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This paper presents a novel approach to the analysis of spatial behavior distribution, utilizing weighted Voronoi diagrams. The objective is to map and understand how an experimental subject moves and spends time in various areas of a given space, thus identifying the areas of greatest behavioral interest. The technique entails the partitioning of the space into a grid, the designation of generator points, and the assignment of weights based on the time the subject spends in each region. The data analyzed were derived from multiple experimental sessions in which subjects were exposed to various conditions, including food deprivation, water deprivation, and combined deprivation and no deprivation. The aforementioned conditions resulted in the formation of clearly delineated spatial patterns. Weighted Voronoi diagrams provided a comprehensive and precise representation of these areas of interest, facilitating an in-depth examination of the evolution of behavioral patterns in diverse contexts, such as under different Motivational Operations. This tool offers a valuable perspective for the dynamic study of spatial behaviors in variable experimental settings., Comment: 10 pages, 3 figures

We have analyzed phenology data and jumps in protein configurations with the non-linear forecasting method proposed by May and Sugihara \cite{MS90}. Full plots of prediction quality as a function of dimensionality and forecasting time give fast and valuable information about Complex Systems dynamics., Comment: 5 pages, 8 figures

We present the Black Hole Explorer (BHEX), a mission that will produce the sharpest images in the history of astronomy by extending submillimeter Very-Long-Baseline Interferometry (VLBI) to space. BHEX will discover and measure the bright and narrow "photon ring" that is predicted to exist in images of black holes, produced from light that has orbited the black hole before escaping. This discovery will expose universal features of a black hole's spacetime that are distinct from the complex astrophysics of the emitting plasma, allowing the first direct measurements of a supermassive black hole's spin. In addition to studying the properties of the nearby supermassive black holes M87* and Sgr A*, BHEX will measure the properties of dozens of additional supermassive black holes, providing crucial insights into the processes that drive their creation and growth. BHEX will also connect these supermassive black holes to their relativistic jets, elucidating the power source for the brightest and most efficient engines in the universe. BHEX will address fundamental open questions in the physics and astrophysics of black holes that cannot be answered without submillimeter space VLBI. The mission is enabled by recent technological breakthroughs, including the development of ultra-high-speed downlink using laser communications, and it leverages billions of dollars of existing ground infrastructure. We present the motivation for BHEX, its science goals and associated requirements, and the pathway to launch within the next decade., Comment: Proceedings for SPIE Astronomical Telescopes and Instrumentation

General relativity predicts that black hole images ought to display a bright, thin (and as-of-yet-unresolved) ring. This "photon ring" is produced by photons that explore the strong gravity of the black hole, flowing along trajectories that experience extreme light bending within a few Schwarzschild radii of the horizon before escaping. The shape of the photon ring is largely insensitive to the precise details of the emission from the astronomical source surrounding the black hole and therefore provides a direct probe of the Kerr geometry and its parameters. The Black Hole Explorer (BHEX) is a proposed space-based experiment targeting the supermassive black holes M87* and Sgr A* with radio-interferometric observations at frequencies of 100 GHz through 300 GHz and from an orbital distance of ~30,000 km. This design will enable measurements of the photon rings around both M87* and Sgr A*, confirming the Kerr nature of these sources and delivering sharp estimates of their masses and spins., Comment: Submitted to SPIE Space Telescopes & Instrumentation

The observed radiation from hot gas accreting onto a black hole depends on both the details of the flow and the spacetime geometry. The lensing behavior of a black hole produces a distinctive pattern of autocorrelations within its photon ring that encodes its mass, spin, and inclination. In particular, the time autocorrelation of the light curve is expected to display a series of peaks produced by light echoes of the source, with each peak delayed by the characteristic time lapse $\tau$ between light echoes. However, such peaks are absent from the light curves of observed black holes. Here, we develop an analytical model for such light curves that demonstrates how, even though light echoes always exist in the signal, they do not produce autocorrelation peaks if the characteristic correlation timescale $\lambda_0$ of the source is greater than $\tau$. We validate our model against simulated light curves of a stochastic accretion model ray traced with a general-relativistic code, and then fit the model to an observed light curve for Sgr A*. We infer that $\lambda_0>\tau$, providing an explanation for the absence of light echoes in the time autocorrelations of Sgr A* light curves. Our results highlight the importance for black hole parameter inference of spatially resolving the photon ring via future space-based interferometry., Comment: 5+8 pages, 1+5 figures

Currently envisioned extensions of the Event Horizon Telescope to space will soon target the black hole photon ring: a narrow ring-shaped imprint of a black hole's strong gravity produced in its images by highly bent photon trajectories. In principle, the shape of the photon ring encodes information about the geometry of the underlying black hole spacetime. In practice, however, whether or not this information can be extracted from the ring shape depends on several factors, ranging from the astrophysical details of the emitting source (such as the magnitude of its plasma fluctuations) to the specific configuration of the interferometric array (such as the separation between its telescopes, or the level of noise in its instruments). Here, we employ a phenomenological model to assess the impact of astrophysical fluctuations and instrument noise on the inferred shape of the photon ring. Our systematic study of several astrophysical profiles suggests that this shape can be measured even in the presence of instrument noise across a wide range of baselines. The measurement accuracy and precision appear relatively insensitive to the noise level, up to a sharp threshold beyond which any measurement becomes incredibly challenging (at least without recourse to more sophisticated data analysis methods). Encouragingly, we find that only a few snapshot images are generally needed to overcome the impact of astrophysical fluctuations and correctly infer the ring diameter. Inference becomes more challenging when analyzing the visibility amplitude in a baseline window that is not entirely dominated by a single photon ring. Nevertheless, in most cases, it is still possible to fit a ring shape with the correct fractional asymmetry. These results provide excellent prospects for future precision measurements of black hole spin and fundamental astrophysics via black hole imaging., Comment: 20+1 pages, 13 figures. V2: Minor changes to match the published version

This study proposes an innovative approach to analyze spatial patterns of behavior by integrating information in weighted Voronoi diagrams. The objective of the research is to analyze the temporal distribution of an experimental subject in different regions of a given space, with the aim of identifying significant areas of interest. The methodology employed involves dividing the experimental space, determining representative points, and assigning weights based on the cumulative time the subject spends in each region. This process results in a set of generator points along with their respective weights, thus defining the Voronoi diagram. The study also presents a detailed and advanced perspective for understanding spatial behavioral patterns in experimental contexts., Comment: 10 pages, 4 figures, 2 tables, Submitted to 16th Mexican Conference on Pattern Recognition 2024

Extreme-mass-ratio inspirals consist of binary systems of compact objects, with orders of magnitude differences in their masses, in the regime where the dynamics are driven by gravitational wave emission. The unique nature of extreme-mass-ratio inspirals facilitates the exploration of diverse and stimulating tests related to various aspects of black holes and General Relativity. These tests encompass investigations into the spacetime geometry, the dissipation of the binary system energy and angular momentum, and the impact of the intrinsic non-linear effects of the gravitational interaction. This review accounts for the manifold opportunities for testing General Relativity, ranging from examinations of black hole properties to cosmological and multimessenger tests., Comment: V2. Updated to match published version. V1: 67+19 pages, 2 figures. Review Chapter for the book "Recent Progress on Gravity Tests" (Eds. C. Bambi and A. C\'ardenas-Avenda\~no, Springer Singapore)

In the context of averaging method, we describe a reconstruction of invariant connection-dependent Poisson structures from canonical actions of compact Lie groups on fibered phase spaces. Some symmetry properties of Wong's type equations are derived from the main results., Comment: 12 pages

General relativity's prediction that all black holes are described by the Kerr metric, irrespective of their size, can now be empirically tested using electromagnetic observations of supermassive black holes and gravitational waves from mergers of stellar-mass black holes. In this work, we focus on the electromagnetic side of this test and quantify the constraining power of very-long-baseline-interferometry (VLBI) observations of emission generated by hot gas surrounding supermassive black holes. We demonstrate how to use lensing bands--annular regions on the observer's screen surrounding the critical curve--to constrain the underlying spacetime geometry. Contingent upon a detection of a lensed VLBI feature, the resulting lensing-band framework allows us to exclude spacetimes for which said feature cannot arise from geodesics that traversed the equatorial plane more than once. Focusing on the first indirect image and tests of black-hole uniqueness, we employ a parametrized spacetime as a case study. We find that resolving geometric information that goes beyond the apparent size of the critical curve has the potential to lift degeneracies between different spacetime parameters. Our work thereby quantifies a conservative estimate of the constraining power of VLBI measurements and contributes to a larger effort to simultaneously constrain geometry and astrophysics., Comment: 16 pages, 9 figures + 4 appendices and references. V2: Minor changes to match the published version

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

The intricacies of black hole ringdown analysis are amplified by the absence of a complete set of orthogonal basis functions for quasinormal modes. Although damped sinusoids effectively fit the ringdown signals from binary black hole mergers, the risk of overfitting remains, due to initial transients and nonlinear effects. In light of this challenge, we introduce two methods for extracting quasinormal modes in numerical simulations and qualitatively study how the transient might affect quasinormal mode fitting. In one method, we accurately fit quasinormal modes by using their spatial functional form at constant time hypersurfaces, while in the other method, we exploit both spatial and temporal aspects of the quasinormal modes. Both fitting methods leverage the spatial behavior of quasinormal eigenfunctions to enhance accuracy, outperforming conventional time-only fitting techniques at null infinity. We also show that we can construct an inner product for which the quasinormal eigenfunctions form an orthonormal (but not complete) set. We then conduct numerical experiments involving linearly perturbed Kerr black holes in horizon penetrating, hyperboloidally compactified coordinates, as this setup enables a more precise isolation and examination of the ringdown phenomenon. From solutions to the Teukolsky equation, describing scattering of an ingoing gravitational wave pulse, we find that the contributions from early-time transients can lead to large uncertainties in the fit to the amplitudes of higher overtones ($n\geq 3$). While the methods we discuss here cannot be applied directly to data from merger observations, our findings underscore the persistence of ambiguities in interpreting ringdown signals, even with access to both temporal and spatial information., Comment: 13+6 pages, 12 figures. V2: Minor changes to match the published version

We prove that the closure of the numerical range of a $(n+1)$-periodic and $(2m+1)$-banded Toeplitz operator can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. In contrast to the periodic $3$-banded (or tridiagonal) case, we show an example of a $2$-periodic and $5$-banded Toeplitz operator such that the closure of its numerical range is not equal to the numerical range of a single finite matrix., Comment: 17 pages, 1 figure

In this paper we initiate the study of the forward and backward shifts on the Hardy space of a tree and the little Hardy space of a tree. In particular, we investigate when these shifts are bounded, find the norm of the shifts if they are bounded, characterize the trees in which they are an isometry, compute the spectrum in some concrete examples, and completely determine when they are hypercyclic., Comment: 23 pages

Black hole images are theoretically predicted (under mild astrophysical assumptions) to display a stack of lensed "photon rings" that carry information about the underlying spacetime geometry. Despite vigorous efforts, no such ring has been observationally resolved thus far. However, planning is now actively under way for space missions targeting the first (and possibly the second) photon rings of the supermassive black holes M87* and Sgr A*. In this work, we study interferometric photon ring signatures in time-averaged images of Kerr black holes surrounded by different astrophysical profiles. We focus on the first, most easily accessible photon ring, which has a larger width-to-diameter ratio than subsequent rings and whose image consequently lacks a sharply defined diameter. Nonetheless, we show that it does admit a precise angle-dependent diameter in visibility space, for which the Kerr metric predicts a specific functional form that tracks the critical curve. We find that a measurement of this interferometric ring diameter is possible for most astrophysical profiles, paving the way for precision tests of strong-field general relativity via near-future observations of the first photon ring., Comment: 16 pages, 6 figures. V2: Minor changes to match the published version

This work investigates pretrained audio representations for few shot Sound Event Detection. We specifically address the task of few shot detection of novel acoustic sequences, or sound events with semantically meaningful temporal structure, without assuming access to non-target audio. We develop procedures for pretraining suitable representations, and methods which transfer them to our few shot learning scenario. Our experiments evaluate the general purpose utility of our pretrained representations on AudioSet, and the utility of proposed few shot methods via tasks constructed from real-world acoustic sequences. Our pretrained embeddings are suitable to the proposed task, and enable multiple aspects of our few shot framework., Comment: IEEE ICASSP 2023

Pre-trained model representations have demonstrated state-of-the-art performance in speech recognition, natural language processing, and other applications. Speech models, such as Bidirectional Encoder Representations from Transformers (BERT) and Hidden units BERT (HuBERT), have enabled generating lexical and acoustic representations to benefit speech recognition applications. We investigated the use of pre-trained model representations for estimating dimensional emotions, such as activation, valence, and dominance, from speech. We observed that while valence may rely heavily on lexical representations, activation and dominance rely mostly on acoustic information. In this work, we used multi-modal fusion representations from pre-trained models to generate state-of-the-art speech emotion estimation, and we showed a 100% and 30% relative improvement in concordance correlation coefficient (CCC) on valence estimation compared to standard acoustic and lexical baselines. Finally, we investigated the robustness of pre-trained model representations against noise and reverberation degradation and noticed that lexical and acoustic representations are impacted differently. We discovered that lexical representations are more robust to distortions compared to acoustic representations, and demonstrated that knowledge distillation from a multi-modal model helps to improve the noise-robustness of acoustic-based models., Comment: 5 pages, conference