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We study the matrix factorizations defined by the generic plane projections of a curve singularity of $\mathbb{C}^3$. On the other hand, given a plane curve singularity $Y\subset \mathbb{C}^2$ we study the family of matrix factorizations defined by the space curve singularities $X\subset \mathbb{C}^3$ such that $Y$ is the generic plane projection of $X$., Comment: To appear in Vietnam Journal of Mathematics

For all $\alpha\in(0,1)$, we construct an explicit divergence-free vector field $V\in L^\infty_tC^\alpha_x \cap C^{\frac{\alpha}{1-\alpha}}_t L^\infty_x$ so that the solutions to the drift-diffusion equations $$\partial_t\theta^\kappa-\kappa\Delta\theta^\kappa+V\cdot\nabla\theta^\kappa=0$$ exhibit asymptotic total dissipation for all mean-zero initial data: $\lim_{\kappa\rightarrow 0}\|\theta^\kappa(1,\cdot)\|_{L^2}=0$. Additionally, we give explicit rates in $\kappa$ and uniform dependence on initial data., Comment: 30 pages, 4 figures

A cuspidal robot can move from one inverse kinematics (IK) solution to another without crossing a singularity. Multiple industrial robots are cuspidal. They tend to have a beautiful mechanical design, but they pose path planning challenges. A task-space path may have a valid IK solution for each point along the path, but a continuous joint-space path may depend on the choice of the IK solution or even be infeasible. This paper presents new analysis, path planning, and optimization methods to enhance the utility of cuspidal robots. We first demonstrate an efficient method to identify cuspidal robots and show, for the first time, that the ABB GoFa and certain robots with three parallel joint axes are cuspidal. We then propose a new path planning method for cuspidal robots by finding all IK solutions for each point along a task-space path and constructing a graph to connect each vertex corresponding to an IK solution. Graph edges are weighted based on the optimization metric, such as minimizing joint velocity. The optimal feasible path is the shortest path in the graph. This method can find non-singular paths as well as smooth paths which pass through singularities. Finally, this path planning method is incorporated into a path optimization algorithm. Given a fixed workspace toolpath, we optimize the offset of the toolpath in the robot base frame while ensuring continuous joint motion. Code examples are available in a publicly accessible repository., Comment: 10 pages, 11 figures

We present new multi-wavelength observations of two ultraluminous X-ray sources (ULXs) hosted by globular clusters (GCs) in the giant elliptical NGC 1399, focusing on CXO J0338318-352604 (GCU7), only the second GC ULX known to have luminous optical emission lines. Notably, only NII and OIII emission is observed in the optical spectra, suggesting H-poor material. Previous work suggested the possibility that the properties of GCU7 could be explained by the tidal disruption of a horizontal branch star by an intermediate-mass black hole. We use new data to show that the lack of evolution in the X-ray or optical properties of the source over the last 20 years rules out this scenario. Instead, we use CLOUDY simulations to demonstrate that the optical emission lines are consistent with an outflow from an ultra-compact X-ray binary where a compact object - likely a neutron star (NS) - is accreting above the Eddington limit from a helium white dwarf (He WD). This binary would have dynamically formed from a direct collision between a NS and a red giant, or else via an exchange interaction. The ULX is predicted to evolve to lower mass transfer rates over time and eventually become a doppelganger to the well-studied ultra-compact X-ray binaries in Galactic GCs such as 4U 1820-30. These results show the utility of using extragalactic GCs to study short-lived phases in dynamical binary evolution that occur too rarely to be observed in Galactic clusters., Comment: 11 pages, 9 figures, 4 tables. Accepted for publication in MNRAS

The Battery-Free Internet of Things might revolutionize our understanding of connected devices, which harvest their operational energy from the environment (e.g., using solar cells). These systems come with the major system-software challenge that the intermittently-powered IoT devices have to checkpoint their state in non-volatile memory to later resume operation with this state when sufficient energy is available. The scarce energy resources demand that only modified data is persisted to non-volatile memory before a power failure, which requires precise modification-tracking. In this paper, we present the first virtually Non-Volatile Heap (vNV-Heap) abstraction for intermittently-powered systems with guaranteed power-failure resilience and non-volatile memory safety (analogous to memory-safety for RAM). The heap exploits ownership systems, a zero-cost (i.e., compile-time) abstraction for example implemented by Rust, to track modifications and virtualize object-persistence. To achieve power-failure resilience, our heap is designed and implemented to guarantee bounded operations by static program code analysis: As an example, the heap allows for determining a worst-case energy consumption for the operation of persisting modified and currently volatile objects. Our evaluations with our open-source implementation on an embedded hardware platform (i.e., ESP32-C3) shows that using our heap abstraction is more energy-efficient than existing approaches, while also providing runtime guarantees by static worst-case analysis bounds.

We develop a linear theory for unsteady aerodynamic effects of the actuator line method (ALM). This theory is validated using ALM simulations, where we compute the lift generated by the harmonic transverse oscillation of a thin airfoil in uniform flow, comparing the results with Theodorsen's theory. This comparison elucidates the underlying characteristics and limitations of ALM when applied to unsteady aerodynamics. Numerical simulations were conducted across a range of chord lengths and oscillation frequencies. Comparison of ALM results with theoretical predictions shows consistent accuracy, with all Gaussian parameter choices yielding accurate results at low reduced frequencies. Furthermore, the study indicates that selecting a width parameter ratio of $\varepsilon/c$ (the Gaussian width parameter over the chord length) between 0.33 and 0.4 in ALM yields the closest alignment with analytical results across a broader frequency range. Additionally, a proper definition of angle of attack for a pitching airfoil is shown to be important for accurate computations. These findings offer valuable guidance for the application of ALM in unsteady aerodynamics and aeroelasticity., Comment: 10 pages, 3 figures

In the near future, autonomous space systems will compose a large number of the spacecraft being deployed. Their tasks will involve autonomous rendezvous and proximity operations with large structures, such as inspections or assembly of orbiting space stations and maintenance and human-assistance tasks over shared workspaces. To promote replicable and reliable scientific results for autonomous control of spacecraft, we present the design of a space systems laboratory based on open-source and modular software and hardware. The simulation software provides a software-in-the-loop (SITL) architecture that seamlessly transfers simulated results to the ATMOS platforms, developed for testing of multi-agent autonomy schemes for microgravity. The manuscript presents the KTH space systems laboratory facilities and the ATMOS platform as open-source hardware and software contributions. Preliminary results showcase SITL and real testing., Comment: Preliminary release, to be submitted

We propose a new strong Riemannian metric on the manifold of (parametrized) embedded curves of regularity $H^s$, $s\in(3/2,2)$. We highlight its close relationship to the (generalized) tangent-point energies and employ it to show that this metric is complete in the following senses: (i) bounded sets are relatively compact with respect to the weak $H^s$ topology; (ii) every Cauchy sequence with respect to the induced geodesic distance converges; (iii) solutions of the geodesic initial-value problem exist for all times; and (iv) there are length-minimizing geodesics between every pair of curves in the same path component (i.e., in the same knot class). As a by-product, we show $C^\infty$-smoothness of the tangent-point energies in the Hilbert case., Comment: 53 pages, 6 figures

Despite coffee's popularity, there are no quantitative methods to measure a chemical property of coffee and relate it to a gustatory experience. Borrowing an electrochemical technique often used to assess the oxidative and reductive features of molecules, we demonstrate that cyclic voltammetry can be used to directly measure the ensemble strength of a coffee beverage and, separately, how dark the coffee has been roasted. We show that the current passed for the protonic features that precede hydrogen evolution are linearly related to beverage strength. The same features are suppressed with subsequent cycling, and we show that the suppression is directly related to composition, which depends on roast. Together, our voltammetric method decouples beverage strength from roast color; the latter is the primary factor determining flavor profiles of coffee extracts.

Frank-Wolfe (FW) algorithms have emerged as an essential class of methods for constrained optimization, especially on large-scale problems. In this paper, we summarize the algorithmic design choices and progress made in the last years of the development of FrankWolfe.jl, a Julia package gathering high-performance implementations of state-of-the-art FW variants. We review key use cases of the library in the recent literature, which match its original dual purpose: first, becoming the de-facto toolbox for practitioners applying FW methods to their problem, and second, offering a modular ecosystem to algorithm designers who experiment with their own variants and implementations of algorithmic blocks. Finally, we demonstrate the performance of several FW variants on important problem classes in several experiments, which we curated in a separate repository for continuous benchmarking.

Text classifiers suffer from small perturbations, that if chosen adversarially, can dramatically change the output of the model. Verification methods can provide robustness certificates against such adversarial perturbations, by computing a sound lower bound on the robust accuracy. Nevertheless, existing verification methods incur in prohibitive costs and cannot practically handle Levenshtein distance constraints. We propose the first method for computing the Lipschitz constant of convolutional classifiers with respect to the Levenshtein distance. We use these Lipschitz constant estimates for training 1-Lipschitz classifiers. This enables computing the certified radius of a classifier in a single forward pass. Our method, LipsLev, is able to obtain $38.80$% and $13.93$% verified accuracy at distance $1$ and $2$ respectively in the AG-News dataset, while being $4$ orders of magnitude faster than existing approaches. We believe our work can open the door to more efficient verification in the text domain., Comment: Accepted in ICLR 2025

There is evidence for interaction between supernova (SN) ejecta and massive circumstellar material (CSM) in various types of SNe. The mass-ejection mechanisms that produce massive CSM are unclear, and studying interacting SNe and their CSM can shed light on these mechanisms and the final stages of stellar evolution. We aim to study the properties of the CSM in the bright, long-lived, hydrogen-rich (Type II) SN 2021irp, which is interacting with a massive aspherical CSM. We present imaging- and spectro-polarimetric observations of SN 2021irp. By modelling its polarisation and bolometric light curve, we derive the mass and distribution of the CSM. SN 2021irp shows a high intrinsic polarisation of $\sim0.8$%. This high continuum polarisation suggests an aspherical photosphere created by an aspherical CSM interaction. Based on the bolometric light curve evolution and the high polarization, SN 2021irp can be explained as a typical Type II SN interacting with a CSM disk with a corresponding mass-loss rate and half-opening angle of $\sim0.035$ - $0.1$ M$_{\odot}$ yr$^{-1}$ and $\sim30$ - $50^{\circ}$, respectively. The total CSM mass derived is $\gtrsim 2$ M$_{\odot}$. We suggest that this CSM disk was created by some process related to binary interaction, and that SN 2021irp is the end product of a typical massive star (i.e. with Zero-Age-Main-Sequence mass of $\sim 8-18$ M$_{\odot}$) that has a separation and/or mass ratio with its companion star that led to an extreme mass ejection within decades of explosion. Based on the observational properties of SN 2021irp and similar SNe, we propose a general picture for the spectroscopic properties of Type II SNe interacting with a massive disk CSM., Comment: 11 pages, 8 figures, submitted to A&A

Some core-collapse supernovae (CCSNe) are too luminous and radiate too much total energy to be powered by the release of thermal energy from the ejecta and radioactive-decay energy from the synthesised $^{56}$Ni/$^{56}$Co. A source of additional power is the interaction between the supernova (SN) ejecta and a massive circumstellar material (CSM). This is an important power source in Type IIn SNe, which show narrow spectral lines arising from the unshocked CSM, but not all interacting SNe show such narrow lines. We present photometric and spectroscopic observations of the hydrogen-rich SN 2021irp, which is both luminous, with $M_{o} < -19.4$ mag, and long-lived, remaining brighter than $M_{o} = -18$ mag for $\sim$ 250 d. We show that an additional energy source is required to power such a SN, and determine the nature of the source. We also investigate the properties of the pre-existing and newly formed dust associated with the SN. Photometric observations show that the luminosity of the SN is an order of magnitude higher than typical Type II SNe and persists for much longer. We detect a infrared excess attributed to dust emission. Spectra show multi-component line profiles, an Fe II pseudo-continuum, and a lack of absorption lines, all typical features of Type IIn SNe. We detect a narrow (< 85 kms$^{-1}$) P-Cygni profile associated with the unshocked CSM. An asymmetry in emission line profiles indicates dust formation occurring from 250-300 d. Analysis of the SN blackbody radius evolution indicates asymmetry in the shape of the emitting region. We identify the main power source of SN 2021irp as extensive interaction with a massive CSM, and that this CSM is distributed asymmetrically around the progenitor star. The infrared excess is explained with emission from newly formed dust although there is also some evidence of an IR echo from pre-existing dust at early times., Comment: 23 pages, 16 figures, submitted to A&A

The 3d $A$-model is a two-dimensional approach to the computation of supersymmetric observables of three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories. In principle, it allows us to compute half-BPS partition functions on any compact Seifert three-manifold (as well as of expectation values of half-BPS lines thereon), but previous results focussed on the case where the gauge group $\widetilde G$ is a product of simply-connected and/or unitary gauge groups. We are interested in the more general case of a compact gauge group $G=\widetilde G/\Gamma$, which is obtained from the $\widetilde G$ theory by gauging a discrete one-form symmetry. In this paper, we discuss in detail the case of pure $\mathcal{N}=2$ Chern-Simons theories (without matter) for simple groups $G$. When $G=\widetilde G$ is simply-connected, we demonstrate the exact matching between the supersymmetric approach in terms of Seifert fibering operators and the 3d TQFT approach based on topological surgery in the infrared Chern-Simons theory $\widetilde G_k$, including through the identification of subtle counterterms that relate the two approaches. We then extend this discussion to the case where the Chern-Simons theory $G_k$ can be obtained from $\widetilde G_k$ by the condensation of abelian anyons which are bosonic. Along the way, we revisit the 3d $A$-model formalism by emphasising its 2d TQFT underpinning., Comment: 56 pages + appendices

We introduce a robust belief-based measure of complexity. The idea is that task A is deemed more complex than task B if the probability of solving A correctly is smaller than the probability of solving B correctly regardless of the reward. We fully characterize the corresponding order over the set of tasks. The main characteristic of this relation is that it depends, not only on difficulty (like most complexity definitions in the literature) but also on ex ante uncertainty. Finally, we show that for every task for which information is optimally acquired, there exists a more complex task which always induces less effort regardless of the reward.

We present the discovery of PSR J1947-1120, a new huntsman millisecond pulsar with a red giant companion star in a 10.3 d orbit. This pulsar was found via optical, X-ray, and radio follow-up of the previously unassociated gamma-ray source 4FGL J1947.6-1121. PSR J1947-1120 is the second confirmed pulsar in the huntsman class and establishes this as a bona fide subclass of millisecond pulsar. We use MESA models to show that huntsman pulsars can be naturally explained as neutron star binaries whose secondaries are currently in the "red bump" region of the red giant branch, temporarily underfilling their Roche lobes and hence halting mass transfer. Huntsman pulsars offer a new view of the formation of typical millisecond pulsars, allowing novel constraints on the efficiency of mass transfer and recycling at an intermediate stage in the process., Comment: ApJ in press

The new era of large-scale data collection and analysis presents an opportunity for diagnosing and understanding the causes of health inequities. In this study, we describe a framework for systematically analyzing health disparities using causal inference. The framework is illustrated by investigating racial and ethnic disparities in intensive care unit (ICU) outcome between majority and minority groups in Australia (Indigenous vs. Non-Indigenous) and the United States (African-American vs. White). We demonstrate that commonly used statistical measures for quantifying inequity are insufficient, and focus on attributing the observed disparity to the causal mechanisms that generate it. We find that minority patients are younger at admission, have worse chronic health, are more likely to be admitted for urgent and non-elective reasons, and have higher illness severity. At the same time, however, we find a protective direct effect of belonging to a minority group, with minority patients showing improved survival compared to their majority counterparts, with all other variables kept equal. We demonstrate that this protective effect is related to the increased probability of being admitted to ICU, with minority patients having an increased risk of ICU admission. We also find that minority patients, while showing improved survival, are more likely to be readmitted to ICU. Thus, due to worse access to primary health care, minority patients are more likely to end up in ICU for preventable conditions, causing a reduction in the mortality rates and creating an effect that appears to be protective. Since the baseline risk of ICU admission may serve as proxy for lack of access to primary care, we developed the Indigenous Intensive Care Equity (IICE) Radar, a monitoring system for tracking the over-utilization of ICU resources by the Indigenous population of Australia across geographical areas.

A variety of high-energy astrophysical phenomena are powered by the release -- via magnetic reconnection -- of the energy stored in oppositely directed fields. Single-fluid resistive magnetohydrodynamic (MHD) simulations with uniform resistivity yield dissipation rates that are much lower (by nearly one order of magnitude) than equivalent kinetic calculations. Reconnection-driven phenomena could be accordingly modeled in resistive MHD employing a non-uniform, ``effective'' resistivity informed by kinetic calculations. In this work, we analyze a suite of fully kinetic particle-in-cell (PIC) simulations of relativistic pair-plasma reconnection -- where the magnetic energy is greater than the rest mass energy -- for different strengths of the guide field orthogonal to the alternating component. We extract an empirical prescription for the effective resistivity, $\eta_{\mathrm{eff}} = \alpha B_0 \mathbf{|J|}^p / \left(|\mathbf{J}|^{p+1}+\left(e n_t c\right)^{p+1}\right)$, where $B_0$ is the reconnecting magnetic field strength, $\bf J$ is the current density, $n_t$ the lab-frame total number density, $e$ the elementary charge, and $c$ the speed of light. The guide field dependence is encoded in $\alpha$ and $p$, which we fit to PIC data. This resistivity formulation -- which relies only on single-fluid MHD quantities -- successfully reproduces the spatial structure and strength of nonideal electric fields, and thus provides a promising strategy for enhancing the reconnection rate in resistive MHD simulations.

While nova eruptions produce some of the most common and dramatic dust formation episodes among astrophysical transients, the demographics of dust-forming novae remain poorly understood. Here, we present a statistical study of dust formation in 40 novae with high-quality optical/IR light curves, quantitatively distinguishing dust-forming from non-dust-forming novae while exploring the properties of the dust events. We find that 50-70% of novae produce dust, significantly higher than previous estimates. Dust-forming novae can be separated from those that do not show dust formation by using the largest redward ($V-K$) colour change from peak visible brightness; ($V-J$) or ($V-H$) offer useful but less sensitive constraints. This makes optical+IR photometry a powerful tool to quantify dust formation in novae. We find that novae detected in GeV $\gamma$-rays by \emph{Fermi}-LAT appear to form dust more often than novae not detected by \emph{Fermi}, implying a possible connection between $\gamma$-ray producing shocks and dust production. We also find that novae that evolve very quickly ($t_2 < 10$ days) are much less likely to form dust, in agreement with previous findings. We confirm a correlation between $t_2$ and the time of the onset of dust formation (which occurs $\sim$1 week--3 months after maximum light), but conclude that it is primarily an observational artifact driven by dust formation determining when a nova drops 2 mag below peak. The significant fraction of novae that form dust make them ideal laboratories in our Galactic backyard to tackle the puzzle of dust formation around explosive transients., Comment: 23 pages, 58 figures, 1 table, submitted to MNRAS

We present optical photometric and spectroscopic observations of the peculiar Type Ia supernova ASASSN-20jq/SN 2020qxp. It is a low-luminosity object with a peak absolute magnitude of $M_B=-17.1\pm0.5$ mag. Despite its low luminosity, its post-peak light-curve decline rate ($\Delta m_{15}(B)=1.35\pm0.09$ mag) and color-stretch parameter (sBV>0.82) are similar to normal SNe Ia, making it an outlier in the luminosity-width and luminosity-color-stretch relations. Early light curves suggest a "bump" during the first 1.4 days of explosion. ASASSN-20jq synthesized a low radioactive $^{56}$Ni mass of $0.09\pm0.01M_\odot$. Near-maximum light spectra reveal strong Si II absorption lines, indicating a cooler photosphere than normal SNe Ia, but lack Ti II absorption lines. Unusually strong O I $\lambda$7773 and Ca II near-infrared triplet absorption features are present. Nebular spectra show a strong, narrow forbidden [Ca II] $\lambda\lambda$7291,7324 doublet emission, rarely seen in SNe Ia except in some Type Iax events. Marginal detection of [O I] $\lambda\lambda$6300,6364 doublet emission, which is extremely rare, is observed. Both [Ca II] and [O I] lines are redshifted by $\sim2000$ km/s. A strong [Fe II] $\lambda$7155 emission line with a tilted-top profile, identical to the [Fe II] $\lambda$16433 profile, is also observed. These asymmetric [Fe II] profiles and redshifted [Ca II] and [O I] emissions suggest a high central density white dwarf progenitor undergoing an off-center delayed-detonation explosion mechanism, producing roughly equal amounts of $^{56}$Ni in deflagration and detonation phases. This distinguishes ASASSN-20jq from normal and subluminous SNe Ia. ASASSN-20jq's light curve and spectra do not align with any single SNe Ia subclass but show similarities to 2002es-like objects. Thus, we add it as an extreme candidate within the heterogeneous parameter space of 2002es-like SNe Ia., Comment: 27 pages, 20 figures, 5 tables, submitted to A&A

This study investigates the use of the $J$-integral to compute the statistics of the energy release rate of a random elastic medium. The spatial variability of the elastic modulus is modeled as a homogeneous lognormal random field. Within the framework of Monte Carlo simulation, a modified contour integral is applied to evaluate the first and second statistical moments of the energy release rate. These results are compared with the energy release rate calculated from the potential energy function. The comparison shows that, if the random field of elastic modulus is homogeneous in space, the path independence of the classical $J$-integral remains valid for calculating the mean energy release rate. However, this path independence does not extend to the higher order statistical moments. The simulation further reveals the effect of the correlation length of the spatially varying elastic modulus on the energy release rate of the specimen., Comment: 10 pages, 4 figures, 3 tables

Localizing the seizure onset zone (SOZ) as a step of presurgical planning leads to higher efficiency in surgical and stimulation treatments. However, the clinical localization including structural, ictal, and invasive data acquisition and assessment is a difficult and long procedure with increasing challenges in patients with complex epileptic foci. The interictal methods are proposed to assist in presurgical planning with simpler data acquisition and higher speed. This study presents a spatiotemporal component classification for the localization of epileptic foci using resting-state functional magnetic resonance imaging data. This method is based on spatiotemporal independent component analysis on rsfMRI with a component-sorting procedure upon dominant power frequency, biophysical constraints, spatial lateralization, local connectivity, temporal energy, and functional non-Gaussianity. This method utilized the rs-fMRI potential to reach a high spatial accuracy in localizing epileptic foci from interictal data while retaining the reliability of results for clinical usage. Thirteen patients with temporal lobe epilepsy who underwent surgical resection and had seizure-free surgical outcomes after a 12-month follow-up were included in this study. All patients had presurgical structural MRI and rsfMRI while postsurgical MRI images were available for ten. Based on the relationship between the localized foci and resection, the results were classified into three groups fully concordant, partially concordant, and discordant. These groups had the resulting cluster aligned with, in the same lobe with, and outside the lobe of the resection area, respectively.

We present a comprehensive photometric and spectroscopic study of the Type IIP SN 2018is. The $V$-band luminosity and the expansion velocity at 50 days post-explosion are $-$15.1$\pm$0.2 mag (corrected for A$_V$=1.34 mag) and 1400 km s$^{-1}$, classifying it as a low-luminosity SN II. The recombination phase in the $V$-band is shorter, lasting around 110 days, and exhibits a steeper decline (1.0 mag per 100 days) compared to most other low-luminosity SNe II. Additionally, the optical and near-infrared spectra display hydrogen emission lines that are strikingly narrow, even for this class. The Fe II and Sc II line velocities are at the lower end of the typical range for low-luminosity SNe II. Semi-analytical modelling of the bolometric light curve suggests an ejecta mass of $\sim$8 M$_\odot$, corresponding to a pre-supernova mass of $\sim$9.5 M$_\odot$, and an explosion energy of $\sim$0.40 $\times$ 10$^{51}$ erg. Hydrodynamical modelling further indicates that the progenitor had a zero-age main sequence mass of 9 M$_\odot$, coupled with a low explosion energy of 0.19 $\times$ 10$^{51}$ erg. The nebular spectrum reveals weak [O I] $\lambda\lambda$6300,6364 lines, consistent with a moderate-mass progenitor, while features typical of Fe core-collapse events, such as He I, [C I], and [Fe I], are indiscernible. However, the redder colours and low ratio of Ni to Fe abundance do not support an electron-capture scenario either. As a low-luminosity SN II with an atypically steep decline during the photospheric phase and remarkably narrow emission lines, SN 2018is contributes to the diversity observed within this population., Comment: 25 pages, 21 figures, accepted for publication in A&A

This research employs Universal Differential Equations (UDEs) alongside differentiable physics to model viscoelastic fluids, merging conventional differential equations, neural networks and numerical methods to reconstruct missing terms in constitutive models. This study focuses on analyzing four viscoelastic models: Upper Convected Maxwell (UCM), Johnson-Segalman, Giesekus, and Exponential Phan-Thien-Tanner (ePTT), through the use of synthetic datasets. The methodology was tested across different experimental conditions, including oscillatory and startup flows. While the UDE framework effectively predicts shear and normal stresses for most models, it demonstrates some limitations when applied to the ePTT model. The findings underscore the potential of UDEs in fluid mechanics while identifying critical areas for methodological improvement. Also, a model distillation approach was employed to extract simplified models from complex ones, emphasizing the versatility and robustness of UDEs in rheological modeling.

The Drinfeld centralizer of a monoidal category $\mathcal{A}$ in a bimodule category $\mathcal{M}$ is the category $\mathcal{Z}(\mathcal{A},\mathcal{M})$ of objects in $\mathcal{M}$ for which the left and right actions by objects of $\mathcal{A}$ coincide, naturally. In this paper we study the interplay between Drinfeld centralizers of $\mathcal{A}$ and its homotopy category $\mathcal{K}^b(\mathcal{A})$, culminating with our ``lifting lemma,'' which provides a sufficient condition for an object of $\mathcal{Z}(\mathcal{A}, \mathcal{K}^b(\mathcal{M}))$ to lift to an object of $\mathcal{Z}(\mathcal{K}^b(\mathcal{A}), \mathcal{K}^b(\mathcal{M}))$. The central application of this lifting lemma is a proof of some folklore facts about conjugation by Rouquier complexes in the Hecke category: the centrality of the full twist, and related properties of half twists and Coxeter braids. We also prove stronger, homotopy coherent versions of these statements, stated using the notion of the $A_{\infty}$-Drinfeld centralizer, which we believe is new.

In this short, elementary note we prove that if a faithful reflection representation of a Coxeter group preserves an orthant, then that Coxeter group is a product of symmetric groups acting on its natural permutation representation. We also prove an affine analogue of this statement, where an orthant is preserved modulo an invariant sublattice. As a consequence, the existence of two different versions of the quantum geometric Satake equivalence is a purely type A phenomenon.

This paper addresses the challenge of multi-agent path planning for efficient data collection in dynamic, uncertain environments, exemplified by autonomous underwater vehicles (AUVs) navigating the Gulf of Mexico. Traditional greedy algorithms, though computationally efficient, often fall short in long-term planning due to their short-sighted nature, missing crucial data collection opportunities and increasing exposure to hazards. To address these limitations, we introduce WAITR (Weighted Aggregate Inter-Temporal Reward), a novel path-planning framework that integrates a knowledge graph with pathlet-based planning, segmenting the environment into dynamic, speed-adjusted sub-regions (pathlets). This structure enables coordinated, adaptive planning, as agents can operate within time-bound regions while dynamically responding to environmental changes. WAITR's cumulative scoring mechanism balances immediate data collection with long-term optimization of Points of Interest (POIs), ensuring safer navigation and comprehensive data coverage. Experimental results show that WAITR substantially improves POI coverage and reduces exposure to hazards, achieving up to 27.1\% greater event coverage than traditional greedy methods., Comment: 10 pages, 8 figures, presented at the 4th Workshop on Knowledge Graphs and Big Data in conjunction with IEEE Big Data 2024

In a previous paper of the first author, the type A affine Cartan matrix was q-deformed to produce a deformation of the reflection representation of the affine Weyl group. This deformation plays a role in the quantum geometric Satake equivalence. In this paper we introduce the study of q-deformed divided difference operators. When q is specialized to a primitive 2m-th root of unity, this affine reflection representation factors through a quotient, the complex reflection group $G(m,m,n)$. The divided difference operators now generate a finite-dimensional algebra we call the exotic nilCoxeter algebra. This algebra is new and has surprising features. In addition to the usual braid relations, we prove a new relation called the roundabout relation. A classic result of Demazure, for Weyl groups, states that the polynomial ring of the reflection representation is a Frobenius extension over its subring of invariant polynomials, and describes how the Frobenius trace can be constructed within the nilCoxeter algebra. We study the analogous Frobenius extension for $G(m,m,n)$, and identify the Frobenius trace within the exotic nilCoxeter algebra for $G(m,m,3)$.

There is a q-deformation of the reflection representation of the affine symmetric group, which arises in the quantum geometric Satake equivalence, and in the study of the complex reflection groups $G(m,m,n)$. Demazure operators (often called divided difference operators) act on the polynomial ring of this deformed representation. When $n=3$ we prove an explicit closed formula for the scalar one obtains when applying a degree $-k$ Demazure operator to a monomial of degree $k$. We also prove a simpler formula for the scalar obtained after specializing q to a root of unity.

The ability of $\theta$-Milstein methods with $\theta\ge 1$ to capture the non-negativity and the mean-reversion property of the exact solution of the CIR model is shown. In addition, the order of convergence and the preservation of the long-term variance is studied. These theoretical results are illustrated with numerical examples.

We present a systematic study of the $BVRI$ colours of novae over the course of their eruptions. Where possible, interstellar reddening was measured using the equivalent widths of Diffuse Interstellar Bands (DIBs). Some novae lack spectra with sufficient resolution and signal-to-noise ratios; therefore, we supplement as necessary with 3D and 2D dust maps. Utilising only novae with DIB- or 3D-map-based $E(B-V)$, we find an average intrinsic $(B-V)_0$ colour of novae at $V$-band light curve peak of 0.18 with a standard deviation of 0.31, based on a sample of 23 novae. When the light curve has declined by 2 magnitudes ($t_2$), we find an average $(B-V)_0 = -0.02$ with a standard deviation of 0.19. These average colours are consistent with previous findings, although the spreads are larger than previously found due to more accurate reddening estimates. We also examined the intrinsic $(R-I)_0$ and $(V-R)_0$ colours across our sample. These colours behave similarly to $(B-V)_0$, except that the $(V-R)_0$ colour gets redder after peak, likely due to the contributions of emission line flux. We searched for correlations between nova colours and $t_2$, peak $V$-band absolute magnitude, and GeV $\gamma$-ray luminosity, but find no statistically significant correlations. Nova colours can therefore be used as standard "crayons" to estimate interstellar reddening from photometry alone, with 0.2--0.3 mag uncertainty. We present a novel Bayesian strategy for estimating distances to Galactic novae based on these $E(B-V)$ measurements, independent of assumptions about luminosity, built using 3D dust maps and a stellar mass model of the Milky Way., Comment: 19 pages, 21 Figures. Submitted to MNRAS

This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024, building on the initial discussions during the inaugural workshop held at CERN in March 2023. Like the summary of the first workshop, this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions., Comment: Summary of the second Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at Imperial College London: https://indico.cern.ch/event/1369392/

We present DriveGPT, a scalable behavior model for autonomous driving. We model driving as a sequential decision making task, and learn a transformer model to predict future agent states as tokens in an autoregressive fashion. We scale up our model parameters and training data by multiple orders of magnitude, enabling us to explore the scaling properties in terms of dataset size, model parameters, and compute. We evaluate DriveGPT across different scales in a planning task, through both quantitative metrics and qualitative examples including closed-loop driving in complex real-world scenarios. In a separate prediction task, DriveGPT outperforms a state-of-the-art baseline and exhibits improved performance by pretraining on a large-scale dataset, further validating the benefits of data scaling., Comment: 14 pages, 16 figures, 9 tables, and 1 video link

In the search for accurate approximate solutions of the many-body Schr\"odinger equation, reduced density matrices play an important role, as they allow to formulate approximate methods with polynomial scaling in the number of particles. However, these methods frequently encounter the issue of $N$-representability, whereby in self-consistent applications of the methods, the reduced density matrices become unphysical. A number of algorithms have been proposed in the past to restore a given set of $N$-representability conditions once the reduced density matrices become defective. However, these purification algorithms have either ignored symmetries of the Hamiltonian related to conserved quantities, or have not incorporated them in an efficient way, thereby modifying the reduced density matrix to a greater extent than is necessary. In this paper, we present an algorithm capable of efficiently performing all of the following tasks in the least invasive manner: restoring a given set of $N$-representability conditions, maintaining contraction consistency between successive orders of reduced density matrices, and preserving all conserved quantities. We demonstrate the superiority of the present purification algorithm over previous ones in the context of the time-dependent two-particle reduced density matrix method applied to the quench dynamics of the Fermi-Hubbard model., Comment: 13 pages, 4 figures

This paper presents a rigorous derivation of equations to evaluate the macroscopic stress tensor, the couple stress tensor, and the flux vector equivalent to underlying microscopic fields in continuous and discrete heterogeneous systems with independent displacements and rotations. Contrary to the classical asymptotic expansion homogenization, finite size representative volume is considered. First, the macroscopic quantities are derived for a heterogeneous Cosserat continuum. The resulting continuum equations are discretized to provide macroscopic quantities in discrete heterogeneous systems. Finally, the expressions for discrete system are derived once again, this time considering the discrete nature directly. The formulations are presented in two variants, considering either internal or external forces, couples, and fluxes. The derivation is based on the virtual work equivalence and elucidates the fundamental significance of the couple stress tensor in the context of balance equations and admissible virtual deformation modes. Notably, an additional term in the couple stress tensor formula emerges, explaining its dependence on the reference system and position of the macroscopic point. The resulting equations are verified by comparing their predictions with known analytical solutions and results of other numerical models under both steady state and transient conditions., Comment: 26 pages, 15 figures

The growing importance of real-time simulation in the medical field has exposed the limitations and bottlenecks inherent in the digital representation of complex biological systems. This paper presents a novel methodology aimed at advancing current lines of research in soft tissue simulation. The proposed approach introduces a hybrid model that integrates the geometric bias of graph neural networks with the physical bias derived from the imposition of a metriplectic structure as soft and hard constrains in the architecture, being able to simulate hepatic tissue with dissipative properties. This approach provides an efficient solution capable of generating predictions at high feedback rate while maintaining a remarkable generalization ability for previously unseen anatomies. This makes these features particularly relevant in the context of precision medicine and haptic rendering. Based on the adopted methodologies, we propose a model that predicts human liver responses to traction and compression loads in as little as 7.3 milliseconds for optimized configurations and as fast as 1.65 milliseconds in the most efficient cases, all in the forward pass. The model achieves relative position errors below 0.15\%, with stress tensor and velocity estimations maintaining relative errors under 7\%. This demonstrates the robustness of the approach developed, which is capable of handling diverse load states and anatomies effectively. This work highlights the feasibility of integrating real-time simulation with patient-specific geometries through deep learning, paving the way for more robust digital human twins in medical applications.

Constructing precise global maps is a key task in robotics and is required for localization, surveying, monitoring, or constructing digital twins. To build accurate maps, data from mobile 3D LiDAR sensors is often used. Mapping requires correctly aligning the individual point clouds to each other to obtain a globally consistent map. In this paper, we investigate the problem of multi-scan alignment to obtain globally consistent point cloud maps. We propose a 3D LiDAR bundle adjustment approach to solve the global alignment problem and jointly optimize the available data. Utilizing a continuous-time trajectory allows us to consider the ego-motion of the LiDAR scanner while recording a single scan directly in the least squares adjustment. Furthermore, pruning the search space of correspondences and utilizing out-of-core circular buffer enables our approach to align thousands of point clouds efficiently. We successfully align point clouds recorded with a handheld LiDAR, as well as ones mounted on a vehicle, and are able to perform multi-session alignment., Comment: Submitted to ICRA 2025

Artificial intelligence-based chatbots are increasingly influencing physics education due to their ability to interpret and respond to textual and visual inputs. This study evaluates the performance of two large multimodal model-based chatbots, ChatGPT-4 and ChatGPT-4o on the Brief Electricity and Magnetism Assessment (BEMA), a conceptual physics inventory rich in visual representations such as vector fields, circuit diagrams, and graphs. Quantitative analysis shows that ChatGPT-4o outperforms both ChatGPT-4 and a large sample of university students, and demonstrates improvements in ChatGPT-4o's vision interpretation ability over its predecessor ChatGPT-4. However, qualitative analysis of ChatGPT-4o's responses reveals persistent challenges. We identified three types of difficulties in the chatbot's responses to tasks on BEMA: (1) difficulties with visual interpretation, (2) difficulties in providing correct physics laws or rules, and (3) difficulties with spatial coordination and application of physics representations. Spatial reasoning tasks, particularly those requiring the use of the right-hand rule, proved especially problematic. These findings highlight that the most broadly used large multimodal model-based chatbot, ChatGPT-4o, still exhibits significant difficulties in engaging with physics tasks involving visual representations. While the chatbot shows potential for educational applications, including personalized tutoring and accessibility support for students who are blind or have low vision, its limitations necessitate caution. On the other hand, our findings can also be leveraged to design assessments that are difficult for chatbots to solve.

To efficiently manage plant diseases, Agriculture Cyber-Physical Systems (A-CPS) have been developed to detect and localize disease infestations by integrating the Internet of Agro-Things (IoAT). By the nature of plant and pathogen interactions, the spread of a disease appears as a focus with density of infected plants and intensity of infection diminishing outwards. This gradient of infection needs variable rate and precision pesticide spraying to efficiently utilize resources and effectively handle the diseases. This article, SprayCraft presents a graph based method for disease management A-CPS to identify disease hotspots and compute near optimal path for a spraying drone to perform variable rate precision spraying. It uses graph to represent the diseased locations and their spatial relation, Message Passing is performed over the graph to compute the probability of a location to be a disease hotspot. These probabilities also serve as disease intensity measures and are used for variable rate spraying at each location. Whereas, the graph is utilized to compute tour path by considering it as Traveling Salesman Problem (TSP) for precision spraying by the drone. Proposed method has been validated on synthetic data of locations of diseased locations in a farmland., Comment: 28 pages, 40 figures, 2 tables

Hamiltonian Truncation (HT) methods provide a powerful numerical approach for investigating strongly coupled QFTs. In this work, we develop HT techniques to analyse a specific Renormalization Group (RG) flow recently proposed in Refs. [1, 3]. These studies put forward Ginzburg-Landau descriptions for the conformal minimal models $M(3,10)$ and $M(3,8)$, as well as the RG flow connecting them. Specifically, the RG-flow is defined by deforming the $M(3,10)$ with the relevant primary operator $\phi_{1,7}$ (whose indices denote its position in the Kac table), yielding $M(3,10)+ \phi_{1,7}$. From the perspective of HT, realising such an RG-flow presents significant challenges, as the $\phi_{1,7}$ deformation requires renormalizing the UV theory up to third order in the coupling constant of the deformation. In this study, we carry out the necessary calculations to formulate HT for this theory and numerically investigate the spectrum of $M(3,10)+ \phi_{1,7}$ in the large coupling regime, finding strong evidence in favour of the proposed flow., Comment: 46 pages, 6 figures and 6 tables

Although pandemics are often studied as if populations are well-mixed, disease transmission networks exhibit a multi-scale structure stretching from the individual all the way up to the entire globe. The COVID-19 pandemic has led to an intense debate about whether interventions should prioritize public health or the economy, leading to a surge of studies analyzing the health and economic costs of various response strategies. Here we show that describing disease transmission in a self-similar (fractal) manner across multiple geographic scales allows for the design of multi-scale containment measures that substantially reduce both these costs. We characterize response strategies using multi-scale reproduction numbers -- a generalization of the basic reproduction number $R_0$ -- that describe pandemic spread at multiple levels of scale and provide robust upper bounds on disease transmission. Stable elimination is guaranteed if there exists a scale such that the reproduction number among regions of that scale is less than $1$, even if the basic reproduction number $R_0$ is greater than $1$. We support our theoretical results using simulations of a heterogeneous SIS model for disease spread in the United States constructed using county-level commuting, air travel, and population data.