We derive a factorization formula for boosted double resonant top-antitop pair production in $e^+e^-$ annihilation with a semileptonic top quark decay in the phase space region where the $b$-jet invariant mass is small. The decaying top quark state is defined through invariant mass measurements on the final states in the top and antitop hemispheres, and the $b$-jet is defined from clustering all hadrons in the top hemisphere. The factorization does not rely on the narrow width limit and accounts for the QCD off-shell and interference effects. The approach employs Soft-Collinear-Effective Theory and boosted Heavy-Quark-Effective-Theory and relies on a combination of factorization theorems known from $e^+e^-$ dijet production and inclusive semileptonic heavy meson endpoint decays. The result provides a first principles treatment of the dominant hadronization effects, which can be determined from $e^+e^-$ event shapes. In the factorization a new distribution function arises, called the ultra-collinear-soft (ucs) function, which encodes the Fermi motion of the decaying top quark within the state defined from the invariant mass measurement. The ucs function is a differential generalization of the inclusive bHQET jet function and shares properties of the shape function in semileptonic heavy meson decays. In frames where the top quark is very slow, it describes the coherent soft radiation arising from top production, propagation and decay, and encodes all effects that are non-factorizable from the perspective of the NW limit. Its form and renormalization depend on two light-cone momenta related to the top-jet and $b$-jet directions and their relative angle. Due to the large top quark width, the ucs function can be computed perturbatively, and we determine the QCD corrections at ${\cal O}(α_s)$. The anomalous dimension is known to three loops.

Gamma-Ray Bursts (GRBs) are the strongest explosions in the Universe, and are powered by initially ultra-relativistic jets. The angular profile of GRB jets encodes important information about their launching and propagation near the central source, and can be probed through their afterglow emission. Detailed analysis of the multi-wavelength afterglow light curves of recent GRBs indeed shows evidence for an extended angular structure beyond the jet's narrow core. The afterglow emission is determined by the jet angular structure, our viewing angle, and the magnetic field structure behind the shock, often leading to degeneracies when considering the light curves and broad-band spectrum alone. Such degeneracies can be lifted with joint modeling of the afterglow light curves and polarization. In this work we study the evolution of the afterglow linear polarization and flux density from steep, core-dominated GRB jets, where most of their energy resides within a narrow core. We explore the dependence of the light and polarization curves on the viewing angle, jet angular energy structure and magnetic field configuration, and provide an analytical approximation for the peak polarization level, which occurs at a time close to that of a break in the light curve. Finally, we demonstrate how our results can be used to determine the nature of orphan GRB afterglows, distinguishing between a quasi-spherical "dirty fireball" and a steep jets viewed far off-axis and apply them on the Zwicky Transient Facility (ZTF) detected orphan afterglow candidate AT2021lfa.

A majority of JWST/NIRSpec/IFU studies at high redshifts to date have focused on UV-bright or massive objects, while our understanding of low-mass galaxies at early cosmic times remains limited. In this work, we present NIRSpec/IFS high-resolution observations of two low-mass ($M_* < 10^9 \ M_\odot$), low-metallicity ($[12 + \log(\text{O/H})] < 8$) galaxies at $z \sim 7.66$, one of which we identify as hosting a Type-II AGN. We measure flat strong-line metallicity gradients, suggestive of ISM redistribution by outflows or past merging, but also identify tension with the direct-$T_\text{e}$ metallicity gradient in one galaxy. We measure $v_\text{rot}/σ< 1$ in both galaxies, consistent with observations of lower rotational support at early cosmic times. We identify broad kinematical components decoupled from galactic rotation with velocities of $\sim 250 - 500 \ \text{km} \ \text{s}^{-1}$ and argue these components trace outflows, for which we infer outflow rates of $\sim 8 - 14 \ M_\odot \ \text{yr}^{-1}$ with $v_\text{out}/v_\text{esc} \sim 1$. We compare our findings to results from the new large-volume AESOPICA simulations, which fully incorporate different models of black hole growth and AGN feedback. We find that our observational results of $v_\text{out}/v_\text{esc}$ are consistent with the simulated dwarf AGN population, hinting AGN-driven feedback may contribute to quenching both in our systems and in a wider population of low-mass galaxies in the early Universe. This novel study illustrates the necessity of deep IFU observations to decompose the complex kinematics and morphology of high-$z$ galaxies, trace outflows, and constrain the effect of feedback in the early Universe.

Recent 3D dust maps of the local Milky Way are revolutionizing our understanding of the Sun's Galactic neighborhood, providing much needed insight into the large-scale organization of the interstellar medium. Focusing on the largest scales in $\textit{Gaia}$-based 3D dust maps, we find a pattern of seven highly elongated, mostly parallel structures in the local $\sim 5\,\mathrm{kpc}^2$, five of which were previously unknown. These structures show pitch angles of $33.5 \pm 4.0 ^\circ$ and masses ranging from $10^5$ to $10^6$ $\mathrm{M}_\odot$. We refer to these structures as superclouds. Nearly all known star-forming regions in the solar neighborhood lie within the superclouds, primarily along their central axes, supporting the idea that they act as gas reservoirs for the formation of giant molecular clouds. All but one of the seven superclouds show an underlying undulation, indicating that this is not a property unique to the Radcliffe Wave. We find that while the superclouds have linear masses that vary by about a factor of 4, their volume densities only vary by about 10$\%$. This suggests that superclouds self-regulate their physical sizes and internal structure to maintain pressure equilibrium with their environment. These findings establish a new framework for understanding how large-scale Galactic structures shape the conditions for star formation in the solar vicinity, and likely in galaxies like the Milky Way.

Many white dwarfs are observed in compact double white dwarf binaries and, through the emission of gravitational waves, a large fraction are destined to merge. The merger remnants that do not explode in a Type Ia supernova are expected to initially be rapidly rotating and highly magnetized. We here present our discovery of the variable white dwarf ZTF J200832.79+444939.67, hereafter ZTF J2008+4449, as a likely merger remnant showing signs of circumstellar material without a stellar or substellar companion. The nature of ZTF J2008+4449 as a merger remnant is supported by its physical properties: hot ($35,500\pm300$ K) and massive ($1.12\pm0.03$ M$_\odot$), the white dwarf is rapidly rotating with a period of $\approx$ 6.6 minutes and likely possesses exceptionally strong magnetic fields ($\sim$ 400-600 MG) at its surface. Remarkably, we detect a significant period derivative of $(1.80\pm0.09)\times10^{-12}$ s/s, indicating that the white dwarf is spinning down, and a soft X-ray emission that is inconsistent with photospheric emission. As the presence of a mass-transferring stellar or brown dwarf companion is excluded by infrared photometry, the detected spin down and X-ray emission could be tell-tale signs of a magnetically driven wind or of interaction with circumstellar material, possibly originating from the fallback of gravitationally bound merger ejecta or from the tidal disruption of a planetary object. We also detect Balmer emission, which requires the presence of ionized hydrogen in the vicinity of the white dwarf, showing Doppler shifts as high as $\approx$ 2000 km s$^{-1}$. The unusual variability of the Balmer emission on the spin period of the white dwarf is consistent with the trapping of a half ring of ionised gas in the magnetosphere of the white dwarf.

In the context of quantum resource theories (QRTs), free states are defined as those which can be obtained at no cost under a certain restricted set of conditions. However, when taking a free state from one QRT and evaluating it through the optics of another QRT, it might well turn out that the state is now extremely resourceful. Such realization has recently prompted numerous works characterizing states across several QRTs. In this work we contribute to this body of knowledge by analyzing the resourcefulness in free states for--and across witnesses of--the QRTs of multipartite entanglement, fermionic non-Gaussianity, imaginarity, realness, spin coherence, Clifford non-stabilizerness, $S_n$-equivariance and non-uniform entanglement. We provide rigorous theoretical results as well as present numerical studies that showcase the rich and complex behavior that arises in this type of cross-examination.

Here we report on a new survey for pulsars and transients in the 10 pc region around Sgr A* using the Effelsberg radio telescope at frequencies between 4 to 8 GHz. Our calibrated full-Stokes data were searched for pulsars and transients using PulsarX, TransientX and PRESTO. Polarisation information is used in the scoring of the candidates. Our periodicity acceleration and jerk searches allowed us to maintain good sensitivity towards binary pulsars in $\gtrsim$ 10-hr orbits. In addition we performed a dedicated search in linear polarisation for slow transients. While our searches yielded no new discovery beyond the redetection of the magnetar SGR J1745-2900, we report on a faint single pulse candidate in addition to several weak periodicity search candidates. After thoroughly assessing our survey's sensitivity, we determined that it is still not sensitive to a population of millisecond pulsars. Next generation radio interferometers can overcome the limitations of traditional single-dish pulsar searches of the Galactic Centre.

Identifying quantum phase transitions poses a significant challenge in condensed matter physics, as this requires methods that both provide accurate results and scale well with system size. In this work, we demonstrate how relaxation methods can be used to generate the phase diagram for one- and two-dimensional quantum systems. To do so, we formulate a relaxed version of the ground-state problem as a semidefinite program, which we can solve efficiently. Then, by taking the resulting vector of moments for different model parameters, we identify all phase transitions based on their cosine similarity. Furthermore, we show how spontaneous symmetry breaking is naturally captured by bounding the corresponding observable. Using these methods, we reproduce the phase transitions for the one-dimensional transverse field Ising model and the two-dimensional frustrated bilayer Heisenberg model. We also illustrate how the phase diagram of the latter changes when a next-nearest-neighbor interaction is introduced. Overall, our work demonstrates how relaxation methods provide a novel framework for studying and understanding quantum phase transitions.

Light reprocessed by dust grains emitting in the infrared allows the study of the physics at play in dusty, embedded regions, where ultraviolet and optical wavelengths are attenuated. Infrared telescopes such as JWST have made it possible to study the earliest feedback phases, when stars are shielded by cocoons of gas and dust. This phase is crucial for unravelling the effects of feedback from young stars, leading to their emergence and the dispersal of their host molecular clouds. Here we show that the transition from the embedded to the exposed phase of star formation is short (< 4 Myr) and sometimes almost absent (< 1 Myr), across a sample of 37 nearby star-forming galaxies, covering a wide range of morphologies from massive barred spirals to irregular dwarfs. The short duration of the dust-clearing timescales suggests a predominant role of pre-supernova feedback mechanisms in revealing newborn stars, confirming previous results on smaller samples and allowing, for the first time, a statistical analysis of their dependencies. We find that the timescales associated with mid-infrared emission at 21 μm, tracing a dust-embedded feedback phase, are controlled by a complex interplay between giant molecular cloud properties (masses and velocity dispersions) and galaxy morphology. We report relatively longer durations of the embedded phase of star formation in barred spiral galaxies, while this phase is significantly reduced in low-mass irregular dwarf galaxies. We discuss tentative trends with gas-phase metallicity, which may favor faster cloud dispersal at low metallicities.

TeV haloes are extended sources of very-high-energy gamma rays found around some middle-aged pulsars. The emission spanning several tens of parsecs suggests an efficient confinement of the ultra-relativistic lepton pairs produced by pulsars in their vicinity. The physical mechanism responsible for this suppressed transport has not yet been identified. In some scenarios, pair confinement may be linked to the medium the pulsars are located in. We aim at understanding the type of medium pulsars probe over their lifetime. We developed a model for the environment probed by moving pulsars, from their birth in core-collapse explosions - where they receive a natal kick - until their entry into the interstellar medium. The model involves: (i) a Monte-Carlo sampling of the properties of the massive-star progenitors of pulsars; (ii) a calculation of the structure of the surrounding medium shaped by these progenitors for the two cases of isolated stars and star clusters; and (iii) a computation of the evolution of supernova remnants in these parent environments. Ultimately, from a distribution of neutron star kick velocities, we assess the medium in which pulsars are located as a function of time. We first derived the statistical properties of a fully synthetic Galactic population and then applied the model to a selection of known pulsars to assess the likely nature of their environment. We show that pulsars escape into the interstellar medium at around 300 kyr, significantly later than assumed in the literature. Given our assumptions, all known pulsars with a confirmed TeV halo have high probabilities of still being in their parent environment, which suggests that efficient pair confinement is connected to the region influenced by progenitor stars. To test this, we provide the probability that known pulsars still reside in their parent environment for a list of known pulsars.

High-cadence microlensing observations uncovered a population of very short-timescale microlensing events, which are believed to be caused by the population of free-floating planets (FFP) roaming the Milky Way. Unfortunately, the light curves of such events are indistinguishable from those caused by wide-orbit planets. To properly differentiate both cases, one needs high-resolution observations that would allow resolving a putative luminous companion to the lens long before or after the event. Usually, the baseline between the event and high-resolution observations needs to be quite long ($\sim 10$ yr), hindering potential follow-up efforts. However, there is a chance to use archival data if they exist. Here, we present an analysis of the microlensing event OGLE-2023-BLG-0524, the site of which was captured in 1997 with the Hubble Space Telescope (HST). Hence, we achieve a record-breaking baseline length of 25 years. A very short duration of the event ($t_E = 0.346 \pm 0.008$ d) indicates an FFP as the explanation. We have not detected any potential companion to the lens with the HST data, which is consistent with the FFP origin of the event. Thanks to the available HST data, we are able to reject from 25% to 48% of potential stellar companions depending on the assumed population model. Based on the finite-source effects in the light curve we measure the angular Einstein radius value $θ_E = 4.78 \pm 0.23 μas$, suggesting a super-Earth in the Galactic disk or a sub-Saturn-mass planet in the Galactic bulge. We show that the archival high-resolution images should be available for several microlensing events, providing us with the unprecedented possibility of seeing the lensing system as it was many years before the event.

This work presents a hardware-efficient and fully parallelizable decoder for quantum LDPC codes that leverages belief propagation (BP) with a speculative post-processing strategy inspired by classical Chase decoding algorithm. By monitoring bit-level oscillation patterns during BP, our method identifies unreliable bits and generates multiple candidate vectors to selectively flip syndromes. Each modified syndrome is then decoded independently using short-depth BP, a process we refer to as BP-SF (syndrome flip). This design eliminates the need for costly Gaussian elimination used in the current BP-OSD approaches. Our implementation achieves logical error rates comparable to or better than BP-OSD while offering significantly lower latency due to its high degree of parallelism for a variety of bivariate bicycle codes. Evaluation on the [[144,12,12]] bivariate bicycle code shows that the proposed decoder reduces average latency to approximately $70\%$ of BP-OSD. When post-processing is parallelized the average latency is reduced by $55\%$ compared to the single process implementation, with the maximum latency reaching as low as $18\%$. These advantages make it particularly well-suited for real-time and resource-constrained quantum error correction systems.

The pulsar J0537$-$6910 undergoes spin-up glitches more frequently than any other known pulsar, at a rate of roughly thrice per year. Its glitches are typically large and accompanied by spin-down rate changes $Δ\dotν$ that partially recover with a nearly constant positive frequency second derivative $\ddotν$ for the post-glitch intervals. The long-term value of $\ddotν$, however, is negative because $\dotν$ has decreased over the years of observations. We wish to determine if permanent shifts (non-relaxing parts of the glitch change $Δ\dotν$ in the spin-down rate, like those observed in the Crab pulsar) can explain the long-term enhancement of the spin-down rate which results in an effective negative braking index. We demonstrate, as a proof of concept, that the actual braking index associated with the pulsar's braking torque can be n~3 if the internal superfluid torque and permanent shifts are considered. We use published RXTE and NICER data to calculate the average permanent shift per glitch needed to bring an underlying braking index $n$ to the effective long-term value n' =-1.2 inferred from the data. We use this average value as the actual permanent shift in each glitch and extract the contributions of the internal and external torques to $\ddotν$, under the assumption that the next glitch occurs when all glitch-induced offsets to internal torques are fully restored. We find that if the braking index of the magnetospheric torque is close to n~3, moderate permanent changes of the spin-down rate are required, similar to those inferred for the Crab pulsar. The natural mechanism to produce such permanent changes is crustquakes. Crustal failure associated with PSR J0537$-$6910 glitches can have interesting and potentially observable consequences, such as transient changes of the X-ray emission, activation of radio emission, or emission of gravitational waves.

We present a detailed analysis of J154506, a strongly lensed submillimeter galaxy behind the Lupus-I molecular cloud, and characterisation of its physical properties using a combination of new and archival data, including VLT/MUSE and FORS2 optical data. We identify two high-significance (SNR>5) emission lines at 97.0 and 145.5 GHz, corresponding to CO(4-3) and CO(6-5), respectively, in the spectral scans from the Atacama Compact Array and the Large Millimetre Telescope and the [CII] 158~$μ$m fine-structure line at 400~GHz using the Atacama Pathfinder Experiment. These detections yield a spectroscopic redshift of $z_{\rm{spec}}=3.7515\pm0.0005$. We also report the detection of [CI], HCN(4-3), and two H$_2\rm{O}^+$ transitions, further confirming the redshift and providing insights into J154506's physical properties. By modeling sub-arcsecond resolution (0.75) ALMA Band 6 and 7 continuum data in the uv-plane, we derive an average magnification factor of $6.0\pm0.4$ and our analysis reveals a relatively cold dust (38K) in a starburst ($\sim900~\rm{M}_{\odot}yr^{-1}$) galaxy with a high intrinsic dust mass ($\sim2.5\times10^{9}~\rm{M}_{\odot}$) and infrared (IR) luminosity ($\sim6\times10^{12}~\rm{L}_{\odot}$). The non-local thermodynamic equilibrium radiative transfer modelling of the joint dust SED and CO line excitation suggests the dust continuum emission is primarily associated with relatively diffuse regions with molecular gas densities of $10^2-10^4\rm{cm}^{-3}$, rather than compact, high-pressure environments typical of extreme starbursts or AGNs. This is supported by the close-to-unity ratio between the dust and gas kinetic temperatures, which argues against highly energetic heating mechanisms. The CO excitation ladder peaks close to CO(5-4) and is dominated by slightly denser molecular gas.

We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition. Starting with the reduced linear problem, we obtain the asymptotic estimates for the solutions, as time $t\to\infty$, depending on the asymptotic behavior of the forcing term and boundary data. These are established in both cases when the drifts are uniformly bounded, and unbounded as $t\to\infty$. For the nonlinear problem, we prove the convergence of the solutions under suitable conditions that balance the growth of the nonlinear term with the decay of the data. To take advantage of the diffusion in the non-divergence form, we prove an inhomogeneous version of the Landis-typed Growth Lemma and apply it to successive time-intervals. At each time step, the center for the barrier function is selected carefully to optimize the contracting factor. Our rigorous results show the robustness of the model.

Monolithic preconditioners applied to the linear systems arising during the solution of the discretized incompressible Navier-Stokes equations are typically more robust than preconditioners based on incomplete block factorizations. Lower number of iterations and a reduced sensitivity to parameters like velocity and viscosity can significantly outweigh the additional cost for their setup. Different monolithic preconditioning techniques are introduced and compared to a selection of block preconditioners. In particular, two-level additive overlapping Schwarz methods (OSM) are used to set up monolithic preconditioners and to approximate the inverses arising in the block preconditioners. GDSW-type (Generalized Dryja-Smith-Widlund) coarse spaces are used for the second level. These highly scalable, parallel preconditioners have been implemented in the solver framework FROSch (Fast and Robust Overlapping Schwarz), which is part of the software library Trilinos. The new GDSW-type coarse space GDSW* is introduced; combining it with other techniques results in a robust algorithm. The block preconditioners PCD (Pressure Convection-Diffusion), SIMPLE (Semi-Implicit Method for Pressure Linked Equations), and LSC (Least-Squares Commutator) are considered to various degrees. The OSM for the monolithic as well as the block approach allows the optimized combination of different coarse spaces for the velocity and pressure components, enabling the use of tailored coarse spaces. The numerical and parallel performance of the different preconditioning methods for finite element discretizations of stationary as well as time-dependent incompressible fluid flow problems is investigated and compared. Their robustness is analyzed for a range of Reynolds and Courant-Friedrichs-Lewy (CFL) numbers with respect to a realistic problem setting.

Clumps in the rest-frame UV emission of galaxies have been observed for decades. Since the launch of the James Webb Space Telescope (JWST), a large population is detected in the rest-frame near-infrared (NIR), raising questions about their formation mechanism. We investigate the presence and properties of NIR over-densities (hereafter substructures) in star-forming and quiescent galaxies at 1 < z < 4 to understand their link to the evolution of their host galaxy. We identify substructures in JWST/NIRCam F277W and F444W residual images at a rest-frame wavelength of 1 um. The fraction of galaxies with substructures with M* > 10^9 Msun has been steadily decreasing with cosmic time from 40% at z = 4 to 10% at z = 1. Clumps, the main small substructures in the rest-frame NIR, are the most common type and are much fainter (2% of the flux) than similar UV clumps in the literature. Nearly all galaxies at the high-mass end of the main sequence (MS), starburst, and green valley regions have substructures. However, we do not find substructures in low-mass galaxies in the green valley and red sequence. Although massive galaxies on the MS and in the green valley have a 40% probability of hosting multiple clumps, the majority of clumpy galaxies host only a single clump. The fraction of clumpy galaxies in the rest-frame NIR is determined by the stellar mass and SFR of the host galaxies. Its evolution with redshift is due to galaxies moving towards lower SFRs at z < 2 and the build-up of low-mass galaxies in the green valley and red sequence. Based on their spatial distribution in edge-on galaxies, we infer that most of substructures are produced in-situ via disk fragmentation. Galaxy mergers may still play an important role at high stellar masses, especially at low SFR.

Neutral atoms recycled from wall interaction interact with confined plasma, thereby refueling it, most strongly in the region closest to the wall. This occurs near the X-point in diverted configurations, or else near the wall itself in limited configurations. A progression of analytic models are developed for neutral density in the vicinity of a planar or linear source in an ionizing domain. First-principles neutral transport simulations with DEGAS2 are used throughout to test the validity and limits of the model when using equivalent sources. The model is further generalized for strong plasma gradients or the inclusion of charge exchange. An important part of the problem of neutral fueling from recycling is thereby isolated and solved with a closed-form analytic model. A key finding is that charge exchange with the confined plasma can be significantly simplified with a reasonable sacrifice of accuracy by treating it as a loss. The several assumptions inherent to the model (and the simulations to which it is compared) can be adapted according to the particular behavior of neutrals in the divertor and the manner in which they cross the separatrix.

We show that an effective gravitational field naturally emerges in quantum materials with long-wavelength spin (or pseudospin) textures. When the itinerant electrons' spin strongly couples to the background spin texture, it effectively behaves as a spinless particle in a curved space, with the curvature arising from quantum corrections to the electron's spin orientation. The emergent curved space gives rise to the electron lensing effect, an analog of the gravitational lensing. The lensing effect can appear in systems without (emergent) magnetic fields, such as those with coplanar spin textures. Our work shows that novel ``gravitational'' phenomena generically appear in quantum systems due to nonadiabaticity, opening new research directions in quantum physics.

While entanglement is a cornerstone of quantum theory and holography, quantum correlations arising from superposition, such as quantum discord, offer a broader perspective that has remained largely unexplored in holography. We construct gravity duals of quantum discord and classical correlation. In both holographic systems and Haar random states, discord exceeds entanglement, revealing an additional quantum correlation linked to the Markov gap and non-distillable entanglement, suggesting holographic states are intrinsically non-bipartite. In black hole setups, discord can increase despite decoherence and persists beyond the sudden death of distillable entanglement. Motivated by the holographic formula, we define reflected discord -- an optimization-free boundary quantity based on reflected entropy -- which remains effective even outside the holographic regime. We also propose several multipartite generalizations of correlation measures. It includes holography-inspired correlations based on multi-entropy, which are shown to be UV-finite and reduce to bipartite measures in the bipartite limit. These results provide new tools for quantifying quantum correlations beyond entanglement in strongly coupled many-body systems and offer a novel approach to multipartite correlation measures.

We establish upper bounds on the lengths of minimal conjugators in 2-step nilpotent groups. These bounds exploit the existence of small integral solutions to systems of linear Diophantine equations. We prove that in some cases these bounds are sharp. This enables us to construct a family of finitely generated 2-step nilpotent groups $(G_m)_{m\in\mathbb{N}}$ such that the conjugator length function of $G_m$ grows like a polynomial of degree $m+1$.

The conjugator length function of a finitely generated group $Γ$ gives the optimal upper bound on the length of a shortest conjugator for any pair of conjugate elements in the ball of radius $n$ in the Cayley graph of $Γ$. We prove that polynomials of arbitrary degree arise as conjugator length functions of finitely presented groups. To establish this, we analyse the geometry of conjugation in the discrete model filiform groups $Γ_d = \mathbb{Z}^d\rtimes_ϕ\mathbb{Z}$ where is $ϕ$ is the automorphism of $\mathbb{Z}^d$ that fixes the last element of a basis $a_1,\dots,a_d$ and sends $a_i$ to $a_ia_{i+1}$ for $i<d$. The conjugator length function of $Γ_d$ is polynomial of degree $d$.

Context. The South Pole Telescope third-generation camera (SPT-3G) has observed over 10,000 square degrees of sky at 95, 150, and 220 GHz (3.3, 2.0, 1.4 mm, respectively) and will significantly overlap the ongoing 14,000 square-degree Euclid Wide Survey. The Euclid collaboration recently released Euclid Deep Field South (EDF-S) observations of 23 square degrees at wide field depths in the first quick data release (Q1). Aims. With the goal of releasing complementary millimeter-wave data and encouraging legacy science, we performed dedicated observations of a 57-square-degree field overlapping the EDF-S. Methods. The observing time totaled 20 days, and we reached noise depths of 4.3, 3.8, and 13.2 $μ$K-arcmin at 95, 150, and 220 GHz, respectively. Results. In this work we present the temperature maps and two catalogs constructed from these data. The emissive source catalog contains 601 objects (334 inside EDF-S) with 54% synchrotron-dominated sources and 46% thermal dust emission-dominated sources. The 5$σ$ detection thresholds are 1.7, 2.0, and 6.5 mJy in the three bands. The cluster catalog contains 217 cluster candidates (121 inside EDF-S) with median mass $M_{500c}=2.12 \times 10^{14} M_{\odot}/h_{70}$ and median redshift $z$ = 0.70, corresponding to an order-of-magnitude improvement in cluster density over previous tSZ-selected catalogs in this region (3.81 clusters per square degree). Conclusions. The overlap between SPT and Euclid data will enable a range of multiwavelength studies of the aforementioned source populations. This work serves as the first step toward joint projects between SPT and Euclid and provides a rich dataset containing information on galaxies, clusters, and their environments.

Graph states are a powerful class of entangled states with numerous applications in quantum communication and quantum computation. Local Clifford (LC) operations that map one graph state to another can alter the structure of the corresponding graphs, including changing the number of edges. Here, we tackle the associated edge-minimisation problem: finding graphs with the minimum number of edges in the LC-equivalence class of a given graph. Such graphs are called minimum edge representatives (MER) and are crucial for minimising the resources required to create a graph state. We leverage Bouchet's algebraic formulation of LC-equivalence to encode the edge-minimisation problem as an integer linear program (EDM-ILP). We further propose a simulated annealing (EDM-SA) approach guided by the local clustering coefficient for edge minimisation. We identify new MERs for graph states with up to 16 qubits by combining EDM-SA and EDM-ILP. We extend the ILP to weighted-edge minimisation, where each edge has an associated weight, and prove that this problem is NP-complete. Finally, we employ our tools to minimise the resources required to create all-photonic generalised repeater graph states using fusion operations.

Precise cosmological constraints from type Ia supernovae require adequately accurate corrections for host-galaxy extinction. Modelling these corrections is challenged by the problem of disentangling supernova intrinsic colours from host-galaxy interstellar reddening. The latter is commonly modelled in a probabilistic way assuming an exponential distribution exp(-E(B-V)/τ) as a universal prior which is applied across all types of supernova host galaxies. We test the robustness of the exponential model and its universality against predictions based on simulating dust and type Ia supernova distributions in host galaxies of different morphological types. We find substantial differences between predicted interstellar reddening in late- and early-type host galaxies, primarily driven by the stellar-to-dust mass ratios. The mean simulated reddening in late-type galaxies matches well those derived from type Ia supernova observations, but it is significantly lower for early-type host galaxies. The reddening distributions exhibit an excess of sight lines with vanishing reddening with respect to the exponential model, although the difference is quite mild for late-type galaxies. On the other hand, the distribution may peak at E(B-V)>0 when considering a population of young type Ia supernovae originating from lower heights within the dust disc. We demonstrate that assuming a universal reddening prior distribution for modeling peak magnitude-colour relation, which is currently a common practice, gives rise to a spurious scatter in the derived extinction properties. It may also bias relative distances between supernovae originating from different host-galaxy populations. The discrepancy between the simulated reddening in average early-type host galaxies and the observed occurrence of reddened supernovae suggests that reddening does not originate from interstellar dust expected in these galaxies.

We study the boundedness of a mutation class for quivers with real weights. The main result is a characterization of bounded mutation classes for real quivers of rank 3.

While 2-level systems, aka qubits, are a natural choice to perform a logical quantum computation, the situation is less clear at the physical level. Encoding information in higher-dimensional physical systems can indeed provide a first level of redundancy and error correction that simplifies the overall fault-tolerant architecture. A challenge then is to ensure universal control over the encoded qubits. Here, we explore an approach where information is encoded in an irreducible representation of a finite subgroup of $U(2)$ through an inverse quantum Fourier transform. We illustrate this idea by applying it to the real Pauli group $\langle X, Z\rangle$ in the bosonic setting. The resulting two-mode Fourier cat code displays good error correction properties and admits an experimentally-friendly universal gate set that we discuss in detail.

The advent of spatiotemporal wave packets (STWPs), represented by spatiotemporal optical vortices (STOVs), has paved the way for the exploration in optics and photonics. To date, despite considerable efforts, a comprehensive and efficient practical means to characterizing wave packets with such complex structures is still lacking. In this study, we introduced a new method designed to achieve high-precision and high-throughput spatiotemporal wave packet measurements using a user-friendly set up. This method is based on a quadriwave lateral shearing interferometric wavefront sensor that utilizes wavelength division multiplexing, termed the "spatiotemporal wavefront sensor (STWFS)." Using this method, we have fabricated a compact prototype with 295 * 295 spatial pixels * 36 wavelength channels of 0.5 nm spectral resolution in a single frame. This STWFS enabled, for the first time, single-shot self-referenced spatiotemporal three-dimensional (3D) optical field characterizations of STOV pulses with transverse orbital angular momenta L of 1 and 2, and obtained the dynamic visualization of the focused propagation of STOV pulses. Furthermore, the STWFS provides a 1.87 nm (0.95%) root mean square (RMS) absolute accuracy for spatiotemporal phase reconstruction. This achievement represents the highest performance compared with other three-dimensional spatiotemporal metrology methods. As a spatiotemporal optical field characterization method, the STWFS offers ultrafast 3D diagnostics, contributing to spatiotemporal photonics and broader applications across different fields, such as light-matter interactions and optical communications.

In this study, we propose a parametric finite element method for a degenerate multi-phase Stefan problem with triple junctions. This model describes the energy-driven motion of a surface cluster whose distributional solution was studied by Garcke and Sturzenhecker. We approximate the weak formulation of this sharp interface model by an unfitted finite element method that uses parametric elements for the representation of the moving interfaces. We establish existence and uniqueness of the discrete solution and prove unconditional stability of the proposed scheme. Moreover, a modification of the original scheme leads to a structure-preserving variant, in that it conserves the discrete analogue of a quantity that is preserved by the classical solution. Some numerical results demonstrate the applicability of our introduced schemes.

We amend and extend the Chiarella model of financial markets to deal with arbitrary long-term value drifts in a consistent way. This allows us to improve upon existing calibration schemes, opening the possibility of calibrating individual monthly time series instead of classes of time series. The technique is employed on spot prices of four asset classes from ca. 1800 onward (stock indices, bonds, commodities, currencies). The so-called fundamental value is a direct output of the calibration, which allows us to (a) quantify the amount of excess volatility in these markets, which we find to be large (e.g. a factor $\approx$ 4 for stock indices) and consistent with previous estimates; and (b) determine the distribution of mispricings (i.e. the difference between market price and value), which we find in many cases to be bimodal. Both findings are strongly at odds with the Efficient Market Hypothesis. We also study in detail the 'sloppiness' of the calibration, that is, the directions in parameter space that are weakly constrained by data. The main conclusions of our study are remarkably consistent across different asset classes, and reinforce the hypothesis that the medium-term fate of financial markets is determined by a tug-of-war between trend followers and fundamentalists.