Search

First we survey and explain the strategy of some recent results that construct holomorphic $\text{sl}(2, \mathbb C)$-differential systems over some Riemann surfaces $\Sigma_g$ of genus $g\geq 2$, satisfying the condition that the image of the associated monodromy homomorphism is (real) Fuchsian \cite{BDHH} or some cocompact Kleinian subgroup $$\Gamma \subset \text{SL}(2, \mathbb C)$$ as in \cite{BDHH2}. As a consequence, there exist holomorphic maps from $\Sigma_g$ to the quotient space $\text{SL}(2, \mathbb C)/ \Gamma$, where $\Gamma \subset \text{SL}(2, \mathbb C)$ is a cocompact lattice, that do not factor through any elliptic curve \cite{BDHH2}. This answers positively a question of Ghys in \cite{Gh}; the question was also raised by Huckleberry and Winkelmann in \cite{HW}. Then we prove that when $M$ is a Riemann surface, a Torelli type theorem holds for the affine group scheme over $\mathbb C$ obtained from the category of holomorphic connections on {\it \'etale trivial} holomorphic bundles. After that, we explain how to compute in a simple way the holonomy of a holomorphic connection on a free vector bundle. Finally, for a compact K\"ahler manifold $M$, we investigate the neutral Tannakian category given by the holomorphic connections on \'etale trivial holomorphic bundles over $M$. If $\varpi$ (respectively, $\Theta$) stands for the affine group scheme over $\mathbb C$ obtained from the category of connections (respectively, connections on free (trivial) vector bundles), then the natural inclusion produces a morphism $v:{\mathcal O}(\Theta)\longrightarrow {\mathcal O}(\varpi)$ of Hopf algebras. We present a description of the transpose of $v$ in terms of the iterated integrals., Comment: To appear in the Int. Jour. Math. volume in honor of Oscar Garcia-Prada

Confidence intervals (CIs) are instrumental in statistical analysis, providing a range estimate of the parameters. In modern statistics, selective inference is common, where only certain parameters are highlighted. However, this selective approach can bias the inference, leading some to advocate for the use of CIs over p-values. To increase the flexibility of confidence intervals, we introduce direction-preferring CIs, enabling analysts to focus on parameters trending in a particular direction. We present these types of CIs in two settings: First, when there is no selection of parameters; and second, for situations involving parameter selection, where we offer a conditional version of the direction-preferring CIs. Both of these methods build upon the foundations of Modified Pratt CIs, which rely on non-equivariant acceptance regions to achieve longer intervals in exchange for improved sign exclusions. We show that for selected parameters out of m > 1 initial parameters of interest, CIs aimed at controlling the false coverage rate, have higher power to determine the sign compared to conditional CIs. We also show that conditional confidence intervals control the marginal false coverage rate (mFCR) under any dependency., Comment: 11 figures, 45 pages

Equilibrium rate theories play a crucial role in understanding rare, reactive events. However, they are inapplicable to a range of irreversible processes in systems driven far from thermodynamic equilibrium like active and biological matter. Here, we develop an efficient numerical method to compute the rate constant of rare nonequilibrium events in the weak-noise limit based on an instanton approximation to the stochastic path integral and illustrate its wide range of application. We demonstrate excellent agreement of the instanton rates with numerically exact results for a particle under a non-conservative force. We also study phase transitions in an active field theory. We elucidate how activity alters the stability of the two phases and their rates of interconversion in a manner that can be well described by modifying classical nucleation theory, Comment: 16 pages, 12 figures

Chaos plays a crucial role in numerous natural phenomena, but its quantum nature has remained large elusive. One intriguing quantum-chaotic phenomenon is the scarring of a single-particle wavefunction, where the quantum probability density is enhanced in the vicinity of a classical periodic orbit. These quantum scars illustrate the quantum suppression of classical chaos, offering a unique way to explore the classical-quantum relationship beyond conventional limits. In this study, we establish an ergodicity theorem for slacking a group of adjacent eigenstates, revealing the aspect of antiscarring -- the reduction of probability density along a periodic orbit generating the corresponding scars. We thereafter apply these two concepts to variational scars in a disordered quantum well, and finally discuss their broader implications, suggesting potential experimental approaches to observe this phenomenon.

With the ever-rising quality of deep generative models, it is increasingly important to be able to discern whether the audio data at hand have been recorded or synthesized. Although the detection of fake speech signals has been studied extensively, this is not the case for the detection of fake environmental audio. We propose a simple and efficient pipeline for detecting fake environmental sounds based on the CLAP audio embedding. We evaluate this detector using audio data from the 2023 DCASE challenge task on Foley sound synthesis. Our experiments show that fake sounds generated by 44 state-of-the-art synthesizers can be detected on average with 98% accuracy. We show that using an audio embedding learned on environmental audio is beneficial over a standard VGGish one as it provides a 10% increase in detection performance. Informal listening to Incorrect Negative examples demonstrates audible features of fake sounds missed by the detector such as distortion and implausible background noise.

This paper explores whether considering alternative domain-specific embeddings to calculate the Fr\'echet Audio Distance (FAD) metric can help the FAD to correlate better with perceptual ratings of environmental sounds. We used embeddings from VGGish, PANNs, MS-CLAP, L-CLAP, and MERT, which are tailored for either music or environmental sound evaluation. The FAD scores were calculated for sounds from the DCASE 2023 Task 7 dataset. Using perceptual data from the same task, we find that PANNs-WGM-LogMel produces the best correlation between FAD scores and perceptual ratings of both audio quality and perceived fit with a Spearman correlation higher than 0.5. We also find that music-specific embeddings resulted in significantly lower results. Interestingly, VGGish, the embedding used for the original Fr\'echet calculation, yielded a correlation below 0.1. These results underscore the critical importance of the choice of embedding for the FAD metric design.

Large language models (LLMs) hold promise to serve complex health information needs but also have the potential to introduce harm and exacerbate health disparities. Reliably evaluating equity-related model failures is a critical step toward developing systems that promote health equity. We present resources and methodologies for surfacing biases with potential to precipitate equity-related harms in long-form, LLM-generated answers to medical questions and conduct a large-scale empirical case study with the Med-PaLM 2 LLM. Our contributions include a multifactorial framework for human assessment of LLM-generated answers for biases, and EquityMedQA, a collection of seven datasets enriched for adversarial queries. Both our human assessment framework and dataset design process are grounded in an iterative participatory approach and review of Med-PaLM 2 answers. Through our empirical study, we find that our approach surfaces biases that may be missed via narrower evaluation approaches. Our experience underscores the importance of using diverse assessment methodologies and involving raters of varying backgrounds and expertise. While our approach is not sufficient to holistically assess whether the deployment of an AI system promotes equitable health outcomes, we hope that it can be leveraged and built upon towards a shared goal of LLMs that promote accessible and equitable healthcare.

In supervised learning, including regression and classification, conformal methods provide prediction sets for the outcome/label with finite sample coverage for any machine learning predictor. We consider here the case where such prediction sets come after a selection process. The selection process requires that the selected prediction sets be `informative' in a well defined sense. We consider both the classification and regression settings where the analyst may consider as informative only the sample with prediction sets small enough, excluding null values, or obeying other appropriate `monotone' constraints. We develop a unified framework for building such informative conformal prediction sets while controlling the false coverage rate (FCR) on the selected sample. While conformal prediction sets after selection have been the focus of much recent literature in the field, the new introduced procedures, called InfoSP and InfoSCOP, are to our knowledge the first ones providing FCR control for informative prediction sets. We show the usefulness of our resulting procedures on real and simulated data., Comment: 50 pages, 15 figures, 1 table

We present the measurements of all-particle energy spectrum and mean logarithmic mass of cosmic rays in the energy range of 0.3-30 PeV using data collected from LHAASO-KM2A between September 2021 and December 2022, which is based on a nearly composition-independent energy reconstruction method, achieving unprecedented accuracy. Our analysis reveals the position of the knee at $3.67 \pm 0.05 \pm 0.15$ PeV. Below the knee, the spectral index is found to be -$2.7413 \pm 0.0004 \pm 0.0050$, while above the knee, it is -$3.128 \pm 0.005 \pm 0.027$, with the sharpness of the transition measured with a statistical error of 2%. The mean logarithmic mass of cosmic rays is almost heavier than helium in the whole measured energy range. It decreases from 1.7 at 0.3 PeV to 1.3 at 3 PeV, representing a 24% decline following a power law with an index of -$0.1200 \pm 0.0003 \pm 0.0341$. This is equivalent to an increase in abundance of light components. Above the knee, the mean logarithmic mass exhibits a power law trend towards heavier components, which is reversal to the behavior observed in the all-particle energy spectrum. Additionally, the knee position and the change in power-law index are approximately the same. These findings suggest that the knee observed in the all-particle spectrum corresponds to the knee of the light component, rather than the medium-heavy components., Comment: 8 pages, 3 figures

This Letter reports a search for charge-parity ($CP$) symmetry violating nonstandard interactions (NSI) of neutrinos with matter using the NOvA Experiment, and examines their effects on the determination of the standard oscillation parameters. Data from $\nu_{\mu}(\bar{\nu}_{\mu})\rightarrow\nu_{\mu}(\bar{\nu}_{\mu})$ and $\nu_{\mu}(\bar{\nu}_{\mu})\rightarrow\nu_{e}(\bar{\nu}_{e})$ oscillation channels are used to measure the effect of the NSI parameters $\varepsilon_{e\mu}$ and $\varepsilon_{e\tau}$. With 90% CL the magnitudes of the NSI couplings are constrained to be $|\varepsilon_{e\mu}| \, \lesssim 0.3$ and $|\varepsilon_{e\tau}| \, \lesssim 0.4$. A degeneracy at $|\varepsilon_{e\tau}| \, \approx 1.8$ is reported, and we observe that the presence of NSI limits sensitivity to the standard $CP$ phase $\delta_{\tiny\text{CP}}$.

Monochromatic gamma-ray signals constitute a potential smoking gun signature for annihilating or decaying dark matter particles that could relatively easily be distinguished from astrophysical or instrumental backgrounds. We provide an updated assessment of the sensitivity of the Cherenkov Telescope Array (CTA) to such signals, based on observations of the Galactic centre region as well as of selected dwarf spheroidal galaxies. We find that current limits and detection prospects for dark matter masses above 300 GeV will be significantly improved, by up to an order of magnitude in the multi-TeV range. This demonstrates that CTA will set a new standard for gamma-ray astronomy also in this respect, as the world's largest and most sensitive high-energy gamma-ray observatory, in particular due to its exquisite energy resolution at TeV energies and the adopted observational strategy focussing on regions with large dark matter densities. Throughout our analysis, we use up-to-date instrument response functions, and we thoroughly model the effect of instrumental systematic uncertainties in our statistical treatment. We further present results for other potential signatures with sharp spectral features, e.g.~box-shaped spectra, that would likewise very clearly point to a particle dark matter origin., Comment: 44 pages JCAP style (excluding author list and references), 19 figures; minor changes to match published version

With growing application of machine learning (ML) technologies in healthcare, there have been calls for developing techniques to understand and mitigate biases these systems may exhibit. Fair-ness considerations in the development of ML-based solutions for health have particular implications for Africa, which already faces inequitable power imbalances between the Global North and South.This paper seeks to explore fairness for global health, with Africa as a case study. We conduct a scoping review to propose axes of disparities for fairness consideration in the African context and delineate where they may come into play in different ML-enabled medical modalities. We then conduct qualitative research studies with 672 general population study participants and 28 experts inML, health, and policy focused on Africa to obtain corroborative evidence on the proposed axes of disparities. Our analysis focuses on colonialism as the attribute of interest and examines the interplay between artificial intelligence (AI), health, and colonialism. Among the pre-identified attributes, we found that colonial history, country of origin, and national income level were specific axes of disparities that participants believed would cause an AI system to be biased.However, there was also divergence of opinion between experts and general population participants. Whereas experts generally expressed a shared view about the relevance of colonial history for the development and implementation of AI technologies in Africa, the majority of the general population participants surveyed did not think there was a direct link between AI and colonialism. Based on these findings, we provide practical recommendations for developing fairness-aware ML solutions for health in Africa., Comment: 11 pages, 4 figures. arXiv admin note: text overlap with arXiv:2304.02190

Surface ion traps with two-dimensional layouts of trapping regions are natural architectures for storing large numbers of ions and supporting the connectivity needed to implement quantum algorithms. Many of the components and operations needed to fully exploit this architecture have already been demonstrated, including operation at cryogenic temperatures with low heating, low excitation transport, and ion control and detection with integrated photonics. Here we demonstrate a trap that addresses the scaling challenge of increasing power dissipation as the RF electrode increases in size. By raising the RF electrode and removing most of the insulating dielectric layer below it we reduce both ohmic and dielectric power dissipation. We also measure heating rates across a range of motional frequencies and for different voltage sources in a trap with a raised RF electrode but solid dielectric., Comment: 7 pages, 4 figures

The dynamic spectra of pulsars frequently exhibit diverse interference patterns, often associated with parabolic arcs in the Fourier-transformed (secondary) spectra. Our approach differs from previous ones in two ways: first, we extend beyond the traditional Fresnel-Kirchhoff method by using the Green's function of the Helmholtz equation, i.e.\ we consider spherical waves originating from three dimensional space, not from a two dimensional screen. Secondly, the discrete structures observed in the secondary spectrum result from discrete scatterer configurations, namely plasma concentrations in the interstellar medium, and not from the selection of points by the stationary phase approximation. Through advanced numerical techniques, we model both the dynamic and secondary spectra, providing a comprehensive framework that describes all components of the latter spectra in terms of physical quantities. Additionally, we provide a thorough analytical explanation of the secondary spectrum., Comment: 13 pages, 6 figures

Human motion prediction is still an open problem extremely important for autonomous driving and safety applications. Due to the complex spatiotemporal relation of motion sequences, this remains a challenging problem not only for movement prediction but also to perform a preliminary interpretation of the joint connections. In this work, we present a Context-based Interpretable Spatio-Temporal Graph Convolutional Network (CIST-GCN), as an efficient 3D human pose forecasting model based on GCNs that encompasses specific layers, aiding model interpretability and providing information that might be useful when analyzing motion distribution and body behavior. Our architecture extracts meaningful information from pose sequences, aggregates displacements and accelerations into the input model, and finally predicts the output displacements. Extensive experiments on Human 3.6M, AMASS, 3DPW, and ExPI datasets demonstrate that CIST-GCN outperforms previous methods in human motion prediction and robustness. Since the idea of enhancing interpretability for motion prediction has its merits, we showcase experiments towards it and provide preliminary evaluations of such insights here. available code: https://github.com/QualityMinds/cistgcn, Comment: 10 pages, 6 figures

We report on the ongoing effort of improving the determination of the gradient flow scale on the (2+1+1)-flavor HISQ ensembles generated by the MILC collaboration. We compute the scales $\sqrt{t_0}/a$ and $w_0/a$ with the Wilson and Symanzik flow using three discretizations for the action density: clover, Wilson and tree-level Symanzik improved. For the absolute scale setting, we intend to employ the $\Omega$-baryon mass, but are also using the pion decay constant while the $\Omega$-mass calculations are in progress., Comment: 10 pages, 6 figures, contribution to the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31 - August 4, 2023, Fermilab, USA

We study which representations $\rho$ of the fundamental group of a compact oriented surface $X$ admit Higgs data that depend holomorphically on the Riemann surface $\Sigma\,=\, (X,\, J)$ via non-abelian Hodge correspondence. For representations $\rho$ into $\mathrm{SL}(2,\mathbb C)$ we show that holomorphic dependency is equivalent to $\rho$ being unitary. For higher ranks this equivalence fails -- we show the existence of non-unitary and irreducible representations of the fundamental group into $\mathrm{SL}(n,\mathbb C)$ admitting Higgs data that are holomorphic in $\Sigma$, for $n$ large enough., Comment: 14 pages