In this article we study the structured distance to singularity for a nonsingular matrix $A\in\mathbb{C}^{n\times n}$, with a prescribed linear structure $\mathcal{S}$ (for instance, a sparsity pattern, or a real Toeplitz structure), i.e., the norm of the smallest perturbation $Δ\in \mathcal{S}$, such that $A + Δ$ is singular. This is an example of structured matrix nearness problem: a family of problems that arise in control and systems theory and in numerical analysis, when characterizing the robustness of a certain property of a system with respect to perturbations that are constrained to a certain structure (for example the structure of the nominal system). We start by highlighting the parallelism between two main tools which have been proposed in the literature: a gradient system approach for a functional in the eigenvalues, which requires the solution of certain low-rank matrix differential equations (see [Guglielmi, Lubich, Sicilia, SINUM 2023]), and a two-level optimization approach in which the inner linear least-squares problem is solved explicitly (see [Usevich, Markovsky, JCAM 2014] and [Gnazzo, Noferini, Nyman, Poloni, FoCM 2025]). In particular, these articles underline the remarkable property that $Δ$ is (at least generically) the orthogonal projection onto the structure $\mathcal{S}$ of a rank-1 matrix $uv^*$. This property and the parallelism suggest a new reformulation of the problem into a system of nonlinear equations in the two vector unknowns $u,v \in\mathbb{C}^n$. We study this new formulation, and propose an algorithm to solve these nonlinear equations directly with the multivariate Newton's method. We discuss how to avoid the singularity of such system of nonlinear equations, and how to ensure monotonic convergence. The resulting algorithm is faster than the existing ones for large matrices, and maintains comparable accuracy.

Quantum tracking control encodes the desired dynamics into a tailored driving field; here, we let the system find its own way there. We propose a real-time feedback control framework in which a proportional controller continuously corrects a simple transform-limited field based on the instantaneous mismatch between two systems' responses - producing the required control on the fly, without prior waveform design. The framework is demonstrated on two distinct examples: a single-active-electron atom, where hydrogen is driven to mimic argon's strong-field optical emission, and a Fermi-Hubbard chain, where a weakly interacting lattice reproduces the transport dynamics of a Mott-insulating reference. By shifting the control paradigm from predesigned inputs to adaptive response tracking, this approach establishes closed-loop feedback as a broadly applicable route to programmable quantum dynamics.

There are precisely four arrangements of two point-hyperplane anti-flags. We consider the corresponding relations on the set of such anti-flags and show that each of them can be recovered from any other except in one special case. If the field consists of two elements, then one of the relations cannot be used to recover each of the remaining three. This is related to a bijection between anti-flags and exterior points of the hyperbolic polar space which exists in this case.

The sub-parsec circumnuclear density profiles of galaxies represent a key element in our understanding of the accretion history and fuel availability of supermassive black holes (SMBHs). Observations that directly resolve sub-parsec scales in galaxies require extremely high resolution and generally hot (bright) environments, making this impossible in all but the nearest active galaxies. Transient accretion events onto previously quiescent SMBHs, such as a tidal disruption event (TDE), offer a new avenue to understand SMBHs and their environments. Radio-bright outflows from TDEs directly probe the ambient density at $10^{-3}-1$ pc scales, allowing direct constraints on the circumnuclear density of TDE host galaxies (i.e., quiescent galaxies). Here we present, using radio observations of a sample of 11 TDE hosts, a new methodology for fitting observed TDE radio emission to constrain their sub-parsec circumnuclear density profiles. Our findings reveal that TDE host galaxies exhibit circumnuclear density profiles remarkably consistent with the expectations of a simple Bondi accretion flow ($n_e\propto R^{-3/2}$). Under the assumption of a Bondi profile, we present a new method to jointly fit the outflow mass and ambient densities, in order to constrain the Bondi accretion rate and temperature. For the TDE host galaxies in our sample, we constrain a sample average Bondi accretion rate Eddington fraction of $\log_{10}f_{\rm{Edd}} = -3.96^{+0.30}_{-0.38}$ (as well as individual fits to each host). This work provides a methodology by which radio observations of TDEs can provide powerful constraints on the sub-parsec density distribution of quiescent SMBHs -- well inside the Bondi sphere. This opens up a new observational avenue to constrain sub-parsec gas distributions in a broad range of galaxies.

We investigate the formation and interaction of solitons in the non-integrable Ostrovsky equation characterized by anomalous (positive) dispersion. This equation is relevant for describing wave phenomena in various media, including plasma, solids, and optical fibers. Our findings indicate that certain Ostrovsky solitons, which possess zero total ''mass'' and exhibit non-monotonic asymptotic behavior, can arise from initial perturbations of a pulse-like nature. These solitons may organize into regular trains, where they are arranged according to their amplitude, or they may form irregular, nonstationary configurations of bound interacting solitons, or even multi-soliton structures. Furthermore, we demonstrate that the interactions between solitons in the Ostrovsky equation are inelastic, resulting in the emergence of a dominant soliton, or ''soliton-champion,'' within closed systems, such as those with periodic boundary conditions. In such systems, the soliton with the highest amplitude acts as a ''terminator,'' annihilating smaller amplitude solitons and absorbing a portion of their energy. We also analyze the recurrence phenomenon and determine that, although it resembles that of the Korteweg-de Vries equation, it exhibits distinct features.

I reduce the cost to prepare magic states with lattice surgery operations on the surface code by using a recursive implementation of 15-to-1 magic state distillation. On a rotated surface code with distance $d$, $|T\rangle$ preparation requires a $d$-by-$3 d$ grid of data qubits for up to $15 d$ error correction cycles, and $|CCZ\rangle$ preparation requires a $3 d$-by-$2 d$ grid for up to $10.5 d$ cycles. However, a significantly lower physical error threshold than that of the underlying surface code is required to match the error probability of the output magic state with the logical error rate of the output surface code at large code distances.

We study the Fourier approximation $\mathcal{F}_N$ of the sign function by the Krawtchouk polynomials. We give numerical evidence that the Gibbs phenomenon of the approximation differs from the classical Gibbs constant; this is in contrast to other families of orthogonal polynomials. We also show that the steepness $\mathcal{F}_N'(0)$ of the approximation is bounded by explicitly proving $\lim_{N \to \infty} \mathcal{F}_N'(0) = \log 4$. This is also in contrast to approximations by classical orthogonal polynomials, where the steepness has been shown to be unbounded as the degree increases.

Shared-nothing geo-distributed SQL databases, such as CockroachDB, are increasingly vital for enterprise applications requiring data resilience and locality. However, we encountered significant performance degradation at the customer side, especially when their deployments span multiple data centers over a Wide Area Network (WAN). Our investigation identifies the bottleneck in the performance of the Distributed Hash Join (Dist-HJ) algorithm, which is contingent upon a crucial balance between communication overhead and computational load. This balance is severely disrupted when processing skewed data from real-world customer workloads, leading to the observed performance decline. To tackle this challenge, we introduce Bala-Join, an adaptive solution to balance the computation and network load in Dist-HJ execution. Our approach consists of the Balanced Partition and Partial Replication (BPPR) algorithm and a distributed online skewed join key detector. The former achieves balanced redistribution of skewed data through a multicast mechanism to improve computational performance and reduce network overhead. The latter provides real-time skewed join key information tailored to BPPR. Furthermore, an Active-Signaling and Asynchronous-Pulling (ASAP) mechanism is incorporated to enable efficient, real-time synchronization between the detector and the redistribution process with minimal overhead. Empirical study shows that Bala-Join outperforms the popular Dist-HJ solutions, increasing throughput by 25%-61%.

We analyze a linear parabolic equation with homogeneous Dirichlet boundary conditions posed in domains whose evolution may involve topological transitions. The domains are described as sublevel sets of a smooth space-time level set function, allowing for transitions such as domain splitting and merging and the creation or vanishing of islands and holes. We introduce anisotropic space-time function spaces that extend the classical Bochner spaces used in cylindrical domains and establish key functional-analytic properties of these spaces, including the density of compactly supported smooth functions. This framework enables the application of the Babuška-Banach theorem, yielding existence, uniqueness, and a priori estimates for weak solutions. The analysis applies to domain evolutions generated by level set functions with isolated nondegenerate critical points, which correspond to the generic topology changes classified by Morse theory in two and three spatial dimensions.

Two-dimensional topological translationally-invariant (TTI) quantum codes, such as the toric code (TC) and bivariate bicycle (BB) codes, are promising candidates for fault-tolerant quantum computation. For such codes to be practically relevant, their decoders must successfully correct the most likely errors while remaining computationally efficient. For the TC, graph-matching decoders satisfy both requirements and, additionally, admit provable performance guarantees. Given the equivalence between TTI codes and (multiple copies of) the TC, one may then ask whether TTI codes also admit analogous graph-matching decoders. In this work, we develop a graph-matching approach to decoding general TTI codes. Intuitively, our approach coarse-grains the TTI code to obtain an effective description of the syndrome in terms of TC excitations, which can then be removed using graph-matching techniques. We prove that our decoders correct errors of weight up to a constant fraction of the code distance and achieve non-zero code-capacity thresholds. We further numerically study a variant optimized for practically relevant BB codes and observe performance comparable to that of the belief propagation with ordered statistics decoder. Our results indicate that graph-matching decoders are a viable approach to decoding BB codes and other TTI codes.

We investigate the Couette-Taylor problem for a steady incompressible viscous fluid in a 3D cylindrical annulus, where one of the two cylinders is still, under both Dirichlet and boundary conditions involving the vorticity that naturally appear in the weak formulation. The outcome of this study is twofold. First, we explicitly determine all the solutions with a specific geometric \emph{partial invariance}, which coincide with the so-called spiral Poiseuille or Poiseuille-Couette flows depending on the boundary conditions. Second, for small boundary data, we provide stability of such solutions, that is, no steady finite-energy perturbations are admissible. To achieve this result in presence of vorticity boundary conditions, we find a substantial analytical difference depending on which cylinder is still.

Quantum error correction is critical to the design and manufacture of scalable quantum computing systems. Recently, there has been growing interest in quantum low-density parity-check codes as a resource-efficient alternative to surface codes. Their adoption is hindered by the difficulty of compiling fault-tolerant logical operations. A key challenge is that logical qubits do not necessarily map to disjoint sets of physical qubits, which limits parallelism. We introduce clustered-cyclic codes, a quantum low-density parity-check code family with finite-size instances such as [[136,8,14]] and [[198,18,10]] that are competitive with state-of-the-art constructions. These codes admit a directly addressable logical basis, enabling highly parallel logical measurement layers. To leverage this structure, we propose parallel product surgery for quantum product codes. Using an auxiliary copy of the data patch and an engineered product-connection structure, the protocol performs many logical Pauli-product measurements in a single surgery round with small, fixed overhead. For clustered-cyclic codes, this yields surface-code-style maximal parallelism: up to k/2 disjoint Pauli-product measurements per round under explicit algebraic conditions. We prove that parallel product surgery preserves the code distance for hypergraph product codes and numerically verify distance preservation for the listed clustered-cyclic instances with k = 8. Finally, for the [[24,8,3]] clustered-cyclic code, treating half of the logical qubits as auxiliaries enables arbitrary parallel CNOTs on disjoint pairs; combined with symmetry-derived operations, these gates generate the full Clifford group fault-tolerantly.

Mutual events of trans-Neptunian binaries (TNBs) provide rare opportunities to measure the physical and orbital properties of small bodies in the outer solar system. However, successful observations of these events have been limited by uncertain predictions. Here, we present probabilistic predictions of TNB mutual events occurring through the 2030s, using high-precision non-Keplerian orbit solutions from the Beyond Point Masses project combined with a Bayesian framework that propagates orbital and size uncertainties. Our methods generate distributions of event timing, duration, depth, and probability of occurrence, enabling direct assessment of observability. We provide predictions for five systems with ongoing or imminent mutual event seasons, including (38628) Huya, (58534) Logos-Zoe, (148780) Altjira, (469705) Kágára and !Hãunu, and (524366) 2001 XR$_{254}$. Preparing for upcoming events with long-baseline light curve monitoring is vital, as events may be difficult to distinguish from a regular rotational light curve. Rapid dissemination of event detections will benefit the entire community, allowing predictions to be updated, ensuring that these rare mutual event opportunities can be fully exploited.

Spin-lattice relaxation theory has been developed over almost a century, but some cardinal assumptions on the nature of the interactions involved have never been fully verified. This includes the weak coupling approximation, which makes it possible to describe spin dynamics perturbatively and leads to the canonical description of spin relaxation in terms of one- and two-phonon processes. Here, we extend the first-principles theory of spin relaxation to three-phonon processes and apply it to the vdW crystal of a spin-1/2 Chromium nitride complex. Results show that three-phonon contributions to spin relaxation only become relevant at temperatures inaccessible to experiments for this molecule, thus providing unprecedented evidence for the validity of the weak spin-phonon coupling assumption in spin relaxation theory. At the same time, we numerically show that a relatively small increase in spin-phonon coupling would lead to a crossover between three- and two-phonon processes' efficiency at room temperature, illustrating the possibility for three-phonon effects in molecular materials as well as paving the way to a systematic exploration of strong coupling in spin systems.

The ability to fault-tolerantly prepare CAT states, also known as multi-qubit GHZ states, is an important primitive for quantum error correction. It is required for Shor-style syndrome extraction, and can also be used as a subroutine for doing fault-tolerant state preparation of CSS codewords. Existing approaches to fault-tolerant CAT state preparations have been found using computationally expensive heuristics involving SAT solving, reinforcement learning, or exhaustive analysis. In this paper, we constructively find optimal circuits for CAT states in a more scalable way. In particular, we derive formal lower bounds on the number of CNOT gates required for circuits implementing $n$-qubit CAT states that do not spread errors of weight at most $t$ for $1\leq t \leq 5$. We do this by using fault-equivalent rewrites of ZX-diagrams to reduce it to a problem of characterising certain 3-regular simple graphs. We then provide families of such optimal graphs for infinitely many values of $n$ and $t\leq5$. By encoding the construction of optimal graphs as a constraint satisfaction problem we find explicit constructions for circuits that match this lower bound on CNOT count for all $n\leq50$ and $t \leq 5$ and for nearly all pairs $(n,t)$ with $n\leq 100$ and $t\leq 5$ or $n\leq 50$ and $t\leq 7$, significantly extending the regimes that were achievable by previous methods and improving the resource counts for existing constructions. We additionally show how to trade CNOT count against depth, allowing us to construct constant-depth fault-tolerant implementations using $O(n)$ ancilla and $O(n)$ CNOT gates.

We develop a calculus of space-time controlled fields for rough stochastic systems. This approach provides a unified composition rule for evaluating random fields along rough semimartingales and yields a rough stochastic Itô-Wentzell formula under natural and verifiable regularity assumptions. Our motivation comes from works of Hudde et al. (2024) and, independently, Del Moral and Singh (2022) where the authors established, respectively, Itô-Alekseev-Gröbner, backward Itô-Wentzell, and diffusion interpolation formulas.

Quantized vortex dynamics in superfluid $^4$He (He~II) are widely regarded as well established: circulation is quantized in units of $κ=h/m_4$, vortices carrying more than one quantum are expected to split into singly quantized filaments, and vortex rings shrink while accelerating due to dissipation from thermal-quasiparticle scattering. Using particle tracking velocimetry with frozen deuterium tracers, we uncover rare vortex-bound particle events that disrupt this canonical picture. In a class of events exhibiting the acceleration characteristic of shrinkage driven vortex ring motion, the measured kinematics cannot be reconciled with a singly quantized ring. Instead, they require an effective circulation $nκ$ with $n>1$, directly challenging the standard expectation that multiquantum vortices are short lived. A more prosaic possibility is that the inferred $nκ$ arises from a bundle of closely spaced singly quantized rings, which could generate similar large-scale motion. However, this scenario is disfavored by vortex-filament simulations that show rapid bundle dispersion. Furthermore, the persistence of particle trapping at the observed high speeds suggests a much deeper core trapping potential, consistent only with a truly multiquantum core. Together, these results point to anomalously long-lived multiquantum rings, a striking puzzle that calls for dedicated scrutiny beyond the prevailing paradigm.

We establish a new global endpoint Sobolev inequality for measures that extends the classical theorem of Meyers-Ziemer by placing a maximal function on the right-hand side. This result has several significant consequences. It extends naturally to functions of weighted bounded variation and yields corresponding capacity and isoperimetric inequalities. The inequality is also closely connected to endpoint estimates for fractional operators, including bounds for fractional maximal functions and Hardy space endpoint estimates for the Riesz potential. Our main inequality yields a family of endpoint inequalities, characterized in terms of subrepresentation formulas, Lorentz space improvements, and isoperimetric inequalities for measures and bounded open sets. When one moves away from the endpoint to $p>1$, the analogous inequalities no longer hold in general; however, we identify a sharp bumped maximal function for which the corresponding non-endpoint inequality is valid. Finally, we show that this framework yields new $(p,p)$ two-weight Sobolev inequalities.

The usual belief propagation (BP) decoders are, in general, exchanging local information on the Tanner graph of the quantum error-correcting (QEC) code and, in particular, are known to not have a threshold for the surface code. We propose novel BP decoders that exchange messages on the decoding graph and obtain code capacity thresholds via standalone BP for the surface code under depolarizing noise. Our approach, similarly to the minimum weight perfect matching (MWPM) decoder, is applicable to any graphlike QEC code. The thresholds observed with our decoders are close to those obtained by MWPM. This result opens the path towards scalable hardware-accelerated implementations of MWPM-compatible decoders.

We study sweeping processes in a Hilbert space driven by time-dependent uniformly prox-regular sets, allowing the moving constraint to exhibit discontinuities of bounded variation. We introduce a new integral formulation for bounded-variation trajectories, given by a global variational inequality tested against continuous admissible trajectories, and we compare it with the standard differential-measure formulation, in which the differential measure of the trajectory is constrained by the proximal normal cone. In the prox-regular (generally nonconvex) framework, the variational inequality necessarily includes a quadratic correction term reflecting the hypomonotonicity of proximal normal cones. Under mild regularity assumptions on the moving set, including lower semicontinuity in time, uniform prox-regularity of the values, and a selection-extension property guaranteeing a rich class of test trajectories (satisfied, for instance, in the convex case and for bounded prox-regular sets), we prove that the new integral formulation is equivalent to the differential-measure formulation. This yields a unified bounded-variation notion of solution for prox-regular sweeping processes. We further establish a Brézis-Ekeland-Nayroles-type variational characterization via a prox-regular variational residual: the residual is nonpositive along every admissible trajectory, and solutions are exactly those trajectories for which this residual attains its maximal value, namely zero. As a consequence, we prove a stability result: a uniform limit of admissible trajectories with vanishing residual is a solution of the limit sweeping process. The resulting variational framework provides a robust tool for stability and approximation analyses in the prox-regular, nonconvex setting.

We investigate the hierarchical flavor structure of the Standard Model in a Froggatt-Nielsen (FN) framework, where the spontaneous breaking of a $U(1)_{\rm FN}$ symmetry by a complex flavon field generates fermion masses and mixing patterns through higher-dimensional operators. Extending the setup with three right-handed neutrinos (RHNs), light neutrino masses arise via the Type-I seesaw mechanism. Allowing complex FN coefficients enables a consistent description of the CKM and PMNS matrices while inducing CP-violating signatures in meson decays. Building on our previous work, where the lightest RHN acts as a viable dark matter (DM) candidate produced through freeze-in or freeze-out mechanisms, we investigate the origin of the baryon asymmetry of the Universe. The heavier RHNs generate a lepton asymmetry through out-of-equilibrium decays, including both Standard Model channels and additional flavon-induced processes in which the flavon appears as an intermediate or final-state particle. We compute the corresponding one-loop CP asymmetries and incorporate these effects in the Boltzmann equations. We show that although freeze-in and freeze-out DM production occur in two qualitatively distinct regions of the FN symmetry-breaking scale $v_ϕ$, successful thermal leptogenesis can be achieved in both regimes. In the large-$v_ϕ$ (freeze-in-compatible) region the results approach the standard leptogenesis limit, while in the freeze-out-compatible region the lower value of $v_ϕ$ implies lighter RHNs, requiring resonant enhancement. This tightly constrained framework, in which $v_ϕ$ simultaneously controls RHN masses and the interaction strengths of the flavon and DM sectors, provides a predictive and unified description of flavor hierarchies, neutrino masses, CP violation, dark matter, and baryogenesis within a single effective theory.

Experiments indicate that collective coupling of molecular ensembles to confined optical modes can modify excited-state dynamics and photochemical reactivity. To describe such cavity-induced effects at atomic resolution, semi-classical molecular dynamics approaches have been developed that treat nuclear motion classically while describing the collective light-matter interaction within the Tavis-Cummings framework of quantum electrodynamics. Here, we benchmark mixed quantum-classical approaches, Ehrenfest dynamics and Fewest-Switches Surface Hopping (FSSH), for simulating nonadiabatic dynamics of electronically strongly coupled carbon monoxide molecules. Their predictions are compared against numerically exact quantum dynamics simulations performed with the multi-configuration time-dependent Hartree (MCTDH) method, which treats both electronic and nuclear degrees of freedom quantum mechanically. We find that the semi-classical approaches reproduce the qualitative features of the full quantum dynamics. Quantitative agreement is best achieved with FSSH when a decoherence correction is included. These results demonstrate that mixed quantum-classical methods provide a computationally efficient and quantitatively reliable alternative to fully quantum simulations for investigating nonadiabatic photochemistry under collective electronic strong coupling in systems beyond the reach of exact quantum treatments.

We study how idiosyncratic firm-level shocks generate aggregate volatility and tail risk when they propagate through a production network under overlapping adjustment: new productivity draws arrive before the economy reaches the static equilibrium associated with earlier draws. Each innovation generates a `productivity wave' that mixes and dissipates over time as it travels through the production network. Macroeconomic fluctuations emerge from the interference between these waves of different vintages. The interference between these waves is governed by the dominant transient eigenvalue of the production network, and therefore so is the macroeconomic fluctuations they generate. In such a dynamic regime, the tail of the degree distribution is a markedly weaker determinant of macro fluctuations than in the fully adjusted static benchmark. And the macroeconomic significance of the degree-heterogeneity of production networks cannot be known without knowing the rate at which the economy converges to equilibrium or equivalently the spectral properties of the production network. More concretely, once we permit the time-averaging of shocks, granular shocks may account for only a small fraction of the empirically observed aggregate volatility.

Writing efficient distributed code remains a labor-intensive and complex endeavor. To simplify application development, the Flexible Computational Science Infrastructure (FleCSI) framework offers a user-oriented, high-level programming interface that is built upon a task-based runtime model. Internally, FleCSI integrates state-of-the-art parallelization backends, including MPI and the asynchronous many-task runtimes (AMTRs) Legion and HPX, enabling applications to fully leverage asynchronous parallelism. In this work, we benchmark two applications using FleCSI's three backends on up to 1024 nodes, intending to quantify the advantages and overheads introduced by the AMTR backends. As representative applications, we select a simple Poisson solver and the multidimensional radiation hydrodynamics code HARD. In the communication-focused Poisson solver benchmark, FleCSI achieves over 97% parallel efficiency using the MPI backend under weak scaling on up to 131072 cores, indicating that only minimal overhead is introduced by its abstraction layer. While the Legion backend exhibits notable overheads and scaling limitations, the HPX backend introduces only marginal overhead compared to MPI+Kokkos. However, the scalability of the HPX backend is currently limited due to the usage of non-optimized HPX collective operations. In the computation-focused radiation hydrodynamics benchmarks, the performance gap between the MPI and HPX backends fades. On fewer than 64 nodes, the HPX backend outperforms MPI+Kokkos, achieving an average speedup of 1.31 under weak scaling and up to 1.27 under strong scaling. For the hydrodynamics-only HARD benchmark, the HPX backend demonstrates superior performance on fewer than 32 nodes, achieving speedups of up to 1.20 relative to MPI and up to 1.64 relative to MPI+Kokkos.

Titan is regarded as a natural laboratory in the Solar System for studying atmospheric photochemistry and the abiotic production of organic molecules on cold small exoplanets. Since the end of the Cassini-Huygens mission, telescope observations have enabled new detections of increasingly complex carbon-based molecules at infrared and sub-millimetre wavelengths, while the optical regime has been largely overlooked. Following a recent tentative detection of the 405 nm absorption band of C3 in Titan in archived optical VLT UVES spectra at resolving power R = 60000, this work reports an eight sigma detection of the C3 405 nm absorption band in Titan using dedicated ultra high resolution VLT ESPRESSO observations at R = 190000, the highest spectral resolution optical observations of Titan to date. The VLT ESPRESSO spectrum is compared to model spectra of Titan with varying C3 abundances. A chi squared analysis is used to assess the agreement between non solar spectral features and C3 absorption as the C3 abundance is varied, and a Bayesian Markov Chain Monte Carlo fit between model and observed spectra is performed. The chi squared analysis yields an eight sigma detection of C3, consistent with a C3 column density of approximately 1.5E13 cm-2, while the MCMC fit retrieves a C3 column density of 1.47E13 cm-2 at five sigma. These values are consistent with the order of magnitude predicted by photochemical models, which reach parts per million levels in the Titan mesosphere. This work demonstrates the usefulness of instruments and techniques originally developed for exoplanet research when applied to Solar System targets.

We establish a trace formula for signatures of hermitian forms over Azumaya algebras with involution, extending Knebusch's work on symmetric bilinear forms over finite étale extensions of commutative base rings. As an application when the base ring is semilocal, we obtain an exact sequence for total signatures, related to Pfister's local-global principle and the notion of stability index.

We analyse an inverse seesaw scenario with 3+3 gauge singlets. The flavour structure is determined by a flavour symmetry, Delta (3 n^2) or Delta (6 n^2), n integer, and CP and their residual groups among charged leptons and the neutral states. For the latter, the Dirac mass matrix of the gauge singlets carries all non-trivial flavour structure. Consequently, the heavy sterile states form three pseudo-Dirac pairs which have in general distinct masses. We discuss the signal strength of different charged lepton flavour violating processes. Ensuring that the lepton mixing angles can be accommodated at the 3 sigma level or better, we find that the current bounds on the branching ratios of mu -> e gamma, mu -> 3 e, tau -> l gamma and tau -> 3 l, l=e, mu, as well as the rate of mu-e conversion in nuclei do not strongly constrain the considered parameter space, while the limits expected from the upcoming experiments Mu3E, COMET and Mu2e will have a relevant impact.

Nonreciprocal phenomena are currently a major focus of research within the fields of classical and quantum technology. In this work, we theoretically investigate the interplay among multiple magnomechanically induced transparency (MMIT) windows, Fano resonances, slow/fast light, and nonreciprocal absorption and group delay in a hybrid cavity magnomechanical system. This system is composed of two yttrium iron garnet (YIG) spheres and a membrane positioned at the center of the cavity. By analyzing the absorption spectrum of a weak probe field in the presence of a strong control field, we demonstrate the emergence of five transparency windows resulting from combined photon-phonon, photon-magnon, and phonon-magnon interactions. The photon-phonon coupling associated with the membrane plays a crucial role in enhancing and tailoring these transparency features. We further examine the impact of the Barnett effect on the absorption and dispersion characteristics, showing that it enables the controllable manipulation of transparency windows and the generation of tunable Fano resonance profiles. The influence of cavity decay and magnon dissipation rates on the spectral response is also analyzed. In addition, we demonstrate that the group delay of the transmitted probe field can be effectively tuned via the photon-phonon coupling strength and the Barnett effect, allowing for a controllable transition between slow and fast light regimes. Finally, nonreciprocal absorption and group delay are achieved through appropriate adjustment of the coupling parameters. These findings highlight the potential of the proposed hybrid system for applications in optical signal processing and quantum information technologies.

For a fixed graph class $Π$, the goal of $Π$-Modification is to transform an input graph $G$ into a graph $H\inΠ$ using at most $k$ modifications. Vertex and edge deletions are common operations, and their (parameterized) complexity for various $Π$ is well-studied. Classic graph modification operations such as edge deletion do not consider the geometric nature of geometric graphs such as (unit) disk graphs. This led Fomin et al. [ITCS' 25] to initiate the study of disk scaling as a geometric graph modification operation for unit disk graphs: For a given radius $r$, each modified disk will be rescaled to radius $r$. In this paper, we generalize their model by allowing rescaled disks to choose a radius within a given interval $[r_{\min}, r_{\max}]$ and study the (parameterized) complexity (with respect to $k$) of the corresponding problem $Π$-Scaling. We show that $Π$-Scaling is in XP for every graph class $Π$ that can be recognized in polynomial time. Furthermore, we show that $Π$-Scaling: (1) is NP-hard and FPT for cluster graphs, (2) can be solved in polynomial time for complete graphs, and (3) is W[1]-hard for connected graphs. In particular, (1) and (2) answer open questions of Fomin et al. and (3) generalizes the hardness result for their variant where the set of scalable disks is restricted.

Thermonuclear X-ray bursts from the surface of accreting neutron stars are the most common astrophysical explosions in our galaxy. They provide a unique window into the physics of neutron stars, the physics of matter under extreme conditions, and the physics of astrophysical thermonuclear explosions. X-ray bursts are powered by a broad range of nuclear reactions that need to be understood to interpret observations. The relevant nuclei are mostly neutron deficient and unstable, and thus experimental information and theoretical understanding is limited and an active area of research in nuclear science. We review the current status of the nuclear physics of X-ray bursts, with special emphasis on new experimental and theoretical information on a large number of reaction rates. As such we provide an overview of the broad experimental and theoretical methods currently used to advance the nuclear physics of X-ray bursts. The new information is used to update the public JINA REACLIB database with 32 new reaction rates based on experimental information, and a new dataset of theoretical statistical model reaction rates where no experimental information is available. Using several models for X-ray bursts that are powered by mixed hydrogen and helium burning, we take advantage of the updated nuclear data to review the current understanding of the nuclear reaction sequences in such X-ray bursts, the modeling of light curves, and predictions of the composition of nuclear ashes.