Search

In this paper we generalize Krylov's theory on parameter-dependent stochastic differential equations to the framework of rough stochastic differential equations (rough SDEs), as initially introduced by Friz, Hocquet and L\^e. We consider a stochastic equation of the form $$ dX_t^\zeta = b_t(\zeta,X_t^\zeta) \ dt + \sigma_t(\zeta,X_t^\zeta) \ dB_t + \beta_t (\zeta,X_t^\zeta) d\mathbf{W}_t,$$ where $\zeta$ is a parameter, $B$ denotes a Brownian motion and $\mathbf{W}$ is a deterministic H\"older rough path. We investigate the conditions under which the solution $X$ exhibits continuity and/or differentiability with respect to the parameter $\zeta$ in the $\mathscr{L}$-sense, as defined by Krylov. As an application, we present an existence-and-uniqueness result for a class of rough partial differential equations (rough PDEs) of the form $$-du_t = L_t u_t dt + \Gamma_t u_t d\mathbf{W}_t, \quad u_T =g.$$ We show that the solution admits a Feynman--Kac type representation in terms of the solution of an appropriate rough SDE, where the initial time and the initial state play the role of parameters.

Deep learning models have shown promise in histopathology image analysis, but their opaque decision-making process poses challenges in high-risk medical scenarios. Here we introduce HIPPO, an explainable AI method that interrogates attention-based multiple instance learning (ABMIL) models in computational pathology by generating counterfactual examples through tissue patch modifications in whole slide images. Applying HIPPO to ABMIL models trained to detect breast cancer metastasis reveals that they may overlook small tumors and can be misled by non-tumor tissue, while attention maps$\unicode{x2014}$widely used for interpretation$\unicode{x2014}$often highlight regions that do not directly influence predictions. By interpreting ABMIL models trained on a prognostic prediction task, HIPPO identified tissue areas with stronger prognostic effects than high-attention regions, which sometimes showed counterintuitive influences on risk scores. These findings demonstrate HIPPO's capacity for comprehensive model evaluation, bias detection, and quantitative hypothesis testing. HIPPO greatly expands the capabilities of explainable AI tools to assess the trustworthy and reliable development, deployment, and regulation of weakly-supervised models in computational pathology.

The Next-generation Extended Wavelength-MUltiband Sub/millimeter Inductance Camera (NEW-MUSIC) on the Leighton Chajnantor Telescope (LCT) will be a first-of-its-kind, six-band, transmillimeter-wave ("trans-mm") polarimeter covering 2.4 octaves of spectral bandwidth to open a new window on the trans-mm time-domain frontier, in particular new frontiers in energy, density, time, and magnetic field. NEW-MUSIC's broad spectral coverage will also enable the use of the Sunyaev-Zeldovich effects to study accretion, feedback, and dust content in the hot gaseous haloes of galaxies and galaxy clusters. Six-band spectral energy distributions, with polarization information, will yield new insights into stellar and planetary nurseries. NEW-MUSIC will employ hierarchical, phased arrays of polarization-sensitive superconducting slot-dipole antennas, coupled to photolithographic bandpass filters, to nearly optimally populate LCT's 14' field-of-view with six spectral bands over 80-420 GHz (1:5.25 spectral dynamic range; 2.4 octaves). Light will be routed to Al or AlMn microstripline-coupled, parallel-plate capacitor, lumped-element kinetic inductance detectors (MS-PPC-LEKIDs), an entirely new KID architecture that substantially enhances design flexibility while providing background-limited performance. Innovative, wide-bandwidth, etched silicon structures will be used to antireflection-treat the back-illuminated focal plane. NEW-MUSIC will cost-effectively reuse much of the MUSIC instrument, initially deploying a quarter-scale focal plane capable of the bulk of NEW-MUSIC science followed later by a full-FoV focal plane needed for NEW-MUSIC wide-area survey science., Comment: 42 pages, 16 figures. This version includes minor corrections relative to the version published at the SPIE website. Versions 2 and 3 include only affiliation corrections

Critical single-particle fluctuations associated with particle displacements are inherent to simple glass-forming liquids in the limit of large dimensions and leave a pseudo-critical trace across all finite dimensions. This characteristic could serve as a crucial test for distinguishing between theories of glass formation. We here examine these critical fluctuations, as captured by the well-established non-Gaussian parameter, within both mode-coupling theory (MCT) and dynamical mean-field theory (DMFT) across dimensions for hard sphere liquids and for the minimally structured Mari--Kurchan model. We establish general scaling laws relevant to any liquid dynamics theory in large dimensions and show that the dimensional scalings predicted by MCT are inconsistent with those from DMFT. Simulation results for hard spheres in moderately high dimensions align with the DMFT scenario, reinforcing the relevance of mean-field theory for capturing glass physics in finite dimensions. We identify potential adjustments to MCT to account for certain mean-field physics. Our findings also highlight that local structure and spatial dimensionality can affect single-particle critical fluctuations in non-trivial ways., Comment: 42 pages, 9 figures

This paper discusses the feasibility of thin-shell wormholes in spacetimes of embedding class one admitting a one-parameter group of conformal motions. It is shown that the surface energy density $\sigma$ is positive, while the surface pressure $\mathcal{P}$ is negative, resulting in $\sigma +\mathcal{P}<0$, thereby signaling a violation of the null energy condition, a necessary condition for holding a wormhole open. For a Morris-Thorne wormhole, matter that violates the null energy condition is referred to as "exotic." For the thin-shell wormholes in this paper, however, the violation has a physical explanation since it is a direct consequence of the embedding theory in conjunction with the assumption of conformal symmetry. These properties avoid the need to hypothesize the existence of the highly problematical exotic matter., Comment: 10 pages, no figures

The concept of signatures and expected signatures is vital in data science, especially for sequential data analysis. The signature transform, a Cartan type development, translates paths into high-dimensional feature vectors, capturing their intrinsic characteristics. Under natural conditions, the expectation of the signature determines the law of the signature, providing a statistical summary of the data distribution. This property facilitates robust modeling and inference in machine learning and stochastic processes. Building on previous work by the present authors [Unified signature cumulants and generalized Magnus expansions, FoM Sigma '22] we here revisit the actual computation of expected signatures, in a general semimartingale setting. Several new formulae are given. A log-transform of (expected) signatures leads to log-signatures (signature cumulants), offering a significant reduction in complexity., Comment: arXiv admin note: text overlap with arXiv:2102.03345

We present optical/UV observations and the spectroscopic classification of the transient AT2023vto as a tidal disruption event (TDE) at z = 0.4846. The spectrum is dominated by a broad He II $\lambda$4686 emission line, with a width of ~ $3.76 \times 10^4$ km/s and a blueshift of ~ $1.05 \times 10^4$ km/s, classifying it as a member of the TDE-He class. The light curve exhibits a long rise and decline timescale, with a large peak absolute magnitude of M$_g$ ~ -23.6, making it the most luminous of the classical optical TDEs (H, H+He, He) discovered to date by about 2 mag (and ~ 4 mag compared to the mean of the population). The light curve exhibits a persistent blue color of g - r ~ -0.4 mag throughout its evolution, similar to other TDEs, but distinct from supernovae. We identify the host galaxy of AT2023vto in archival Pan-STARRS images and find that the transient is located at the galaxy center, and that its inferred central black hole mass is ~ $10^7~M_{\odot}$. Modeling the light curves of AT2023vto, we find that it resulted from the disruption of a ~ 9 $M_{\odot}$ star by a ~$10^7~M_{\odot}$ supermassive black hole. The star mass is about 5 times larger than the highest star masses previously inferred in TDEs, and the black hole mass is at the high end of the distribution. AT2023vto is comparable in luminosity and timescale to some putative TDEs (with a blue featureless continuum), as well as to the mean of the recently identified population of ambiguous nuclear transients (ANTs), although the latter are spectroscopically distinct and tend to have longer timescales. ANTs have been speculated to arise from tidal disruptions of massive stars, perhaps in active galactic nuclei, and AT2023vto may represent a similar case but in a dormant black hole, thereby bridging the TDE and ANT populations. We anticipate that Rubin Observatory / LSST will uncover similar luminous TDEs to z ~ 3., Comment: 21 pages, 8 figures

Radio frequency (rf) receivers using Rydberg atoms offer appealing features over classical sensors, such as their size, frequency tuning range, and lack of field absorption. In this work, we extend the application space by demonstrating a Rydberg atom rf polarimeter. Using rf heterodyne with three independent and orthogonal local oscillators, we are able to extract the polarization ellipse of the field in three dimensions, in addition to the total amplitude of the field. We use the relative phases and amplitudes of the three generated heterodyne signals to measure the field amplitudes and phases along three cardinal axes giving the full three-dimensional polarization. We demonstrate this polarization measurement for incoming fields at different angles around the sensor. Lastly, we investigate the reception of data symbols encoded in the horizontal and vertical signal field polarizations and the phase between them. Our measurements yield an amplitude noise of 57 $\mu$V/m/$\sqrt{\text{Hz}}$ for horizontal polarization, 66 $\mu$V/m/$\sqrt{\text{Hz}}$ for vertical polarization, and a standard deviation of 0.094 rad in the phase between the field components., Comment: 10 pages, 6 figures

We present the most comprehensive catalog to date of Type I Superluminous Supernovae (SLSNe), a class of stripped envelope supernovae (SNe) characterized by exceptionally high luminosities. We have compiled a sample of 262 SLSNe reported through 2022 December 31. We verified the spectroscopic classification of each SLSN and collated an exhaustive data set of UV, optical and IR photometry from both publicly available data and our own FLEET observational follow-up program, totaling over 30,000 photometric detections. Using these data we derive observational parameters such as the peak absolute magnitudes, rise and decline timescales, as well as bolometric luminosities, temperature and photospheric radius evolution for all SLSNe. Additionally, we model all light curves using a hybrid model that includes contributions from both a magnetar central engine and the radioactive decay of $^{56}$Ni. We explore correlations among various physical and observational parameters, and recover the previously found relation between ejecta mass and magnetar spin, as well as the overall progenitor pre-explosion mass distribution with a peak at $\approx 6.5$ M$_\odot$. We find no significant redshift dependence for any parameter, and no evidence for distinct sub-types of SLSNe. We find that $< 3$\% of SLSNe are best fit with a significant contribution from radioactive decay $\gtrsim 50$\%, representing a set of relatively dim and slowly declining SNe. We provide several analytical tools designed to simulate typical SLSN light curves across a broad range of wavelengths and phases, enabling accurate K-corrections, bolometric scaling calculations, and inclusion of SLSNe in survey simulations or future comparison works. The complete catalog, including all of the photometry, models, and derived parameters, is made available as an open-source resource on GitHub., Comment: 59 pages, 22 Figures, Submitted to MNRAS

As survey methods adapt to technological and societal changes, a growing body of research seeks to understand the tradeoffs associated with various sampling methods and administration modes. We show how the NSF-funded 2022 Collaborative Midterm Survey (CMS) can be used as a dynamic and transparent framework for evaluating which sampling approaches - or combination of approaches - are best suited for various research goals. The CMS is ideally suited for this purpose because it includes almost 20,000 respondents interviewed using two administration modes (phone and online) and data drawn from random digit dialing, random address-based sampling, a probability-based panel, two nonprobability panels, and two nonprobability marketplaces. The analysis considers three types of population benchmarks (election data, administrative records, and large government surveys) and focuses on the national-level estimates as well as oversamples in three states (California, Florida, and Wisconsin). In addition to documenting how each of the survey strategies performed, we develop a strategy to assess how different combinations of approaches compare to different population benchmarks in order to guide researchers combining sampling methods and sources. We conclude by providing specific recommendations to public opinion and election survey researchers and demonstrating how our approach could be applied to a large government survey conducted at regular intervals to provide ongoing guidance to researchers, government, businesses, and nonprofits regarding the most appropriate survey sampling and administration methods.

The skew-stickiness-ratio (SSR), examined in detail by Bergomi in his book, is critically important to options traders, especially market makers. We present a model-free expression for the SSR in terms of the characteristic function. In the diffusion setting, it is well-known that the short-term limit of the SSR is 2; a corollary of our results is that this limit is $H+3/2$ where $H$ is the Hurst exponent of the volatility process. The general formula for the SSR simplifies and becomes particularly tractable in the affine forward variance case. We explain the qualitative behavior of the SSR with respect to the shape of the forward variance curve, and thus also path-dependence of the SSR., Comment: 22 pages, 4 figures

The rapid advancements in quantum computing necessitate a scientific and rigorous approach to the construction of a corresponding software ecosystem, a topic underexplored and primed for systematic investigation. This chapter takes an important step in this direction: It presents scientific considerations essential for building a quantum software ecosystem that makes quantum computing available for scientific and industrial problem solving. Central to this discourse is the concept of hardware-software co-design, which fosters a bidirectional feedback loop from the application layer at the top of the software stack down to the hardware. This approach begins with compilers and low-level software that are specifically designed to align with the unique specifications and constraints of the quantum processor, proceeds with algorithms developed with a clear understanding of underlying hardware and computational model features, and extends to applications that effectively leverage the capabilities to achieve a quantum advantage. We analyze the ecosystem from two critical perspectives: the conceptual view, focusing on theoretical foundations, and the technical infrastructure, addressing practical implementations around real quantum devices necessary for a functional ecosystem. This approach ensures that the focus is towards promising applications with optimized algorithm-circuit synergy, while ensuring a user-friendly design, an effective data management and an overall orchestration. Our chapter thus offers a guide to the essential concepts and practical strategies necessary for developing a scientifically grounded quantum software ecosystem.

We present a new deep learning paradigm for the generation of sparse approximate inverse (SPAI) preconditioners for matrix systems arising from the mesh-based discretization of elliptic differential operators. Our approach is based upon the observation that matrices generated in this manner are not arbitrary, but inherit properties from differential operators that they discretize. Consequently, we seek to represent a learnable distribution of high-performance preconditioners from a low-dimensional subspace through a carefully-designed autoencoder, which is able to generate SPAI preconditioners for these systems. The concept has been implemented on a variety of finite element discretizations of second- and fourth-order elliptic partial differential equations with highly promising results., Comment: 15 pages, 8 figures, International conference on Computational Science

We perform a detailed dynamical system analysis for the behaviour of a Dirac-Born-Infeld (DBI) field in a spatially closed Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmology. The DBI field is characterised by a potential and brane tension. We study power-law or exponential functions for the potential and tension. We find that in a spatially closed FLRW cosmology, a DBI field in the ultra-relativistic limit allows for a broader range of initial conditions resulting in a bouncing universe than in the non-relativistic limit. We further note that the range of initial conditions allowing for a bounce is larger if we consider power-law functions for the potential and tension, compared to the exponential case. Our dynamical analysis shows that a DBI field does not exhibit stable cyclical behaviour, including the case in which a negative cosmological constant is present., Comment: 18 pages, 5 figures, 3 tables

Numerous applications in biology, statistics, science, and engineering require generating samples from high-dimensional probability distributions. In recent years, the Hamiltonian Monte Carlo (HMC) method has emerged as a state-of-the-art Markov chain Monte Carlo technique, exploiting the shape of such high-dimensional target distributions to efficiently generate samples. Despite its impressive empirical success and increasing popularity, its wide-scale adoption remains limited due to the high computational cost of gradient calculation. Moreover, applying this method is impossible when the gradient of the posterior cannot be computed (for example, with black-box simulators). To overcome these challenges, we propose a novel two-stage Hamiltonian Monte Carlo algorithm with a surrogate model. In this multi-fidelity algorithm, the acceptance probability is computed in the first stage via a standard HMC proposal using an inexpensive differentiable surrogate model, and if the proposal is accepted, the posterior is evaluated in the second stage using the high-fidelity (HF) numerical solver. Splitting the standard HMC algorithm into these two stages allows for approximating the gradient of the posterior efficiently, while producing accurate posterior samples by using HF numerical solvers in the second stage. We demonstrate the effectiveness of this algorithm for a range of problems, including linear and nonlinear Bayesian inverse problems with in-silico data and experimental data. The proposed algorithm is shown to seamlessly integrate with various low-fidelity and HF models, priors, and datasets. Remarkably, our proposed method outperforms the traditional HMC algorithm in both computational and statistical efficiency by several orders of magnitude, all while retaining or improving the accuracy in computed posterior statistics.

In physical science, the concept of \emph{emergence} is often used to describe phenomena that occur at macroscopic scales but not at microscopic scales. The latter is usually referred to as a \emph{fundamental property} and the former as an \emph{emergent property}. In this paper, noncommutative geometry, often viewed as an offshoot of string theory, is the primary fundamental theory that gives rise to macroscopic wormholes and their properties, thereby becoming an emergent phenomenon. As a consequence of these considerations, we will reexamine the boundary conditions that characterize a Morris-Thorne wormhole, resulting in a modification of the wormhole structure., Comment: 10 pages, no figures. arXiv admin note: text overlap with arXiv:2312.08392

Multiplexed imaging data are revolutionizing our understanding of the composition and organization of tissues and tumors. A critical aspect of such tissue profiling is quantifying the spatial relationship relationships among cells at different scales from the interaction of neighboring cells to recurrent communities of cells of multiple types. This often involves statistical analysis of 10^7 or more cells in which up to 100 biomolecules (commonly proteins) have been measured. While software tools currently cater to the analysis of spatial transcriptomics data, there remains a need for toolkits explicitly tailored to the complexities of multiplexed imaging data including the need to seamlessly integrate image visualization with data analysis and exploration. We introduce SCIMAP, a Python package specifically crafted to address these challenges. With SCIMAP, users can efficiently preprocess, analyze, and visualize large datasets, facilitating the exploration of spatial relationships and their statistical significance. SCIMAP's modular design enables the integration of new algorithms, enhancing its capabilities for spatial analysis., Comment: 6 pages, 1 figure

We present results from a search for radio emission in 77 stellar systems hosting 140 exoplanets, predominantly within 17.5 pc using the Very Large Array (VLA) at $4-8$ GHz. This is the largest and most sensitive search to date for radio emission in exoplanetary systems in the GHz frequency range. We obtained new observations of 58 systems, and analyzed archival observations of an additional 19 systems. Our choice of frequency and volume limit are motivated by radio detections of ultracool dwarfs (UCDs), including T dwarfs with masses at the exoplanet threshold of $\sim\!13\,M_J$. Our surveyed exoplanets span a mass range of $\approx\,10^{-3}-10\,M_J$ and semi-major axes of $\approx\,10^{-2}-10\,$AU. We detect a single target - GJ 3323 (M4) hosting two exoplanets with minimum masses of 2 and 2.3$\,M_\oplus$ - with a circular polarization fraction of $\approx\,40\%$; the radio luminosity agrees with its known X-ray luminosity and the G\"udel-Benz relation for stellar activity suggesting a likely stellar origin, but the high circular polarization fraction may also be indicative of star-planet interaction. For the remaining sources our $3\sigma$ upper limits are generally $L_\nu\lesssim\,10^{12.5}\,\mathrm{erg}\,\mathrm{s}^{-1}\,\mathrm{Hz}^{-1}$, comparable to the lowest radio luminosities in UCDs. Our results are consistent with previous targeted searches of individual systems at GHz frequencies while greatly expanding the sample size. Our sensitivity is comparable to predicted fluxes for some systems considered candidates for detectable star-planet interaction. Observations with future instruments such as the Square Kilometer Array and Next Generation Very Large Array will be necessary to further constrain emission mechanisms from exoplanet systems at GHz frequencies., Comment: Submitted to ApJ, 18 pages, 8 figures

In previous work [Phys. Rev. X 5, 021020 (2015)], it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier-space in the sense that the the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. In this work, we exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice. This is in contrast to real-space hard-spheres, whose densest configuration is conjectured to be disordered. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions $d=2$-$8$., Comment: 9 pages; 6 figures

We study the causal dynamics of an embedded null horizon foliated by marginally outer trapped surfaces (MOTS) for a locally rotationally symmetric background spacetime subjected to linear perturbations. We introduce a simple procedure which characterizes the transition of the causal character of the null horizon. We apply our characterization scheme to non-dissipative perturbations of the Schwarzschild and spatially homogeneous backgrounds. For the latter, a linear equation of state was imposed. Assuming a harmonic decomposition of the linearized field equations, we clarify the variables of a formal solution to the linearized system that determine how the null horizon evolves. For both classes of backgrounds, the shear and vorticity 2-vectors are essential to the characterization, and their roles are made precise. Finally, we discuss aspects of the relationship between the characterizing conditions. Various properties related to the self-adjointness of the MOTS stability operator are extensively discussed., Comment: 18 pages, no figures, all comments are welcome

Physics-informed neural networks (PINNs) provide a means of obtaining approximate solutions of partial differential equations and systems through the minimisation of an objective function which includes the evaluation of a residual function at a set of collocation points within the domain. The quality of a PINNs solution depends upon numerous parameters, including the number and distribution of these collocation points. In this paper we consider a number of strategies for selecting these points and investigate their impact on the overall accuracy of the method. In particular, we suggest that no single approach is likely to be ``optimal'' but we show how a number of important metrics can have an impact in improving the quality of the results obtained when using a fixed number of residual evaluations. We illustrate these approaches through the use of two benchmark test problems: Burgers' equation and the Allen-Cahn equation., Comment: 15 pages, 8 figures, 2 tables. Accepted for publication in the conference proceedings of the International Conference on Computational Science (ICCS) 2024

We report measurements characterizing the performance of a kinetic inductance detector array designed for a wavelength of 25 microns and very low optical background level suitable for applications such as a far-infrared instrument on a cryogenically cooled space telescope. In a pulse counting mode of operation at low optical flux, the detectors can resolve individual 25-micron photons. In an integrating mode, the detectors remain photon noise limited over more than six orders of magnitude in absorbed power from 70 zW to 200 fW, with a limiting NEP of 4.6 x 10^-20 W/rtHz at 1 Hz. In addition, the detectors are highly stable with flat power spectra under optical load down to 1 mHz. Operational parameters of the detector are determined including the efficiency of conversion of the incident optical power into quasiparticles in the aluminum absorbing element and the quasiparticle self-recombination constant., Comment: 35 pages, 18 figures

We present a dynamical system formulation for inhomogeneous LRS-II spacetimes using the covariant 1+1+2 decomposition approach. Our approach describes the LRS-II dynamics from the point of view of a comoving observer. Promoting the covariant radial derivatives of the covariant dynamical quantities to new dynamical variables and utilizing the commutation relation between the covariant temporal and radial derivatives, we were able to construct an autonomous system of first-order ordinary differential equations along with some purely algebraic constraints. Using our dynamical system formulation we found several interesting features in the LRS-II phase space with dust, one of them being that the homogeneous solutions constitute an invariant submanifold. For the particular case of LTB, we were also able to recover the previously known result that an expanding LTB tends to Milne in the absence of a cosmological constant, providing a potential validation of our formalism., Comment: JCAP accepted version. Acknowledgement modified

We consider a double polytropic cosmological fluid and demonstrate that, when one constituent resembles a bare cosmological constant while the other emulates a generalized Chaplygin gas, a good description of the Universe's large-scale dynamics is obtained. In particular, our double polytropic reduces to the Murnaghan equation of state, whose applications are already well established in solid state physics and classical thermodynamics. Intriguingly, our model approximates the conventional $\Lambda$CDM paradigm while reproducing the collective effects of logotropic and generalized Chaplygin fluids across different regimes. To check the goodness of our fluid description, we analyze first order density perturbations, refining our model through various orders of approximation, utilizing $\sigma_8$ data alongside other cosmological data sets. Encouraging results suggest that our model, based on the Murnaghan equation of state, outperforms the standard cosmological background within specific approximate regimes and, on the whole, surpasses the standard phenomenological reconstruction of dark energy., Comment: 13 pages, 3 figures, 1 table

We introduce an invariant of negative definite plumbed knot complements unifying knot lattice homology, due to Ozsv\'ath, Stipsicz, and Szab\'o, and the BPS $q$-series of Gukov and Manolescu. This invariant is a natural extension of weighted graded roots of negative definite plumbed 3-manifolds introduced earlier by the first two authors and Krushkal. We prove a surgery formula relating our invariant with the weighted graded root of the surgered 3-manifold., Comment: 52 pages

Protocol-dependent states in structural glasses can encode a disordered, yet retrievable memory. While training such materials is typically done via a global drive, such as external shear, in dense active matter the driving is instead local and spatio-temporally correlated. Here we focus on the impact of such spatial correlation on memory formation. We investigate the mechanical response of a dense amorphous packing of athermal particles, subject to an oscillatory quasistatic driving with a tunable spatial correlation, akin to the instantaneous driving pattern in active matter. We find that the capacity to encode memory can be rendered comparable upon a proper rescaling on the spatial correlation, whereas the efficiency in memory formation increases with motion cooperativity.

The Euler-Maclaurin formula which relates a discrete sum with an integral, is generalised to the setting of Riemann-Stieltjes sums and integrals on stochastic processes whose paths are a.s. rectifiable, that is continuous and bounded variation. For this purpose, new variants of the signature are introduced, such as the flip and the sawtooth signature. The counterparts of the Bernoulli numbers that arise in the classical Euler-Maclaurin formula are obtained by choosing the appropriate integration constants in the repeated integration by parts to ``minimise the error'' of every truncation level.

We present a covariant description of non-vacuum static spherically symmetric spacetimes in $f(R)$ gravity applying the (1+1+2) covariant formalism. The propagation equations are then used to derive a covariant and dimensionless form of the Tolman-Oppenheimer-Volkoff (TOV) equations. We then give a solution strategy to these equations and obtain some new exact solutions for the particular case $f(R)=R+\alpha R^{2}$, which have the correct thermodynamic properties for standard matter. We find that one of the solutions represents a stellar object with a unique structure called a double layer., Comment: 21 pages, 15 figures

Holding a Morris-Thorne wormhole open requires a violation of the null energy condition, calling for the need for so-called exotic matter near the throat. Many researchers consider exotic matter to be completely unphysical in classical general relativity. It has been shown, however, that the existence of an extra macroscopic dimension can resolve this issue: the throat could be lined with ordinary matter, while the extra dimension is then responsible for the unavoidable energy violation. The purpose of this paper is to show that the extra dimension can be microscopic, a result that is consistent with string theory., Comment: 7 pages, no figures

The combination of functional limit theorems with the pathwise analysis of deterministic and stochastic differential equations has proven to be a powerful approach to the analysis of fast-slow systems. In a multivariate setting, this requires rough path ideas, as already suggested in the seminal work [Melbourne-Stuart, Nonlinearity, 24, 2011]. This initiated a program pursued by numerous authors and which has required substantial results on invariance principles (also known as functional central limit theorems) in rough path topologies. We take a unified point of view and provide simple and exact formulas, of the Green-Kubo type, that characterize the relevant Brownian rough path limits and discuss how they naturally apply in different settings., Comment: 23 pages

Radio interferometers targeting the 21cm brightness temperature fluctuations at high redshift are subject to systematic effects that operate over a range of different timescales. These can be isolated by designing appropriate Fourier filters that operate in fringe-rate (FR) space, the Fourier pair of local sidereal time (LST). Applications of FR filtering include separating effects that are correlated with the rotating sky vs. those relative to the ground, down-weighting emission in the primary beam sidelobes, and suppressing noise. FR filtering causes the noise contributions to the visibility data to become correlated in time however, making interpretation of subsequent averaging and error estimation steps more subtle. In this paper, we describe fringe rate filters that are implemented using discrete prolate spheroidal sequences, and designed for two different purposes -- beam sidelobe/horizon suppression (the `mainlobe' filter), and ground-locked systematics removal (the `notch' filter). We apply these to simulated data, and study how their properties affect visibilities and power spectra generated from the simulations. Included is an introduction to fringe-rate filtering and a demonstration of fringe-rate filters applied to simple situations to aid understanding., Comment: 21 pages, 18 figures, submitted to Monthly Notices of the Royal Astronomical Society

Microwave Kinetic Inductance Detectors (MKIDs) have been demonstrated as capable phonon sensors when coupled to crystalline substrates, and have been proposed as detectors for next-generation rare-event searches such as for the direct detection of dark matter. These Kinetic Inductance Phonon Mediated (KIPM) detector designs, favoring large superconducting absorber volumes and high readout powers, are oftentimes limited in their sensitivity by low temperature amplifier noise introduced in the signal readout chain. We report here an effort to couple a wideband Kinetic Inductance Travelling Wave Parametric Amplifier (KI-TWPA), operated near the Standard Quantum Limit of minimal added amplifier noise, to sensors spanning a 70 MHz bandwidth at 3.5 GHz. This results in a ~5x improvement in the inferred detector energy resolution in the best sensor and highlights the potential of constructing O(100) meV resolving phonon-mediated particle detectors. We detail limitations introduced by lossy passive components, degraded RF responsivity, and microphysical noise sources like two-level systems (TLS), in achieving ultimate quantum-limited system noise levels., Comment: 7 pages, 4 figures

This work culminates in a demonstration of an alternative Frequency Domain Multiplexing (FDM) scheme for Superconducting Nanowire Single-Photon Detectors (SNSPDs) using the Kinetic inductance Parametric UP-converter (KPUP) made out of NbTiN. There are multiple multiplexing architectures for SNSPDs that are already in use, but FDM could prove superior in applications where the operational bias currents are very low, especially for mid- and far-infrared SNSPDs. Previous FDM schemes integrated the SNSPD within the resonator, while in this work we use an external resonator, which gives more flexibility to optimize the SNSPD architecture. The KPUP is a DC-biased superconducting resonator in which a nanowire is used as its inductive element to enable sensitivity to current perturbations. When coupled to an SNSPD, the KPUP can be used to read out current pulses on the few $\mu$A scale. The KPUP is made out of NbTiN, which has high non-linear kinetic inductance for increased sensitivity at higher current bias and high operating temperature. Meanwhile, the SNSPD is made from WSi, which is a popular material for broadband SNSPDs. To read out the KPUP and SNSPD array, a software-defined radio platform and a graphics processing unit are used. Frequency Domain Multiplexed SNSPDs have applications in astronomy, remote sensing, exoplanet science, dark matter detection, and quantum sensing.

We present the optical characterization of two-scale hierarchical phased-array antenna kinetic inductance detectors (KIDs) for millimeter/submillimeter wavelengths. Our KIDs have a lumped-element architecture with parallel plate capacitors and aluminum inductors. The incoming light is received with a hierarchical phased array of slot-dipole antennas, split into 4 frequency bands (between 125 GHz and 365 GHz) with on-chip lumped-element band-pass filters, and routed to different KIDs using microstriplines. Individual pixels detect light for the 3 higher frequency bands (190-365 GHz) and the signals from four individual pixels are coherently summed to create a larger pixel detecting light for the lowest-frequency band (125-175 GHz). The spectral response of the band-pass filters was measured using Fourier transform spectroscopy (FTS), the far-field beam pattern of the phased-array antennas was obtained using an infrared source mounted on a 2-axis translating stage, and the optical efficiency of the KIDs was characterized by observing loads at 294 K and 77 K. We report on the results of these three measurements., Comment: 6 pages of main text, 8 pages total, 4 figures, 1 table. Presented at conference LTD20

We study the existence of gradient conformal Killing vectors (CKVs) in the class of locally rotationally symmetric (LRS) spacetimes which generalizes spherically symmetric spacetimes, and investigate some implications for the evolutionary character of marginally outer trapped surfaces. We first study existence of gradient CKVs via the obtention of a relationship between the Ricci curvature and the gradient of the divergence of the CKV. This provides an alternative set of equations, for which the integrability condition is obtained, to analyze the existence of gradient CKVs. A uniqueness result is obtained in the case of perfect fluids, where it is demonstrated that the Robertson-Walker solution is the unique perfect fluid solution with a nonvanishing pressure, admitting a timelike gradient CKV. The constant mean curvature condition for LRS spacetimes is also obtained, characterized by three distinct conditions which are specified by a set of three scalars. Linear combinations of these scalars, whose vanishing define the constant mean curvature condition, turn out to be related to the evolutions of null expansions of 2-spheres along their null normal directions. As such, some implications for the existence of black holes and the character of the associated horizons are obtained. It is further shown that dynamical black holes of increasing area, with a non-vanishing heat flux across the horizon, will be in equilibrium, with respect to the frame of the conformal observers., Comment: 25 pages; typos corrected; Abstract and references updated; some additional details, including calculations, provided for clarity; accepted for publication in CQG

This paper presents the design and deployment of the Hydrogen Epoch of Reionization Array (HERA) phase II system. HERA is designed as a staged experiment targeting 21 cm emission measurements of the Epoch of Reionization. First results from the phase I array are published as of early 2022, and deployment of the phase II system is nearing completion. We describe the design of the phase II system and discuss progress on commissioning and future upgrades. As HERA is a designated Square Kilometer Array (SKA) pathfinder instrument, we also show a number of "case studies" that investigate systematics seen while commissioning the phase II system, which may be of use in the design and operation of future arrays. Common pathologies are likely to manifest in similar ways across instruments, and many of these sources of contamination can be mitigated once the source is identified.