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At least 487 records · Page 27

Quality quandaries: Experiencing the practice of statistics with simple experiments

This article illustrates the practice of statistics through simple experiments. In running ex- periments that involve blowing bubbles, collecting rain, and spinning propellers, issues arise that in the practice of statistics require being carefully addressed to correctly apply statisti- cal methods. Addressing these issues involves developing statistical models, simulation, and optimization. Sometimes the solutions require research, i.e., applied research.

42 ENGINEERING↗

A SIMPLE TECHNIQUE FOR PREDICTING HIGH-REDSHIFT GALAXY EVOLUTION

We show that the ratio of galaxies' specific star formation rates (SSFRs) to their host halos' specific mass accretion rates (SMARs) strongly constrains how the galaxies' stellar masses, SSFRs, and host halo masses evolve over cosmic time. This evolutionary constraint provides a simple way to probe z > 8 galaxy populations without direct observations. Tests of the method with galaxy properties at z = 4 successfully reproduce the known evolution of the stellar mass-halo mass (SMHM) relation, galaxy SSFRs, and the cosmic star formation rate (CSFR) for 5 < z < 8. We then predict the continued evolution of these properties for 8 < z < 15. In contrast to the nonevolution in the SMHM relation at z < 4, the median galaxy mass at fixed halo mass increases strongly at z > 4. We show that this result is closely linked to the flattening in galaxy SSFRs at z > 2 compared to halo SMARs; we expect that average galaxy SSFRs at fixed stellar mass will continue their mild evolution to z ∼ 15. The expected CSFR shows no breaks or features at z > 8.5; this constrains both reionization and the possibility of a steep falloff in the CSFR at z = 9-10. Finally, we make predictions for stellar mass and luminosity functions for the James Webb Space Telescope, which should be able to observe one galaxy with M {sub *} ≳ 10{sup 8} M {sub ☉} per 10{sup 3} Mpc{sup 3} at z = 9.6 and one such galaxy per 10{sup 4} Mpc{sup 3} at z = 15.

79 ASTRONOMY AND ASTROPHYSICS↗

A SIMPLE GRAVITATIONAL LENS MODEL FOR COSMIC VOIDS

We present a simple gravitational lens model to illustrate the ease of using the embedded lensing theory when studying cosmic voids. It confirms the previously used repulsive lensing models for deep voids. We start by estimating magnitude fluctuations and weak-lensing shears of background sources lensed by large voids. We find that sources behind large (∼90 Mpc) and deep voids (density contrast about −0.9) can be magnified or demagnified with magnitude fluctuations of up to ∼0.05 mag and that the weak-lensing shear can be up to the ∼10{sup −2} level in the outer regions of large voids. Smaller or shallower voids produce proportionally smaller effects. We investigate the “wiggling” of the primary cosmic microwave background (CMB) temperature anisotropies caused by intervening cosmic voids. The void-wiggling of primary CMB temperature gradients is of the opposite sign to that caused by galaxy clusters. Only extremely large and deep voids can produce wiggling amplitudes similar to galaxy clusters, ∼15 μK by a large void of radius ∼4° and central density contrast −0.9 at redshift 0.5 assuming a CMB background gradient of ∼10 μK arcmin{sup −1}. The dipole signal is spread over the entire void area, and not concentrated at the lens center as it is for clusters. Finally, we use our model to simulate CMB sky maps lensed by large cosmic voids. Our embedded theory can easily be applied to more complicated void models and used to study gravitational lensing of the CMB, to probe dark matter profiles, to reduce the lensing-induced systematics in supernova Hubble diagrams, and to study the integrated Sachs–Wolfe effect.

79 ASTRONOMY AND ASTROPHYSICS↗

A simple data-driven level finding method of many-electron atoms and heavy nuclei based on statistical outlier detection

Here, we report a simple and pure data-driven method to find new energy levels of quantum many-body systems only from observed line wavelengths. In our method, all the possible combinations are computed from known energy levels and wavelengths of unidentified lines. As each excited state exhibits many transition lines to different lower levels, the true levels should be reconstructed coincidentally from many level-line combinations, while the wrong combinations distribute randomly. Such a coincidence can be easily detected statistically. We demonstrate this statistical method by finding new levels for various atomic and nuclear systems from unidentified line lists available online.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Simple and statistically sound recommendations for analysing physical theories

Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Furthermore, our examples can be reproduced with the code publicly available at Zenodo.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

It's a dark, dark world: background evolution of interacting φCDM models beyond simple exponential potentials

We study the background cosmological dynamics with a three component source content: a radiation fluid, a barotropic fluid to mimic the matter sector and a single scalar field which can act as dark energy giving rise to the late-time accelerated phase. Using the well-known dimensionless variables, we cast the dynamical equations into an autonomous system of ordinary differential equations (ASODE), which are studied by computing the fixed points and the conditions for their stability. The matter fluid and the scalar field are taken to be uncoupled at first and later, we consider a coupling between the two of the form Q = √(2/3)κβρ{sub m} φ̇ where ρ{sub m} is the barotropic fluid density. The key point of our analysis is that for the closure of ASODE, we only demand that the jerk, Γ = V V ''/ V '{sup 2} is a function of acceleration, z = −M{sub p}V'/V, that is, Γ = 1+ f ( z ). In this way, we are able to accommodate a large class of potentials that goes beyond the simple exponential potentials. The analysis is completely generic and independent of the form of the potential for the scalar field. As an illustration and confirmation of the analysis, we consider f ( z ) of the forms μ/ z {sup 2}, μ/ z , (μ− z )/ z {sup 2} and (μ− z ) to numerically compute the evolution of cosmological parameters with and without coupling. Implications of the approach and the results are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

A simple model for the evolution of a non-Abelian cosmic string network

In this paper we present the results of numerical simulations intended to study the behavior of non-Abelian cosmic strings networks. In particular we are interested in discussing the variations in the asymptotic behavior of the system as we variate the number of generators for the topological defects. A simple model which allows for cosmic strings is presented and its lattice discretization is discussed. The evolution of the generated cosmic string networks is then studied for different values for the number of generators for the topological defects. Scaling solution appears to be approached in most cases and we present an argument to justify the lack of scaling for the residual cases.

79 ASTRONOMY AND ASTROPHYSICS↗

Fermionic dark matter in a simple t-channel model

We consider a fermionic dark matter (DM) particle in renormalizable Standard Model (SM) gauge interactions in a simple t-channel model. The DM particle interactions with SM fermions is through the exchange of scalar and vector mediators which carry colour or lepton number. In the case of coloured mediators considered in this study, we find that if the DM is thermally produced and accounts for the observed relic density almost the entire parameter space is ruled out by the direct detection observations. The bounds from the monojet plus missing energy searches at the Large Hadron Collider are less stringent in this case. In contrast for the case of Majorana DM, we obtain strong bounds from the monojet searches which rule out DM particles of mass less than about a few hundred GeV for both the scalar and vector mediators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Modeling electron temperature profiles in the pedestal with simple formulas for ETG transport

Abstract This paper reports on the refinement (building on (Hatch D.R. et al 2022 Phys. Plasmas 29 062501)) and application of simple formulas for electron heat transport from electron temperature gradient (ETG) driven turbulence in the pedestal. The formulas are improved by (1) improving the parameterization for certain key parameters and (2) carefully accounting for the impact of geometry and shaping in the underlying gyrokinetic simulation database. Comparisons with nonlinear gyrokinetic simulations of ETG transport in the MAST pedestal demonstrate the model’s applicability to spherical tokamaks in addition to standard aspect ratio tokamaks. We identify bounds for model applicability: the model is accurate in the steep gradient region, where the ETG turbulence is largely slab-like, but accuracy decreases as the temperature gradient becomes weaker in the pedestal top. We use the formula to model the electron temperature profile in the pedestal for four experimental scenarios while extensively varying input parameters to represent uncertainties. In all cases, the predicted electron temperature profile exhibits extreme sensitivity to separatrix temperature and density, which has implications for core-edge integration. The model reproduces the electron temperature profile for high η e = L n e / L T e scenarios but not for low η e scenarios in which microtearing modes (MTMs) have been identified. We develop a proof-of-concept model for MTM transport and explore the relative roles of ETG and MTM in setting the electron temperature profile.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A simple model of hohlraum power balance and mitigation of SRS

A simple energy balance model has been obtained for laser-plasma heating in indirect drive hohlraum plasma that allows rapid temperature scaling and evolution with parameters such as plasma density and composition. Furthermore, this model enables assessment of the effects on plasma temperature of, e.g., adding high-Z dopant to the gas fill or magnetic fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A simple, flexible technique for RF cavity wake-field calculations

It is typical in the accelerator field to model machine components, especially RF cavities, as parallel RLC resonators. In the interest of simulating and diagnosing beam instabilities, knowledge of the time-domain voltage waveform over an equivalent resonator by a bunch current often proves useful. This waveform may be found by convolving the bunch current with the RLC resonator impulse response. While analytical and quasi-analytical expressions are available in this regime for common distributions such as the Gaussian, analogous results for less standard distributions are difficult to obtain using direct methods, which opens the door for the development of a more generalized technique. In this paper, a formulation is created that allows for the simple computation of the time-domain voltage waveform of and RLC resonator. The formulation uses the Cauchy Residue Theorem to extract the convolution result from the Fourier Domain, and it only requires that the current distribution Fourier Transform be holomorphic and known at one specific evaluation point. This greatly simplifies the computation of the time domain voltage for a large amount of bunch distributions both common and uncommon.

43 PARTICLE ACCELERATORS↗

A simple framework to characterize land aridity based on surface energy partitioning regimes

Land aridity is often characterized by the aridity index (AI), which does not account for land surface water-energy interactions that are crucially important in determining regional climate. Such interactions can be captured by the evaporative fraction (EF, ratio of evapotranspiration to available energy) regimes. As EF is subject to energy and water limitations in humid and dry areas, respectively, EF regimes may be used to characterize land aridity to account for the influence of complex land characteristics and their impact on water availability. Here, we propose a simple framework to characterize land aridity by statistically ranking the coupling strength between EF and surface energy and water terms. The framework is demonstrated using gridded data and compared with AI over the U.S. and China. Results show that regionalization of aridity zones based on EF regimes and a two-tiered classification scheme may provide information such as surface energy and water variability complementary to the background aridity depicted by AI, with implications for extreme events.

54 ENVIRONMENTAL SCIENCES↗

A SIMPLE PHYSICAL MODEL FOR THE GAS DISTRIBUTION IN GALAXY CLUSTERS

The dominant baryonic component of galaxy clusters is hot gas whose distribution is commonly probed through X-ray emission arising from thermal bremsstrahlung. The density profile thus obtained has been traditionally modeled with a β-profile, a simple function with only three parameters. However, this model is known to be insufficient for characterizing the range of cluster gas distributions and attempts to rectify this shortcoming typically introduce additional parameters to increase the fitting flexibility. We use cosmological and physical considerations to obtain a family of profiles for the gas with fewer parameters than the β-model but which better accounts for observed gas profiles over wide radial intervals.

79 ASTRONOMY AND ASTROPHYSICS↗

Clusterdv: a simple density-based clustering method that is robust, general and automatic

Abstract Motivation How to partition a dataset into a set of distinct clusters is a ubiquitous and challenging problem. The fact that data vary widely in features such as cluster shape, cluster number, density distribution, background noise, outliers and degree of overlap, makes it difficult to find a single algorithm that can be broadly applied. One recent method, clusterdp, based on search of density peaks, can be applied successfully to cluster many kinds of data, but it is not fully automatic, and fails on some simple data distributions. Results We propose an alternative approach, clusterdv, which estimates density dips between points, and allows robust determination of cluster number and distribution across a wide range of data, without any manual parameter adjustment. We show that this method is able to solve a range of synthetic and experimental datasets, where the underlying structure is known, and identifies consistent and meaningful clusters in new behavioral data. Availability and implementation The clusterdv is implemented in Matlab. Its source code, together with example datasets are available on: https://github.com/jcbmarques/clusterdv. Supplementary information Supplementary data are available at Bioinformatics online.

Marques, João C.↗

Simple, direct and efficient multi-way spectral clustering

Abstract We present a new algorithm for spectral clustering based on a column-pivoted QR factorization that may be directly used for cluster assignment or to provide an initial guess for k-means. Our algorithm is simple to implement, direct and requires no initial guess. Furthermore, it scales linearly in the number of nodes of the graph and a randomized variant provides significant computational gains. Provided the subspace spanned by the eigenvectors used for clustering contains a basis that resembles the set of indicator vectors on the clusters, we prove that both our deterministic and randomized algorithms recover a basis close to the indicators in Frobenius norm. We also experimentally demonstrate that the performance of our algorithm tracks recent information theoretic bounds for exact recovery in the stochastic block model. Finally, we explore the performance of our algorithm when applied to a real-world graph.

Damle, Anil↗

Formation and evolution of protostellar accretion discs – II. From 3D simulation to a simple semi-analytic model of Class 0/I discs

Here we use a 3D radiative non-ideal magnetohydrodynamic simulation to investigate the formation and evolution of a young protostellar disc from a magnetized pre-stellar core. The simulation covers the first ${\sim }10\, {\rm kyr}$ after protostar formation and shows a massive, weakly magnetized disc with radius that initially grows and then saturates at ${\sim }30\, {\rm au}$. The disc is gravitationally unstable with prominent large-amplitude spiral arms. We use our simulation results and a series of physical arguments to construct a predictive and quantitative physical picture of Class 0/I protostellar disc evolution from several aspects, including (i) the angular-momentum redistribution in the disc, self-regulated by gravitational instability to make most of the disc marginally unstable; (ii) the thermal profile of the disc, well-approximated by a balance between radiative cooling and accretion heating; and (iii) the magnetic-field strength and magnetic-braking rate inside the disc, regulated by non-ideal magnetic diffusion. Using these physical insights, we build a simple 1D semi-analytic model of disc evolution. We show that this 1D model, when coupled to a computationally inexpensive simulation for the evolution of the surrounding pseudo-disc, can be used reliably to predict disc evolution in the Class 0/I phase. The predicted long-term evolution of disc size, which saturates at ${\sim }30\, {\rm au}$ and eventually shrinks, is consistent with a recent observational survey of Class 0/I discs. Such hierarchical modelling of disc evolution circumvents the computational difficulty of tracing disc evolution through Class 0/I phase with direct, numerically converged simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

Simple, efficient and open-source CRISPR/Cas9 strategy for multi-site genome editing in Populus tremula × alba

Although the CRISPR/Cas9 system has been successfully used for crop breeding, its application remains limited in forest trees. Here, we describe an efficient gene editing strategy for hybrid poplar, (Populus tremula × alba INRA clone 717-1B4) based on the Golden Gate MoClo cloning. To test the system efficiency for generating single gene mutants, two single guide RNAs (sgRNAs) were designed and incorporated into the MoClo Tool Kit level 2 binary vector with the Cas9 expression cassette to mutate the SHORT ROOT (SHR) gene. Moreover, we also tested its efficiency for introducing mutations in two genes simultaneously by expressing one sgRNA targeting a single site of the YUC4 gene and the other sgRNA targeting the PLT1 gene. For a robust evaluation of the approach, we repeated the strategy to target the LBD12 and LBD4 genes simultaneously, using an independent construct. We generated hairy roots by Agrobacterium rhizogenes-mediated leaf transformation. Sequencing results confirmed the CRISPR/Cas9-mediated mutation in the targeted sites of PtaSHR. Biallelic and homozygous knockout mutations were detected. A deletion spanning both target sites and small insertions/deletions were the most common mutations. Out of the 22 SHR alleles sequenced, 21 were mutated. The phenotype’s characterization showed that transgenic roots with biallelic mutations for the SHR gene lacked a defined endodermal single cell layer, suggesting a conserved gene function similar to its homolog in Arabidopsis Arabidopsis thaliana (L.) Heynh. Sequencing results also revealed the high efficiency of the system for generating double mutants. Biallelic mutations for both genes in the yuc4/plt1 and lbd12/lbd4 roots were detected in three (yuc4/plt1) and two (lbd12/lbd4) out of four transgenic roots evaluated. A small deletion or a single nucleotide insertion at the single target site was the most common mutations. This CRISPR/Cas9 strategy arises as a rapid, simple and standardized gene-editing tool to evaluate the gene role in essential developmental programs such as radial cell differentiation of poplar roots.

59 BASIC BIOLOGICAL SCIENCES↗

From diamond to BC8 to simple cubic and back: Kinetic pathways to post-diamond carbon phases from metadynamics

Understanding the kinetic pathways connecting carbon polymorphs at multimegabar pressures remains a major unsolved problem in high-pressure physics. Here, we provide insights into the long-standing question of BC8 formation and stability by combining a state-of-the-art SNAP machine-learning interatomic potential with enhanced sampling via metadynamics, enabling direct access to transition mechanisms far beyond the reach of standard molecular dynamics. Our simulations show that carbon phase transformations are intrinsically complex, proceeding through multiple intermediate disordered and crystalline states governed by nontrivial kinetic ordering. We determine the upper pressure limit for BC8 formation and reveal that hexagonal diamond transforms to BC8 faster than cubic diamond—an unexpected and experimentally testable prediction. We also identify a 𝑃⁢222 carbon phase that becomes competitive with diamond and simple cubic above 1.8 TPa, and we demonstrate that BC8 may be quenched to ambient conditions at moderate temperatures. Altogether, these results establish a general and transferable framework for resolving kinetic pathways in solid-solid phase transitions and provide physical insights into carbon's complex high-pressure landscape.

36 MATERIALS SCIENCE↗