compact radio sources selected from the literature in order to determine the impact of the radio-jet in their circumnuclear environment. Our sample includes 58 Compact Steep Spectrum (CSS) and GigaHertz Peaked Spectrum (GPS) and 14 Megahertz-Peaked spectrum (MPS) radio sources located at $z\leq 1$. The radio luminosity ($L_R$) of the sample varies between Log\,L$_R\sim$ 23.2 and 27.7 W\,Hz$^{-1}$. We obtained optical spectra for all sources from SDSS-DR12 and performed a stellar population synthesis using the {\sc starlight} code. We derived stellar masses (M$_\star$), ages $\langle t_\star \rangle$, star formation rates (SFR), metallicities $\langle Z_\star \rangle$ and internal reddening A$_V$ for all young AGNs of our sample. A visual inspection of the SDSS images was made to assign a morphological class for each source. Our results indicate that the sample is dominated by intermediate to old stellar populations and there is no strong correlation between optical and radio properties of these sources. Also, we found that young AGNs can be hosted by elliptical, spiral and interacting galaxies, confirming recent findings. When comparing the optical properties of CSS/GPS and MPS sources, we do not find any significant difference. Finally, the Mid-Infrared WISE colours analysis suggest that compact radio sources defined as powerful AGNs are, in general, gas-rich systems.
Active Galactic NucleiStellar populationsRadio sourcesStar formation rateGalaxySloan Digital Sky SurveyStarStar formationHost galaxyMilky Way...
• #### Magnetic Spirals in Accretion Flows Originated from Misaligned Magnetic Field

Misalignment between rotation and magnetic field has been suggested to be one type of physical mechanisms which can easen the effects of magnetic braking during collapse of cloud cores leading to formation of protostellar disks. However, its essential factors are poorly understood. Therefore, we perform a more detailed analysis of the physics involved. We analyze existing simulation data to measure the system torques, mass accretion rates and Toomre Q parameters. We also examine the presence of shocks in the system. While advective torques are generally the strongest, we find that magnetic and gravitational torques can play substantial roles in how angular momentum is transferred during the disk formation process. Magnetic torques can shape the accretion flows, creating two-armed magnetized inflow spirals aligned with the magnetic field. We find evidence of an accretion shock that is aligned according to the spiral structure of the system. Inclusion of ambipolar diffusion as explored in this work has shown a slight influence in the small scale structures but not in the main morphology. We discuss potential candidate systems where some of these phenomena could be present.
Spiral structureAccretionJeans instabilityMagnetohydrodynamicsAccretion flowMass accretion ratePitch angleAmbipolar diffusionIRASMomentum transfer...
• #### Analytic torsion for graphs

Analytic torsion is a functional on graphs which only needs linear algebra to be defined. In the continuum it corresponds to the Ray-Singer analytic torsion. We have formulas for analytic torsion if the graph is contractible or if it is a discrete sphere. A key insight is that analytic torsion is the super determinant of the Dirac operator of the graph.
GraphSpanning treeTorsion tensorAnalytic torsionManifoldDirac operatorCohomologyOdd dimensionalDual graphSimple graph...
• #### Modern Koopman Theory for Dynamical Systemsver. 2

The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches that formulate models in operator theoretic or probabilistic frameworks. Koopman spectral theory has emerged as a dominant perspective over the past decade, in which nonlinear dynamics are represented in terms of an infinite-dimensional linear operator acting on the space of all possible measurement functions of the system. This linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. However, obtaining finite-dimensional coordinate systems and embeddings in which the dynamics appear approximately linear remains a central open challenge. The success of Koopman analysis is due primarily to three key factors: 1) there exists rigorous theory connecting it to classical geometric approaches for dynamical systems, 2) the approach is formulated in terms of measurements, making it ideal for leveraging big-data and machine learning techniques, and 3) simple, yet powerful numerical algorithms, such as the dynamic mode decomposition (DMD), have been developed and extended to reduce Koopman theory to practice in real-world applications. In this review, we provide an overview of modern Koopman operator theory, describing recent theoretical and algorithmic developments and highlighting these methods with a diverse range of applications. We also discuss key advances and challenges in the rapidly growing field of machine learning that are likely to drive future developments and significantly transform the theoretical landscape of dynamical systems.
Machine learningData scienceBig dataOperator theoryTheoryDynamical systemsMeasurementAlgorithmsFieldPotential...
• #### Physics-informed dynamic mode decomposition (piDMD)

In this work, we demonstrate how physical principles -- such as symmetries, invariances, and conservation laws -- can be integrated into the dynamic mode decomposition (DMD). DMD is a widely-used data analysis technique that extracts low-rank modal structures and dynamics from high-dimensional measurements. However, DMD frequently produces models that are sensitive to noise, fail to generalize outside the training data, and violate basic physical laws. Our physics-informed DMD (piDMD) optimization, which may be formulated as a Procrustes problem, restricts the family of admissible models to a matrix manifold that respects the physical structure of the system. We focus on five fundamental physical principles -- conservation, self-adjointness, localization, causality, and shift-invariance -- and derive several closed-form solutions and efficient algorithms for the corresponding piDMD optimizations. With fewer degrees of freedom, piDMD models are less prone to overfitting, require less training data, and are often less computationally expensive to build than standard DMD models. We demonstrate piDMD on a range of challenging problems in the physical sciences, including energy-preserving fluid flow, travelling-wave systems, the Schr\"odinger equation, solute advection-diffusion, a system with causal dynamics, and three-dimensional transitional channel flow. In each case, piDMD significantly outperforms standard DMD in metrics such as spectral identification, state prediction, and estimation of optimal forcings and responses.
RankManifoldOptimizationTotal least squaresTraining setMachine learningRegressionCirculant matrixExact solutionHamiltonian...
• #### Self-Attentional Credit Assignment for Transfer in Reinforcement Learningver. 2

The ability to transfer knowledge to novel environments and tasks is a sensible desiderata for general learning agents. Despite the apparent promises, transfer in RL is still an open and little exploited research area. In this paper, we take a brand-new perspective about transfer: we suggest that the ability to assign credit unveils structural invariants in the tasks that can be transferred to make RL more sample-efficient. Our main contribution is SECRET, a novel approach to transfer learning for RL that uses a backward-view credit assignment mechanism based on a self-attentive architecture. Two aspects are key to its generality: it learns to assign credit as a separate offline supervised process and exclusively modifies the reward function. Consequently, it can be supplemented by transfer methods that do not modify the reward function and it can be plugged on top of any RL algorithm.
AttentionArchitectureMarkov decision processReinforcement learningSupervised learningHyperparameterSparsityGround truthComputational linguisticsMachine translation...
• #### alpha-Deep Probabilistic Inference (alpha-DPI): efficient uncertainty quantification from exoplanet astrometry to black hole feature extraction

Inference is crucial in modern astronomical research, where hidden astrophysical features and patterns are often estimated from indirect and noisy measurements. Inferring the posterior of hidden features, conditioned on the observed measurements, is essential for understanding the uncertainty of results and downstream scientific interpretations. Traditional approaches for posterior estimation include sampling-based methods and variational inference. However, sampling-based methods are typically slow for high-dimensional inverse problems, while variational inference often lacks estimation accuracy. In this paper, we propose alpha-DPI, a deep learning framework that first learns an approximate posterior using alpha-divergence variational inference paired with a generative neural network, and then produces more accurate posterior samples through importance re-weighting of the network samples. It inherits strengths from both sampling and variational inference methods: it is fast, accurate, and scalable to high-dimensional problems. We apply our approach to two high-impact astronomical inference problems using real data: exoplanet astrometry and black hole feature extraction.
InferenceDouble-parton interactionsExtrasolar planetAstrometryFeature extractionBlack holeNeural networkInverse problemsOptimizationDeep learning...
• #### Digital Rock Typing DRT Algorithm Formulation with Optimal Supervised Semantic Segmentationver. 2

Each grid block in a 3D geological model requires a rock type that represents all physical and chemical properties of that block. The properties that classify rock types are lithology, permeability, and capillary pressure. Scientists and engineers determined these properties using conventional laboratory measurements, which embedded destructive methods to the sample or altered some of its properties (i.e., wettability, permeability, and porosity) because the measurements process includes sample crushing, fluid flow, or fluid saturation. Lately, Digital Rock Physics (DRT) has emerged to quantify these properties from micro-Computerized Tomography (uCT) and Magnetic Resonance Imaging (MRI) images. However, the literature did not attempt rock typing in a wholly digital context. We propose performing Digital Rock Typing (DRT) by: (1) integrating the latest DRP advances in a novel process that honors digital rock properties determination, while; (2) digitalizing the latest rock typing approaches in carbonate, and (3) introducing a novel carbonate rock typing process that utilizes computer vision capabilities to provide more insight about the heterogeneous carbonate rock texture.
Semantic segmentationPermeabilityMagnetic resonance imagingEngineeringImage ProcessingCapillary pressureCarbonateAlgorithmsMeasurement...
• #### The Understanding of Intertwined Physics: Discovering Capillary Pressure and Permeability Co-Determinationver. 2

Although capillary and permeability are the two most important physical properties controlling fluid distribution and flow in nature, the interconnectivity function between them was a pressing challenge. Because knowing permeability leads to determining capillary pressure. Geodynamics (e.g., subsurface water, CO2 sequestration) and organs (e.g., plants, blood vessels) depend on capillary pressure and permeability. The first determines how far the fluid can reach, while the second determines how fast the fluid can flow in porous media. They are also vital to designing synthetic materials and micro-objects like membranes and micro-robotics. Here, we reveal the capillary and permeability intertwined behavior function. And demonstrate the unique physical connectors: pore throat size and network, linking capillary pressure and permeability. Our discovery quantifies the inverse relationship between capillary pressure and permeability for the first time, which we analytically derived and experimentally proved.
PermeabilityCapillary pressurePorous mediumCarbon dioxideRoboticsMembraneObjectMaterialsNetworks...
• #### Morphology Decoder: A Machine Learning Guided 3D Vision Quantifying Heterogenous Rock Permeability for Planetary Surveillance and Robotic Functionsver. 2

Permeability has a dominant influence on the flow properties of a natural fluid. Lattice Boltzmann simulator determines permeability from the nano and micropore network. The simulator holds millions of flow dynamics calculations with its accumulated errors and high consumption of computing power. To efficiently and consistently predict permeability, we propose a morphology decoder, a parallel and serial flow reconstruction of machine learning segmented heterogeneous Cretaceous texture from 3D micro computerized tomography and nuclear magnetic resonance images. For 3D vision, we introduce controllable-measurable-volume as new supervised segmentation, in which a unique set of voxel intensity corresponds to grain and pore throat sizes. The morphology decoder demarks and aggregates the morphologies boundaries in a novel way to produce permeability. Morphology decoder method consists of five novel processes, which describes in this paper, these novel processes are: (1) Geometrical 3D Permeability, (2) Machine Learning guided 3D Properties Recognition of Rock Morphology, (3) 3D Image Properties Integration Model for Permeability, (4) MRI Permeability Imager, and (5) Morphology Decoder (the process that integrates the other four novel processes).
PermeabilityMachine learningRoboticsLattice (order)IntensityNuclear magnetic resonanceMagnetic resonance imagingNetworksAggregate...
• #### Deducing Optimal Classification Algorithm for Heterogeneous Fabricver. 3

For defining the optimal machine learning algorithm, the decision was not easy for which we shall choose. To help future researchers, we describe in this paper the optimal among the best of the algorithms. We built a synthetic data set and performed the supervised machine learning runs for five different algorithms. For heterogeneous rock fabric, we identified Random Forest, among others, to be the appropriate algorithm.
Machine learningSynthetic DataRandom forestAlgorithms...
• #### Machine Learning Guided 3D Image Recognition for Carbonate Pore and Mineral Volumes Determinationver. 2

Automated image processing algorithms can improve the quality, efficiency, and consistency of classifying the morphology of heterogeneous carbonate rock and can deal with a massive amount of data and images seamlessly. Geoscientists face difficulties in setting the direction of the optimum method for determining petrophysical properties from rock images, Micro-Computed Tomography (uCT), or Magnetic Resonance Imaging (MRI). Most of the successful work is from the homogeneous rocks focusing on 2D images with less focus on 3D and requiring numerical simulation. Currently, image analysis methods converge to three approaches: image processing, artificial intelligence, and combined image processing with artificial intelligence. In this work, we propose two methods to determine the porosity from 3D uCT and MRI images: an image processing method with Image Resolution Optimized Gaussian Algorithm (IROGA); advanced image recognition method enabled by Machine Learning Difference of Gaussian Random Forest (MLDGRF). We have built reference 3D micro models and collected images for calibration of IROGA and MLDGRF methods. To evaluate the predictive capability of these calibrated approaches, we ran them on 3D uCT and MRI images of natural heterogeneous carbonate rock. We measured the porosity and lithology of the carbonate rock using three and two industry-standard ways, respectively, as reference values. Notably, IROGA and MLDGRF have produced porosity results with an accuracy of 96.2% and 97.1% on the training set and 91.7% and 94.4% on blind test validation, respectively, in comparison with the three experimental measurements. We measured limestone and pyrite reference values using two methods, X-ray powder diffraction, and grain density measurements. MLDGRF has produced lithology (limestone and Pyrite) volumes with 97.7% accuracy.
Image ProcessingMagnetic resonance imagingImage recognitionMachine learningCalibrationNumerical simulationDifference of GaussiansTraining setRandom forestPowder diffraction...
• #### Quantum Dipolar Coupling Thermal Correction for NMR Signal during Natural Rock Flooding by Melding Experimentation and Numerical Simulation (Th-CENS)

Researchers have used NMR to measure multi-phase fluid saturation and distribution inside porous media of natural rock. However, the NMR signal amplitude suffers reduction with the increase of temperature. The main reason is the Transverse Overhauser Effect, where heating increases the freedom for ionic motion, affecting spinning behavior by having two spins go in two opposite directions to form the Dipolar Coupling. We approach solving NMR thermal effects correction by melding experimentation and numerical simulation method. We use NMR for Cretaceous carbonate rock multi-phase flow research. We conduct time step in-situ temperature measurement for four different sections of the flooding system at the inlet, center, and outlet along the flooding path. In addition, we conduct a temperature measurement at the NMR device radial axis, representing the permanent magnet temperature. We build a 3D cylindrical heat transfer model for the numerical simulator that simulates thermal effect distribution on the NMR for optimally generating the correction model. The insight provided by the simulator improved the understanding of the thermal distribution at the natural rock core plug to produce a better thermal correction model that meld experimentation and simulation, a method we call Th-CENS.
Nuclear magnetic resonanceNumerical simulationTemperature measurementPorous mediumTemperatureSpinAmplitudeSimulationsMagnetCarbonate...
• #### Tearing instability and current-sheet disruption in the turbulent dynamo

Turbulence in a conducting plasma can amplify seed magnetic fields in what is known as the turbulent, or small-scale, dynamo. The associated growth rate and emergent magnetic-field geometry depend sensitively on the material properties of the plasma, in particular on the Reynolds number ${\rm Re}$, the magnetic Reynolds number ${\rm Rm}$, and their ratio ${\rm Pm}\equiv{\rm Rm}/{\rm Re}$. For ${\rm Pm} > 1$, the amplified magnetic field is gradually arranged into a folded structure, with direction reversals at the resistive scale and field lines curved at the larger scale of the flow. As the mean magnetic energy grows to come into approximate equipartition with the fluid motions, this folded structure is thought to persist. Using analytical theory and high-resolution MHD simulations with the Athena++ code, we show that these magnetic folds become unstable to tearing during the nonlinear stage of the dynamo for ${\rm Rm}\gtrsim 10^4$ and ${\rm Re}\gtrsim 10^3$. An ${\rm Rm}$- and ${\rm Pm}$-dependent tearing scale, at and below which folds are disrupted, is predicted theoretically and found to match well the characteristic field-reversal scale measured in the simulations. The disruption of folds by tearing increases the ratio of viscous-to-resistive dissipation. In the saturated state, the magnetic-energy spectrum exhibits a sub-tearing-scale steepening to a slope consistent with that predicted for tearing-mediated Alfv\'enic turbulence. Its spectral peak appears to be independent of the resistive scale and comparable to the driving scale of the flow, while the magnetic energy resides in a broad range of scales extending down to the field-reversal scale set by tearing. Emergence of a degree of large-scale magnetic coherence in the saturated state of the turbulent dynamo may be consistent with observations of magnetic-field fluctuations in galaxy clusters and recent laboratory experiments.
Magnetic energyKinematicsInstabilityTurbulenceTurbulent dynamoHigh-resolutionDissipationPlasmoidEddyNumerical simulation...
• #### Fast radio bursts at the dawn of the 2020sver. 2

Since the discovery of the first fast radio burst (FRB) in 2007, and their confirmation as an abundant extragalactic population in 2013, the study of these sources has expanded at an incredible rate. In our 2019 review on the subject we presented a growing, but still mysterious, population of FRBs -- 60 unique sources, 2 repeating FRBs, and only 1 identified host galaxy. However, in only a few short years new observations and discoveries have given us a wealth of information about these sources. The total FRB population now stands at over 600 published sources, 24 repeaters, and 19 host galaxies. Higher time resolution data, sustained monitoring, and precision localisations have given us insight into repeaters, host galaxies, burst morphology, source activity, progenitor models, and the use of FRBs as cosmological probes. The recent detection of a bright FRB-like burst from the Galactic magnetar SGR~1935+2154 provides an important link between FRBs and magnetars. There also continue to be surprising discoveries, like periodic modulation of activity from repeaters and the localisation of one FRB source to a relatively nearby globular cluster associated with the M81 galaxy. In this review, we summarise the exciting observational results from the past few years. We also highlight their impact on our understanding of the FRB population and proposed progenitor models. We build on the introduction to FRBs in our earlier review, update our readers on recent results, and discuss interesting avenues for exploration as the field enters a new regime where hundreds to thousands of new FRBs will be discovered and reported each year.
• #### PT challenge: Validation of ShapeFit on large-volume, high-resolution mocks

The ShapeFit compression method has been shown to be a powerful tool to gain cosmological information from galaxy power spectra in an effective, model-independent way. Here we present its performance on the blind PT challenge mock products presented in [1]. Choosing a set-up similar to that of other participants to the blind challenge we obtained $\Delta \ln\left(10^{10} A_s\right) = -0.018 \pm 0.014$, $\Delta \Omega_\mathrm{m} = 0.0039 \pm 0.0021$ and $\Delta h =-0.0009 \pm 0.0034$, remaining below $2\sigma$ deviations for a volume of $566 \left[ h^{-1}\mathrm{Gpc}\right]^3$. This corresponds to a volume 10 times larger than the volume probed by future galaxy surveys. We also present an analysis of these mocks oriented towards an actual data analysis using the full redshift evolution, using all three redshift bins $z_1 = 0.38$, $z_2=0.51$, and $z_3 = 0.61$, and exploring different set-ups to quantify the impact of choices or assumptions on noise, bias, scale range, etc. We find consistency across reasonable changes in set-up and across redshifts and that, as expected, mapping the redshift evolution of clustering helps constraining cosmological parameters within a given model.
Perturbation theoryCosmological parametersRedshift binsGalaxyCosmologyBaryon acoustic oscillationsRedshift-space distortionNuisance parameterLarge scale structureCosmological model...
• #### The Evolution of AGN Activity in Brightest Cluster Galaxies

We present the results of an analysis of Wide-field Infrared Survey Explorer (WISE) observations on the full 2500 deg^2 South Pole Telescope (SPT)-SZ cluster sample. We describe a process for identifying active galactic nuclei (AGN) in brightest cluster galaxies (BCGs) based on WISE mid-infrared color and redshift. Applying this technique to the BCGs of the SPT-SZ sample, we calculate the AGN-hosting BCG fraction, which is defined as the fraction of BCGs hosting bright central AGNs over all possible BCGs. Assuming {\bf an evolving} single-burst stellar population model, we find statistically significant evidence (>99.9%) for a mid-IR excess at high redshift compared to low redshift, suggesting that the fraction of AGN-hosting BCGs increases with redshift over the range of 0 < z < 1.3. The best-fit redshift trend of the AGN-hosting BCG fraction has the form (1+z)^(4.1+/-1.0). These results are consistent with previous studies in galaxy clusters as well as field galaxies. One way to explain this result is that member galaxies at high redshift tend to have more cold gas. While BCGs in nearby galaxy clusters grow mostly by dry mergers with cluster members, leading to no increase in AGN activity, BCGs at high redshift could primarily merge with gas-rich satellites, providing fuel for feeding AGNs. If this observed increase in AGN activity is linked to gas-rich mergers, rather than ICM cooling, we would expect to see an increase in scatter in the P_cav vs L_cool relation at z > 1. Lastly, this work confirms that the runaway cooling phase, as predicted by the classical cooling flow model, in the Phoenix cluster is extremely rare and most BCGs have low (relative to Eddington) black hole accretion rates.
Brightest cluster galaxyActive Galactic NucleiCluster of galaxiesWide-field Infrared Survey ExplorerSouth Pole TelescopeCoolingGalaxyAGN feedbackAccreting black holeStellar populations...
• #### Canonical Purification of Evaporating Black Holes

We show that the canonical purification of an evaporating black hole after the Page time consists of a short, connected, Lorentzian wormhole between two asymptotic boundaries, one of which is unitarily related to the radiation. This provides a quantitative and general realization of the predictions of ER=EPR in an evaporating black hole after the Page time; this further gives a standard AdS/CFT calculation of the entropy of the radiation (without modifications of the homology constraint). Before the Page time, the canonical purification consists of two disconnected, semiclassical black holes. From this, we construct two bipartite entangled holographic CFT states, with equal (and large) amount of entanglement, where the semiclassical dual of one has a connected ERB and the other does not. From this example, we speculate that that measures of multipartite entanglement may offer a more complete picture into the emergence of spacetime.
• #### Comments on the negative specific heat of the $T \bar T$ deformed symmetric product CFT

We show that the $T \bar T$ deformation of conformal field theories whose entropy grows as $S(E) \sim E^\gamma$ for $\gamma > 1/2$ exhibits negative specific heat in its microcanonical thermodynamic function $S({\cal E})$. We analyze the large $N$ symmetric product CFT as a concrete example of a CFT with this property and compute the thermodynamic functions such as $S({\cal E})$ and ${\cal E}(T)$. The negative specific heat in the microcanonical data is interpreted as signaling the first order phase transition when the system is coupled to a heat bath.
Conformal field theoryFirst-order phase transitionsEntropyHagedorn behaviorCanonical ensembleCentral chargeOrbifoldPhase transitionsDensity of statesField theory...
• #### Leptogenesis from a feebly interacting dark matter sector

We perform an analysis of leptogenesis in the context of a simple extension of the Standard Model by two fermions; one charged ($\chi$) and one neutral ($\psi$), in addition to three right-handed neutrinos, $N_i$, interacting through a charged gauge singlet scalar $S$. The dark sector ($\chi$, $\psi$ and $S$) interacts feebly and produces a relic density consistent with measurements. The decay of right-handed neutrinos into the charged scalar $S$ and lepton provides an additional source of CP asymmetry, along with contributing through the virtual exchange of $S$ in the standard decay channel. With this the out-of-equilibrium decay of right-handed neutrinos, combined with lepton number changing scattering processes can generate the required baryon asymmetry of the universe even for right-handed neutrino masses in 10 TeV region, without requiring neutrinos to have degenerate masses.
LeptogenesisDark matterSterile neutrinoStandard ModelNeutrinoYukawa couplingWeakly interacting massive particleBaryon asymmetry of the UniverseCP asymmetryDark matter particle...
• #### Triple nodal points characterized by their nodal-line structure in all magnetic space groups

We analyze triply degenerate nodal points [or triple points (TPs) for short] in energy bands of crystalline solids. Specifically, we focus on spinless band structures, i.e., when spin-orbit coupling is negligible, and consider TPs formed along high-symmetry lines in the momentum space by a crossing of three bands transforming according to a 1D and a 2D irreducible corepresentation (ICR) of the little co-group. The result is a complete classification of such TPs in all magnetic space groups, including the non-symmorphic ones, according to several characteristics of the nodal-line structure at and near the TP. We show that the classification of the presently studied TPs is exhausted by 13 magnetic point groups (MPGs) that can arise as the little co-group of a high-symmetry line and which support both 1D and 2D spinless ICRs. For 10 of the identified MPGs, the TP characteristics are uniquely determined without further information; in contrast, for the 3 MPGs containing sixfold rotation symmetry, two types of TPs are possible, depending on the choice of the crossing ICRs. The classification result for each of the 13 MPGs is illustrated with first-principles calculations of a concrete material candidate.
Magnetic space groupMomentum spaceTriple pointSpin-orbit interactionSymmetryEnergyMaterialsPoint group...
• #### Holographic R\'enyi Entropies at Finite Coupling

We compute R\'enyi entropies for a spherical entangling surface in four-dimensional N=4 super-Yang-Mills at strong coupling using the AdS/CFT correspondence. Incorporating the effects of the leading \alpha' corrections to the low energy effective action of type IIB string theory, we calculate the leading corrections in inverse powers of the 't Hooft coupling (and the number of colours). The results are compared with known weak coupling calculations. Setting the order of the R\'enyi entropy q to one, it reduces to the entanglement entropy and the strong and weak coupling results match without any corrections, as expected. In the limit of q going to 0, the relation between the strong and weak coupling entropies is connected to the known corrections for the thermal free energy in flat space. We also compute the correction to the scaling dimension of twist operators.
EntropyEntanglementSuper Yang-Mills theoryConformal field theoryCurvatureRenyi entropyBlack holeType IIB string theoryHorizonEffective action...
• #### Notes on Entanglement Entropy in String Theoryver. 2

In this paper, we study the entanglement entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on the Rindler space. This entropy is also called the conical entropy and includes surface term contributions. We first derive a new simple formula of the conical entropy for any free higher spin fields. Then we apply this formula to computations of conical entropy in open and closed superstring. In our analysis of closed string, we study the twisted conical entropy defined by making use of string theory on Melvin backgrounds. This quantity is easier to calculate owing to the folding trick. Our analysis shows that the entanglement entropy in closed superstring is UV finite owing to the string scale cutoff.
OrbifoldPartition functionTachyonEntropyBosonizationTorusFree field theoryAnalytic continuationEntanglement entropyTwisted sector...
• #### Varying fundamental constants and dark energy in the ESPRESSO era

The observational evidence for the recent acceleration of the universe shows that canonical theories of cosmology and particle physics are incomplete and that new physics is out there, waiting to be discovered. A compelling task for astrophysical facilities is to search for, identify and ultimately characterize this new physics. I present very recent developments in tests of the stability of nature's fundamental constants, as well as their impact on physics paradigms beyond the standard model. Specifically I discuss new observational constraints at low redshifts and at the BBN epoch, and highlight their different implications for canonical quintessence-type models and for non-canonical string-theory inspired models. Finally I also present new forecasts, based on realistic simulated data, of the gains in sensitivity for these constraints expected from ELT-HIRES, on its own and in combination with Euclid.
Dark energyESPRESSOBig bang nucleosynthesisCosmologyEuropean Extremely Large TelescopeLithium-7 problemEuclid missionFine structure constantScalar fieldHIRES spectrometer...

The aim of this paper is to describe a novel non-parametric noise reduction technique from the point of view of Bayesian inference that may automatically improve the signal-to-noise ratio of one- and two-dimensional data, such as e.g. astronomical images and spectra. The algorithm iteratively evaluates possible smoothed versions of the data, the smooth models, obtaining an estimation of the underlying signal that is statistically compatible with the noisy measurements. Iterations stop based on the evidence and the $\chi^2$ statistic of the last smooth model, and we compute the expected value of the signal as a weighted average of the whole set of smooth models. In this paper, we explain the mathematical formalism and numerical implementation of the algorithm, and we evaluate its performance in terms of the peak signal to noise ratio, the structural similarity index, and the time payload, using a battery of real astronomical observations. Our Fully Adaptive Bayesian Algorithm for Data Analysis (FABADA) yields results that, without any parameter tuning, are comparable to standard image processing algorithms whose parameters have been optimized based on the true signal to be recovered, something that is impossible in a real application. State-of-the-art non-parametric methods, such as BM3D, offer slightly better performance at high signal-to-noise ratio, while our algorithm is significantly more accurate for extremely noisy data (higher than $20-40\%$ relative errors, a situation of particular interest in the field of astronomy). In this range, the standard deviation of the residuals obtained by our reconstruction may become more than an order of magnitude lower than that of the original measurements. The source code needed to reproduce all the results presented in this report, including the implementation of the method, is publicly available at https://github.com/PabloMSanAla/fabada
Signal to noise ratioMean squared errorWiener filterBayesianStatisticsOptimizationImage ProcessingAbsorption lineBayesian evidenceBayesian approach...
• #### The Road to Precision Cosmology

The past 50 years has seen cosmology go from a field known for the errors being in the exponents to precision science. The transformation, powered by ideas, technology, a paradigm shift and culture change, has revolutionized our understanding of the Universe, with the $\Lambda$CDM paradigm as its crowning achievement. I chronicle the journey of precision cosmology and finish with my thoughts about what lies ahead.
CosmologyInflationDark matterBig BangPrecision cosmologyGravitational waveGalaxyNeutralinoDark energyCMB temperature anisotropy...
• #### Morphology of dark matter haloes beyond triaxiality

The morphology of haloes inform about both cosmological and galaxy formation models. We use the Minkowski Functionals (MFs) to characterize the actual morphology of haloes, only partially captured by smooth density profile, going beyond the spherical or ellipsoidal symmetry. We employ semi-analytical haloes with NFW and $\alpha\beta\gamma$-profile and spherical or ellipsoidal shape to obtain a clear interpretation of MFs as function of inner and outer slope, concentration and sphericity parameters. We use the same models to mimic the density profile of $N$-body haloes, showing that their MFs clearly differ as sensitive to internal substructures. This highlights the benefit of MFs at the halo scales as promising statistics to improve the spatial modeling of dark matter, crucial for future lensing, Sunyaev-Zel'dovich, and X-ray mass maps as well as dark matter detection based on high-accuracy data.
Minkowski functionalNavarro-Frenk-White profileDark matter haloStatisticsCosmologyDark matterCluster of galaxiesDark matter subhaloStandard deviationInner slope...
• #### Simultaneously constraining cosmology and baryonic physics via deep learning from weak lensingver. 2

Ongoing and planned weak lensing (WL) surveys are becoming deep enough to contain information on angular scales down to a few arcmin. To fully extract information from these small scales, we must capture non-Gaussian features in the cosmological WL signal while accurately accounting for baryonic effects. In this work, we account for baryonic physics via a baryonic correction model that modifies the matter distribution in dark matter-only $N$-body simulations, mimicking the effects of galaxy formation and feedback. We implement this model in a large suite of ray-tracing simulations, spanning a grid of cosmological models in $\Omega_\mathrm{m}-\sigma_8$ space. We then develop a convolutional neural network (CNN) architecture to learn and constrain cosmological and baryonic parameters simultaneously from the simulated WL convergence maps. We find that in a Hyper-Suprime Cam (HSC)-like survey, our CNN achieves a 1.7$\times$ tighter constraint in $\Omega_\mathrm{m}-\sigma_8$ space ($1\sigma$ area) than the power spectrum and 2.1$\times$ tighter than the peak counts, showing that the CNN can efficiently extract non-Gaussian cosmological information even while marginalizing over baryonic effects. When we combine our CNN with the power spectrum, the baryonic effects degrade the constraint in $\Omega_\mathrm{m}-\sigma_8$ space by a factor of 2.4, compared to the much worse degradation by a factor of 4.7 or 3.7 from either method alone.
Convolution Neural NetworkWeak lensingCosmologyStatisticsHyper Suprime-CamArchitectureCosmological parametersRay tracingSigma8Dark matter...
• #### Structure Formation in Dark Matter Particle Production Cosmology

We investigate a cosmological scenario in which the dark matter particles can be created during the evolution of the Universe. By regarding the Universe as an open thermodynamic system and using non-equilibrium thermodynamics, we examine the mechanism of gravitational particle production. In this setup, we study the large-scale structure (LSS) formation of the Universe in the Newtonian regime of perturbations and derive the equations governing the evolution of the dark matter overdensities. Then, we implement the cosmological data from Planck 2018 CMB measurements, SNe Ia and BAO observations, as well as the SH0ES local measurement for $H_0$ to provide some cosmological constraints for the parameters of our model. We see that the best case of our scenario ($\chi_{{\rm tot}}^{2}=3834.40$) fits the observational data better than the baseline $\Lambda$CDM model ($\chi_{{\rm tot}}^{2} = 3838.00$) at the background level. We also see that this case results in the Hubble constant as $H_0 = 68.79\pm 0.59\,{\rm km\,s^{-1}\,Mpc^{-1}}$ which is greater than $H_0 = 68.20^{+0.42}_{-0.38}\,{\rm km\,s^{-1}\,Mpc^{-1}}$ given by the $\Lambda$CDM model, and hence we can alleviate the $H_0$ tension to some extent in our framework. Furthermore, the best case of our scenario gives a lower value for the best-fit of the $S_8$ parameter than the $\Lambda$CDM result, and therefore it also reduces the LSS tension slightly. We moreover estimate the growth factor of linear perturbations and show that the best case of our model ($\chi_{f\sigma_{8}}^{2}=40.84$) fits the LSS data significantly better than the $\Lambda$CDM model ($\chi_{f\sigma_{8}}^{2}=44.29$). Consequently, our model also makes a better performance at the level of the linear perturbations compared to the standard cosmological model.
Large scale structureLambda-CDM modelSupernovae H0 for the Equation of StateBaryon acoustic oscillationsCosmologyDark matter particleHubble parameterPlanck missionDensity contrastDark matter...