- Prime number (Prime number)

by Wilson Yu04 Feb 2019 03:47 - Lower and upper (Lower and upper)

by Dr. Wei Wang28 Dec 2018 02:32 - Electrical conductivity (Electrical conductivity)

by Dr. Farhad Daneshvar20 Nov 2018 19:00 - On Measurement Assessment and Division Matrices (On Measurement Assessment and Division Matrices)

by Prof. Hasan Keleş01 Aug 2018 11:58 - Pauli matrices (Pauli matrices)

by Prof. Hasan Keleş16 Feb 2018 07:45 - Wigner transform (Wigner transform)

by Dr. Claude Becker06 Apr 2011 14:04 - Geometric flattening (Geometric flattening)

by Dr. Ganna Ivashchenko05 Dec 2010 22:14 - Neutrino Minimal Standard Model (Neutrino Minimal Standard Model)

by Prof. Mikhail Shaposhnikov15 Nov 2016 16:20 - RKKY interaction (RKKY interaction)

by Dr. Vadim Cheianov31 Aug 2009 09:28 - Fingers of God (Fingers of God)

by Dr. Ganna Ivashchenko18 May 2011 22:42

- Gaia DR2 provides unprecedented precision in measurements of the distance and kinematics of stars in the solar neighborhood. Through applying unsupervised machine learning on DR2's 5-dimensional dataset (3d position + 2d velocity), we identify a number of clusters, associations, and co-moving groups within 1 kpc and $|b|<30^\circ$ (many of which have not been previously known). We estimate their ages with the precision of $\sim$0.15 dex. Many of these groups appear to be filamentary or string-like, oriented in parallel to the Galactic plane, and some span hundreds of pc in length. Most of these string lack a central cluster, indicating that their filamentary structure is primordial, rather than the result of tidal stripping or dynamical processing. The youngest strings ($<$100 Myr) are orthogonal to the Local Arm. The older ones appear to be remnants of several other arm-like structures that cannot be presently traced by dust and gas. The velocity dispersion measured from the ensemble of groups and strings increase with age, suggesting a timescale for dynamical heating of $\sim$300 Myr. This timescale is also consistent with the age at which the population of strings begins to decline, while the population in more compact groups continues to increase, suggesting that dynamical processes are disrupting the weakly bound string populations, leaving only individual clusters to be identified at the oldest ages. These data shed a new light on the local galactic structure and a large scale cloud collapse. \end{abstract}StarParallaxMilky WayKinematicsVelocity dispersionSolar neighborhoodProper motionGalactic planeConvolutional neural networkOf stars...
- Detecting emotions from text is an extension of simple sentiment polarity detection. Instead of considering only positive or negative sentiments, emotions are conveyed using more tangible manner; thus, they can be expressed as many shades of gray. This paper manifests the results of our experimentation for fine-grained emotion analysis on Bangla text. We gathered and annotated a text corpus consisting of user comments from several Facebook groups regarding socio-economic and political issues, and we made efforts to extract the basic emotions (sadness, happiness, disgust, surprise, fear, anger) conveyed through these comments. Finally, we compared the results of the five most popular classical machine learning techniques namely Naive Bayes, Decision Tree, k-Nearest Neighbor (k-NN), Support Vector Machine (SVM) and K-Means Clustering with several combinations of features. Our best model (SVM with a non-linear radial-basis function (RBF) kernel) achieved an overall average accuracy score of 52.98% and an F1 score (macro) of 0.3324Support vector machineMachine learningRadial basis functionPart-of-speechClassificationFacebookF1 scoreK-means clusteringText corpusNearest-neighbor site...
- Local Universe observations find a value of the Hubble constant $H_0$ that is larger than the value inferred from the Cosmic Microwave Background and other early Universe measurements, assuming known physics and the $\Lambda$CDM cosmological model. We show that additional radiation in active neutrinos produced just before Big Bang Nucleosynthesis by an unstable sterile neutrino with mass $m_s=$ O(10) MeV can alleviate this discrepancy. The necessary masses and couplings of the sterile neutrino, assuming it mixes primarily with $\nu_{\tau}$ and/or $\nu_{\mu}$ neutrinos, are within reach of Super-Kamiokande as well as upcoming laboratory experiments such as NA62.Sterile neutrinoActive neutrinoBig bang nucleosynthesisNeutrinoCosmic microwave backgroundHubble parameterSuper-KamiokandeNA62 experimentLambda-CDM modelSterile neutrino decay...
- We use high-resolution hydrodynamical simulations run with the EAGLE model of galaxy formation to study the differences between the properties of - and subsequently the lensing signal from subhaloes of massive elliptical galaxies at redshift 0.2, in Cold and Sterile Neutrino Dark matter models. We focus on the two 7 keV SN models that bracket the range of matter power spectra compatible with resonantly-produced SN as the source of the observed 3.5 keV line. We derive an accurate parametrization for the subhalo mass function in these two SN models relative to CDM, as well as the subhalo spatial distribution, density profile, and projected number density and the dark matter fraction in subhaloes. We create mock lensing maps from the simulated haloes to study the differences in the lensing signal in the framework of subhalo detection. We find that subhalo convergence is well described by a log-normal distribution and that signal of subhaloes in the power spectrum is lower in SN models with respect to CDM, at a level of 10 to 80 per cent, depending on the scale. However, the scatter between different projections is large and might make the use of power-spectrum studies on the typical scales of current lensing images very difficult. Moreover, in the framework of individual detections through gravitational imaging a sample of ~30 lenses with an average sensitivity of M_sub=5 10^7 M_sun would be required to discriminate between CDM and the considered sterile neutrino models.Dark matter subhaloSterile neutrinoCold dark matterSubhalo mass functionDark matter modelDark matter fractionWarm dark matterDark matterLensing signalElliptical galaxy...
- The impacts of the light sterile neutrino hypothesis in particle physics and cosmology are reviewed. The observed short baseline neutrino anomalies challenging the standard explanation of neutrino oscillations within the framework of three active neutrinos are addressed. It is shown that they can be interpreted as the experimental hints pointing towards the existence of sterile neutrino at the eV scale. While the electron neutrino appearance and disappearance data are in favor of such a sterile neutrino, the muon disappearance data disfavor it, which gives rise to a strong appearance-disappearacne tension. After a brief review on the cosmological effects of light sterile neutrinos, proposed signatures of light sterile neutrinos in the existing cosmological data are discussed. The keV-scale sterile neutrinos as possible dark matter candidates are also discussed by reviewing different mechanisms of how they can be produced in the early Universe and how their properties can be constrained by several cosmological observations. We give an overview of the possibility that keV-scale sterile neutrino can be a good DM candidate and play a key role in achieving low scale leptogenesis simultaneously by introducing a model where an extra light sterile neutrino is added on top of type I seesaw model.Sterile neutrinoNeutrinoActive neutrinoNeutrino massNeutrino oscillationsDark matterCosmologyLeptogenesisMixing angleLiquid Scintillator Neutrino Detector...
- New physics in the neutrino sector might be necessary to address anomalies between different neutrino oscillation experiments. Intriguingly, it also offers a possible solution to the discrepant cosmological measurements of $H_0$ and $\sigma_8$. We show here that delaying the onset of neutrino free-streaming until close to the epoch of matter-radiation equality can naturally accommodate a larger value for the Hubble constant $H_0=72.3 \pm 1.4$ km/s/Mpc and a lower value of the matter fluctuations $\sigma_8=0.786\pm 0.020$, while not degrading the fit to the cosmic microwave background (CMB) damping tail. We achieve this by introducing neutrino self-interactions in the presence of a non-vanishing sum of neutrino masses. This strongly interacting neutrino cosmology prefers $N_{\rm eff} = 4.02 \pm 0.29$, which has interesting implications for particle model-building and neutrino oscillation anomalies. We show that the absence of the neutrino free-streaming phase shift on the CMB can be compensated by shifting the value of other cosmological parameters, hence providing an important caveat to the detections made in the literature. Due to their impact on the evolution of the gravitational potential at early times, self-interacting neutrinos and their subsequent decoupling leave a rich structure on the matter power spectrum. In particular, we point out the existence of a novel localized feature appearing on scales entering the horizon at the onset of neutrino free-streaming. While the interacting neutrino cosmology provides a better global fit to current cosmological data, we find that traditional Bayesian analyses penalize the model as compared to the standard cosmological. Our analysis shows that it is possible to find radically different cosmological models that nonetheless provide excellent fits to the data, hence providing an impetus to thoroughly explore alternate cosmological scenarios.NeutrinoFree streaming of particlesCold dark matterCosmologyCosmic microwave backgroundBaryon acoustic oscillationsHorizonNeutrino massMatter power spectrumDark matter...
- We argue that the observed baryon asymmetry of the Universe can be explained within the minimal Standard Model, from the ``sphaleron freezeout" reached when the electroweak sphaleron rate becomes equal to the Hubble rate of the Universe expansion. This freezeout drives the system out of equilibrium, and prevents the sphalerons from washing out the baryon asymmetry; we find that this mechanism can explain the observed magnitude of baryon asymmetry in the Universe. The test of the proposed scenario is possible through the study of magnetic helicity at intergalactic scales, as the baryon asymmetry appears tightly linked to the magnetic helicity at intergalactic scales.SphaleronBaryon asymmetry of the UniverseStandard ModelCP violationElectroweak phase transitionHiggs bosonGravitational waveSphaleron rateMagnetic helicityElectroweak...
- We study the laser control of magnon topological phases induced by the Aharonov-Casher effect in insulating antiferromagnets (AFs). Since the laser electric field can be considered as a time-periodic perturbation, we apply the Floquet theory and perform the inverse frequency expansion by focusing on the high frequency region. Using the obtained effective Floquet Hamiltonian, we study nonequilibrium magnon dynamics away from the adiabatic limit and its effect on topological phenomena. We show that a linearly polarized laser can generate helical edge magnon states and induce the magnonic spin Nernst effect, whereas a circularly polarized laser can generate chiral edge magnon states and induce the magnonic thermal Hall effect. In particular, in the latter, we find that the direction of the magnon chiral edge modes and the resulting thermal Hall effect can be controlled by the chirality of the circularly polarized laser through the change from the left-circular to the right-circular polarization. Our results thus provide a handle to control and design magnon topological properties in the insulating AF.MagnonLasersHamiltonianTopological orderTime-reversal symmetryHall effectChiralityTopological insulatorCyclotronEdge excitations...
- We introduce natural adversarial examples -- real-world, unmodified, and naturally occurring examples that cause classifier accuracy to significantly degrade. We curate 7,500 natural adversarial examples and release them in an ImageNet classifier test set that we call ImageNet-A. This dataset serves as a new way to measure classifier robustness. Like l_p adversarial examples, ImageNet-A examples successfully transfer to unseen or black-box classifiers. For example, on ImageNet-A a DenseNet-121 obtains around 2% accuracy, an accuracy drop of approximately 90%. Recovering this accuracy is not simple because ImageNet-A examples exploit deep flaws in current classifiers including their over-reliance on color, texture, and background cues. We observe that popular training techniques for improving robustness have little effect, but we show that some architectural changes can enhance robustness to natural adversarial examples. Future research is required to enable robust generalization to this hard ImageNet test set.Adversarial examplesAttentionClassificationConvolutional neural networkCalibrationArchitectureImage ProcessingGenerative modelTraining ImageGenerative Adversarial Net...
- An exact spacetime parity replicates the $SU(2) \times U(1)$ electroweak interaction, the Higgs boson $H$, and the matter of the Standard Model. This "Higgs Parity" and the mirror electroweak symmetry are spontaneously broken at scale $v' = \left\langle{H'} \right\rangle \gg \left\langle{H}\right\rangle$, yielding the Standard Model below $v'$ with a quartic coupling that essentially vanishes at $v'$: $\lambda_{SM}(v') \sim 10^{-3}$. The strong CP problem is solved as Higgs parity forces the masses of mirror quarks and ordinary quarks to have opposite phases. Dark matter is composed of mirror electrons, $e'$, stabilized by unbroken mirror electromagnetism. These interact with Standard Model particles via kinetic mixing between the photon and the mirror photon, which arises at four-loop level and is a firm prediction of the theory. Physics below $v'$, including the mass and interaction of $e'$ dark matter, is described by $\textit{one fewer parameter}$ than in the Standard Model. The allowed range of $m_{e'}$ is determined by uncertainties in $(\alpha_s, m_t, m_h)$, so that future precision measurements of these will be correlated with the direct detection rate of $e'$ dark matter, which, together with the neutron electric dipole moment, will probe the entire parameter space.Standard ModelDark matterHiggs bosonAbundanceMeteoritesKinetic mixingHiggs boson massStrong CP-problemMirror quarksTop quark mass...
- In this work we study generalization of neural networks in gradient-based meta-learning by analyzing various properties of the objective landscapes. We experimentally demonstrate that as meta-training progresses, the meta-test solutions, obtained after adapting the meta-train solution of the model, to new tasks via few steps of gradient-based fine-tuning, become flatter, lower in loss, and further away from the meta-train solution. We also show that those meta-test solutions become flatter even as generalization starts to degrade, thus providing an experimental evidence against the correlation between generalization and flat minima in the paradigm of gradient-based meta-leaning. Furthermore, we provide empirical evidence that generalization to new tasks is correlated with the coherence between their adaptation trajectories in parameter space, measured by the average cosine similarity between task-specific trajectory directions, starting from a same meta-train solution. We also show that coherence of meta-test gradients, measured by the average inner product between the task-specific gradient vectors evaluated at meta-train solution, is also correlated with generalization. Based on these observations, we propose a novel regularizer for MAML and provide experimental evidence for its effectiveness.Meta learningArchitectureNeural networkCurvatureCosine similarityHyperparameterClassificationOptimization landscapeSupervised learningOverfitting...
- A possible connection between the existence of three quark-lepton generations and the triality property of SO(8) group (the equality between 8-dimensional vectors and spinors) is investigated.SO(8)TrialityAutomorphismSubgroupFlavourWeak interactionCyclic permutationDegree of freedomPati Salam modelIrreducible representation...
- The universe goes through several phase transitions during its formative stages. Cosmic reionization is the last of them, where ultraviolet and X-ray radiation escape from the first generations of galaxies heating and ionizing their surroundings and subsequently the entire intergalactic medium. There is strong observational evidence that cosmic reionization ended approximately one billion years after the Big Bang, but there are still uncertainties that will be clarified with upcoming optical, infrared, and radio facilities in the next decade. This article gives an introduction to the theoretical and observational aspects of cosmic reionization and discusses their role in our understanding of early galaxy formation and cosmology.ReionizationGalaxyIntergalactic mediumIonizationIonizing radiationRecombinationStarQuasarStar formationPopulation III...
- We provide a deep Boltzmann machine (DBM) for the AdS/CFT correspondence. Under the philosophy that the bulk spacetime is a neural network, we give a dictionary between those, and obtain a restricted DBM as a discretized bulk scalar field theory in curved geometries. The probability distribution as training data is the generating functional of the boundary quantum field theory, and it trains neural network weights which are the metric of the bulk geometry. The deepest layer implements black hole horizons, and an employed regularization for the weights is an Einstein action. A large $N_c$ limit in holography reduces the DBM to a folded feed-forward architecture. We also neurally implement holographic renormalization into an autoencoder. The DBM for the AdS/CFT may serve as a platform for studying mechanisms of spacetime emergence in holography.Deep Boltzmann machineAdS/CFT correspondenceBoltzmann machineNeural networkArchitectureQuantum field theoryAnti de Sitter spaceDiscretizationRegularizationAutoencoder...
- How can we understand classification decisions made by deep neural nets? We propose answering this question by using ideas from causal inference. We define the ``Causal Concept Effect'' (CaCE) as the causal effect that the presence or absence of a concept has on the prediction of a given deep neural net. We then use this measure as a mean to understand what drives the network's prediction and what does not. Yet many existing interpretability methods rely solely on correlations, resulting in potentially misleading explanations. We show how CaCE can avoid such mistakes. In high-risk domains such as medicine, knowing the root cause of the prediction is crucial. If we knew that the network's prediction was caused by arbitrary concepts such as the lighting conditions in an X-ray room instead of medically meaningful concept, this would prevent us from disastrous deployment of such models. Estimating CaCE is difficult in situations where we cannot easily simulate the do-operator. As a simple solution, we propose learning a generative model, specifically a Variational AutoEncoder (VAE) on image pixels or image embeddings extracted from the classifier to measure VAE-CaCE. We show that VAE-CaCE is able to correctly estimate the true causal effect as compared to other baselines in controlled settings with synthetic and semi-natural high dimensional images.ClassificationGenerative modelCausal inferenceEmbeddingOrientationDeclinationGraphTraining setBinary classificationMachine learning...
- Instance segmentation is a promising yet challenging topic in computer vision. Recent approaches such as Mask R-CNN typically divide this problem into two parts -- a detection component and a mask generation branch, and mostly focus on the improvement of the detection part. In this paper, we present an approach that extends Mask R-CNN with five novel optimization techniques for improving the mask generation branch and reducing the conflicts between the mask branch and the detection component in training. These five techniques are independent to each other and can be flexibly utilized in building various instance segmentation architectures for increasing the overall accuracy. We demonstrate the effectiveness of our approach with tests on the COCO dataset.Convolutional neural networkRegion of interestCOCO simulationOptimizationArchitectureAblationSemantic segmentationImage ProcessingClassificationEmbedding...
- One of the most important parameters in characterizing the Epoch of Reionization, the escape fraction of ionizing photons, $f_\mathrm{esc}$, remains unconstrained both observationally and theoretically. With recent work highlighting the impact of galaxy-scale feedback on the instantaneous value of $f_\mathrm{esc}$, it is important to develop a model in which reionization is self-consistently coupled to galaxy evolution. In this work, we present such a model and explore how physically motivated functional forms of $f_\mathrm{esc}$ affect the evolution of ionized hydrogen within the intergalactic medium. Using the $21$cm power spectrum evolution, we investigate the likelihood of observationally distinguishing between a constant $f_\mathrm{esc}$ and other models that depend upon different forms of galaxy feedback. We find that changing the underlying connection between $f_\mathrm{esc}$ and galaxy feedback drastically alters the large-scale $21$cm power. The upcoming Square Kilometre Array Low Frequency instrument possesses the sensitivity to differentiate between our models at a fixed optical depth, requiring only $200$ hours of integration time focused on redshifts $z = 7.5-8.5$. Generalizing these results to account for a varying optical depth will require multiple $800$ hour observations spanning redshifts $z = 7-10$. This presents an exciting opportunity to observationally constrain one of the most elusive parameters during the Epoch of Reionization.ReionizationGalaxyStellar massEpoch of reionizationStar formation rateIonizing radiationGalactic evolutionSquare Kilometre ArrayStar formationIntergalactic medium...
- Nonlinear objects like halos and voids exhibit a scale-dependent bias on linear scales in massive neutrino cosmologies. The shape of this scale-dependent bias is a unique signature of the neutrino masses, but the amplitude of the signal is generally small, of the order of $f_\nu$, the contribution of neutrinos to the total matter content ($\lesssim 1\%$). In this paper, we demonstrate for the first time how the strength of this signal can be substantially enhanced by using information about the halo environment at a range of scales. This enhancement is achieved by using certain combinations of the large scale Cold Dark Matter and total matter environments of halos, both of which are measurable from galaxy clustering and weak lensing surveys.NeutrinoCold dark matterNeutrino massMassive neutrinoCosmologyTransfer functionGalaxyCosmic voidLarge scale structureFree streaming of particles...
- Since two-dimensional boron sheet (borophene) synthesized on Ag substrates in 2015, research on borophene has grown fast in the fields of condensed matter physics, chemistry, material science, and nanotechnology. Due to the unique physical and chemical properties, borophene has various potential applications. In this review, we summarize the progress on borophene with a particular emphasis on the recent advances. First, we introduce the phases of borophene by experimental synthesis and theoretical predictions. Then, the physical and chemical properties, such as mechanical, thermal, electronic, optical and superconducting properties are summarized. We also discuss in detail the utilization of the borophene for wide ranges of potential application among the alkali metal ion batteries, Li-S batteries, hydrogen storage, supercapacitor, sensor and catalytic in hydrogen evolution, oxygen reduction, oxygen evolution, and CO2 electroreduction reaction. Finally, the challenges and outlooks in this promising field are featured on the basis of its current development.SupercapacitorNanotechnologyCarbon dioxideCondensed matter physicsPotentialFieldLithiumIonMetalsMaterials...
- We revisit spatially flat FLRW cosmology in light of recent advances in standard model relativistic fluid dynamics. Modern fluid dynamics requires the presence of curvature-matter terms in the energy-momentum tensor for consistency. These terms are linear in the Ricci scalar and tensor, such that the corresponding cosmological model is referred to as ``Ricci cosmology''. No cosmological constant is included, there are no inflaton fields, bulk viscosity is assumed to be zero and we only employ standard Einstein gravity. Analytic solutions to Ricci cosmology are discussed, and we find that it is possible to support an early-time inflationary universe using only well-known ingredients from the Standard Model of physics and geometric properties of space-time.CosmologyFluid dynamicsStandard ModelFriedmann-Lemaitre-Robertson-Walker metricCurvatureTransport coefficientVolume viscosityDe Sitter spaceDark energyPerfect fluid...
- Ten years ago, relativistic viscous fluid dynamics was formulated from first principles in an effective field theory framework, based entirely on the knowledge of symmetries and long-lived degrees of freedom. In the same year, numerical simulations for the matter created in relativistic heavy-ion collision experiments became first available, providing constraints on the shear viscosity in QCD. The field has come a long way since then. We present the current status of the theory of non-equilibrium fluid dynamics in 2017, including the divergence of the fluid dynamic gradient expansion, resurgence, non-equilibrium attractor solutions, the inclusion of thermal fluctuations as well as their relation to microscopic theories. Furthermore, we review the theory basis for numerical fluid dynamics simulations of relativistic nuclear collisions, and comparison of modern simulations to experimental data for nucleus-nucleus, nucleus-proton and proton-proton collisions.Fluid dynamicsEnergy-momentum tensorAttractorKinetic theoryHeavy ion collisionTransport coefficientIdeal fluidDegree of freedomMonte Carlo methodTwo-point correlation function...
- Recent researches attempt to improve the detection performance by adopting the idea of cascade for single-stage detectors. In this paper, we analyze and discover that inconsistency is the major factor limiting the performance. The refined anchors are associated with the feature extracted from the previous location and the classifier is confused by misaligned classification and localization. Further, we point out two main designing rules for the cascade manner: improving consistency between classification confidence and localization performance, and maintaining feature consistency between different stages. A multistage object detector named Cas-RetinaNet, is then proposed for reducing the misalignments. It consists of sequential stages trained with increasing IoU thresholds for improving the correlation, and a novel Feature Consistency Module for mitigating the feature inconsistency. Experiments show that our proposed Cas-RetinaNet achieves stable performance gains across different models and input scales. Specifically, our method improves RetinaNet from 39.1 AP to 41.1 AP on the challenging MS COCO dataset without any bells or whistles.ClassificationRegressionObject detectionCOCO simulationGround truthArchitectureMain sequence starFeature extractionConvolutional neural networkInference...
- End-to-end learning has recently emerged as a promising technique to tackle the problem of autonomous driving. Existing works show that learning a navigation policy from raw sensor data may reduce the system's reliance on external sensing systems, (e.g. GPS), and/or outperform traditional methods based on state estimation and planning. However, existing end-to-end methods generally trade off performance for safety, hindering their diffusion to real-life applications. For example, when confronted with an input which is radically different from the training data, end-to-end autonomous driving systems are likely to fail, compromising the safety of the vehicle. To detect such failure cases, this work proposes a general framework for uncertainty estimation which enables a policy trained end-to-end to predict not only action commands, but also a confidence about its own predictions. In contrast to previous works, our framework can be applied to any existing neural network and task, without the need to change the network's architecture or loss, or to train the network. In order to do so, we generate confidence levels by forward propagation of input and model uncertainties using Bayesian inference. We test our framework on the task of steering angle regression for an autonomous car, and compare our approach to existing methods with both qualitative and quantitative results on a real dataset. Finally, we show an interesting by-product of our framework: robustness against adversarial attacks.Neural networkAutonomous drivingData uncertaintyTraining setDeep learningBayesianArchitectureRegressionBayesian approachConvolutional neural network...
- Many automated processes such as auto-piloting rely on a good semantic segmentation as a critical component. To speed up performance, it is common to downsample the input frame. However, this comes at the cost of missed small objects and reduced accuracy at semantic boundaries. To address this problem, we propose a new content-adaptive downsampling technique that learns to favor sampling locations near semantic boundaries of target classes. Cost-performance analysis shows that our method consistently outperforms the uniform sampling improving balance between accuracy and computational efficiency. Our adaptive sampling gives segmentation with better quality of boundaries and more reliable support for smaller-size objects.Semantic segmentationClassificationConvolutional neural networkArchitectureGround truthAutonomous drivingImage ProcessingDeep learningCurvatureSparsity...
- Calculating the value of $C^{k\in\{1,\infty\}}$ class of smoothness real-valued function's derivative in point of $\mathbb{R}^+$ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and $q$-difference operator. $(P,q)$-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using $q$-difference and $p,q$-power difference is shown.Radius of convergenceFinite differenceWolfram MathematicaPower closedAuxiliary functionPolynomialNewtonTaylor seriesAnalytic function...
- An open secret in contemporary machine learning is that many models work beautifully on standard benchmarks but fail to generalize outside the lab. This has been attributed to training on biased data, which provide poor coverage over real world events. Generative models are no exception, but recent advances in generative adversarial networks (GANs) suggest otherwise -- these models can now synthesize strikingly realistic and diverse images. Is generative modeling of photos a solved problem? We show that although current GANs can fit standard datasets very well, they still fall short of being comprehensive models of the visual manifold. In particular, we study their ability to fit simple transformations such as camera movements and color changes. We find that the models reflect the biases of the datasets on which they are trained (e.g., centered objects), but that they also exhibit some capacity for generalization: by "steering" in latent space, we can shift the distribution while still creating realistic images. We hypothesize that the degree of distributional shift is related to the breadth of the training data distribution, and conduct experiments that demonstrate this. Code is released on our project page: https://ali-design.github.io/gan_steerability/Latent spaceGenerative Adversarial NetGenerative modelTraining setNeural networkArchitectureVolcanoesManifoldObject detectionStatistics...
- Leading terms of asymptotic expansions for the general complex solutions of the fifth Painlev\'e equation as $t\to\imath\infty$ are found. These asymptotics are parameterized by monodromy data of the associated linear ODE. $$ \frac{d}{d\lambda}Y= \left(\frac t2\sigma_3 + \frac{A_0}\lambda+\frac{A_1}{\lambda-1}\right)Y. $$ The parametrization allows one to derive connection formulas for the asymptotics. We provide numerical verification of the results. Important special cases of the connection formulas are also considered.MonodromyAsymptotic expansionBäcklund transformMonodromy matrixAnalytic continuationWentzel-Kramers-Brillouin approximationGraphManifoldComplex numberPainlevé transcendents...
- Einstein-Boltzmann Solvers (EBSs) are run on a massive scale by the cosmology community when fitting cosmological models to data. We present a new concept for speeding up such codes with neural networks. The originality of our approach stems from not substituting the whole EBS by a machine learning algorithm, but only its most problematic and least parallelizable step: the integration of perturbation equations over time. This approach offers two significant advantages: the task depends only on a subset of cosmological parameters, and it is blind to the characteristics of the experiment for which the output must be computed (for instance, redshift bins). These allow us to construct a fast and highly re-usable network. In this proof-of-concept paper, we focus on the prediction of CMB source functions, and design our networks according to physical considerations and analytical approximations. This allows us to reduce the depth and training time of the networks compared to a brute-force approach. Indeed, the calculation of the source functions using the networks is fast enough so that it is not a bottleneck in the EBS anymore. Finally, we show that their accuracy is more than sufficient for accurate MCMC parameter inference from Planck data. This paves the way for a new project, CosmicNet, aimed at gradually extending the use and the range of validity of neural networks within EBSs, and saving massive computational time in the context of cosmological parameter extraction.Einstein-Boltzmann SolversCosmic microwave backgroundCosmologyNeural networkTransfer functionReionizationCosmological modelCosmological parametersHyperparameterArchitecture...
- A quantum spin liquid (QSL) is a state of matter where unpaired electrons' spins in a solid are quantum entangled, but do not show magnetic order in the zero-temperature limit. Because such a state may be important to the microscopic origin of high-transition temperature superconductivity and useful for quantum computation, the experimental realization of QSL is a long-sought goal in condensed matter physics. Although neutron scattering experiments on the two-dimensional (2D) spin-1/2 kagome-lattice ZnCu3(OD)6Cl2 and effective spin-1/2 triangular lattice YbMgGaO4 have found evidence for a continuum of magnetic excitations, the hallmark of a QSL carrying 'fractionalized quantum excitations', at very low temperature, magnetic and nonmagnetic site chemical disorder complicates the interpretation of the data. Recently, the three-dimensional (3D) Ce3+ pyrochlore lattice Ce2Sn2O7 has been suggested as a clean, effective spin-1/2 QSL candidate, but there is no evidence of a spin excitation continuum. Here we use thermodynamic, muon spin relaxation ({\mu} SR), and neutron scattering experiments on single crystals of Ce2Zr2O7, a compound isostructural to Ce2Sn2O7, to demonstrate the absence of magnetic ordering and the presence of a spin excitation continuum at 35 mK, consistent with the expectation of a QSL. Since our neutron diffraction and diffuse scattering measurements on Ce2Zr2O7 reveal no evidence of oxygen deficiency and magnetic/nonmagnetic ion disorder as seen in other pyrochlores, Ce2Zr2O7 may be the first example of a 3D QSL material with minimum magnetic and nonmagnetic chemical disorder.PyrochloreSpin liquidMagnetic orderNeutron scatteringSingle crystalTriangular latticeSuperconductivityState of matterCondensed matter physicsRelaxation...
- Machine learning methods are powerful in distinguishing different phases of matter in an automated way and provide a new perspective on the study of physical phenomena. We train a Restricted Boltzmann Machine (RBM) on data constructed with spin configurations sampled from the Ising Hamiltonian at different values of temperature and external magnetic field using Monte Carlo methods. From the trained machine we obtain the flow of iterative reconstruction of spin state configurations to faithfully reproduce the observables of the physical system. We find that the flow of the trained RBM approaches the spin configurations of the maximal possible specific heat which resemble the near criticality region of the Ising model. In the special case of the vanishing magnetic field the trained RBM converges to the critical point of the Renormalization Group (RG) flow of the lattice model. Our results suggest an alternative explanation of how the machine identifies the physical phase transitions, by recognizing certain properties of the configuration like the maximization of the specific heat, instead of associating directly the recognition procedure with the RG flow and its fixed points. Then from the reconstructed data we deduce the critical exponent associated to the magnetization to find satisfactory agreement with the actual physical value. We assume no prior knowledge about the criticality of the system and its Hamiltonian.Restricted Boltzmann MachinesIsing modelPhase transitionsRenormalisation group flowHamiltonianMachine learningCritical pointMagnetizationRenormalization groupCritical exponent...
- Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute. (Notebooks are available at https://physics.bu.edu/~pankajm/MLnotebooks.html )Neural networkDeep Neural NetworksRegularizationRegressionLogistic regressionConvolutional neural networkMachine learningDeep learningSupervised learningArchitecture...
- We present version X of the hammurabi package, the HEALPix-based numeric simulator for Galactic polarized emission. Improving on its earlier design, we have fully renewed the framework with modern c++ standards and features. Multi-threading support has been built in to meet the growing computational workload in future research. For the first time, we present precision profiles of hammurabi line-of-sight integral kernel with multi-layer HEALPix shells. In addition to fundamental improvements, this report focuses on simulating polarized synchrotron emission with Gaussian random magnetic fields. Two fast methods are proposed for realizing divergence-free random magnetic fields either on the Galactic scale where a field alignment and strength modulation are imposed, or on a local scale where more physically motivated models like a parameterized magneto-hydrodynamic (MHD) turbulence can be applied. As an example application, we discuss the phenomenological implications of Gaussian random magnetic fields for high Galactic latitude synchrotron foregrounds. In this, we numerically find B/E polarization mode ratios lower than unity based on Gaussian realizations of either MHD turbulent spectra or in spatially aligned magnetic fields.Galactic magnetic fieldRandom FieldSynchrotronSynchrotron radiationLine of sightFaraday rotationCosmic ray electronTurbulenceMagnetohydrodynamic turbulenceInterstellar medium...
- Fundamental mathematical constants like $e$ and $\pi$ are ubiquitous in diverse fields of science, from abstract mathematics and geometry to physics, biology and chemistry. Nevertheless, for centuries new mathematical formulas relating fundamental constants have been scarce and usually discovered sporadically. In this paper we propose a novel and systematic approach that leverages algorithms for deriving new mathematical formulas for fundamental constants and help reveal their underlying structure. Our algorithms find dozens of well-known as well as previously unknown continued fraction representations of $\pi$, $e$, and the Riemann zeta function values. Two new conjectures produced by our algorithm, along with many others, are: \begin{equation*} e = 3 + \frac{-1}{4+\frac{-2}{5+\frac{-3}{6+\frac{-4}{7+\ldots}}}} \quad\quad,\quad\quad \frac{4}{\pi-2} = 3+\frac{1\cdot3}{5+\frac{2\cdot 4}{7+\frac{3\cdot 5}{9+\frac{4\cdot 6}{11+\ldots}}}} \end{equation*} We present two algorithms that proved useful in finding new results: a variant of the Meet-In-The-Middle (MITM) algorithm and a Gradient Descent (GD) tailored to the recurrent structure of continued fractions. Both algorithms are based on matching numerical values and thus find new conjecture formulas without providing proofs and without requiring prior knowledge on any mathematical structure. This approach is especially attractive for fundamental constants for which no mathematical structure is known, as it reverses the conventional approach of sequential logic in formal proofs. Instead, our work presents a new conceptual approach for research: computer algorithms utilizing numerical data to unveil new internal structures and conjectures, thus playing the role of mathematical intuition of great mathematicians of the past, providing leads to new mathematical research.OptimizationNumber theoryGeneralized continued fractionTheorem proverFormal proofRational functionRiemann zeta functionSparsityGround truthMathematical proof...
- We propose a procedure to cross-validate Monte Carlo implementations of the standard model effective field theory. It is based on the numerical comparison of squared amplitudes computed at specific phase-space and parameter points in pairs of implementations. Interactions are fully linearised in the effective field theory expansion. The squares of linear effective field theory amplitudes and their interference with standard-model contributions are compared separately. Such pairwise comparisons are primarily performed at tree level and a possible extension to the one-loop level is also briefly considered. We list the current standard model effective field theory implementations and the comparisons performed to date.Effective field theoryMonte Carlo methodStandard ModelDimension-six operatorsInterferencePhase spaceHiggs bosonTop quarkElectroweakHelicity...
- Ho\v{r}ava gravity breaks boost invariance in the gravitational sector by introducing a preferred time foliation. The dynamics of this preferred slicing is governed, in the low-energy limit suitable for most astrophysical applications, by three dimensionless parameters $\alpha$, $\beta$ and $\lambda$. The first two of these parameters are tightly bounded by solar system and gravitational wave propagation experiments, but $\lambda$ remains relatively unconstrained ($0\leq\lambda\lesssim 0.01-0.1$). We restrict here to the parameter space region defined by $\alpha=\beta=0$ (with $\lambda$ kept generic), which in a previous paper we showed to be the only one where black hole solutions are non-pathological at the universal horizon, and we focus on possible violations of the strong equivalence principle in systems involving neutron stars. We compute neutron star "sensitivities", which parametrize violations of the strong equivalence principle, and find that they vanish identically, like in the black hole case, for $\alpha=\beta=0$ and generic $\lambda\neq0$. This implies that no violations of the strong equivalence principle (neither in the conservative sector nor in gravitational wave fluxes) can occur at the leading post-Newtonian order in binaries of compact objects, and that data from binary pulsars and gravitational interferometers are unlikely to further constrain $\lambda$.Black holeNeutron starGravitational waveGeneral relativityGW170817Equivalence principleStarFoliationBinary pulsarSolar system...
- Recently, there is a growing interest in the study of rank metric codes. These codes have applications in network coding and cryptography. In this paper, we investigate some automorpshisms on polynomial rings over finite fields. We show how the linear operators from these automorphisms can be used to construct some maximum rank distance (MRD) codes. First we work on rank metric codes over arbitrary extension and then we reduce these to finite fields extension. Some particular constructions give MRD codes which are not equivalent to the twisted Gabidulin codes. Another application is to use these linear operators to construct some optimal rank metric codes for some Ferrers diagrams. In fact we give some examples of Ferrers diagrams for which there was no known construction of optimal rank metric codes.RankAutomorphismRational functionGalois fieldNetwork CodingCryptographyPolynomial ringMultiplicative groupVector spaceSecurity...
- The distributions of dark matter and baryons in the Universe are known to be very different: the dark matter resides in extended halos, while a significant fraction of the baryons have radiated away much of their initial energy and fallen deep into the potential wells. This difference in morphology leads to the widely held conclusion that dark matter cannot cool and collapse on any scale. We revisit this assumption, and show that a simple model where dark matter is charged under a "dark electromagnetism" can allow dark matter to form gravitationally collapsed objects with characteristic mass scales much smaller than that of a Milky Way-type galaxy. Though the majority of the dark matter in spiral galaxies would remain in the halo, such a model opens the possibility that galaxies and their associated dark matter play host to a significant number of collapsed substructures. The observational signatures of such structures are not well explored, but potentially interesting.Dark matterCoolingMilky WayDark matter haloGalaxyVirial massDark sectorThe early UniverseDegree of freedomDwarf galaxy...
- We present a new and independent determination of the local value of the Hubble constant based on a calibration of the Tip of the Red Giant Branch (TRGB) applied to Type Ia supernovae (SNeIa). We find a value of Ho = 69.8 +/- 0.8 (+/-1.1\% stat) +/- 1.7 (+/-2.4\% sys) km/sec/Mpc. The TRGB method is both precise and accurate, and is parallel to, but independent of the Cepheid distance scale. Our value sits midway in the range defined by the current Hubble tension. It agrees at the 1.2-sigma level with that of the Planck 2018 estimate, and at the 1.7-sigma level with the SHoES measurement of Ho based on the Cepheid distance scale. The TRGB distances have been measured using deep Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) imaging of galaxy halos. The zero point of the TRGB calibration is set with a distance modulus to the Large Magellanic Cloud of 18.477 +/- 0.004 (stat) +/-0.020 (sys) mag, based on measurement of 20 late-type detached eclipsing binary (DEB) stars, combined with an HST parallax calibration of a 3.6 micron Cepheid Leavitt law based on Spitzer observations. We anchor the TRGB distances to galaxies that extend our measurement into the Hubble flow using the recently completed Carnegie Supernova Project I sample containing about 100 well-observed SNeIa. There are several advantages of halo TRGB distance measurements relative to Cepheid variables: these include low halo reddening, minimal effects of crowding or blending of the photometry, only a shallow (calibrated) sensitivity to metallicity in the I-band, and no need for multiple epochs of observations or concerns of different slopes with period. In addition, the host masses of our TRGB host-galaxy sample are higher on average than the Cepheid sample, better matching the range of host-galaxy masses in the CSP distant sample, and reducing potential systematic effects in the SNeIa measurements.Tip of the red giant branchCepheidGalaxyCalibrationLarge Magellanic CloudStarMilky WaySystematic errorCepheid distanceReddening...
- Deep neural networks have achieved tremendous success in various fields including medical image segmentation. However, they have long been criticized for being a black-box, in that interpretation, understanding and correcting architectures is difficult as there is no general theory for deep neural network design. Previously, precision learning was proposed to fuse deep architectures and traditional approaches. Deep networks constructed in this way benefit from the original known operator, have fewer parameters, and improved interpretability. However, they do not yield state-of-the-art performance in all applications. In this paper, we propose to analyze deep networks using known operators, by adopting a divide-and-conquer strategy to replace network components, whilst retaining its performance. The task of retinal vessel segmentation is investigated for this purpose. We start with a high-performance U-Net and show by step-by-step conversion that we are able to divide the network into modules of known operators. The results indicate that a combination of a trainable guided filter and a trainable version of the Frangi filter yields a performance at the level of U-Net (AUC 0.974 vs. 0.972) with a tremendous reduction in parameters (111,536 vs. 9,575). In addition, the trained layers can be mapped back into their original algorithmic interpretation and analyzed using standard tools of signal processing.Deep Neural NetworksArchitectureRegion of interestImage segmentationGround truthF1 scoreMaculaTraining setField of viewNetworks...
- We present a method for gating deep-learning architectures on a fine-grained level. Individual convolutional maps are turned on/off conditionally on features in the network. This method allows us to train neural networks with a large capacity, but lower inference time than the full network. To achieve this, we introduce a new residual block architecture that gates convolutional channels in a fine-grained manner. We also introduce a generally applicable tool "batch-shaping" that matches the marginal aggregate posteriors of features in a neural network to a pre-specified prior distribution. We use this novel technique to force gates to be more conditional on the data. We present results on CIFAR-10 and ImageNet datasets for image classification and Cityscapes for semantic segmentation. Our results show that our method can slim down large architectures conditionally, such that the average computational cost on the data is on par with a smaller architecture, but with higher accuracy. In particular, our ResNet34 gated network achieves a performance of 72.55% top-1 accuracy compared to the 69.76% accuracy of the baseline ResNet18 model, for similar complexity. We also show that the resulting networks automatically learn to use more features for difficult examples and fewer features for simple examples.ArchitectureNeural networkInferenceSparsitySemantic segmentationClassificationConvolutional neural networkMagnetic adiabatic collimationDeep learningRegularization...
- Monocular depth estimation is an essential task for scene understanding. The underlying structure of objects and stuff in a complex scene is critical to recovering accurate and visually-pleasing depth maps. Global structure conveys scene layouts, while local structure reflects shape details. Recently developed approaches based on convolutional neural networks (CNNs) significantly improve the performance of depth estimation. However, few of them take into account multi-scale structures in complex scenes. In this paper, we propose a Structure-Aware Residual Pyramid Network (SARPN) to exploit multi-scale structures for accurate depth prediction. We propose a Residual Pyramid Decoder (RPD) which expresses global scene structure in upper levels to represent layouts, and local structure in lower levels to present shape details. At each level, we propose Residual Refinement Modules (RRM) that predict residual maps to progressively add finer structures on the coarser structure predicted at the upper level. In order to fully exploit multi-scale image features, an Adaptive Dense Feature Fusion (ADFF) module, which adaptively fuses effective features from all scales for inferring structures of each scale, is introduced. Experiment results on the challenging NYU-Depth v2 dataset demonstrate that our proposed approach achieves state-of-the-art performance in both qualitative and quantitative evaluation. The code is available at https://github.com/Xt-Chen/SARPN.Depth estimationConvolutional neural networkSemantic segmentationGround truthArchitectureAttentionF1 scorePoint cloudRegressionInference...
- Understanding the world in 3D is a critical component of urban autonomous driving. Generally, the combination of expensive LiDAR sensors and stereo RGB imaging has been paramount for successful 3D object detection algorithms, whereas monocular image-only methods experience drastically reduced performance. We propose to reduce the gap by reformulating the monocular 3D detection problem as a standalone 3D region proposal network. We leverage the geometric relationship of 2D and 3D perspectives, allowing 3D boxes to utilize well-known and powerful convolutional features generated in the image-space. To help address the strenuous 3D parameter estimations, we further design depth-aware convolutional layers which enable location specific feature development and in consequence improved 3D scene understanding. Compared to prior work in monocular 3D detection, our method consists of only the proposed 3D region proposal network rather than relying on external networks, data, or multiple stages. M3D-RPN is able to significantly improve the performance of both monocular 3D Object Detection and Bird's Eye View tasks within the KITTI urban autonomous driving dataset, while efficiently using a shared multi-class model.Object detectionLiDARPoint cloudOptimizationAutonomous drivingConvolutional neural networkOrientationGround truthStatisticsClassification...
- We show that the special values at tuples of positive integers of the $p$-adic multiple $L$-function introduced by the first-named author et al. can be expressed in terms of the cyclotomic multiple harmonic values introduced by the second-named author.Prime numberIterated integralMultiple zeta functionMultiple polylogarithmsDifferential formAutomorphismGalois theoryRiemann zeta functionPolylogarithmVon Staudt-Clausen theorem...
- Voronoi cells of varieties encode many features of their metric geometry. We prove that each Voronoi or Delaunay cell of a plane curve appears as the limit of a sequence of cells obtained from point samples of the curve. We then use this result to study metric features of plane curves, including the medial axis, curvature, evolute, bottlenecks, and reach. In each case, we provide algebraic equations defining the object and, where possible, give formulas for the degrees of these algebraic varieties. We then show how to identify the desired metric feature from Voronoi or Delaunay cells, and therefore how to approximate it by a finite point sample from the variety.CurvatureAlgebraic varietyConvex setCenter of curvatureCritical pointAlgebraic geometryWijsman convergenceVoronoi tessellationOsculating circleMetric geometry...
- The generation of magnetic field in an electrically conducting fluid generally involves the complicated nonlinear interaction of flow turbulence, rotation and field. This dynamo process is of great importance in geophysics, planetary science and astrophysics, since magnetic fields are known to play a key role in the dynamics of these systems. This paper gives an introduction to dynamo theory for the fluid dynamicist. It proceeds by laying the groundwork, introducing the equations and techniques that are at the heart of dynamo theory, before presenting some simple dynamo solutions. The problems currently exercising dynamo theorists are then introduced, along with the attempts to make progress. The paper concludes with the argument that progress in dynamo theory will be made in the future by utilising and advancing some of the current breakthroughs in neutral fluid turbulence such as those in transition, self-sustaining processes, turbulence/mean-flow interaction, statistical methods and maintenance and loss of balance.Dynamo theoryTurbulenceTurbulent dynamoPlanetary scienceMagnetic fieldField...
- Reionization leads to large spatial fluctuations in the intergalactic temperature that can persist well after its completion. We study the imprints of such fluctuations on the $z\sim5$ Ly$\alpha$ forest flux power spectrum using a set of radiation-hydrodynamic simulations that model different reionization scenarios. We find that large-scale coherent temperature fluctuations bring $\sim20-60\%$ extra power at $k\sim0.002$ s/km, with the largest enhancements in the models where reionization is extended or ends the latest. On smaller scales ($k\gtrsim0.1$ s/km), we find that temperature fluctuations suppress power by $\lesssim10\%$. We find that the shape of the power spectrum is mostly sensitive to the reionization midpoint rather than temperature fluctuations from reionization's patchiness. However, for all of our models with reionization midpoints of $z\le 8$ ($z\le 12$) the shape differences are $\lesssim20\%$ ($\lesssim40\%$) because of a surprisingly well-matched cancellation between thermal broadening and pressure smoothing that occurs for realistic thermal histories. We also consider fluctuations in the ultraviolet background, finding their impact on the power spectrum to be much smaller than temperature fluctuations at $k\gtrsim0.01$ s/km. Furthermore, we compare our models to power spectrum measurements, finding that none of our models with reionization midpoints of $z<8$ is strongly preferred over another and that all of our models with midpoints of $z\geq8$ are excluded at $2.5\sigma$. Future measurements may be able to distinguish between viable reionization models if they can be performed at lower $k$ or, alternatively, if the error bars on the high-$k$ power can be reduced by a factor of $1.5$.ReionizationFlux power spectrumUltraviolet backgroundLyman-alpha forestPressure smoothingLine thermal broadeningIGM temperatureMean transmitted fluxFluid dynamicsUVB fluctuations...
- The neutral hydrogen (HI) and its 21 cm line are promising probes to the reionization process of the intergalactic medium (IGM). To use this probe effectively, it is imperative to have a good understanding on how the neutral hydrogen traces the underlying matter distribution. Here we study this problem using semi-numerical modeling by combining the HI in the IGM and the HI from halos during the epoch of reionization (EoR), and investigate the evolution and the scale-dependence of the neutral fraction bias as well as the 21 cm line bias. We find that the neutral fraction bias on large scales is negative during reionization, and its absolute value on large scales increases during the early stage of reionization and then decreases during the late stage. During the late stage of reionization, there is a transition scale at which the HI bias transits from negative on large scales to positive on small scales, and this scale increases as the reionization proceeds to the end.ReionizationEpoch of reionizationIntergalactic mediumDark matterHydrogen 21 cm lineNeutral hydrogen gasBrightness temperature21-cm power spectrumIonizationCross-correlation...