arXiv subjects

Brendan Miller

Publications and source records attributed to Brendan Miller.

15 recordsLinked to original sources

arXiv2026

Frames from Functional Calculus

We introduce frames generated by applying families of functions to a diagonal operator through functional calculus, with diagonal entries forming a Carleson interpolating sequence. First, for separated spectra contained in a Stolz domain and an angular sector, we prove that systems of fractional operator powers remain frames whenever the step size satisfies the natural angular restriction. This extends earlier results for positive real spectra and permits noninteger powers. We also show that the angular restriction is sharp in general. Second, we give an $\ell^2$-perturbation criterion for frames generated by more general continuous functions, assuming a density condition on a curve containing the spectrum. The results broaden the class of structured frames available in dynamical sampling and related operator-orbit problems.

math.FA↗

arXiv2026

Block Diagonal Carleson Frames

We introduce \textit{block diagonal Carleson frames}, i.e. singly generated dynamical frames in which the generating operator is block diagonal. We classify all such frames when the generating operator is a direct sum of Jordan blocks, the sizes of which are uniformly bounded. Furthermore, block diagonal Carleson frames are shown to enjoy the high redundancy properties observed for Carleson frames. When the generating operator has nonnegative spectrum, we provide a complete description of the redundancy of such frames under the assumption of the existence of natural density.

math.FA↗

arXiv2026

Gabor duals with minimal L1-norm

It is well-known that for a Gabor frame in L2, the canonical dual window is the dual window with the minimal L2-norm. In this paper, we address the problem of finding dual windows for a Gabor frame that minimizes the L1-norm. Since it has been shown that minimizing the L1-norm often coincides with minimizing the L0-norm, we also investigate the support of the dual Gabor window that achieves the minimal L1-norm.

math.FA↗

arXiv2025

Demystifying Carleson Frames

We study spanning properties of Carleson systems and prove a recent conjecture on frame subsequences of Carleson frames. In particular, we show that if $\{T^k\varphi\}_{k=0}^\infty$ is a Carleson frame, then every subsequence of the form $\{T^{Nk+j_k}\varphi\}_{k=0}^\infty$ where $N\in\mathbb{N}$ and $0 \leq j_k < N$ is also a frame.

math.FA↗

arXiv2024

Reconstructing Graph Signals from Noisy Dynamical Samples

We investigate the dynamical sampling space-time trade-off problem within a graph setting. Specifically, we derive necessary and sufficient conditions for space-time sampling that enable the reconstruction of an initial band-limited signal on a graph. Additionally, we develop and test numerical algorithms for approximating the optimal placement of sensors on the graph to minimize the mean squared error when recovering signals from time-space measurements corrupted by i.i.d.~additive noise. Our numerical experiments demonstrate that our approach outperforms previously proposed algorithms for related problems.

cs.IT↗

arXiv2024

Kadec-type theorems for sampled group orbits

We extend the classical Kadec 1/4 theorem for systems of exponential functions on an interval to frames and atomic decompositions formed by sampling an orbit of a vector under an isometric group representation.

math.FA↗

arXiv2024

Reconstruction algorithms for source term recovery from dynamical samples in catalyst models

This paper investigates the problem of recovering source terms in abstract initial value problems (IVP) commonly used to model various scientific phenomena in physics, chemistry, economics, and other fields. We consider source terms of the form $F=h+\eta$, where $\eta$ is a Lipschitz continuous background source. The primary objective is to estimate the unknown parameters of non-instantaneous sources $h(t)=\sum\limits_{j=0}^M h_je^{-\rho_j(t-t_j)}\chi_{[t_j,\infty)}(t)$, such as the decay rates, initial intensities and activation times. We present two novel recovery algorithms that employ distinct sampling methods of the solution of the IVP. Algorithm 1 combines discrete and weighted average measurements, whereas Algorithm 2 uses a different variant of weighted average measurements. We analyze the performance of these algorithms, providing upper bounds on the recovery errors of the model parameters. Our focus is on the structure of the dynamical samples used by the algorithms and on the error guarantees they yield.

math.DS↗

arXiv2023

On Low-Rank Convex-Convex Quadratic Fractional Programming

We present an efficient algorithm for solving fractional programming problems whose objective functions are the ratio of a low-rank quadratic to a positive definite quadratic with convex constraints. The proposed algorithm for these convex-convex problems is based on the Shen-Yu Quadratic Transform which finds stationary points of concave-convex sum-of-ratios problems. We further use elements of the algorithm proposed in [arXiv:1802.10192] and the classic Dinkelbach approach to ensure convergence. We show that our algorithm performs better than previous algorithms for low-rank problems.

math.OC↗

arXiv2019

Agent Probing Interaction Policies

Reinforcement learning in a multi agent system is difficult because these systems are inherently non-stationary in nature. In such a case, identifying the type of the opposite agent is crucial and can help us address this non-stationary environment. We have investigated if we can employ some probing policies which help us better identify the type of the other agent in the environment. We've made a simplifying assumption that the other agent has a stationary policy that our probing policy is trying to approximate. Our work extends Environmental Probing Interaction Policy framework to handle multi agent environments.

cs.MA↗

arXiv2019

Sub-Eddington super-massive black hole activity in Fornax early type galaxies

We characterize the incidence and intensity of low-level super-massive black hole activity within the Fornax cluster, through X-ray observations of the nuclei of 29 quiescent early-type galaxies. Using the \textit{Chandra X-ray Telescope}, we target 17 galaxies from the HST Fornax Cluster Survey, down to a uniform (3$σ$) limiting X-ray luminosity threshold of $5\cdot10^{38}$ergs$^{-1}$, which we combine with deeper, archival observations for an additional 12 galaxies. A nuclear X-ray point-source is detected in 11 out of 29 targets. After accounting for the low mass X-ray binary contamination to the nuclear X-ray signal, the X-ray active fraction is measured at $26.6\% \pm 9.6\%$. The results from this analysis are compared to similar investigations targeting quiescent early types in the Virgo cluster, as well as the field. After correcting for the different mass distributions, the measured Fornax active fraction is less than the field fraction, at more than 3$σ$, confirming that the funneling of gas to the nuclear regions of cluster members is inhibited compared to those galaxies in the field. At the same time, we find no statistically significant difference between Fornax and Virgo galaxies, with only marginal evidence for a lower active fraction in Fornax (1 $σ$); if real, owing to Fornax's higher galaxy number density, this could indicate that galaxy-galaxy interactions are more effective at gas removal than galaxy-gas effects.

astro-ph.HE↗

arXiv2012

Assessing luminosity correlations via cluster analysis: Evidence for dual tracks in the radio/X-ray domain of black hole X-ray binaries

[abridged] The radio:X-ray correlation for hard and quiescent state black hole X-ray binaries is critically investigated in this paper. New observations of known sources, along with newly discovered ones, have resulted in an increasingly large number of outliers lying well outside the scatter about the quoted best-fit relation. Here, we employ and compare state of the art data clustering techniques in order to identify and characterize different data groupings within the radio:X-ray luminosity plane for 18 hard and quiescent state black hole X-ray binaries with nearly simultaneous multi-wavelength coverage. Linear regression is then carried out on the clustered data to infer the parameters of a relationship of the form {ell}_{r}=alpha+beta {ell}_x through a Bayesian approach (where {ell} denotes log lum). We conclude that the two cluster model, with independent linear fits, is a significant improvement over fitting all points as a single cluster. While the upper track slope (0.63\pm0.03) is consistent, within the errors, with the fitted slope for the 2003 relation (0.7\pm0.1), the lower track slope (0.98\pm0.08) is not consistent with the upper track, nor it is with the widely adopted value of ~1.4 for the neutron stars. The two luminosity tracks do not reflect systematic differences in black hole spins as estimated either from reflection, or continuum fitting method. These results are insensitive to the selection of sub-samples, accuracy in the distances, and to the treatment of upper limits. Besides introducing a further level of complexity in understanding the interplay between synchrotron and Comptonised emission from black hole X-ray binaries, the existence of two tracks in the radio:X-ray domain underscores that a high level of caution must be exercised when employing black hole luminosity relations for the purpose of estimating a third parameter, such as distance or mass.

astro-ph.HE↗

arXiv2012

AMUSE-Field I: Nuclear X-ray Properties of Local Field and Group Spheroids across the Stellar Mass Scale

We present the first results from AMUSE-Field, a Chandra survey designed to characterize the occurrence and intensity of low-level accretion onto supermassive black holes (SMBHs) at the center of local early-type field galaxies. This is accomplished by means of a Large Program targeting a distance-limited (<30 Mpc) sample of 103 early types spanning a wide range in stellar masses. We acquired new ACIS-S observations for 61 objects down to a limiting (0.3-10 keV) luminosity of 2.5x10^38 erg/s, and we include an additional 42 objects with archival (typically deeper) coverage. A nuclear X-ray source is detected in 52 out of the 103 galaxies. After accounting for potential contamination from low-mass X-ray binaries, we estimate that the fraction of accreting SMBHs within the sample is 45+/-7 percent, which sets a firm lower limit on the occupation fraction within the field. The measured nuclear X-ray luminosities are invariably highly sub-Eddington, with -8<log(L_X/L_Edd)<-4. As also found in a companion survey targeting Virgo early types, the active fraction increases with increasing host galaxy stellar mass, reflective of "Eddington incompleteness" within the lower-mass objects. For the Field sample, the average nuclear X-ray luminosity scales with the host stellar mass as M_star^(0.71+/-0.10), with an intrinsic scatter of 0.73+/-0.09 dex. A majority of the AMUSE-Field galaxies (78%) inhabits groups, enabling us to investigate the influence of group richness upon nuclear activity. We see no evidence for a positive correlation between nuclear X-ray luminosity, normalized to host properties, and galaxy density. Rather, while the scatter is substantial, it appears that the Eddington-scaled X-ray luminosity of group members may be slightly lower than for isolated galaxies, and that this trend continues to cluster early-types.

astro-ph.HE↗

arXiv2012

The role of environment in low-level active galactic nucleus activity: no evidence for cluster enhancement

We use the AMUSE-Virgo and AMUSE-Field surveys for nuclear X-ray emission in early-type galaxies to conduct a controlled comparison of low-level supermassive black hole activity within cluster and field spheroids. While both the Virgo and the Field samples feature highly sub-Eddington X-ray luminosities (log L_x/L_Edd between -8 and -4), we find that after accounting for the influence of host galaxy stellar mass, the field early-type galaxies tend toward marginally greater (0.38+/-0.14 dex) nuclear X-ray luminosities, at a given black hole mass, than their cluster counterparts. This trend is qualitatively consistent with the field black holes having access to a greater reservoir of fuel, plausibly in the form of cold gas located near the nucleus. We are able to rule out at high confidence the alternative of enhanced X-ray activity within clusters. Presuming nuclear X-ray emission correlates with the total energy and momentum output of these weakly accreting black holes, this indicates that low-level active galactic nucleus feedback is not generally stronger within typical cluster galaxies than in the field. These results confirm that for most cluster early-type galaxies (i.e., excluding brightest cluster galaxies) direct environmental effects, such as gas stripping, are more relevant in quenching star formation.

astro-ph.HE↗

arXiv2006

Revealing the Nature of Algol Disks through Optical and UV Spectroscopy, Synthetic Spectra, and Tomography of TT Hydrae

We have developed a systematic procedure to study the disks in Algol-type binaries using spectroscopic analysis, synthetic spectra, and tomography. We analyzed 119 H-alpha spectra of TT Hya, an Algol-type eclipsing interacting binary, collected from 1985-2001. The new radial velocities enabled us to derive reliable orbital elements, including a small non-zero eccentricity, and to improve the accuracy of the absolute dimensions of the system. High resolution IUE spectra were also analyzed to study the formation of the ultraviolet lines and continuum. Synthetic spectra of the iron curtain using our new shellspec program enabled us to derive a characteristic disk temperature of 7000K. We have demonstrated that the UV emission lines seen during total primary eclipse cannot originate from the accretion disk, but most likely arise from a hotter disk-stream interaction region. The synthetic spectra of the stars, disk, and stream allowed us to derive a lower limit to the mass transfer rate of 2e-10 solar masses per year. Doppler tomography of the observed H-alpha profiles revealed a distinct accretion disk. The difference spectra produced by subtracting the synthetic spectra of the stars resulted in an image of the disk, which virtually disappeared once the composite synthetic spectra of the stars and disk were used to calculate the difference spectra. An intensity enhancement of the resulting tomogram revealed images of the gas stream and an emission arc. We successfully modeled the gas stream using shellspec and associated the emission arc with an asymmetry in the accretion disk.

astro-ph↗

arXiv2005

A Study of Synthetic and Observed H_alpha Spectra of TT Hydrae

The formation and properties of accretion discs and circumstellar material in Algol-type systems is not very well understood. In order to study the underlying physics of these structures, we have calculated synthetic Halpha spectra of TT Hya, which is an Algol-type eclipsing binary with an accretion disc. Both the primary and secondary stars were considered in the calculations as well as a disc surrounding the primary. The Roche model for the secondary star was assumed. The synthetic spectra cover all the phases including primary eclipse and are compared with the observed spectra. The influence of various effects and free parameters of the disc on the emerging spectrum was studied. This enabled us to put some constraints on the geometry, temperature, density and velocity fields within the disc. Differences found between the observed and synthetic spectra unravel the existence of a gas stream as well as a hotter disc-gas interaction region. An additional cooler circumstellar region between the C1 and C2 Roche surfaces is suggested to account for various observed effects. A new computer code called {\sc{shellspec}} was created for this purpose and is briefly described in this work as well. It is designed to solve simple radiative transfer along the line of sight in 3D moving media. The scattered light from a central object is taken into account assuming an optically thin environment. Output intensities are then integrated through the 2D projection surface of a 3D object. The assumptions of the code include LTE and optional known state quantities and velocity fields in 3D.

astro-ph↗