Showing 1–17 of 17 results for author: Goes, J

Parts-per-million-accurate determination of the K$α$ photoionization resonance of Be-like oxygen with resolution of its $^{16}$O-$^{18}$O isotopic shift

Authors: Jonas Danisch, Marc Botz, Chintan Shah, Moto Togawa, Joschka Goes, Dominic Hache, Filipe Grilo, Pedro Amaro, Vladimir A. Yerokhin, Steffen Kühn, Awad Mohamed, Roberta Totani, Monica de Simone, Stefano Orlando, Thomas Pfeifer, Fabrizio Nicastro, Marcello Coreno, José R. Crespo López-Urrutia

Abstract: We determine with high accuracy the energy of the inner-shell transition $1s^2 2s^2~{}^1\mathrm{S}_0 \rightarrow 1s~2s^2~2p_{3/2}~{}^1\mathrm{P}_1$ ${}^{16}\mathrm{O}_{Kα}^{4+}$ at $554.372(3)~\mathrm{eV}$ ($λ$ = $22.36480(12)~\unicode{x212B}$) as well as its small shift of $2.2 \pm 1.3~\mathrm{meV}$ ($Δλ$ = $0.089(52)~\mathrm{m}\unicode{x212B}$) for the ${}^{18}\mathrm{O}$ isotope. This transitio… ▽ More We determine with high accuracy the energy of the inner-shell transition $1s^2 2s^2~{}^1\mathrm{S}_0 \rightarrow 1s~2s^2~2p_{3/2}~{}^1\mathrm{P}_1$ ${}^{16}\mathrm{O}_{Kα}^{4+}$ at $554.372(3)~\mathrm{eV}$ ($λ$ = $22.36480(12)~\unicode{x212B}$) as well as its small shift of $2.2 \pm 1.3~\mathrm{meV}$ ($Δλ$ = $0.089(52)~\mathrm{m}\unicode{x212B}$) for the ${}^{18}\mathrm{O}$ isotope. This transition blends with a $K_α$ line of $\mathrm{O}^{5+}$ used in astrophysical diagnostics, potentially affecting its reliability. In contrast to our experimental uncertainty of $\pm 3~\mathrm{meV}$, advanced electronic structure predictions for this four-electron system, including quantum electrodynamic (QED) corrections on the order of $100~\mathrm{meV}$, still scatter by more than $\pm 250~\mathrm{meV}$. Ions generated and stored in an electron beam ion trap were excited at the ELETTRA synchrotron facility with monochromatic soft x rays, with photon energies corrected by an additional spectrometer. Upon resonant excitation of $\mathrm{O}^{4+}$ and subsequent autoionization, we separate the photoions of each isotope by a time-of-flight measurement. This way, we resolve soft x-ray isotopic shifts of a few meV, obtain very accurate data on an essential astrophysical ion, and test calculations down to the level of QED contributions. △ Less

Submitted 1 July, 2026; originally announced July 2026.

Comments: 9 pages, 6 figures, 4 tables, published in Physical Review A

Journal ref: Physical Review A 113, 022811 (2026)

A laboratory plasma experiment for X-ray astronomy using a compact electron beam ion trap (EBIT)

Authors: Yuki Amano, Leo Hirata, Moto Togawa, Hiromasa Suzuki, Hiroyuki A. Sakaue, Naoki Kimura, Nobuyuki Nakamura, Makoto Sawada, Masaki Oura, Jonas Danisch, Joschka Goes, Marc Botz, José R. Crespo López-urrutia, Hiroya Yamaguchi

Abstract: We present the basic performance and experimental results of an electron beam ion trap (JAXA-EBIT), newly introduced to the Japanese astronomical community. Accurate atomic data are indispensable for the reliable interpretation of high-resolution X-ray spectra of astrophysical plasmas. The JAXA-EBIT generates highly charged ions under well-controlled laboratory conditions, providing experimental b… ▽ More We present the basic performance and experimental results of an electron beam ion trap (JAXA-EBIT), newly introduced to the Japanese astronomical community. Accurate atomic data are indispensable for the reliable interpretation of high-resolution X-ray spectra of astrophysical plasmas. The JAXA-EBIT generates highly charged ions under well-controlled laboratory conditions, providing experimental benchmarks for atomic data. The JAXA-EBIT shows performance comparable to the Heidelberg compact EBIT through dielectronic recombination measurements of highly charged Ar ions. Furthermore, we conducted resonant photoexcitation spectroscopy of highly charged ions using the soft X-ray beamline BL17SU at the synchrotron radiation facility SPring-8. As a result, we successfully detected resonance transitions of He-like O$^{6+}$ and Ne-like Fe$^{16+}$. These results demonstrate the capability of the JAXA-EBIT for precise measurement of atomic data and show that it serves as a powerful tool for advancing astrophysical research. △ Less

Submitted 25 November, 2025; originally announced November 2025.

Comments: 8pages, 4 figures, accepted for publication in Plasma and Fusion Research

Enhanced One-Color-Two-Photon Resonant Ionization in Highly Charged Ions by Fine-Structure Effects

Authors: Moto Togawa, Chunhai Lyu, Chintan Shah, Marc Botz, Joschka Goes, Jonas Danisch, Marleen Maxton, Kai Köbnick, Filipe Grilo, Pedro Amaro, Katharina Kubicek, Mohammed Sekkal, Awad Mohamed, Rebecca Boll, Alberto De Fanis, Simon Dold, Tommaso Mazza, Jacobo Montano, Nils Rennhack, Björn Senfftleben, Sergey Usenko, Zoltan Harman, Christoph H. Keitel, Maurice Leutenegger, Michael Meyer , et al. (3 additional authors not shown)

Abstract: Ultraintense pulses from X-ray free-electron lasers can drive, within femtoseconds, multiple processes in the inner shells of atoms and molecules in all phases of matter. The ensuing complex ionization pathways of outer-shell electrons from the neutral to the final highly charged states make a comparison with theory enormously difficult. We resolve these pathways by preparing highly charged ions i… ▽ More Ultraintense pulses from X-ray free-electron lasers can drive, within femtoseconds, multiple processes in the inner shells of atoms and molecules in all phases of matter. The ensuing complex ionization pathways of outer-shell electrons from the neutral to the final highly charged states make a comparison with theory enormously difficult. We resolve these pathways by preparing highly charged ions in an electron beam ion trap before exposing them to the pulsed radiation. This reveals how relativistic fine-structure effects shift electronic energies, largely compensate the core-screening potential, and enable the consecutive, resonant absorption of two quasi-monochromatic X-ray photons that would generally be unfeasible. This doubly-resonant channel enhances the efficiency of two-photon ionization by more than two orders of magnitude, dominating in this regime the nonlinear interaction of light and matter with possible application for future precision X-ray metrology. △ Less

Submitted 7 November, 2025; originally announced November 2025.

DQS: A Low-Budget Query Strategy for Enhancing Unsupervised Data-driven Anomaly Detection Approaches

Authors: Lucas Correia, Jan-Christoph Goos, Thomas Bäck, Anna V. Kononova

Abstract: Truly unsupervised approaches for time series anomaly detection are rare in the literature. Those that exist suffer from a poorly set threshold, which hampers detection performance, while others, despite claiming to be unsupervised, need to be calibrated using a labelled data subset, which is often not available in the real world. This work integrates active learning with an existing unsupervised… ▽ More Truly unsupervised approaches for time series anomaly detection are rare in the literature. Those that exist suffer from a poorly set threshold, which hampers detection performance, while others, despite claiming to be unsupervised, need to be calibrated using a labelled data subset, which is often not available in the real world. This work integrates active learning with an existing unsupervised anomaly detection method by selectively querying the labels of multivariate time series, which are then used to refine the threshold selection process. To achieve this, we introduce a novel query strategy called the dissimilarity-based query strategy (DQS). DQS aims to maximise the diversity of queried samples by evaluating the similarity between anomaly scores using dynamic time warping. We assess the detection performance of DQS in comparison to other query strategies and explore the impact of mislabelling, a topic that is underexplored in the literature. Our findings indicate that DQS performs best in small-budget scenarios, though the others appear to be more robust when faced with mislabelling. Therefore, in the real world, the choice of query strategy depends on the expertise of the oracle and the number of samples they are willing to label. Regardless, all query strategies outperform the unsupervised threshold even in the presence of mislabelling. Thus, whenever it is feasible to query an oracle, employing an active learning-based threshold is recommended. △ Less

Submitted 10 August, 2026; v1 submitted 6 September, 2025; originally announced September 2025.

Soil moisture estimation of bare and vegetation-covered areas using a P/L/C-band SAR

Authors: Gian Oré, Jhonnatan Yepes, Juliana A. Góes, Luciano P. Oliveira, Bárbara Teruel, Hugo E. Hernandez-Figueroa

Abstract: The paper introduces a novel approach for estimating soil moisture in vegetated surfaces, specifically focusing on sugarcane crops throughout various growth stages in agriculture applications. While existing models typically address bare soil scenarios, this model utilizes data from P-, L-, and C-band Synthetic Aperture Radar (SAR) to estimate soil moisture. The semi-empirical Dubois model forms t… ▽ More The paper introduces a novel approach for estimating soil moisture in vegetated surfaces, specifically focusing on sugarcane crops throughout various growth stages in agriculture applications. While existing models typically address bare soil scenarios, this model utilizes data from P-, L-, and C-band Synthetic Aperture Radar (SAR) to estimate soil moisture. The semi-empirical Dubois model forms the basis of the proposed model, which has been adapted to accommodate multiband operation and crop height variations. Synthetic datasets are generated using the adjusted model to train two neural networks incorporated into the overall model. Additionally, a linear expression for estimating crop height is integrated into the model. The model is validated in an Experimental Site at the School of Agricultural Engineering, UNICAMP, and an independent area at the Sugarcane Technology Center in Piracicaba, Brazil. The model utilizes a multiband drone-borne SAR system with a 3-meter image resolution and radiometric accuracy of 0.5 dB. The results indicate that the model can estimate soil moisture with root-mean-square errors of 0.05 cm3.cm-3 (5 vol. %) across crop heights ranging from zero to 2.5 meters. △ Less

Submitted 16 December, 2024; originally announced December 2024.

Comments: 9 pages, 12 figures, 2 tables, 17 equations

ACM Class: I.4.7

PATH: A Discrete-sequence Dataset for Evaluating Online Unsupervised Anomaly Detection Approaches for Multivariate Time Series

Authors: Lucas Correia, Jan-Christoph Goos, Thomas Bäck, Anna V. Kononova

Abstract: Benchmarking anomaly detection approaches for multivariate time series is a challenging task due to a lack of high-quality datasets. Current publicly available datasets are too small, not diverse and feature trivial anomalies, which hinders measurable progress in this research area. We propose a solution: a diverse, extensive, and non-trivial dataset generated via state-of-the-art simulation tools… ▽ More Benchmarking anomaly detection approaches for multivariate time series is a challenging task due to a lack of high-quality datasets. Current publicly available datasets are too small, not diverse and feature trivial anomalies, which hinders measurable progress in this research area. We propose a solution: a diverse, extensive, and non-trivial dataset generated via state-of-the-art simulation tools that reflects realistic behaviour of an automotive powertrain, including its multivariate, dynamic and variable-state properties. Additionally, our dataset represents a discrete-sequence problem, which remains unaddressed by previously-proposed solutions in literature. To cater for both unsupervised and semi-supervised anomaly detection settings, as well as time series generation and forecasting, we make different versions of the dataset available, where training and test subsets are offered in contaminated and clean versions, depending on the task. We also provide baseline results from a selection of approaches based on deterministic and variational autoencoders, as well as a non-parametric approach. As expected, the baseline experimentation shows that the approaches trained on the semi-supervised version of the dataset outperform their unsupervised counterparts, highlighting a need for approaches more robust to contaminated training data. Furthermore, results show that the threshold used can have a large influence on detection performance, hence more work needs to be invested in methods to find a suitable threshold without the need for labelled data. △ Less

Submitted 12 November, 2025; v1 submitted 21 November, 2024; originally announced November 2024.

Hanle effect for lifetime determinations in the soft X-ray regime

Authors: Moto Togawa, Jan Richter, Chintan Shah, Marc Botz, Joshua Nenninger, Jonas Danisch, Joschka Goes, Steffen Kühn, Pedro Amaro, Awad Mohamed, Yuki Amano, Stefano Orlando, Roberta Totani, Monica de Simone, Stephan Fritzsche, Thomas Pfeifer, Marcello Coreno, Andrey Surzhykov, José R. Crespo López-Urrutia

Abstract: By exciting a series of $1\mathrm{s}^{2}\, ^{1}\mathrm{S}_{0} \to 1\mathrm{s}n\mathrm{p}\, ^{1}\mathrm{P}_{1}$ transitions in helium-like nitrogen ions with linearly polarized monochromatic soft X-rays at the Elettra facility, we found a change in the angular distribution of the fluorescence sensitive to the principal quantum number $n$. In particular it is observed that the ratio of emission in d… ▽ More By exciting a series of $1\mathrm{s}^{2}\, ^{1}\mathrm{S}_{0} \to 1\mathrm{s}n\mathrm{p}\, ^{1}\mathrm{P}_{1}$ transitions in helium-like nitrogen ions with linearly polarized monochromatic soft X-rays at the Elettra facility, we found a change in the angular distribution of the fluorescence sensitive to the principal quantum number $n$. In particular it is observed that the ratio of emission in directions parallel and perpendicular to the polarization of incident radiation increases with higher $n$. We find this $n$-dependence to be a manifestation of the Hanle effect, which served as a practical tool for lifetime determinations of optical transitions since its discovery in 1924. In contrast to traditional Hanle effect experiments, in which one varies the magnetic field and considers a particular excited state, we demonstrate a 'soft X-ray Hanle effect' which arises in a static magnetic field but for a series of excited states. By comparing experimental data with theoretical predictions, we were able to determine lifetimes ranging from hundreds of femtoseconds to tens of picoseconds of the $1\mathrm{s}n\mathrm{p}\, ^{1}\mathrm{P}_{1}$ levels, which find excellent agreement with atomic-structure calculations. We argue that dedicated soft X-ray measurements could yield lifetime data that is beyond current experimental reach and cannot yet be predicted with sufficient accuracy. △ Less

Submitted 22 August, 2024; originally announced August 2024.

Comments: 7 pages, 4 figures

Online Model-based Anomaly Detection in Multivariate Time Series: Taxonomy, Survey, Research Challenges and Future Directions

Authors: Lucas Correia, Jan-Christoph Goos, Philipp Klein, Thomas Bäck, Anna V. Kononova

Abstract: Time-series anomaly detection plays an important role in engineering processes, like development, manufacturing and other operations involving dynamic systems. These processes can greatly benefit from advances in the field, as state-of-the-art approaches may aid in cases involving, for example, highly dimensional data. To provide the reader with understanding of the terminology, this survey introd… ▽ More Time-series anomaly detection plays an important role in engineering processes, like development, manufacturing and other operations involving dynamic systems. These processes can greatly benefit from advances in the field, as state-of-the-art approaches may aid in cases involving, for example, highly dimensional data. To provide the reader with understanding of the terminology, this survey introduces a novel taxonomy where a distinction between online and offline, and training and inference is made. Additionally, it presents the most popular data sets and evaluation metrics used in the literature, as well as a detailed analysis. Furthermore, this survey provides an extensive overview of the state-of-the-art model-based online semi- and unsupervised anomaly detection approaches for multivariate time-series data, categorising them into different model families and other properties. The biggest research challenge revolves around benchmarking, as currently there is no reliable way to compare different approaches against one another. This problem is two-fold: on the one hand, public data sets suffers from at least one fundamental flaw, while on the other hand, there is a lack of intuitive and representative evaluation metrics in the field. Moreover, the way most publications choose a detection threshold disregards real-world conditions, which hinders the application in the real world. To allow for tangible advances in the field, these issues must be addressed in future work. △ Less

Submitted 19 September, 2024; v1 submitted 7 August, 2024; originally announced August 2024.

TeVAE: A Variational Autoencoder Approach for Discrete Online Anomaly Detection in Variable-state Multivariate Time-series Data

Authors: Lucas Correia, Jan-Christoph Goos, Philipp Klein, Thomas Bäck, Anna V. Kononova

Abstract: As attention to recorded data grows in the realm of automotive testing and manual evaluation reaches its limits, there is a growing need for automatic online anomaly detection. This real-world data is complex in many ways and requires the modelling of testee behaviour. To address this, we propose a temporal variational autoencoder (TeVAE) that can detect anomalies with minimal false positives when… ▽ More As attention to recorded data grows in the realm of automotive testing and manual evaluation reaches its limits, there is a growing need for automatic online anomaly detection. This real-world data is complex in many ways and requires the modelling of testee behaviour. To address this, we propose a temporal variational autoencoder (TeVAE) that can detect anomalies with minimal false positives when trained on unlabelled data. Our approach also avoids the bypass phenomenon and introduces a new method to remap individual windows to a continuous time series. Furthermore, we propose metrics to evaluate the detection delay and root-cause capability of our approach and present results from experiments on a real-world industrial data set. When properly configured, TeVAE flags anomalies only 6% of the time wrongly and detects 65% of anomalies present. It also has the potential to perform well with a smaller training and validation subset but requires a more sophisticated threshold estimation method. △ Less

Submitted 12 November, 2025; v1 submitted 9 July, 2024; originally announced July 2024.

High-Precision Transition Energy Measurements of Neon-like Fe XVII Ions

Authors: Chintan Shah, Moto Togawa, Marc Botz, Jonas Danisch, Joschka J. Goes, Sonja Bernitt, Marleen Maxton, Kai Köbnick, Jen Buck, Jörn Seltmann, Moritz Hoesch, Ming Feng Gu, F. Scott Porter, Thomas Pfeifer, Maurice A. Leutenegger, Charles Cheung, Marianna S. Safronova, José R. Crespo López-Urrutia

Abstract: We improve by a factor of 4-20 the energy accuracy of the strongest soft X-ray transitions of Fe XVII ions by resonantly exciting them in an electron beam ion trap with a monochromatic beam at the P04 beamline of the PETRA III synchrotron facility. By simultaneously tracking instantaneous photon-energy fluctuations with a high-resolution photoelectron spectrometer, we minimize systematic uncertain… ▽ More We improve by a factor of 4-20 the energy accuracy of the strongest soft X-ray transitions of Fe XVII ions by resonantly exciting them in an electron beam ion trap with a monochromatic beam at the P04 beamline of the PETRA III synchrotron facility. By simultaneously tracking instantaneous photon-energy fluctuations with a high-resolution photoelectron spectrometer, we minimize systematic uncertainties down to 10-15 meV, or velocity equivalent $\pm\sim$5 km s$^{-1}$ in their rest energies, substantially improving our knowledge of this key astrophysical ion. Our large-scale configuration-interaction computations include more than four million relativistic configurations and agree with the experiment at a level without precedent for a 10-electron system. Thereby, theoretical uncertainties for interelectronic correlations become far smaller than those of quantum electrodynamics (QED) corrections. The present QED benchmark strengthens our trust in future calculations of many other complex atomic ions of interest to astrophysics, plasma physics, and for the development of optical clocks with highly charged ions. △ Less

Submitted 15 July, 2024; v1 submitted 16 January, 2024; originally announced January 2024.

Comments: 14 pages, 2 figures, 4 tables, published version

Journal ref: The Astrophysical Journal, 969, 52 (2024)

Bayesian mortality modelling with pandemics: a vanishing jump approach

Authors: Julius Goes, Karim Barigou, Anne Leucht

Abstract: This paper extends the Lee-Carter model for single- and multi-populations to account for pandemic jump effects of vanishing kind, allowing for a more comprehensive and accurate representation of mortality rates during a pandemic, characterised by a high impact at the beginning and gradually vanishing effects over subsequent periods. While the Lee-Carter model is effective in capturing mortality tr… ▽ More This paper extends the Lee-Carter model for single- and multi-populations to account for pandemic jump effects of vanishing kind, allowing for a more comprehensive and accurate representation of mortality rates during a pandemic, characterised by a high impact at the beginning and gradually vanishing effects over subsequent periods. While the Lee-Carter model is effective in capturing mortality trends, it may not be able to account for large, unexpected jumps in mortality rates caused by pandemics or wars. Existing models allow either for transient jumps with an effect of one period only or persistent jumps. However, there is no literature on estimating mortality time series with jumps having an effect over a small number of periods as typically observed in pandemics. The Bayesian approach allows to quantify the uncertainty around the parameter estimates. Empirical data from the COVID-19 pandemic shows the superiority of the proposed approach, compared to models with a transitory shock effect. △ Less

Submitted 29 August, 2024; v1 submitted 2 November, 2023; originally announced November 2023.

MA-VAE: Multi-head Attention-based Variational Autoencoder Approach for Anomaly Detection in Multivariate Time-series Applied to Automotive Endurance Powertrain Testing

Authors: Lucas Correia, Jan-Christoph Goos, Philipp Klein, Thomas Bäck, Anna V. Kononova

Abstract: A clear need for automatic anomaly detection applied to automotive testing has emerged as more and more attention is paid to the data recorded and manual evaluation by humans reaches its capacity. Such real-world data is massive, diverse, multivariate and temporal in nature, therefore requiring modelling of the testee behaviour. We propose a variational autoencoder with multi-head attention (MA-VA… ▽ More A clear need for automatic anomaly detection applied to automotive testing has emerged as more and more attention is paid to the data recorded and manual evaluation by humans reaches its capacity. Such real-world data is massive, diverse, multivariate and temporal in nature, therefore requiring modelling of the testee behaviour. We propose a variational autoencoder with multi-head attention (MA-VAE), which, when trained on unlabelled data, not only provides very few false positives but also manages to detect the majority of the anomalies presented. In addition to that, the approach offers a novel way to avoid the bypass phenomenon, an undesirable behaviour investigated in literature. Lastly, the approach also introduces a new method to remap individual windows to a continuous time series. The results are presented in the context of a real-world industrial data set and several experiments are undertaken to further investigate certain aspects of the proposed model. When configured properly, it is 9% of the time wrong when an anomaly is flagged and discovers 67% of the anomalies present. Also, MA-VAE has the potential to perform well with only a fraction of the training and validation subset, however, to extract it, a more sophisticated threshold estimation method is required. △ Less

Submitted 19 September, 2024; v1 submitted 5 September, 2023; originally announced September 2023.

Prototype of an affordable pressure-controlled emergency mechanical ventilator for COVID-19

Authors: Américo Pereira, Luís Lopes, Paulo Fonte, Pedro Póvoa, Telmo G. Santos, Alberto Martinho, Ângela Neves, António Bugalho, António Gabriel-Santos, Gonçalo Gaspar Bentes Pimenta, João Goês, João Martins, João Pedro Oliveira, José Paulo Santos, Luís C. Gil, Miguel Onofre Domingues, Orlando Cunha, Pedro Pinheiro de Sousa, Tiago A. Rodrigues, Valdemar R. Duarte, Antero Abrunhosa, António Grilo, João Agostinho do Nascimento, Mário Pimenta

Abstract: We present a viable prototype of a simple mechanical ventilator intended as a last resort to ventilate COVID-19 patients. The prototype implements the pressure-controlled continuous mandatory ventilation mode (PC-CMV) with settable breathing rates, inspiration/expiration time ratios and FiO2 modulation. Although safe, the design aims to minimize the use of technical components and those used are c… ▽ More We present a viable prototype of a simple mechanical ventilator intended as a last resort to ventilate COVID-19 patients. The prototype implements the pressure-controlled continuous mandatory ventilation mode (PC-CMV) with settable breathing rates, inspiration/expiration time ratios and FiO2 modulation. Although safe, the design aims to minimize the use of technical components and those used are common in industry, so its construction may be possible in times of logistical shortage or disruption or in areas with reduced access to technical materials and at a moderate cost, affordable to lower income countries. Most of the device can be manufactured by modest technical means and construction plans are provided. △ Less

Submitted 21 July, 2020; v1 submitted 1 April, 2020; originally announced April 2020.

Comments: This version differs from version 2 in that it includes toxicological and bio-safety tests and updated electronics

Robust Sparse Covariance Estimation by Thresholding Tyler's M-Estimator

Authors: John Goes, Gilad Lerman, Boaz Nadler

Abstract: Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental problem in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Towards bridging this gap, in this work we consider estimating a sparse shape matrix from $n$ samples following a possibly heavy tailed elliptical distribution. We propose estimato… ▽ More Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental problem in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Towards bridging this gap, in this work we consider estimating a sparse shape matrix from $n$ samples following a possibly heavy tailed elliptical distribution. We propose estimators based on thresholding either Tyler's M-estimator or its regularized variant. We derive bounds on the difference in spectral norm between our estimators and the shape matrix in the joint limit as the dimension $p$ and sample size $n$ tend to infinity with $p/n\toγ>0$. These bounds are minimax rate-optimal. Results on simulated data support our theoretical analysis. △ Less

Submitted 19 September, 2018; v1 submitted 24 June, 2017; originally announced June 2017.

Journal ref: Annals of Statistics, 48(1):86-110, 2020

Towards an 'average' version of the Birch and Swinnerton-Dyer Conjecture

Authors: John Goes, Steven J Miller

Abstract: The Birch and Swinnerton-Dyer conjecture states that the rank of the Mordell-Weil group of an elliptic curve E equals the order of vanishing at the central point of the associated L-function L(s,E). Previous investigations have focused on bounding how far we must go above the central point to be assured of finding a zero, bounding the rank of a fixed curve or on bounding the average rank in a fa… ▽ More The Birch and Swinnerton-Dyer conjecture states that the rank of the Mordell-Weil group of an elliptic curve E equals the order of vanishing at the central point of the associated L-function L(s,E). Previous investigations have focused on bounding how far we must go above the central point to be assured of finding a zero, bounding the rank of a fixed curve or on bounding the average rank in a family. Mestre showed the first zero occurs by O(1/loglog(N_E)), where N_E is the conductor of E, though we expect the correct scale to study the zeros near the central point is the significantly smaller 1/log(N_E). We significantly improve on Mestre's result by averaging over a one-parameter family of elliptic curves, obtaining non-trivial upper and lower bounds for the average number of normalized zeros in intervals on the order of 1/log(N_E) (which is the expected scale). Our results may be interpreted as providing further evidence in support of the Birch and Swinnerton-Dyer conjecture, as well as the Katz-Sarnak density conjecture from random matrix theory (as the number of zeros predicted by random matrix theory lies between our upper and lower bounds). These methods may be applied to additional families of L-functions. △ Less

Submitted 21 November, 2009; v1 submitted 15 November, 2009; originally announced November 2009.

Comments: 20 pages, 2 figures, revised first draft (fixed some typos)

MSC Class: 11M41 (primary); 11G40; 15B52 (secondary).}

Journal ref: Journal of Number Theory 130 (2010) 2341-2358

A unitary test of the Ratios Conjecture

Authors: John Goes, Steven Jackson, Steven J. Miller, David Montague, Kesinee Ninsuwan, Ryan Peckner, Thuy Pham

Abstract: The Ratios Conjecture of Conrey, Farmer and Zirnbauer predicts the answers to numerous questions in number theory, ranging from n-level densities and correlations to mollifiers to moments and vanishing at the central point. The conjecture gives a recipe to generate these answers, which are believed to be correct up to square-root cancelation. These predictions have been verified, for suitably re… ▽ More The Ratios Conjecture of Conrey, Farmer and Zirnbauer predicts the answers to numerous questions in number theory, ranging from n-level densities and correlations to mollifiers to moments and vanishing at the central point. The conjecture gives a recipe to generate these answers, which are believed to be correct up to square-root cancelation. These predictions have been verified, for suitably restricted test functions, for the 1-level density of orthogonal and symplectic families of L-functions. In this paper we verify the conjecture's predictions for the unitary family of all Dirichlet $L$-functions with prime conductor; we show square-root agreement between prediction and number theory if the support of the Fourier transform of the test function is in (-1,1), and for support up to (-2,2) we show agreement up to a power savings in the family's cardinality. △ Less

Submitted 21 January, 2010; v1 submitted 27 September, 2009; originally announced September 2009.

Comments: Version 2: 24 pages, provided additional details, fixed some small mistakes and expanded the exposition in places

MSC Class: 11M26 (primary); 11M41; 15B52 (secondary)

Journal ref: Journal of Number Theory 130 (2010), pp. 2238-2258

Fluctuating Interfaces in Microemulsion and Sponge Phases

Authors: G. Gompper, J. Goos

Abstract: A simple Ginzburg-Landau theory with a single, scalar order parameter is used to study the microscopic structure of microemulsions and sponge phases. The scattering intensity in both film and bulk contrast, as well as averages of the internal area $S$, the Euler characteristic $χ_E$, and the mean curvature squared $<H^2>$, are calculated by Monte Carlo methods. The results are compared with resu… ▽ More A simple Ginzburg-Landau theory with a single, scalar order parameter is used to study the microscopic structure of microemulsions and sponge phases. The scattering intensity in both film and bulk contrast, as well as averages of the internal area $S$, the Euler characteristic $χ_E$, and the mean curvature squared $<H^2>$, are calculated by Monte Carlo methods. The results are compared with results obtained from a variational approach in combination with the theory of Gaussian random fields and level surfaces. The results for the location of the transition from the microemulsion to oil/water coexistence, for the scattering intensity in bulk contrast, and for the dimensionless ratio $χ_E V^2/S^3$ (where $V$ is the volume) are found to be in good quantitative agreement. However, the variational approach fails to give a peak in the scattering intensity in film contrast at finite wavevector, a peak which is observed both in the Monte Carlo simulations and in experiment. Also, the variational approach fails to produce a transition from the microemulsion to the lamellar phase. △ Less

Submitted 28 June, 1994; originally announced June 1994.

Comments: 23 pages (LaTeX) + 15 figures appended, figures 10-13 upon request, LMU-WAG-940530