Equivalence between two charged black holes in dynamics of orbits outside the event horizons

Using the FermiDirac distribution function, Balart and Vagenas gave a charged spherically symmetric regular black hole, which is a solution of Einstein field equations coupled to a nonlinear electrodynamics. In fact, the regular black hole is a Reissner-Nordstrom (RN) black hole when a metric function is given a Taylor expansion to first order approximations. It does not have a curvature singularity at the origin,but the RN black hole does. Both black hole metrics have horizons and similar asymptotic behaviors, and satisfy the weak energy conditions everywhere. They are almost the same in photon effective potentials, photon circular orbits and photon spheres outside the event horizons. There are relatively minor differences between effective potentials, stable circular orbits and innermost stable circular orbits of charged particles outside the event horizons of the two black holes immersed in external magnetic fields. Although the twomagnetized black holes allow different construction methods of explicit symplectic integrators, they exhibit approximately consistent results in the regular and chaotic dynamics of charged particles outside the event horizons. Chaos gets strong as the magnetic field parameter or the magnitude of negative Coulomb parameter increases, but becomes weak when the black hole charge or the positive Coulomb parameter increases. A variation of dynamical properties is not sensitive dependence on an appropriate increase of the black hole charge. The basic equivalence between the two black hole gravitational systems in the dynamics of orbits outside the event horizons is due to the two metric functions having an extremely small difference. This implies that the RN black hole is reasonably replaced by the regular black hole without curvature singularity in many situations.Comment: 18 pages, 12 figure

T-COL: Generating Counterfactual Explanations for General User Preferences on Variable Machine Learning Systems

Machine learning (ML) based systems have been suffering a lack of interpretability. To address this problem, counterfactual explanations (CEs) have been proposed. CEs are unique as they provide workable suggestions to users, in addition to explaining why a certain outcome was predicted. However, the application of CEs has been hindered by two main challenges, namely general user preferences and variable ML systems. User preferences, in particular, tend to be general rather than specific feature values. Additionally, CEs need to be customized to suit the variability of ML models, while also maintaining robustness even when these validation models change. To overcome these challenges, we propose several possible general user preferences that have been validated by user research and map them to the properties of CEs. We also introduce a new method called \uline{T}ree-based \uline{C}onditions \uline{O}ptional \uline{L}inks (T-COL), which has two optional structures and several groups of conditions for generating CEs that can be adapted to general user preferences. Meanwhile, a group of conditions lead T-COL to generate more robust CEs that have higher validity when the ML model is replaced. We compared the properties of CEs generated by T-COL experimentally under different user preferences and demonstrated that T-COL is better suited for accommodating user preferences and variable ML systems compared to baseline methods including Large Language Models

Laboratory Simulation of an Iron(II)-rich Precambrian Marine Upwelling System to Explore the Growth of Photosynthetic Bacteria

A conventional concept for the deposition of some Precambrian Banded Iron Formations (BIF) proceeds on the assumption that ferrous iron [Fe(II)] upwelling from hydrothermal sources in the Precambrian ocean was oxidized by molecular oxygen [O2] produced by cyanobacteria. The oldest BIFs, deposited prior to the Great Oxidation Event (GOE) at about 2.4 billion years (Gy) ago, could have formed by direct oxidation of Fe(II) by anoxygenic photoferrotrophs under anoxic conditions. As a method for testing the geochemical and mineralogical patterns that develop under different biological scenarios, we designed a 40 cm long vertical flow-through column to simulate an anoxic Fe(II)-rich marine upwelling system representative of an ancient ocean on a lab scale. The cylinder was packed with a porous glass bead matrix to stabilize the geochemical gradients, and liquid samples for iron quantification could be taken throughout the water column. Dissolved oxygen was detected non-invasively via optodes from the outside. Results from biotic experiments that involved upwelling fluxes of Fe(II) from the bottom, a distinct light gradient from top, and cyanobacteria present in the water column, show clear evidence for the formation of Fe(III) mineral precipitates and development of a chemocline between Fe(II) and O2. This column allows us to test hypotheses for the formation of the BIFs by culturing cyanobacteria (and in the future photoferrotrophs) under simulated marine Precambrian conditions. Furthermore we hypothesize that our column concept allows for the simulation of various chemical and physical environments — including shallow marine or lacustrine sediments

The diagnostic value of four-dimensional ultrasound examination of perineum in the diagnosis of postpartum pelvic floor dysfunction

Objective to explore the diagnostic value of perineal four-dimensional ultrasound (4D-US) in postpartum pelvic floor dysfunction (PFD) disease. 328 postpartum PFD patients diagnosed by clinical pelvic floor palpation from June 2018 to December 2020 were selected as the PFD group, and 328 patients without PFD were selected as the control group. All participants underwent perineal 4D-US, the indicators were statistically analyzed. The results showed that the LAT of left and right, LHLR, LHAP, LHA, resting state and holding the breath in the PFD group were higher than those in the control group, and the difference was statistically significant (P<0.05). From cervix to lower margin of pubic symphysis, bladder to lower margin of pubic symphysis of the pubic symphysis, and from the ampulla of the rectum to the lower margin of the pubic symphysis, the PFD group was larger than the control group, but the result of urethral rotation was reversed, and the difference was statistically significant (P<0.05). The morphologic features of the levator ani muscle and pelvic fissure can be detected early using 4D-US, which is a reliable technique that can be learned in a short period of time

MM-BigBench: Evaluating Multimodal Models on Multimodal Content Comprehension Tasks

The popularity of multimodal large language models (MLLMs) has triggered a recent surge in research efforts dedicated to evaluating these models. Nevertheless, existing evaluation studies of MLLMs primarily focus on the comprehension and reasoning of unimodal (vision) content, neglecting performance evaluations in the domain of multimodal (vision-language) content understanding. Beyond multimodal reasoning, tasks related to multimodal content comprehension necessitate a profound understanding of multimodal contexts, achieved through the multimodal interaction to obtain a final answer. In this paper, we introduce a comprehensive assessment framework called MM-BigBench, which incorporates a diverse range of metrics to offer an extensive evaluation of the performance of various models and instructions across a wide spectrum of diverse multimodal content comprehension tasks. Consequently, our work complements research on the performance of MLLMs in multimodal comprehension tasks, achieving a more comprehensive and holistic evaluation of MLLMs. To begin, we employ the Best Performance metric to ascertain each model's performance upper bound on different datasets. Subsequently, the Mean Relative Gain metric offers an assessment of the overall performance of various models and instructions, while the Stability metric measures their sensitivity. Furthermore, previous research centers on evaluating models independently or solely assessing instructions, neglecting the adaptability between models and instructions. We propose the Adaptability metric to quantify the adaptability between models and instructions. Our paper evaluates a total of 20 language models (14 MLLMs) on 14 multimodal datasets spanning 6 tasks, with 10 instructions for each task, and derives novel insights. Our code will be released at https://github.com/declare-lab/MM-BigBench.Comment: Undervie

Iron Isotope Fractionation during Fe(II) Oxidation Mediated by the Oxygen-Producing Marine Cyanobacterium Synechococcus PCC 7002

In this study, we couple iron isotope analysis to microscopic and mineralogical investigation of iron speciation during circumneutral Fe(II) oxidation and Fe(III) precipitation with photosynthetically produced oxygen. In the presence of the cyanobacterium Synechococcus PCC 7002, aqueous Fe(II) (Fe(II)aq) is oxidized and precipitated as amorphous Fe(III) oxyhydroxide minerals (iron precipitates, Feppt), with distinct isotopic fractionation (ε56Fe) values determined from fitting the δ56Fe(II)aq (1.79‰ and 2.15‰) and the δ56Feppt (2.44‰ and 2.98‰) data trends from two replicate experiments. Additional Fe(II) and Fe(III) phases were detected using microscopy and chemical extractions and likely represent Fe(II) and Fe(III) sorbed to minerals and cells. The iron desorbed with sodium acetate (FeNaAc) yielded heavier δ56Fe compositions than Fe(II)aq. Modeling of the fractionation during Fe(III) sorption to cells and Fe(II) sorption to Feppt, combined with equilibration of sorbed iron and with Fe(II)aq using published fractionation factors, is consistent with our resulting δ56FeNaAc. The δ56Feppt data trend is inconsistent with complete equilibrium exchange with Fe(II)aq. Because of this and our detection of microbially excreted organics (e.g., exopolysaccharides) coating Feppt in our microscopic analysis, we suggest that electron and atom exchange is partially suppressed in this system by biologically produced organics. These results indicate that cyanobacteria influence the fate and composition of iron in sunlit environments via their role in Fe(II) oxidation through O2 production, the capacity of their cell surfaces to sorb iron, and the interaction of secreted organics with Fe(III) minerals