Search

We show that if $G$ is an amenable group and $A\subseteq G$ has positive upper Banach density, then there is an identity neighborhood $B$ in the Bohr topology on $G$ that is almost contained in $AA^{-1}$ in the sense that $B\backslash AA^{-1}$ has upper Banach density $0$. This generalizes the abelian case (due to F{\o}lner) and the countable case (due to Beiglb\"{o}ck, Bergelson, and Fish). The proof is indirectly based on local stable group theory in continuous logic. The main ingredients are Grothendieck's double-limit characterization of relatively weakly compact sets in spaces of continuous functions, along with results of Ellis and Nerurkar on the topological dynamics of weakly almost periodic flows., Comment: 9 pages, correction made to discussion in 4.2 and other typos fixed

The PROSPECT experiment is designed to perform precise searches for antineutrino disappearance at short distances (7 - 9~m) from compact nuclear reactor cores. This Letter reports results from a new neutrino oscillation analysis performed using the complete data sample from the PROSPECT-I detector operated at the High Flux Isotope Reactor in 2018. The analysis uses a multi-period selection of inverse beta decay neutrino interactions with reduced backgrounds and enhanced statistical power to set limits on electron-flavor disappearance caused by mixing with sterile neutrinos with 0.2 - 20 eV$^2$ mass splittings. Inverse beta decay positron energy spectra from six different reactor-detector distance ranges are found to be statistically consistent with one another, as would be expected in the absence of sterile neutrino oscillations. The data excludes at 95% confidence level the existence of sterile neutrinos in regions above 3~eV$^2$ previously unexplored by terrestrial experiments, including all space below 10~eV$^2$ suggested by the recently strengthened Gallium Anomaly. The best-fit point of the Neutrino-4 reactor experiment's claimed observation of short-baseline oscillation is ruled out at more than five standard deviations., Comment: 6 pages, 4 figures

The PROSPECT-I detector has several features that enable measurement of the direction of a compact neutrino source. In this paper, a detailed report on the directional measurements made on electron antineutrinos emitted from the High Flux Isotope Reactor is presented. With an estimated true neutrino (reactor to detector) direction of $\phi = 40.8\unicode{xB0} \pm 0.7\unicode{xB0}$ and $\theta = 98.6\unicode{xB0} \pm 0.4\unicode{xB0}$, the PROSPECT-I detector is able to reconstruct an average neutrino direction of $\phi = 39.4\unicode{xB0} \pm 2.9\unicode{xB0}$ and $\theta = 97.6\unicode{xB0} \pm 1.6\unicode{xB0}$. This measurement is made with approximately 48000 Inverse Beta Decay signal events and is the most precise directional reconstruction of reactor antineutrinos to date.

We prove a structure theorem for stable functions on amenable groups, which extends the arithmetic regularity lemma for stable subsets of finite groups. Given a group $G$, a function $f\colon G\to [-1,1]$ is called stable if the binary function $f(x\cdot y)$ is stable in the sense of continuous logic. Roughly speaking, our main result says that if $G$ is amenable, then any stable function on $G$ is almost constant on all translates of a unitary Bohr neighborhood in $G$ of bounded complexity. The proof uses ingredients from topological dynamics and continuous model theory. We also prove several applications which generalize results in arithmetic combinatorics to nonabelian groups., Comment: 28 pages; substantial changes to first version; the previous subsection 4.3 (on applications) has been turned into Section 5 and expanded significantly

We give three counterexamples to the folklore claim that in an arbitrary theory, if a complete type $p$ over a set $B$ does not divide over $C\subseteq B$, then no extension of $p$ to a complete type over $\text{acl}(B)$ divides over $C$. Two of our examples are also the first known theories where all sets are extension bases for nonforking, but forking and dividing differ for complete types (answering a question of Adler). One example is an NSOP$_1$ theory with a complete type that forks, but does not divide, over a model (answering a question of d'Elb\'{e}e). Moreover, dividing independence fails to imply M-independence in this example (which refutes another folklore claim). In addition to these counterexamples, we summarize various related properties of dividing that are still true. We also address consequences for previous literature, including an earlier unpublished result about forking and dividing in free amalgamation theories, and some claims about dividing in the theory of generic $K_{m,n}$-free incidence structures., Comment: 19 pages, minor revisions from first version, to appear in JSL

This expository article is based on two lectures given by the first author at the Fields Institute in the Fall 2021 Thematic Program on Trends in Pure and Applied Model Theory. We give a detailed proof of a qualitative version of the Mallaris-Shelah regularity lemma for stable graphs using only basic local stability theory and an ultraproduct construction. This proof strategy was first established by Malliaris and Pillay, and later simplified by Pillay. We provide some further simplifications, and also explain how the pseudofinite approach can be used to obtain a qualitative strengthening (compared to previous proofs) in terms of "functional error". To illustrate the extra leverage obtained by functional error, we give an elementary argument for extracting equipartitions from arbitrary partitions., Comment: 15 pages, submitted as a chapter in a forthcoming title of the Fields Institute Monographs book series

We first give simplified and corrected accounts of some results in \cite{PiRCP} on compactifications of pseudofinite groups. For instance, we use a classical theorem of Turing \cite{Turing} to give a simplified proof that any definable compactification of a pseudofinite group has an abelian connected component. We then discuss the relationship between Turing's work, the Jordan-Schur Theorem, and a (relatively) more recent result of Kazhdan \cite{Kazh} on approximate homomorphisms, and we use this to widen our scope from finite groups to amenable groups. In particular, we develop a suitable continuous logic framework for dealing with definable homomorphisms from pseudo-amenable groups to compact Lie groups. Together with the stabilizer theorems of \cite{HruAG,MOS}, we obtain a uniform (but non-quantitative) analogue of Bogolyubov's Lemma for sets of positive measure in discrete amenable groups. We conclude with brief remarks on the case of amenable topological groups., Comment: 23 pages

We prove a number of results relating the concepts of Keisler measures, generic stability, randomizations, and NIP formulas. Among other things, we do the following: (1) We introduce the notion of a Keisler-Morley measure, which plays the role of a Morley sequence for a Keisler measure. We prove that if $\mu$ is fim over $M$, then for any Keisler-Morley measure $\lambda$ in $\mu$ over $M$ and any formula $\varphi(x,b)$, $\lim_{i \to \infty} \lambda(\varphi(x_i,b)) = \mu(\varphi(x,b))$. We also show that any measure satisfying this conclusion must be fam. (2) We study the map, defined by Ben Yaacov, taking a definable measure $\mu$ to a type $r_\mu$ in the randomization. We prove that this map commutes with Morley products, and that if $\mu$ is fim then $r_\mu$ is generically stable. (3) We characterize when generically stable types are closed under Morley products by means of a variation of ict-patterns. Moreover, we show that NTP$_2$ theories satisfy this property. (4) We prove that if a local measure admits a suitably tame global extension, then it has finite packing numbers with respect to any definable family. We also characterize NIP formulas via the existence of tame extensions for local measures., Comment: 37 pages; Added section 3.4 on fam measures and some general clarifying remarks

The $k$-dimensional functional order property ($\text{FOP}_k$) is a combinatorial property of a $(k+1)$-partitioned formula. This notion arose in work of Terry and Wolf, which identified $\text{NFOP}_2$ as a ternary analogue of stability in the context of two finitary combinatorial problems related to hypergraph regularity and arithmetic regularity. In this paper we show $\text{NFOP}_k$ has equally strong implications in model-theoretic classification theory, where its behavior as a $(k+1)$-ary version of stability is in close analogy to the behavior of $k$-dependence as a $(k+1)$-ary version of $\text{NIP}$. Our results include several new characterizations of $\text{NFOP}_k$, including a characterization in terms of collapsing indiscernibles, combinatorial recharacterizations, and a characterization in terms of type-counting when $k=2$. As a corollary of our collapsing theorem, we show $\text{NFOP}_k$ is closed under Boolean combinations, and that $\text{FOP}_k$ can always be witnessed by a formula where all but one variable have length $1$. When $k=2$, we prove a composition lemma analogous to that of Chernikov and Hempel from the setting of $2$-dependence. Using this, we provide a new class of algebraic examples of $\text{NFOP}_2$ theories. Specifically, we show that if $T$ is the theory of an infinite dimensional vector space over a field $K$, equipped with a bilinear form satisfying certain properties, then $T$ is $\text{NFOP}_2$ if and only if $K$ is stable. Along the way we provide a corrected and reorganized proof of Granger's quantifier elimination and completeness results for these theories.

This Letter reports one of the most precise measurements to date of the antineutrino spectrum from a purely U235-fueled reactor, made with the final dataset from the PROSPECT-I detector at the High Flux Isotope Reactor. By extracting information from previously unused detector segments, this analysis effectively doubles the statistics of the previous PROSPECT measurement. The reconstructed energy spectrum is unfolded into antineutrino energy and compared with both the Huber-Mueller model and a spectrum from a commercial reactor burning multiple fuel isotopes. A local excess over the model is observed in the 5MeV to 7MeV energy region. Comparison of the PROSPECT results with those from commercial reactors provides new constraints on the origin of this excess, disfavoring at 2.2 and 3.2 standard deviations the hypotheses that antineutrinos from U235 are solely responsible and non-contributors to the excess observed at commercial reactors respectively., Comment: The paper has been updated to match publication at PRL

The Capacitated Vehicle Routing Problem is a well-known NP-hard problem that poses the challenge of finding the optimal route of a vehicle delivering products to multiple locations. Recently, new efforts have emerged to create constructive and perturbative heuristics to tackle this problem using Deep Learning. In this paper, we join these efforts to develop the Combined Deep Constructor and Perturbator, which combines two powerful constructive and perturbative Deep Learning-based heuristics, using attention mechanisms at their core. Furthermore, we improve the Attention Model-Dynamic for the Capacitated Vehicle Routing Problem by proposing a memory-efficient algorithm that reduces its memory complexity by a factor of the number of nodes. Our method shows promising results. It demonstrates a cost improvement in common datasets when compared against other multiple Deep Learning methods. It also obtains close results to the state-of-the art heuristics from the Operations Research field. Additionally, the proposed memory efficient algorithm for the Attention Model-Dynamic model enables its use in problem instances with more than 100 nodes.

This paper presents an energy calibration scheme for an upgraded reactor antineutrino detector for the Precision Reactor Oscillation and Spectrum Experiment (PROSPECT). The PROSPECT collaboration is preparing an upgraded detector, PROSPECT-II (P-II), to advance capabilities for the investigation of fundamental neutrino physics, fission processes and associated reactor neutrino flux, and nuclear security applications. P-II will expand the statistical power of the original PROSPECT (P-I) dataset by at least an order of magnitude. The new design builds upon previous P-I design and focuses on improving the detector robustness and long-term stability to enable multi-year operation at one or more sites. The new design optimizes the fiducial volume by elimination of dead space previously occupied by internal calibration channels, which in turn necessitates the external deployment. In this paper, we describe a calibration strategy for P-II. The expected performance of externally deployed calibration sources is evaluated using P-I data and a well-benchmarked simulation package by varying detector segmentation configurations in the analysis. The proposed external calibration scheme delivers a compatible energy scale model and achieves comparable performance with the inclusion of an additional AmBe neutron source, in comparison to the previous internal arrangement. Most importantly, the estimated uncertainty contribution from the external energy scale calibration model meets the precision requirements of the P-II experiment., Comment: 19 pages, 10 figures

In this study, we automate quantitative mammographic breast density estimation with neural networks and show that this tool is a strong use case for federated learning on multi-institutional datasets. Our dataset included bilateral CC-view and MLO-view mammographic images from two separate institutions. Two U-Nets were separately trained on algorithm-generated labels to perform segmentation of the breast and dense tissue from these images and subsequently calculate breast percent density (PD). The networks were trained with federated learning and compared to three non-federated baselines, one trained on each single-institution dataset and one trained on the aggregated multi-institution dataset. We demonstrate that training on multi-institution datasets is critical to algorithm generalizability. We further show that federated learning on multi-institutional datasets improves model generalization to unseen data at nearly the same level as centralized training on multi-institutional datasets, indicating that federated learning can be applied to our method to improve algorithm generalizability while maintaining patient privacy., Comment: Deep learning, federated learning, mammography, breast density, risk assessment

Several high efficiency, low cost, RF sources are in development or recently completed. All are designed to provide operating efficiencies exceeding 80% and provide more than 100 kW of output power with a focus on high average power or CW operation. The sources include (1) a magnetron system with amplitude and phase control, a multiple beam, power grid-tube based source, a multiple beam inductive output tube, and a klystron using the core oscillation method. The estimated cost for the magnetron system and multiple beam power grid-tube source are one dollar per Watt and 75 cents per Watt, respectively. Operating frequencies span the range from 300 MHz (power grid tube) to 1.3 GHz (magnetron and klystron). This paper describes the basic operation of the sources, indicates the status and schedule, and provides available experimental results., Comment: contribution to Snowmass 2021

Given a structure $\mathcal{M}$ and a stably embedded $\emptyset$-definable set $Q$, we prove tameness preservation results when enriching the induced structure on $Q$ by some further structure $\mathcal{Q}$. In particular, we show that if $T=\text{Th}(\mathcal{M})$ and $\text{Th}(\mathcal{Q})$ are stable (resp., superstable, $\omega$-stable), then so is the theory $T[\mathcal{Q}]$ of the enrichment of $\mathcal{M}$ by $\mathcal{Q}$. Assuming simplicity of $T$, elimination of hyperimaginaries and a further condition on $Q$ related to the behavior of algebraic closure, we also show that simplicity and NSOP$_1$ pass from $\text{Th}(\mathcal{Q})$ to $T[\mathcal{Q}]$. We then prove several applications for tame expansions of weakly minimal structures and, in particular, the group of integers. For example, we construct the first known examples of strictly stable expansions of $(\mathbb{Z},+)$. More generally, we show that any stable (resp., superstable, simple, NIP, NTP$_2$, NSOP$_1$) countable graph can be defined in a stable (resp., superstable, simple, NIP, NTP$_2$, NSOP$_1$) expansion of $(\mathbb{Z},+)$ by some unary predicate $A\subseteq\mathbb{N}$.

Nuclear reactors are uniquely powerful, abundant, and flavor-pure sources of antineutrinos that continue to play a vital role in the US neutrino physics program. The US reactor antineutrino physics community is a diverse interest group encompassing many detection technologies and many particle physics topics, including Standard Model and short-baseline oscillations, BSM physics searches, and reactor flux and spectrum modeling. The community's aims offer strong complimentary with numerous aspects of the wider US neutrino program and have direct relevance to most of the topical sub-groups composing the Snowmass 2021 Neutrino Frontier. Reactor neutrino experiments also have a direct societal impact and have become a strong workforce and technology development pipeline for DOE National Laboratories and universities. This white paper, prepared as a submission to the Snowmass 2021 community organizing exercise, will survey the state of the reactor antineutrino physics field and summarize the ways in which current and future reactor antineutrino experiments can play a critical role in advancing the field of particle physics in the next decade., Comment: Contribution to Snowmass 2021

The PROSPECT experiment has substantially addressed the original 'Reactor Antineutrino Anomaly' by performing a high-resolution spectrum measurement from an enriched compact reactor core and a reactor model-independent sterile neutrino oscillation search based on the unique spectral distortions the existence of eV$^2$-scale sterile neutrinos would impart. But as the field has evolved, the current short-baseline (SBL) landscape supports many complex phenomenological interpretations, establishing a need for complementary experimental approaches to resolve the situation. While the global suite of SBL reactor experiments, including PROSPECT, have probed much of the sterile neutrino parameter space, there remains a large region above 1 eV$^2$ that remains unaddressed. Recent results from BEST confirm the Gallium Anomaly, increasing its significance to $\sim 5\sigma$, with sterile neutrinos providing a possible explanation of this anomaly. Separately, the MicroBooNE exclusion of electron-like signatures causing the MiniBooNE low-energy excess does not eliminate the possibility of sterile neutrinos as an explanation. Focusing specifically on the future use of reactors as a neutrino source for beyond-the-standard-model physics and applications, higher-precision spectral measurements still have a role to play. These recent results have created a confusing landscape which requires new data to disentangle the seemingly contradictory measurements. To directly probe $\overline{\nu}_{e}$ disappearance from high $\Delta m^2$ sterile neutrinos, the PROSPECT collaboration proposes to build an upgraded and improved detector, PROSPECT-II. It features an evolutionary detector design which can be constructed and deployed within one year and have impactful physics with as little as one calendar year of data., Comment: contribution to Snowmass 2021

The large quantities of antineutrinos produced through the decay of fission fragments in nuclear reactors provide an opportunity to study the properties of these particles and investigate their use in reactor monitoring. The reactor antineutrino spectra are measured using specialized, large area detectors that detect antineutrinos through inverse beta decay, electron elastic scattering, or coherent elastic neutrino nucleus scattering; although, inverse beta decay is the only demonstrated method so far. Reactor monitoring takes advantage of the differences in the antineutrino yield and spectra resulting from uranium and plutonium fission providing an opportunity to estimate the fissile material composition in the reactor. Recent experiments reveal a deviation between the measured and calculated antineutrino flux and spectra indicating either the existence of yet undiscovered neutrino physics, uncertainties in the reactor source term calculation, incorrect nuclear data, or a combination of all three. To address the nuclear data that impact the antineutrino spectrum calculations and measurements, an international group of over 180 experts in antineutrino physics, reactor analysis, detector development, and nuclear data came together during the Workshop on Nuclear Data for Reactor Antineutrino Measurements (WoNDRAM) to discuss nuclear data needs and achieve concordance on a set of recommended priorities for nuclear data improvements. Three topical sessions provided a forum to gain consensus amongst the participants on the most important data improvements to address two goals: 1) understand the reactor anomaly and 2) improve the ability to monitor reactors using antineutrinos. This report summarizes the outcomes of the workshop discussions and the recommendations for nuclear data efforts that reduce reactor antineutrino measurement uncertainties., Comment: 26 pages

For decades, physicists have used neutrinos from nuclear reactors to advance basic science. These pursuits have inspired many ideas for application of neutrino detectors in nuclear energy and security. While developments in neutrino detectors are now making some of these ideas technically feasible, their value in the context of real needs and constraints has been unclear. This report seeks to help focus the picture of where neutrino technology may find practical roles in nuclear energy and security. This report is the final product of the Nu Tools study, commissioned in 2019 by the DOE National Nuclear Security Administration (NNSA) Office of Defense Nuclear Nonproliferation Research and Development (DNN R&D). The study was conducted over two years by a group of neutrino physicists and nuclear engineers. A central theme of the study and this report is that useful application of neutrinos will depend not only on advancing physics and technology but also on understanding the needs and constraints of potential end-users. The Study Approach emphasized broad end-user engagement. The major effort, undertaken from May to December 2020, was a series of engagements with the wider nuclear energy and security communities. Interviews with 41 experts revealed points of common understanding, which this report captures in three Cross-Cutting Findings, a Framework for Evaluating Utility, and seven Use Case Findings. The report concludes with two Recommendations. The findings and recommendations are summarized below. The respective ordering within each category does not represent a prioritization or implied value judgement.

We prove an analytic version of the stable graph regularity lemma from \cite{MaSh}, which applies to stable functions $f\colon V\times W\to [0,1]$. Our methods involve continuous model theory and, in particular, results on the structure of local Keisler measures for stable continuous formulas. Along the way, we develop some basic tools around ultraproducts of metric structures and linear functionals on continuous formulas, and we also describe several concrete families of examples of stable functions., Comment: 32 pages, final version

We generalize P. M. Neumann's Lemma to the setting of isometric actions on metric spaces and use it to prove several results in continuous logic related to algebraic independence. In particular, we show that algebraic independence satisfies the full existence axiom (which answers a question of Goldbring) and is implied by dividing independence. We also use the relationship between hyperimaginaries and continuous imaginaries to derive further results that are new even for discrete theories. Specifically, we show that if $\mathbb{M}$ is a monster model of a discrete or continuous theory, then bounded-closure independence in $\mathbb{M}^{\text{heq}}$ satisfies full existence (which answers a question of Adler) and is implied by dividing independence., Comment: 11 pages

The Precision Reactor Oscillation and Spectrum Experiment, PROSPECT, has made world-leading measurements of reactor antineutrinos at short baselines. In its first phase, conducted at the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory, PROSPECT produced some of the strongest limits on eV-scale sterile neutrinos, made a precision measurement of the reactor antineutrino spectrum from $^{235}$U, and demonstrated the observation of reactor antineutrinos in an aboveground detector with good energy resolution and well-controlled backgrounds. The PROSPECT collaboration is now preparing an upgraded detector, PROSPECT-II, to probe yet unexplored parameter space for sterile neutrinos and contribute to a full resolution of the Reactor Antineutrino Anomaly, a longstanding puzzle in neutrino physics. By pressing forward on the world's most precise measurement of the $^{235}$U antineutrino spectrum and measuring the absolute flux of antineutrinos from $^{235}$U, PROSPECT-II will sharpen a tool with potential value for basic neutrino science, nuclear data validation, and nuclear security applications. Following a two-year deployment at HFIR, an additional PROSPECT-II deployment at a low enriched uranium reactor could make complementary measurements of the neutrino yield from other fission isotopes. PROSPECT-II provides a unique opportunity to continue the study of reactor antineutrinos at short baselines, taking advantage of demonstrated elements of the original PROSPECT design and close access to a highly enriched uranium reactor core.

The PROSPECT and STEREO collaborations present a combined measurement of the pure $^{235}$U antineutrino spectrum, without site specific corrections or detector-dependent effects. The spectral measurements of the two highest precision experiments at research reactors are found to be compatible with $\chi^2/\mathrm{ndf} = 24.1/21$, allowing a joint unfolding of the prompt energy measurements into antineutrino energy. This $\bar{\nu}_e$ energy spectrum is provided to the community, and an excess of events relative to the Huber model is found in the 5-6 MeV region. When a Gaussian bump is fitted to the excess, the data-model $\chi^2$ value is improved, corresponding to a $2.4\sigma$ significance.

A joint determination of the reactor antineutrino spectra resulting from the fission of $^{235}$U and $^{239}$Pu has been carried out by the Daya Bay and PROSPECT collaborations. This Letter reports the level of consistency of $^{235}$U spectrum measurements from the two experiments and presents new results from a joint analysis of both data sets. The measurements are found to be consistent. The combined analysis reduces the degeneracy between the dominant $^{235}$U and $^{239}$Pu isotopes and improves the uncertainty of the $^{235}$U spectral shape to about 3\%. The ${}^{235}$U and $^{239}$Pu antineutrino energy spectra are unfolded from the jointly deconvolved reactor spectra using the Wiener-SVD unfolding method, providing a data-based reference for other reactor antineutrino experiments and other applications. This is the first measurement of the $^{235}$U and $^{239}$Pu spectra based on the combination of experiments at low- and highly enriched uranium reactors., Comment: 8 pages, 5 figures, Supplementary Material Included

If dark matter has mass lower than around 1 GeV, it will not impart enough energy to cause detectable nuclear recoils in many direct-detection experiments. However, if dark matter is upscattered to high energy by collisions with cosmic rays, it may be detectable in both direct-detection experiments and neutrino experiments. We report the results of a dedicated search for boosted dark matter upscattered by cosmic rays using the PROSPECT reactor antineutrino experiment. We show that such a flux of upscattered dark matter would display characteristic diurnal sidereal modulation, and use this to set new experimental constraints on sub-GeV dark matter exhibiting large interaction cross-sections., Comment: 11 pages, 8 figures

In light of a gap found by Krupi\'{n}ski, we give a new proof of associativity for the Morley (or "nonforking") product of invariant measures in NIP theories., Comment: 7 pages

We investigate Keisler measures in arbitrary theories. Our initial focus is on Borel definability. We show that when working over countable parameter sets in countable theories, Borel definable measures are closed under Morley products and satisfy associativity. However, we also demonstrate failures of both properties over uncountable parameter sets. In particular, we show that the Morley product of Borel definable types need not be Borel definable (correcting an erroneous result from the literature). We then study various notions of generic stability for Keisler measures and generalize several results from the NIP setting to arbitrary theories. We also prove some positive results for the class of frequency interpretation measures in arbitrary theories, namely, that such measures are closed under convex combinations and commute with all Borel definable measures. Finally, we construct the first example of a complete type which is definable and finitely satisfiable in a small model, but not finitely approximated over any small model., Comment: 56 pages. Final version incorporating referee comments; minor changes from previous version (e.g. Prop 4.3, Remark 7.4, Remark 7.16 are new)

Breast density is an important risk factor for breast cancer that also affects the specificity and sensitivity of screening mammography. Current federal legislation mandates reporting of breast density for all women undergoing breast screening. Clinically, breast density is assessed visually using the American College of Radiology Breast Imaging Reporting And Data System (BI-RADS) scale. Here, we introduce an artificial intelligence (AI) method to estimate breast percentage density (PD) from digital mammograms. Our method leverages deep learning (DL) using two convolutional neural network architectures to accurately segment the breast area. A machine-learning algorithm combining superpixel generation, texture feature analysis, and support vector machine is then applied to differentiate dense from non-dense tissue regions, from which PD is estimated. Our method has been trained and validated on a multi-ethnic, multi-institutional dataset of 15,661 images (4,437 women), and then tested on an independent dataset of 6,368 digital mammograms (1,702 women; cases=414) for both PD estimation and discrimination of breast cancer. On the independent dataset, PD estimates from Deep-LIBRA and an expert reader were strongly correlated (Spearman correlation coefficient = 0.90). Moreover, Deep-LIBRA yielded a higher breast cancer discrimination performance (area under the ROC curve, AUC = 0.611 [95% confidence interval (CI): 0.583, 0.639]) compared to four other widely-used research and commercial PD assessment methods (AUCs = 0.528 to 0.588). Our results suggest a strong agreement of PD estimates between Deep-LIBRA and gold-standard assessment by an expert reader, as well as improved performance in breast cancer risk assessment over state-of-the-art open-source and commercial methods.

We comment on the claimed observation [arXiv:arXiv:2005.05301] of sterile neutrino oscillations by the Neutrino-4 collaboration. Such a claim, which requires the existence of a new fundamental particle, demands a level of rigor commensurate with its impact. The burden lies with the Neutrino-4 collaboration to provide the information necessary to prove the validity of their claim to the community. In this note, we describe aspects of both the data and analysis method that might lead to an oscillation signature arising from a null experiment and describe additional information needed from the Neutrino-4 collaboration to support the oscillation claim. Additionally, as opposed to the assertion made by the Neutrino-4 collaboration, we also show that the method of 'coherent summation' using the $L/E$ parameter produces similar results to the methods used by the PROSPECT and the STEREO collaborations., Comment: 5 pages, 3 figures

We present a detailed report on sterile neutrino oscillation and U-235 antineutrino energy spectrum measurement results from the PROSPECT experiment at the highly enriched High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory. In 96 calendar days of data taken at an average baseline distance of 7.9 m from the center of the 85 MW HFIR core, the PROSPECT detector has observed more than 50,000 interactions of antineutrinos produced in beta decays of U-235 fission products. New limits on the oscillation of antineutrinos to light sterile neutrinos have been set by comparing the detected energy spectra of ten reactor-detector baselines between 6.7 and 9.2 meters. Measured differences in energy spectra between baselines show no statistically significant indication of antineutrinos to sterile neutrino oscillation and disfavor the Reactor Antineutrino Anomaly best-fit point at the 2.5$\sigma$ confidence level. The reported U-235 antineutrino energy spectrum measurement shows excellent agreement with energy spectrum models generated via conversion of the measured U-235 beta spectrum, with a $\chi^2$/DOF of 31/31. PROSPECT is able to disfavor at 2.4$\sigma$ confidence level the hypothesis that U-235 antineutrinos are solely responsible for spectrum discrepancies between model and data obtained at commercial reactor cores. A data-model deviation in PROSPECT similar to that observed by commercial core experiments is preferred with respect to no observed deviation, at a 2.2$\sigma$ confidence level., Comment: 42 pages, 52 Figures. Submitted to Phys. Rev. D. Supplementary Material Included

We show that for each $k\in\mathbb{N}$, a link $L\subset S^3$ bounds a degree $k$ Whitney tower in the 4-ball if and only if it is \emph{$C_k$-concordant} to the unlink. This means that $L$ is obtained from the unlink by a finite sequence of concordances and degree $k$ clasper surgeries. In our construction the trees associated to the Whitney towers coincide with the trees associated to the claspers. As a corollary to our previous obstruction theory for Whitney towers in the 4-ball, it follows that the $C_k$-concordance filtration of links is classified in terms of Milnor invariants, higher-order Sato-Levine and Arf invariants. Using a new notion of $k$-repeating twisted Whitney towers, we also classify a natural generalization of the notion of link homotopy, called twisted \emph{self $C_k$-concordance}, in terms of $k$-repeating Milnor invariants and $k$-repeating Arf invariants., Comment: 30 pages, 9 figures

We show that a $k$-stable set in a finite group can be approximated, up to given error $\epsilon>0$, by left cosets of a subgroup of index $\epsilon^{\text{-}O_k(1)}$. This improves the bound in a similar result of Terry and Wolf on stable arithmetic regularity in finite abelian groups, and leads to a quantitative account of work of the author, Pillay, and Terry on stable sets in arbitrary finite groups. We also prove an analogous result for finite stable sets of small tripling in arbitrary groups, which provides a quantitative version of recent work by Martin-Pizarro, Palac\'{i}n, and Wolf. Our proofs use results on VC-dimension, and a finitization of model-theoretic techniques from stable group theory., Comment: 14 pages, final version incorporating referee comments

Reactor neutrino experiments have seen major improvements in precision in recent years. With the experimental uncertainties becoming lower than those from theory, carefully considering all sources of $\overline{\nu}_{e}$ is important when making theoretical predictions. One source of $\overline{\nu}_{e}$ that is often neglected arises from the irradiation of the nonfuel materials in reactors. The $\overline{\nu}_{e}$ rates and energies from these sources vary widely based on the reactor type, configuration, and sampling stage during the reactor cycle and have to be carefully considered for each experiment independently. In this article, we present a formalism for selecting the possible $\overline{\nu}_{e}$ sources arising from the neutron captures on reactor and target materials. We apply this formalism to the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory, the $\overline{\nu}_{e}$ source for the the Precision Reactor Oscillation and Spectrum Measurement (PROSPECT) experiment. Overall, we observe that the nonfuel $\overline{\nu}_{e}$ contributions from HFIR to PROSPECT amount to 1\% above the inverse beta decay threshold with a maximum contribution of 9\% in the 1.8--2.0~MeV range. Nonfuel contributions can be particularly high for research reactors like HFIR because of the choice of structural and reflector material in addition to the intentional irradiation of target material for isotope production. We show that typical commercial pressurized water reactors fueled with low-enriched uranium will have significantly smaller nonfuel $\overline{\nu}_{e}$ contribution.