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Validation of Machine Learning-Based Automated Surgical Instrument Annotation Using Publicly Available Intraoperative Video
No full textBACKGROUND: Intraoperative tool movement data have been demonstrated to be clinically useful in quantifying surgical performance. However, collecting this information from intraoperative video requires laborious hand annotation. The ability to automatically annotate tools in surgical video would advance surgical data science by eliminating a time-intensive step in research.
OBJECTIVE: To identify whether machine learning (ML) can automatically identify surgical instruments contained within neurosurgical video.
METHODS: A ML model which automatically identifies surgical instruments in frame was developed and trained on multiple publicly available surgical video data sets with instrument location annotations. A total of 39 693 frames from 4 data sets were used (endoscopic endonasal surgery [EEA] [30 015 frames], cataract surgery [4670], laparoscopic cholecystectomy [2532], and microscope-assisted brain/spine tumor removal [2476]). A second model trained only on EEA video was also developed. Intraoperative EEA videos from YouTube were used for test data (3 videos, 1239 frames).
RESULTS: The YouTube data set contained 2169 total instruments. Mean average precision (mAP) for instrument detection on the YouTube data set was 0.74. The mAP for each individual video was 0.65, 0.74, and 0.89. The second model trained only on EEA video also had an overall mAP of 0.74 (0.62, 0.84, and 0.88 for individual videos). Development costs were 100 for computation.
CONCLUSION: Surgical instruments contained within endoscopic endonasal intraoperative video can be detected using a fully automated ML model. The addition of disparate surgical data sets did not improve model performance, although these data sets may improve generalizability of the model in other use cases
An AGN with an Ionized Gas Outflow in a Massive Quiescent Galaxy in a Protocluster at z = 3.09
No full textWe report the detection of an ionized gas outflow from an X-ray active galactic nucleus hosted in a massive quiescent galaxy in a protocluster at z = 3.09 (J221737.29+001823.4). It is a type-2 QSO with broad (W_80 > 1000 km s^(−1)) and strong (log(L[OIII]/erg s^(−1)) ≈ 43.4) [O III]λλ 4959,5007 emission lines detected by slit spectroscopy in three-position angles using Multi-Object Infra-Red Camera and Spectrograph (MOIRCS) on the Subaru telescope and the Multi-Object Spectrometer For Infra-Red Exploration (MOSFIRE) on the Keck-I telescope. In the all slit directions, [O III] emission is extended to ∼15 physical kpc and indicates a powerful outflow spreading over the host galaxy. The inferred ionized gas mass outflow rate is 22 ± 3 M_⊙ yr^(−1). Although it is a radio source, according to the line diagnostics using Hβ, [O II], and [O III], photoionization by the central QSO is likely the dominant ionization mechanism rather than shocks caused by radio jets. On the other hand, the spectral energy distribution of the host galaxy is well characterized as a quiescent galaxy that has shut down star formation several hundred Myr ago. Our results suggest a scenario that QSOs are powered after the shutdown of the star formation and help complete the quenching of massive quiescent galaxies at high redshift
A New Method for In Situ Measurement of the Erosion Threshold of River Channels
No full textThe vast majority of alluvial deposits have some degree of cohesion, typically due to the presence of clays and/or organic matter. Determining the threshold fluid shear stress, τc, necessary to entrain these sediments is essential for predicting erosion rates and morphodynamics of rivers, tidal channels, and coasts. Cohesive sediments present a greater challenge than noncohesive sand and gravel beds due to the sensitivity of τc to such factors as compaction, aggregation, and particle surface chemistry. All of those factors may be altered if bed and bank sediments are extracted for later analysis in the laboratory. Environments with mixed cohesive and noncohesive materials are common, such as sand-bedded rivers with muddy banks; it is therefore desirable to have a method for in situ measurement of τ_c across a very wide range. We present a novel instrument that is capable of reproducibly determining τ_c for submerged cohesive and noncohesive sediments in situ. The instrument has several advantages over alternative methods, including ease of implementation in the field, and a fluid shear that is more representative of natural flows. The device incorporates common and low-cost components integrated with an Arduino microcontroller, which may receive commands from a mobile phone. We demonstrate our instrument's capabilities in gravel, sand, and clay-sand mixtures prepared in the laboratory, and present a proof of concept field deployment in a wadeable stream. Additionally, we provide the necessary schematics, parts lists, code, and calibration procedures for the interested reader to build their own version of the instrument
Spectral exponential sums on hyperbolic surfaces
No full textWe study an exponential sum over Laplacian eigenvalues of Maaß forms on Γ∖ℍ, where Γ is a congruence subgroup of SL₂(ℤ) and ℍ is the upper half-plane. The goal is to establish an asymptotic formula that expresses the spectral exponential sum in terms of an oscillatory main term, the von Mangoldt function and the Selberg zeta function
Efficient Fair Division with Minimal Sharing
No full textA collection of objects, some of which are good and some of which are bad, is to be divided fairly among agents with different tastes, modeled by additive utility functions. If the objects cannot be shared, so that each of them must be entirely allocated to a single agent, then a fair division may not exist. What is the smallest number of objects that must be shared between two or more agents to attain a fair and efficient division? In this paper, fairness is understood as proportionality or envy-freeness and efficiency as fractional Pareto-optimality. We show that, for a generic instance of the problem (all instances except a zero-measure set of degenerate problems), a fair fractionally Pareto-optimal division with the smallest possible number of shared objects can be found in polynomial time, assuming that the number of agents is fixed. The problem becomes computationally hard for degenerate instances, where agents’ valuations are aligned for many objects
Online EV Scheduling Algorithms for Adaptive Charging Networks with Global Peak Constraints
No full textThis paper tackles online scheduling of electric vehicles (EVs) in an adaptive charging network (ACN) with local and global peak constraints. Given the aggregate charging demand of the EVs and the peak constraints of the ACN, it might be infeasible to fully charge all the EVs according to their charging demand. Two alternatives in such resource-limited scenarios are to maximize the social welfare by partially charging the EVs (fractional model) or selecting a subset of EVs and fully charge them (integral model). The technical challenge is the need for online solution design since in practical scenarios the scheduler has no or limited information of future arrivals in a time-coupled underlying problem. For the fractional model, we devise both offline and online algorithms. We prove that the offline algorithm is optimal. Using competitive ratio as the performance measure, we prove the online algorithm achieves a competitive ratio of 2. The integral model, however, is more challenging since the underlying problem is strongly NP-hard due to 0/1 selection criteria of EVs. Hence, efficient solution design is challenging even in offline setting. For offline setting, we devise a low-complexity primal-dual scheduling algorithm that achieves a bounded approximation ratio. Built upon the offline approximate algorithm, we propose an online algorithm and analyze its competitive ratio in special cases. Extensive trace-driven experimental results show that the performance of the proposed online algorithms is close to the offline optimum, and outperform the existing solutions
Potentially Singular Behavior of the 3D Navier-Stokes Equations
No full textWhether the 3D incompressible Navier-Stokes equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this paper, we present some new numerical evidence that the incompressible axisymmetric Navier-Stokes equations with smooth initial data of finite energy seem to develop potentially singular behavior at the origin. This potentially singular behavior is induced by a potential finite time singularity of the 3D Euler equations that we reported in the companion paper (arXiv:2107.05870). We present numerical evidence that the 3D Navier--Stokes equations develop nearly self-similar singular scaling properties with maximum vorticity increased by a factor of 10⁷. We have applied several blow-up criteria to study the potentially singular behavior of the Navier--Stokes equations. The Beale-Kato-Majda blow-up criterion and the blow-up criteria based on the growth of enstrophy and negative pressure seem to imply that the Navier--Stokes equations using our initial data develop a potential finite time singularity. We have also examined the Ladyzhenskaya-Prodi-Serrin regularity criteria. Our numerical results for the cases of (p,q) = (4,8), (6,4), (9,3) and (p,q) = (∞,2) provide strong evidence for the potentially singular behavior of the Navier--Stokes equations. Our numerical study shows that while the global L^3 norm of the velocity grows very slowly, the localized version of the L³ norm of the velocity experiences rapid dynamic growth relative to the localized L³ norm of the initial velocity. This provides further evidence for the potentially singular behavior of the NavieStokes equations
Potential Singularity of the 3D Euler Equations in the Interior Domain
No full textWhether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this paper, we present some new numerical evidence that the 3D axisymmetric incompressible Euler equations with smooth initial data of finite energy develop a potential finite time singularity at the origin. This potential singularity is different from the blow-up scenario revealed by Luo and Hou (111:12968–12973, 2014) and (12:1722–1776, 2014), which occurs on the boundary. Our initial condition has a simple form and shares several attractive features of a more sophisticated initial condition constructed by Hou and Huang in (arXiv:2102.06663, 2021) and (435:133257, 2022). One important difference between these two blow-up scenarios is that the solution for our initial data has a one-scale structure instead of a two-scale structure reported in Hou and Huang (arXiv:2102.06663, 2021) and (435:133257, 2022). More importantly, the solution seems to develop nearly self-similar scaling properties that are compatible with those of the 3D Navier–Stokes equations. We will present numerical evidence that the 3D Euler equations seem to develop a potential finite time singularity. Moreover, the nearly self-similar profile seems to be very stable to the small perturbation of the initial data
Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics
No full textWe asymptotically estimate the variance of the number of lattice points in a thin, randomly rotated annulus lying on the surface of the sphere. This partially resolves a conjecture of Bourgain, Rudnick, and Sarnak. We also obtain estimates that are valid for all balls and annuli that are not too small. Our results have several consequences: for a conjecture of Linnik on sums of two squares and a “microsquare”, a conjecture of Bourgain and Rudnick on the number of lattice points lying in small balls on the surface of the sphere, the covering radius of the sphere, and the distribution of lattice points in almost all thin regions lying on the surface of the sphere. Finally, we show that for a density 1. subsequence of squarefree integers, the variance exhibits a different asymptotic behaviour for balls of volume (log n)^(−δ) with 0 < δ < 1/16.
We also obtain analogous results for Heegner points and closed geodesics. Interestingly, we are able to prove some slightly stronger results for closed geodesics than for Heegner points or lattice points on the surface of the sphere. A crucial observation that underpins our proof is the different behaviour of weighting functions for annuli and for balls
Interferometer Response to Geontropic Fluctuations
No full textWe model vacuum fluctuations in quantum gravity with a scalar field,
characterized by a high occupation number, coupled to the metric. The
occupation number of the scalar is given by a thermal density matrix, whose
form is motivated by fluctuations in the vacuum energy, which have been shown
to be conformal near a light-sheet horizon. For the experimental measurement of
interest in an interferometer, the size of the energy fluctuations is fixed by
the area of a surface bounding the volume of spacetime being interrogated by an
interferometer. We compute the interferometer response to these "geontropic"
scalar-metric fluctuations, and apply our results to current and future
interferometer measurements, such as LIGO and the proposed GQuEST experiment