We study radiative processes of two qubits coupled to a massless scalar field prepared in the Minkowski vacuum state. The analyze the effects of vacuum fluctuations in the generation of qubits' entangled states is performed. We assume one of the qubits is at rest in an inertial frame while the other comoves with a uniformly rotating frame, i.e., undergoing circular motion. We investigate how the entanglement harvesting phenomenon depends on the radius and angular velocity of the non-inertial qubit. We compute the concurrence and mutual information to identify the set of circular motion parameters that maximizes entanglement generation.

A central challenge in financial economics is understanding how credit networks form under informational noise. We introduce the concept of topological capital, arguing that banks increasingly rely on topological certification, interpreting a borrower's connectivity as a primary proxy for creditworthiness. Using a novel dataset of bank-firm relationships manually extracted from Italian financial statements, we implement a multi-stage empirical framework, benchmarking empirical patterns against a maximum-entropy benchmark, to separate the determinants of credit access from those of loan volumes. Our results indicate that network topology systematically outperforms traditional fundamentals. In the link-formation stage, connectivity breeds further connectivity through an amplified preferential attachment mechanism. In the loan-sizing stage, network strength absorbs the explanatory power of balance-sheet metrics, documenting a profound network substitution effect where topological signals effectively replace physical collateral across all corporate segments. For SMEs, we identify a critical signal divergence: reported debt acts as a risk signal, while network footprint serves as market validation. Furthermore, we reveal a diversification paradox: while firms fragment debt to avoid hold-up risks, over-diversification leads to a complexity penalty that stagnates credit depth and inflates systemic Loss Given Default. Ultimately, our findings signal the twilight of the balance sheet as the primary anchor of corporate lending, calling for a shift toward topological macro-prudential supervision to manage vulnerabilities invisible to traditional bilateral indicators.

Computational workloads are growing exponentially, driving power consumption to unsustainable levels. Efficiently distributing large-scale networks is an NP-Complete problem equivalent to Boolean satisfiability (SAT), making it one of the core challenges in modern computation. To address this, physics and device inspired methods such as Ising systems have been explored for solving SAT more efficiently. In this work, we implement an Ising model equivalence of the 3-SAT problem using a ReRAM crossbar fabricated in the Skywater 130 nm CMOS process. Our ReRAM-based algorithm achieves $91.0\%$ accuracy in matrix representation across iterative reprogramming cycles. Additionally, we establish a foundational energy profile by measuring the energy costs of small sub-matrix structures within the problem space, demonstrating under linear growth trajectory for combining sub-matrices into larger problems. These results demonstrate a promising platform for developing scalable architectures to accelerate NP-Complete problem solving.

We investigate how chemical substitution reshapes the energetics of twin formation in non-modulated (NM) Ni-Mn-Ga martensite. Using density functional theory, we compute generalized planar fault energy (GPFE) curves for the $(101)[10\bar{1}]$ shear system in stoichiometric Ni$_{2}$MnGa and in a set of doped supercells containing Cu, Co, Fe, or Zn on different sublattices. The GPFE landscape is used as a microscopic descriptor of twinning behavior: the first barrier reflects intrinsic stacking-fault formation (twin nucleation), whereas subsequent barriers govern twin thickening and boundary motion. We show that the impact of dopants is strongly site dependent. Substitutions Cu$\rightarrow$Mn, Cu$\rightarrow$Ni, Co$\rightarrow$Ni, and Zn$\rightarrow$Mn lower the nucleation barrier and generally soften the GPFE profile, indicating more favorable conditions for twin formation and propagation; these cases also correlate with a reduced tetragonality $c/a$, which implies a smaller twinning shear and a reduced energetic cost of twin formation. In contrast, Cu$\rightarrow$Ga, Co$\rightarrow$Mn, Co$\rightarrow$Ga, Fe$\rightarrow$Ga, and Zn$\rightarrow$Ga increase GPFE barriers and hinder twinning, even though such substitutions are often used to enhance martensite stability and raise $T_{m}$. Fe$\rightarrow$Mn leaves barrier heights largely unchanged, while Fe$\rightarrow$Ni produces an anomalous GPFE response indicative of unstable twin configurations. Finally, inspired by the nanotwinning characterisation of 10M/14M modulation, we link the depth of the two-layer nanotwin minimum to modulation stability. The substitutions Fe$\rightarrow$Mn, Cu$\rightarrow$Ni, and Zn$\rightarrow$Mn result in a lower energy minimum compared to the structure without the double-layered twin. The other substitutions favor the twin-free NM structure.

Distributing quantum workloads over many Quantum Processing Units (QPUs) is a crucial step in scaling up quantum computers toward practical quantum advantage due to the limitations in size of a single QPU. In the absence of high-fidelity quantum interconnects, circuit knitting could provide a path to computing certain properties of large quantum systems on many QPUs of limited size in a distributed fashion using only classical communication. Circuit knitting partitions large quantum circuits into manageable sub-circuits, however, reconstructing observables in a straightforward manner comes at an exponential cost in sampling and classical post-processing. To mitigate the overhead this technique incurs, we introduce an Adaptive Circuit Knitting (ACK) method that finds efficient partitions of quantum circuits by discovering regions of minimal entanglement between subsystems. We simulate 1D and 2D disordered mixed-field Ising models up to 60 qubits and show that the ACK approach can reduce circuit knitting sampling overheads by up to four orders of magnitude for observables of interest. We highlight our parallel GPU-accelerated implementation and discuss the need for efficient classical simulators to enable distributed quantum algorithm development. Our techniques could enable efficient distribution of quantum simulation for both near-term and fault-tolerant architectures.

The Tate conjecture predicts that Galois-invariant classes in $\ell$-adic cohomology, and Frobenius-invariant classes in crystalline cohomology, arise from algebraic cycles. We prove an unconditional p-adic analogue of this principle in the 1-motivic range. Our starting point is a full-faithfulness theorem for Deligne 1-motives: after p-adic scalar extension, the Barsotti-Tate crystal functor identifies Hom-groups of 1-motives with Hom-groups in the category of filtered Dieudonne modules. Using the equivalence between the derived category of 1-motives up to isogeny and the 1-motivic part of Voevodsky's triangulated category of effective motives with rational coefficients, we extend this full-faithfulness result to the entire 1-motivic thick subcategory. More precisely, over a finite field $k = F_q$, we show that every Frobenius-compatible morphism between Barsotti-Tate crystalline realizations is induced by a unique 1-motivic morphism. Consequently, the Frobenius-invariant classes that occur in this range are already motivic and therefore algebraic. This yields an explicit linear-algebraic description of motivic morphisms and extension classes in level at most 1 in terms of Frobenius-equivariant maps preserving the Hodge filtration, giving a crystalline analogue of the principle that Tate classes are algebraic without invoking cycle conjectures in codimension at least 2.

\textbf{Background:} Fairness and diversity are receiving growing attention in software engineering, particularly as AI and machine learning systems increasingly influence decision-making processes. While fairness is often examined at the algorithmic or data level, there is limited understanding of how it is addressed during the early stages of software development. Moreover, little is known about how team diversity affects fairness-related decisions in software projects. \textbf{Aims:} This study investigates how diversity in software teams influences fairness-aware behavior during requirements prioritization. \textbf{Method:} A controlled experiment was conducted with 27 pairs of software engineering students, including 13 LGBTQ diverse pairs and 14 non diverse pairs. Each pair prioritized user stories with varying fairness implications. Descriptive statistics were used to analyze attitudes and prioritization outcomes, and thematic analysis was applied to examine the reasoning behind participants' decisions. \textbf{Results:} Both groups demonstrated general alignment with fairness principles, prioritizing features that promoted equitable treatment and rejecting those that posed fairness risks. However, LGBTQ diverse pairs were more consistent in rejecting fairness risking stories and made fewer fairness related misprioritization errors. Their reasoning emphasized inclusion, non discrimination, and ethical responsibility, whereas non diverse pairs adopted a more pragmatic, goal oriented perspective. \textbf{Conclusions:} The findings indicate that fairness should be considered from the earliest stages of software development. Team diversity can enhance the identification and interpretation of fairness issues during requirements analysis, fostering more reflective and inclusive decision making.

Let a torus $T$ act on a symplectic manifold $(M,ω)$ with moment map $ϕ$. We say that the Hamiltonian $T$-manifold $(M,ω,ϕ)$ has complexity one if $\frac{1}{2} \dim M - \dim T = 1$, and that it is Kähler if it admits an invariant compatible complex structure. In this paper, we show how the class of Kähler complexity one Hamiltonian $T$-manifolds sits inside the class of complexity one Hamiltonian $T$-manifolds by proving that every compact, connected Kähler complexity one Hamiltonian $T$-manifold has a trivial painting. As a corollary, we show that two tall compact, connected Kähler complexity one Hamiltonian $T$-manifolds are symplectomorphic exactly if they have the same genus, Duistermaat-Heckman measure, and skeleton. Here, $(M,ω,ϕ)$ is tall exactly if every non-empty fiber $ϕ^{-1}(α)$ contains more than one orbit.

We study a setting where a set of agents engage in pairwise exchanges of freely replicable goods (e.g., digital goods such as data), where two agents grant each other a copy of a good they possess in exchange for a good they lack. Such exchanges introduce a fundamental tension: while agents benefit from acquiring additional goods, they incur negative externalities when others do the same. This dynamic typically arises in real-world scenarios where competing entities may benefit from selective collaboration. For example, in a data sharing consortium, pharmaceutical companies might share (copies of) drug discovery data, when the value of accessing a competitor's data outweighs the risk of revealing their own. In our model, an altruistic central planner wishes to design an exchange protocol (without money), to structure such exchanges between agents. The protocol operates over multiple rounds, proposing sets of pairwise exchanges in each round, which agents may accept or reject. We formulate three key desiderata for such a protocol: (i) individual rationality: agents should not be worse off by participating in the protocol; (ii) incentive-compatibility: agents should be incentivized to share as much as possible by accepting all exchange proposals by the planner; (iii) stability: there should be no further mutually beneficial exchanges upon termination. We design an exchange protocol for the planner that satisfies all three desiderata. While the above desiderata are inspired by classical models for exchange, free-replicability and negative externalities necessitate novel and nontrivial reformalizations of these goals. We also argue that achieving Pareto-efficient agent utilities -- often a central goal in exchange models without externalities -- may be ill-suited in this setting.

The images of Sagittarius A${}^*$ published by the Event Horizon Telescope (ETH) Collaboration in 2022 present features that were associated with an emission ring consistent with what is expected from an accretion disc surrounding the supermassive black hole at the center of our Galaxy. Here, we generate images of Sgr~A${}^*$ across different configurations of a simple accretion disc model that became successful, in our previous work, in reproducing the main features observed in M87*. Their best image, here reproduced in Fig. 1, suggests a geometric configuration of an inclined disk with three bright regions; which we have considered as our first configuration. Since we were not convinced with the results of this first configuration, we also explore in detail the case of nearly edge-on orientations which are a priori the expected geometry for a relaxed disc, as seen from the plane of the galaxy. We have produced simulated images using an efficient ray tracing and geodesic deviation methodology that allows to account for deformation, relativistic and magnification effects. We compare our synthetic images with the EHT images reconstructed with data from April 6 and 7 of 2017. We found that, although the EHT Collaboration seems to discard the image from April 6, our best suggested image resembles the output from the {\sc Themis} pipeline for April 6; which for us gives support for the edge-on configuration.

In a recent paper, Thejitha and Fathima introduced the overcolored partition function $\bar{a}_{r,s}(n)$, which enumerates overpartitions in which even parts may appear in one of $r$ colors and odd parts in one of $s$ colors, for fixed integers $r,s \geq 1$. They also proposed several conjectures concerning families of congruences modulo powers of $2$ for specific arithmetic progressions of $\bar{a}_{r,s}(n)$. In this paper, we provide an elementary proof of this conjecture that relies only on classical $q$-series manipulations and properties of Ramanujan's theta function.

Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the large number of degrees of freedom, and it is challenging on quantum computers due to the linear and unitary nature of quantum mechanics. We develop a quantum algorithm to tackle nonlinear differential equations driven by the Ornstein-Uhlenbeck (OU) stochastic process. The query complexity of our algorithm scales logarithmically with the error tolerance and nearly quadratically with the simulation time. Our algorithmic framework comprises probabilistic Carleman linearization (PCL) to tackle nonlinearity coupled with stochasticity, and stochastic linear combination of Hamiltonian simulations (SLCHS) to simulate stochastic non-unitary dynamics. We obtain probabilistic exponential convergence for the Carleman linearization of Liu et al. [1], provided the NSDE is stable and reaches a steady state. We extend deterministic LCHS to stochastic linear differential equations, retaining near-optimal parameter scaling from An et al. [2] except for the nearly quadratic time scaling. This is achieved by using Monte Carlo integration for time discretization of both the stochastic inhomogeneous term in LCHS and the truncated Dyson series for each Hamiltonian simulation.

With more than 6000 exoplanets discovered so far, about 12 percent are hot Jupiters. Their large sizes and short orbital periods make them valuable targets for studying planetary formation, atmospheres, and orbital evolution. We present a homogeneous analysis of the WASP-19 b system using a 15 year dataset to investigate both its orbital dynamics and atmospheric properties. We test whether the transit times show evidence for tidal orbital decay, apsidal precession, or periodic perturbations from an additional body, and we also construct a photometric transmission spectrum. Multi-wavelength light curves are modeled with PRISM to account for starspots, and linear, quadratic, and cubic ephemeris models are fitted to the transit timing residuals. Our dataset includes 27 new transits and reveals no statistically significant periodic signal. Although none of the tested models fully reproduces the timing scatter, the transit times show systematic deviations from a constant period and are best described by the cubic ephemeris, indicating a slow long-term trend over the full baseline. This behavior is more consistent with gradual apsidal precession than with monotonic tidal decay. A precession model yields a rate of 1.00 +/- 0.12 x 10^-4 rad per orbit and a planetary Love number k2p = 0.107 +/- 0.08. The transmission spectrum shows signatures of Na, K, and H2O, with no strong evidence for TiO or VO. These results suggest that apsidal precession may dominate the long-term orbital evolution of WASP-19 b. Continued high-precision timing and spectroscopic observations are needed to further test this scenario.

Surface temperature is a fundamental Essential Climate Variable, serving as a primary indicator of climate change and exerting a profound influence on ecosystems, agriculture, and human livelihoods. Although existing research provides a foundation for understanding the climate of Ghana, there remains an opportunity to enhance this landscape with granular station-level analysis. Such high-resolution analysis complements existing studies by capturing localised climatic nuances. This study conducts a detailed spatio-temporal analysis of temperature trends across 22 meteorological stations from 1983 to 2021. Using daily maximum (Tmax) and minimum (Tmin) observations, data were subjected to quality control, homogeneity testing, and homogenisation according to World Meteorological Organisation (WMO) standards, using AgERA5 reanalysis as a reference.The significance and magnitude of trends were determined using the Modified Mann-Kendall test, which is robust in handling potential effects of autocorrelation, and Sen's slope estimator. Results revealed that temperature trends in Ghana are highly localised and seasonal, highlighting the necessity for more studies of this nature. A critical finding is the asymmetric warming across the country, with minimum temperatures rising at an accelerated rate compared to maximum temperatures. This narrowing of the diurnal temperature range poses significant threats to agricultural stability and public health because nocturnal cooling is diminished. These findings underscore the urgent need for site-specific, seasonal climate monitoring to inform customised adaptation strategies. To mitigate these impacts, the study recommends a robust policy framework focusing on afforestation and the transition to green energy.

In quantum information theory and statistical physics, symmetries of multiple copies, or replicas, of a system play a pivotal role. For unitary ensembles, these symmetries are encoded in the replicated commutant: the algebra of operators commuting with the ensemble across $k$ replicas. Determining the commutant is straightforward for the full unitary group, but remains a major obstacle for structured, computationally relevant circuit families. We solve this problem for matchgate circuits, which prepare fermionic Gaussian states on $n$ qubits. Using a Majorana fermion representation, we show that operators coupling different system copies generate the orthogonal Lie algebra $\mathfrak{so}(k)$, endowing the space of invariants with rich and tractable structure. This underlying symmetry decomposes the matchgate commutant into irreducible sectors, which we completely resolve via a Gelfand--Tsetlin construction. We provide an explicit orthonormal basis of the matchgate commutant for all $k$ and $n$, together with a formula for its dimension that grows polynomially in $n$. Furthermore, we characterize the commutant of the Clifford--matchgate subgroup, showing that restricting to signed permutations of Majorana modes yields a commutant that qualitatively diverges from the matchgate case for $k \geq 4$ replicas. Ultimately, our orthonormal basis turns algebraic classification into a working toolbox. Using it, we derive closed-form expressions for matchgate twirling channels and a fermionic analogue of Weingarten calculus, the projector encoding all moments of the Gaussian state orbit, state and unitary frame potentials, the average nonstabilizerness of fermionic Gaussian states, a systematic hierarchy of non-Gaussianity measures, and a fermionic de Finetti theorem.

To investigate gauge theories with near-term quantum computers warrants exploration of nontraditional quantum simulators to find resource-efficient simulation protocols and ultimately access exotic features of different field theories, including unexplored regimes of the QCD phase diagram. In this work, using superconducting transmon qutrit processors, we formulate and implement a pulse-based, three-level, hybrid analog-digital simulation protocol of the (1+1) dimensional Abelian Higgs model (AHM) on two sites. Alongside this approach, we experimentally realize a gate-based implementation of the same model. Using the natural mapping of the three-level truncation of the transmon Hilbert space to the spin-1 truncated AHM, we observe real time dynamics of AHM field observables, which are analogous to electric field operators, with both protocols. For the analog-digital protocol, we engineer a Floquet simulation with a combination of local analog drives, driven modification of the natural interaction Hamiltonian of the two transmons, and dynamical decoupling pulses. For the digital protocol, we use a state-of-the-art qutrit processor to implement a Trotterized simulation of the model incorporating advanced error mitigation techniques. We further discuss the scalability of the two approaches, and their potential to be extended to the simulation of other model Hamiltonians. Our experiments demonstrate a viable platform for future studies of spin-1 and SU(3) based gauge theory models on current and near-term transmon qutrit processors.

We present some of the first infrared spectral maps acquired by SPHEREx. These maps, which to our knowledge are the largest of their type ever compiled in the near-infrared, reveal multiple strong lines due to interstellar ices and polycyclic aromatic hydrocarbons (PAHs) throughout the Cygnus X and North American Nebula regions. The maps emphasize the strongest features arising from the 3 $μ$m H$_2$O, 4.27 $μ$m CO$_2$, and 4.67 $μ$m CO lines and the 3.28 $μ$m PAH feature, all of which are detected over large areas with complex and filamentary spatial distributions. The ice absorption maps of H$_2$O and CO$_2$ in particular broadly trace dense, cold, and well-shielded regions across Cygnus X, consistent with the established picture of efficient ice formation in dense molecular clouds. The interstellar ice features are also detected abundantly in diffuse absorption over wide areas. The relative strength of the H$_2$O and CO$_2$ features varies among different lines of sight, indicating possible differences in local physical conditions or chemical variations. The 3.28 $μ$m PAH emission correlates with the emission from the 7.7 and 11.2 $μ$m features, but shows small differences that may trace the grain size distribution and variations in the ambient UV field. SPHEREx all-sky spectral imaging, of which only a small fraction is showcased in this work, will support numerous science investigations including the structure of the Galaxy, the physics of the interstellar medium, and the chemistry of stars.

In this paper, we introduce ribbon TQFTs via Edge Contraction/Construction Axioms of colored ribbon graphs as an extension of the 2D TQFT axioms for ribbon graphs formulated in arXiv:1508.05922. We investigate nearly Frobenius structures and Almost TQFTs defined in arXiv:1907.05470 together with ribbon TQFTs. We give a classification result for ribbon TQFTs that extends the one obtained for Frobenius algebras in arXiv:1508.05922. In particular, the Edge Contraction/Construction Axioms of colored ribbon graphs in this work become equivalent to the functorial Axioms of TQFTs governed by the sewing principle of Atiyah and Segal discussed in arXiv:2510.03128 and arXiv:1907.05470. As an application, we obtain that the recursion of generalized Catalan numbers can be twisted by Almost TQFT for co-unital nearly Frobenius algebra.

We prove a conjecture of Kumbhakar, Roy, and Srinivasan (2024) on the classification of order one differential equations, and a conjecture of Kumbhakar and Srinivasan (2025) on higher order equations. Both conjectures are shown to be results of recent work in differential Galois theory. In both cases, stronger versions of the conjectures hold when working over the field of constants. We use inverse Galois theory to show the conjectures cannot be improved over any nonconstant differential field. We also show how certain recent results of Jaoui and Moosa (2024) on abelian reductions of differential equations can be recovered from the work of Kumbhakar and Srinivasan (2025) and vice versa.

Paper I in this series introduced a model in which seed radio bursts produced by a hotspot anchored in the magnetosphere of a highly-magnetic neutron star (NS) are greatly amplified by strong gravitational self-lensing and thus give rise to Fast Radio Bursts (FRBs). Key features of the FRB population such as the observed dichotomy between repeating and non-repeating sources, their large luminosities and the high-energy power-law distribution of their bursts naturally arise in the model from the amplification dependence on the relative orientation of the rotation axis with respect to the hotspot and the line of sight. Here we compare the model predictions with Five-hundred-meter Aperture Spherical radio Telescope (FAST) data from repeaters and with the general population of FRBs. We find that the burst energy distribution from FRB 20121102A can be explained by assuming two antipodal hotspots in the NS magnetosphere, both producing seed bursts with the same log-normal energy distribution. This scenario implies a well-aligned system geometry, with the rotation axis, line of sight, and hotspot sites separated by $\lesssim 2$°. Similar constraints are found for FRB 20201124A and FRB 20220912A, and weaker ones for FRB 20190520B, owing to its smaller burst sample. We also show that precession of the NS rotation axis can explain the time evolution of the burst energy distribution from FRB 20121102A as well as its temporary disappearance. In application to a cosmological population of randomly-oriented sources the model predicts distance and fluence distributions of FRBs in good agreement with those from a completeness-selected subsample of the first CHIME/FRB catalogue, provided the energy distribution of seed bursts spans a range of ${\sim10^{35}-10^{38}}$ erg.

We propose a novel test of the unitarity of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix at collider experiments. Our approach exploits the incomplete cancellation between $t$-channel neutrino exchange and $s$-channel gauge-boson contributions that arises in the presence of violation of the flavor-diagonal PMNS unitarity conditions, leading to an anomalous growth of the cross section with energy. Such effects are generic in extensions of the Standard Model in which light neutrinos mix with heavier states, and can manifest at colliders as long as the characteristic energy of the process remains below the mass threshold of the new degrees of freedom. After briefly reviewing these scenarios, we employ our strategy to derive model-independent bounds on flavor diagonal unitarity-violating effects using LEP-II data. We then present sensitivity projections for future lepton and hadron colliders, demonstrating that they are well suited to probe the unitarity of the neutrino mixing matrix with this method.

We present a method to construct approximate analytic expressions for Ricci-flat Kähler metrics on Calabi-Yau threefolds with explicit dependence on the Kähler moduli. Our strategy combines numerical data obtained from machine learning with an explicit analytic Ansatz for the Kähler potential and symbolic regression methods. Specifically, we use neural networks to learn the Kähler potential at selected points in Kähler moduli space, fit this data to analytic expressions with Kähler moduli-dependent parameters, and determine an analytic form of these coefficients as functions of the Kähler moduli using symbolic regression. In this way, we reconstruct closed-form approximations to the Ricci-flat metric that retain explicit Kähler-moduli dependence. We apply this method to two Calabi-Yau threefolds with $h^{1,1}=2$, namely a bicubic hypersurface in $\mathbb{P}^2 \times \mathbb{P}^2$ and a bi-degree $(2,4)$ hypersurface in $\mathbb{P}^1 \times \mathbb{P}^3$, both of which admit nontrivial discrete symmetry groups that simplify the structure of the metric. In both cases, the resulting analytic expressions reproduce the numerically learned Kähler potentials with percent-level accuracy and respect the discrete symmetry of the underlying manifold. Our results represent a concrete bridge between purely numerical results for Calabi-Yau metrics and analytic constructions, opening the door to a systematic study of their dependence on Kähler moduli.

We derive a novel factorization theorem for $N$-jettiness at hadron colliders, which incorporates coherence-violating effects induced by Glauber gluons and several new momentum modes. Their interplay generates coherence-violating logarithms (CVLs) starting at four-loop ($N\ge1$) or five-loop order ($N=0$). We calculate the anomalous dimensions required for the resummation of CVLs and establish a general framework for the systematic treatment of coherence violation. Our findings imply that most existing factorization formulas for global LHC observables must be revised.

Precise halo mass ($M_h$) measurements are crucial for cosmology and galaxy formation. HaloFlow introduced a simulation-based inference (SBI) framework that uses state-of-the-art simulated galaxy images to precisely infer $M_h$. However, for HaloFlow to be applied to observations, it must be generalizable even when the underlying galaxy formation physics differ from those in the simulations on which it was trained. Without this generalization, HaloFlow produces biased and overconfident $M_h$ posteriors when applied to simulations with different physics. We introduce HaloFlow$^{\rm DA}$, an extension of HaloFlow that integrates domain adaptation (DA) with SBI to mitigate these cross-simulation shifts. Using synthetic galaxy images forward-modeled from the IllustrisTNG, EAGLE, and SIMBA simulations, we test two DA methods: Domain-Adversarial Neural Networks (DANN) and Maximum Mean Discrepancy (MMD). Incorporating DA significantly reduces bias and improves calibration, with MMD achieving the most stable performance, lowering the normalized residual metric, $β$, by an average of 31% and up to 57% when trained and tested on different simulations. Overall, HaloFlow$^{\rm DA}$ produces more robust, less biased with similar precision, $M_h$ constraints than the standard approach using the stellar-to-halo mass relation. HaloFlow$^{\rm DA}$ enables consistent, simulation-trained inference models to generalize across domains, establishing a foundation for robust $M_h$ inference from real HSC-SSP observations.

Due to their simultaneous optimization for radial and parallel neoclassical transport, quasi-isodynamic fields have been the main choice of stellarator magnetic configuration for most fusion reactor candidates in recent years. However, achieving a high degree of quasi-isodynamicity often comes at the cost of a strong shaping of the flux surfaces of the stellarator and complex coil geometries. In this work, the concepts of quasi-isodynamicity and piecewise omnigenity are combined to form QI-pwO fields. These fields are quasi-isodynamic in the low-field region of the magnetic surface, whereas they significantly depart from quasi-isodynamicity in the high-field region without sacrificing the neoclassical transport properties of quasi-isodynamic fields. This departure could make it easier to integrate the optimization of neoclassical transport with other physical and technological aspects of a stellarator reactor.

We introduce a detailed analysis of the convergence of first-order methods with composite noise (sum of relative and absolute) in gradient for convex and smooth function minimization. This paper illustrates instances of practical problems where the utilization of inexact oracles becomes necessary, such as biased compressors, use of floating-point arithmetic and gradient-free optimization. We propose an algorithm that optimally accumulates absolute error, with intermediate convergence depending on the relative component of the noise. Usage of restart technique, regularization transformation, and stopping criteria has been demonstrated to yield results for various function classes. Also, gradient descent adaptive to relative error parameter is provided. For relative noise, lower bounds of convergence are given, confirming the dependence of the parameter of the noise on the condition number of the problem.

This paper introduces a no-arbitrage, Monte Carlo-free approach to pricing path-dependent interest rate derivatives. The Heath-Jarrow-Morton model gives arbitrage-free contingent claims prices but is infinite-dimensional, making traditional numerical methods computationally prohibitive. To make the problem computationally tractable, I cast the stochastic pricing problem as a deterministic partial differential equation (PDE). Finance-Informed Neural Networks (FINNs) solve this PDE directly by minimizing violations of the differential equation and boundary condition, with automatic differentiation efficiently computing the exact derivatives needed to evaluate PDE terms. FINNs achieve pricing accuracy within 0.04 to 0.07 cents per dollar of contract value compared to Monte Carlo benchmarks. Once trained, FINNs price caplets in a few microseconds regardless of dimension, delivering speedups ranging from 300,000 to 4.5 million times faster than Monte Carlo simulation as the state space discretization of the forward curve grows from 10 to 150 nodes. The major Greeks-theta and curve deltas-come for free, computed automatically during PDE evaluation at zero marginal cost, whereas Monte Carlo requires complete re-simulation for each sensitivity. The framework generalizes naturally beyond caplets to other path-dependent derivatives-caps, swaptions, callable bonds-requiring only boundary condition modifications while retaining the same core PDE structure.

Plasmonic nanocavities are a promising platform for strong light-matter coupling and enhanced spectroscopies at the single-molecule level. These nanoscale environments are challenging to model due to their strongly multimodal character and short cavity lifetimes. Herein, we study the effects of these environments using real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) coupled to multiple classical cavity modes in a manner that includes cavity loss. In RT-NEO-TDDFT, the quantum mechanical densities of all electrons and specified nuclei, typically protons, are propagated in real time. We show that a cavity with many modes at different frequencies can be used to probe and modify the nuclear-electronic quantum dynamics of chemical systems. Ultrafast excited-state proton transfer reactions can be probed through the time- and energy-resolved cavity emission of a multimode cavity. Under strong coupling conditions, the cavity can modify the dynamics, in some cases suppressing proton transfer and exhibiting Rabi-like oscillations of the cavity emission due to polariton formation. Utilizing the spectral density for an experimentally relevant nanoparticle-on-mirror single-molecule cavity, we show that an excited-state proton transfer system can evolve into resonance with the cavity even when initially out of resonance with the dominant cavity peak. In this case, tuning the dominant cavity peak to be resonant with the electronic transition leads to polariton formation for a small collection of molecules. The RT-NEO framework with multimode cavities enables the efficient simulation of chemical reactions in physically realistic electromagnetic environments, providing fundamental insights into the dynamics and associated spectroscopic signatures.

We prove that the Dirichlet eigenvalues of the Laplace-Beltrami operator on a compact Riemannian manifold with cylindrical boundary can be approximated by the spectrum of truncated graph Laplacians constructed from $(\varepsilon,ρ)$-proximity graphs on the manifold. The approximation is uniform over a class $\mathcal{M}$ of manifolds, characterized by bounds on Ricci curvature, a lower bound on the injectivity radius, and an upper bound on the diameter. We show that the $k$-th eigenvalue of the truncated graph Laplacian lies between the $k$-th Dirichlet eigenvalues of truncated domains of the manifold. As the parameters $\varepsilon$ and $ρ$ and the ratio $\frac{\varepsilon}ρ$ tend to zero, these estimates yield convergence of the eigenvalues of the truncated graph Laplacian to the Dirichlet eigenvalues of the Laplace-Beltrami operator.

The generalized BBM studied in this paper contains an additional dissipative term. Thus instead of solitons for the classic BBM there exists a lot of travelling shock wave solutions. The rules of their interactions or superposition is of high importance. The paper gives a detailed description of the two-parameter family of travelling wave solutions and proves their stability using a conservation law. Based on these results, effective rules of superposition are obtained. Moreover these rules are applicable not exclusively to the travelling wave solutions of BBM, but also to a wider class of shock waves, in particular discontinuous. Characteristic examples are illustrated by numerically worked out graphs.