In equilibrium self-assembly, microscopic building blocks spontaneously self-organize into stable structures as dictated by their interaction potentials, which limits the accessible structural features to those that correspond to global minima in free energy landscapes; they are often ordered and periodic on length scales comparable to the building block size. Coupling the assembly process to an exergonic reaction drives the system out of equilibrium so that an assembly pathway can be engineered to target a specific kinetically stabilized state, which in principle opens up a vast design space with access to diverse complex structures with features on multiple length scales. However, the question of how such features might be specifically targeted remains unanswered. Here, we explore this design space using a DNA-encoded recipe consisting of multiple biomolecular reactions that dictate the time-dependent binding strength and specificity of each type of subunit in the sample independently, which makes it possible to program an assembly pathway that leads to a kinetically trapped final state. With this kinetic control, we show that the same set of building blocks can form clusters with different final structures. These structures, with tunable core-shell compositions, have feature sizes much larger than the building block size and are governed by the DNA-encoded assembly kinetics. Contrasting global kinetic control strategies such as thermal annealing, tuning the timing of individual biomolecular reactions offers the opportunity to regulate how the activity of each separate co-assembling component of a large set varies over time, opening up the potential for morphogenesis-like assembly processes involving engineered species.

CARMENES is a dual-channel high-resolution spectrograph at the 3.5 m Calar Alto telescope designed to detect low-mass planets around late-type dwarfs by measuring their radial velocities (RVs). High thermal stability in both the visible (VIS) and near infrared channels is essential to achieve the precision required for these measurements. In particular, stabilising the NIR channel to the millikelvin level, which operates at cryogenic temperatures (140 K), poses significant engineering challenges.The CARMENES-PLUS project was initiated to improve the instruments intrinsic RV precision. In this article, we focus on the thermal stability improvements made to the NIR channels cooling system. The NIR cooling system was originally conceived to operate with a discontinuous flow of cryogenic nitrogen gas. As part of CARMENES-PLUS, this was upgraded to a continuous flow configuration. Additional changes included the installation of an automatic vacuum system, a proportional control valve, and a pressure regulation system. These upgrades were designed to reduce thermal fluctuations and enhance long-term stability. The implemented upgrades significantly improved the intrinsic RV precision of the NIR channel. We quantified this improvement using Fabry Perot calibration spectra, obtaining an intrinsic RV precision of 0.67 ms after the interventions, an improvement of nearly 2 ms . We also assessed the stability of the nightly zero points, finding a reduced scatter of 3.9 ms post upgrade, compared to 6.1 ms before. For a sample of slowly rotating stars (vsin i below 2 kms), the median scatter decreased from 8.8 ms to 6.7 ms after the upgrades. These results demonstrate that the thermal control upgrades introduced in CARMENES PLUS have enhanced the NIR channels RV performance, bringing it closer to the VIS channels stability and reinforcing CARMENES capabilities for exoplanet detection around M dwarfs.

This paper investigates a new black hole solution within the framework of bumblebee gravity, incorporating non-commutative corrections parameterized by $Θ$ and implemented through the Moyal twist $\partial_r \wedge \partial_θ$. Notably, the event horizon remains unaffected by $Θ$, while the surface gravity becomes ill-defined, in agreement with the behavior previously reported for the non-commutative Schwarzschild black hole [1]. The propagation of light is examined by analyzing null geodesics, identifying critical orbits, and determining the resulting black hole shadow. To complement these analyses, we explore gravitational lensing by evaluating the deflection angle in both the weak- and strong-field regimes. Using these results, constraints are derived for the lensing observables by comparing with the Event Horizon Telescope data for $Sgr A^{*}$ and $M87^{*}$. Finally, we close the analysis by deriving additional constraints from standard Solar System experiments, including Mercury's orbital precession, gravitational light bending, and time-delay measurements.

In surface diffusion, one of the key observables is the so-called intermediate scattering function which is measured directly from the surface technique called Helium spin echo. In this work, we show that this function can be seen as a characteristic function of probability theory. From the characteristic function, the moments and cumulants of the probability distribution function of the position of the adsorbate are straightforward obtained in an analytical way; in particular, the second order which is related to the diffusion coefficient. In order to illustrate this simple theory, we have focused on the incoherent tunneling of H and D on a Pt(111) surface where only jumps between nearest neighbor sites have been reported experimentally. Finally, an extension to jumps to more than nearest neighbors has also been considered.

Asymptotic velocity domination (AVD) posits that when back-propagated to the Big Bang generic cosmological spacetimes solve a drastically simplified version of the Einstein field equations, where all dynamical spatial gradients are absent (similar as in the Belinski-Khalatnikov-Lifshitz scenario). Conversely, a solution can in principle be reconstructed from its behavior near the Big Bang. This property has been rigorously proven for the Gowdy class of cosmologies, both polarized and unpolarized. Here we establish for the polarized case a quantum version of the AVD property formulated in terms of two-point functions of (the integrands of) Dirac observables: these correlators approach their much simpler velocity dominated counterparts when the time support is back-propagated to the Big Bang. Conversely, the full correlators can be expressed as a uniformly convergent series in averaged spatial gradients of the velocity dominated ones.

We present benchmarking results for single-qubit gates implemented on a neutral atom quantum processor using Direct Randomized Benchmarking (DRB) and Gate Set Tomography (GST). The DRB protocol involves preparing stabilizer states, applying $m$ layers of native single-qubit gates, and measuring in the computational basis, providing an efficient error characterization under a stochastic Pauli noise model. GST enables the full, self-consistent reconstruction of quantum processes, including gates, input states, and measurements. Both protocols provide robust to state preparation and measurement (SPAM) errors estimations of gate performance, offering complementary perspectives on quantum gate fidelity. For single-qubit gates, DRB yields an average fidelity of $99.963 \%$. The protocol was further applied to a 25-qubit array under global single-qubit control. GST results are consistent with those obtained via DRB. We also introduce a gauge optimization procedure for GST that brings the reconstructed gates, input states, and measurements into a canonical frame, enabling meaningful fidelity comparisons while preserving physical constraints. These constraints of the operators -- such as complete positivity and trace preservation -- are enforced by performing the optimization over the Stiefel manifold. The combined analysis supports the use of complementary benchmarking techniques for characterizing scalable quantum architectures.

Simulation-based testing of cyber-physical systems (CPS) is costly due to the time-consuming execution of CPS simulators. In addition, CPS simulators may be flaky, leading to inconsistent test outcomes and requiring repeated test re-execution for reliable test verdicts. Many test inputs within the input space of CPS may not effectively exercise the behaviour of the system under test (SUT) -- for instance, those that violate system preconditions, exceed operational design domain (ODD) limits, or represent inherently safe scenarios. In this article, we propose to use test validators to filter out such test inputs before execution. We describe two methods for generating test validators: one using genetic programming (GP) that employs well-known spectrum-based fault localization (SBFL) ranking formulas, namely Ochiai, Tarantula, and Naish, as fitness functions; and the other using decision trees (DT) and decision rules (DR). We evaluate our test validators through case studies in the domains of aerospace, networking and autonomous driving. We show that test validators generated using GP with Ochiai are significantly more accurate than those generated using GP with Tarantula and Naish or using DT or DR. Moreover, this accuracy advantage remains even when accounting for the flakiness of the simulator. We further show that our test validators generated by GP with Ochiai are robust against flakiness with only 4% average variation in their accuracy results across four different network and autonomous-driving systems with flaky behaviours. Finally, we show that, on average, 88.7% of the assertions inferred by our approach align or overlap with requirements precondition violations, ODD-limit violations, and nominal safe conditions extracted from technical standards and empirical results in the literature.

Galaxy profile fitting is a ubiquitous technique that provides the backbone for photometric and morphological measurements in modern extragalactic surveys. A recent innovation in profile fitting algorithms is to render, or create, the model profile in Fourier space, which aims to provide faster and more accurate results. However, the most common parameterization, the Sérsic profile, has no closed form Fourier transform, requiring the use of computationally expensive approximations. In this paper our goal is to develop an emulator to mimic the radial Fourier transform of the Sérsic profile, for use in profile fitting. We first numerically compute the radial Fourier transform and demonstrate that it varies smoothly as a function of the Sérsic index and $k$, the spatial frequency coordinate. Using this set of numerically calculated transforms as a training set, we use symbolic regression to discover an equation which approximates its behavior. This ensures the emulator will be based on computationally efficient and differentiable building blocks. We implement this novel rendering method in the pysersic profile fitter, and ensure it is accurate by conducting both injection-recovery tests using model galaxy profiles and applying multiple rendering methods to a real sample of galaxies in HSC-SSP imaging. Crucially, the Fourier emulator rendering technique enables measurements of morphological parameters of galaxies 2.5 times faster than standard methods with minimal loss in accuracy. This increased performance while maintaining accuracy is a step that ensures these tools can continue to scale with the ever-increasing flow of incoming data.

For any extension of commutative rings $A\subseteq B$, by using invertible ideals, we first define an Abelian group $\Cl(A,B)$, that we call the ideal class group of this extension. Then we study the main properties of this group. Among them, we prove that the group $\Cl(A,B)$ is indeed the kernel of the natural group morphism $\Pic(A)\rightarrow \Pic(B)$ which is given by $L\mapsto L\otimes_{A}B$. Then we show that both the classical ideal class group and, surprisingly, the Picard group are special cases of this structure. Next, we prove that ...

We extend Priestley Duality to suitable categories of fuzzy topological spaces and ordered algebraic structures that generalize bounded distributive lattices. The duality we prove extends not only classical Priestley Duality between Priestley Spaces and bounded distributive lattices, but also the duality between limit cut complete MV-algebras and Stone MV-topological spaces (proved by the second author in a previous paper) which, on its turn, is an extension of classical Stone Duality.

We present a theoretical investigation of entanglement generation in an external quantum system via interaction with a quantum autonomous thermal machine (QATM) under non-Markovian dynamics. The QATM, composed of two qubits each coupled to independent thermal reservoirs, interacts with an external system of two additional qubits. By analyzing the Hilbert space structure, energy level configurations, and temperature gradients, we define a common interaction between the QATM qubits and the external system qubits, which allows the definition of two thermodynamic cycles (A and B) governed by virtual temperatures and energy-conserving transitions. We demonstrate that the QATM can act as a structured reservoir capable of inducing non-Markovian memory effects, as highlighted by negative entropy production rates. Using mutual information and concurrence, we show that entanglement is generated only under cycle A, which is associated with stronger non-Markovian behavior and higher coherence correlations. Our results demonstrate that temperature differences, Hilbert space structure, and coherence serve as quantum resources for controlling and enhancing entanglement in quantum thermodynamic settings, with parameters consistent with experimental superconducting qubit platforms.

Let $(R,M,k)$ be a complete local ring (not necessarily Noetherian). As the first main result of this article, we prove that in the unequal characteristic case $\Char(R)\neq\Char(k)$, the natural surjective map between the groups of units $R^{\ast}\rightarrow k^{\ast}$ admits a splitting. \\ Next, we reprove by a new method that in the equi-characteristic case $\Char(R)=\Char(k)$, the natural surjective ring map $R\rightarrow k$ admits a splitting. In our proof there is no need for the existence of the coefficient fields for equi-characteristic complete local rings, whose existence is the most difficult part of the known proof. \\ As an application, we show that for any complete local ring $(R,M,k)$ the following short exact sequence of Abelian groups: $$\xymatrix{1\ar[r]&1+M\ar[r]& R^{\ast}\ar[r]&k^{\ast} \ar[r]&1}$$ is always split. In particular, we have an isomorphism of Abelian groups $R^{\ast}\simeq(1+M)\times k^{\ast}$. We also show with an example that the above exact sequence does not split for many incomplete local rings.

Post-growth has emerged as an umbrella term for various sustainability visions that advocate the pursuit of environmental sustainability, social equity, and human wellbeing, while questioning the continued pursuit of economic growth. Although there are increasing calls to include post-growth scenarios in high-level assessments, a coherent framework with what is required to model post-growth adequately remains absent. This article addresses this gap by: (1) identifying the minimum requirements for post-growth models, and (2) establishing a set of model elements for representing specific policy themes. Drawing on a survey of modellers and on relevant post-growth literature, we develop a framework of minimum requirements for post-growth modelling that integrates three spheres: biophysical, economic, and social, and links them to post-growth goals. Within the biophysical sphere, we argue that embeddedness requires the inclusion of resource use and pollution, environmental limits, and feedback mechanisms from the environment onto society. Within the economic sphere, models should disaggregate households, incorporate limits to technological change and decoupling, include different types of government interventions, and calculate GDP or output endogenously. Within the social sphere, models should represent time use, material and non-material need satisfiers, and the affordability of essential goods and services. Specific policies and transformation scenarios require additional features, such as sectoral disaggregation or representation of the financial system. Our framework guides the development of models that can simulate both post-growth and pro-growth policies and scenarios, an urgently needed tool for informing policymakers and stakeholders about the full range of options for pursuing sustainability, equity, and wellbeing.

Short-range correlation (SRC) in nuclei refers to nucleons forming temporally correlated pairs in close proximity, giving rise to the high momentum of the nucleons beyond the Fermi surface. It has been reported that bremsstrahlung $γ$ production from neutron-proton process in heavy-ion reactions provides a potential probe to the SRC abundance in nuclei. In this paper, we present in detail the precision measurement of bremsstrahlung $γ$-rays in $\rm ^{124}Sn$+$\rm ^{124}Sn$ reactions at 25 MeV/u using the Compact Spectrometer for Heavy IoN Experiment (CSHINE). A comprehensive experimental and analysis framework is established to ensure the reliability and robustness of the extracted results. Background contributions are evaluated and subtracted using independent methods, and the consistency of the analysis is systematically validated. By comparing the experimental $γ$ spectrum with the Isospin-dependent Boltzmann-Uehling-Uhlenbeck simulations, the high momentum tail (HMT) fraction of $R_{\rm HMT}=(20 \pm 3)\%$ is derived in $^{124}$Sn nuclei. This work provides a detailed and validated experimental framework for extracting SRC information from bremsstrahlung $γ$-ray emission and demonstrates the feasibility of studying nucleon SRCs with high precision in low-energy heavy-ion collisions.

We estimate the degree of squeezing possible in gravitational waves due to nonlinear gravitational effects in the weakly perturbative regime. Using the predicted amplitude ratios for higher harmonic generation in the ringdown phase of a black hole merger event, we estimate the relevant degree of squeezing produced by a Schwarzschild singularity to be of the order of one percent.

Motivated by game-theoretic models of crowd motion dynamics, this paper analyzes a broad class of distributed games with jump diffusions within the recently developed $α$-potential game framework. We demonstrate that analyzing the $α$-Nash equilibria reduces to solving a finite-dimensional control problem. Beyond the viscosity and verification characterizations for the general games, we examine explicitly and in detail how spatial population distributions and interaction rules influence the structure of $α$-Nash equilibria in these distributed settings. For crowd motion network games, we show that $α= 0$ for all symmetric interaction networks, and or asymmetric networks. We quantify the precise polynomial and logarithmic decays of $α$ in terms of the number of players, the degree of the network, and the decay rate of interaction asymmetry. We also exploit the $α$-potential game framework to analyze an $N$-player portfolio selection game under a mean-variance criterion. We show that this portfolio game constitutes a potential game and explicitly construct its Nash equilibrium. Our analysis allows for heterogeneous preference parameters, going beyond the mean-field interactions considered in the existing game literature. Our theoretical results are supported by numerical implementations using policy gradient-based algorithms, demonstrating the computational advantages of the $α$-potential game framework in computing Nash equilibria for general dynamic games.

Background: In pair programming, Togetherness (the partners understand each other's mental state well) is a main success factor. Maintaining high Togetherness is an element of pair programming skill. Some sessions appear to go badly although Togetherness appears good. Objective: Understand under what circumstances this is possible. Method: Grounded Theory Methodology based on 21 recorded pair programming sessions with 22 developers from 5 German software companies and 6 interviews with different developers from 4 other German companies. Results: We explain how a Power Gap can make a session dysfunctional despite the presence of high Togetherness, how it comes into existence due to a Knowledge Gap and Hierarchical Behavior, why its consequences (Defensive Behavior and Disengaging Behavior) are problematic, and how it can be reduced or prevented by Equalizing Behavior. Conclusions: Pair programming practitioners can improve their pair programming skill by unlearning problematic behaviors related to Power Gaps and by learning to recognize Power Gaps and apply Equalizing Behavior.

We propose a quantum algorithm for computing the n-gluon maximally helicity violating (MHV) tree-level scattering amplitude. We revisit a newly proposed method for unitarisation of non-unitary operations and present how this implementation can be used to create quantum gates responsible for the color and kinematic factors of the gluon scattering amplitude. As a proof-of-concept, we detail the full conceptual algorithm that yields the squared amplitude and implement the corresponding building blocks on simulated noiseless quantum circuits for n = 4 to analyze its performance. The algorithm is found to perform well with parameter optimizations, suggesting it to be a good candidate for implementing on quantum computers also for higher multiplicities.

One of the ultimate goals of the Hassett-Keel program is the determination of the log canonical models of the moduli spaces of pointed rational curves $\overline{M}_{0,n}$. In this paper, we study log canonical models of $\overline{M}_{0,5}$ with \textit{asymmetric} boundary divisors. Our results generalize previous work by Alexeev-Swinarski, Fedorchuk-Smyth, Kiem-Moon and Simpson for the first non-trivial case, namely $n=5$. We prove that all moduli spaces of weighted pointed rational curves $\overline{M}_{0,A}$ arise as log canonical models of $\overline{M}_{0,5}$ for suitable choices of boundary coefficients, thereby also recovering a theorem of Fedorchuk and Moon. In addition, we relate these moduli spaces to Deligne-Mostow ball quotients. We further study log canonical models of the moduli spaces $\overline{M}_{0,n\cdot (1/k)}$ with symmetric weight, which differ from $\overline{M}_{0,n}$. The case $n=5$ can be viewed as an explicit guiding example in a very general program and the paper can thus also serve as an expository introduction.

The Koba-Nielsen local zeta functions are integrals depending on several complex parameters, used to regularize the Koba-Nielsen string amplitudes. These integrals are convergent and admit meromorphic continuations in the complex parameters. In the original case, the integration is carried out on the n-dimensional Euclidean space. In this work, the integration is over a variety of (bounded or unbounded) convex subsets; the resulting integrals also admit meromorphic continuations in the complex parameters. We describe the meromorphic continuation's polar locus explicitly, using the technique of embedded resolution. This result can be reinterpreted as saying that the meromorphic continuations are weighted sums of Gamma functions, evaluated at linear combinations of the complex parameters, where the weights are holomorphic functions. The integrals announced in the title of this paper occur as a particular case of these new Koba-Nielsen local zeta functions, or of a further generalization to arbitrary hyperplane arrangements.

In the framework of light-cone gauge vector superspace, a continuous-spin field propagating in AdS space of dimension greater than or equal to four is studied. Use of such framework allows us to find a simple solution for spin operators entering our light-cone gauge Lagrangian formulation. Bosonic continuous-spin field is considered in AdS space of arbitrary dimensions, while the use of a helicity basis in four-dimensional AdS space allows us to consider bosonic and fermionic continuous-spin fields on an equal footing. Classification of continuous-spin fields is proposed. Conjectures on the notion of masslessness for continuous-spin field are made. All unitary irreps of non-linear spin algebra for four-dimensional AdS are also obtained.

We present a comprehensive study of the galaxy size-stellar mass relation (SMR) at low redshift (z <= 0.125), using a large spectroscopic sample from the SDSS-DR13 survey. Our goal is to investigate how environment affects galaxy structural properties across multiple spatial scales. Galaxies are classified by specific star formation rate, optical color, and bulge-to-total light ratio, allowing us to disentangle environmental effects from intrinsic galaxy properties. We examine the SMR in three contexts: (1) comparing galaxy sizes in two extreme environments-dense clusters versus cosmic voids; (2) analyzing cluster galaxies across a range of cluster masses; and (3) studying member galaxies located in different cluster regions, from the core to the infall zone. In all three cases, we find no significant dependence of the SMR on environment at fixed stellar mass and galaxy type. Cluster and void galaxies follow consistent SMR trends, and no measurable variation is observed with cluster mass or cluster-centric distance. We also confirm that early-type galaxies exhibit steeper SMR slopes than late types. Notably, this consistent lack of environmental dependence on the SMR persists even when accounting for the differing galaxy number densities in voids, supporting the universality of this SMR scaling relation across diverse environments.

Clouds are important features of the atmosphere, determining the energy budget by interacting with incoming solar radiation and outgoing thermal radiation, respectively. For pure ice clouds, the net effect of radiative effect is still unknown. In this study we develop a simple but physically consistent ice cloud model, and analyze it using methods from the theory of dynamical systems. We find that the model constitutes a nonlinear oscillator with two Hopf bifurcations in the relevant parameter regime. In addition to the characterization of the equilibrium states and the occurring limit cycle, we find scaling behaviors of the bifurcations and the limit cycle, reducing the parameter space crucially. Finally, the model shows very good agreement with real measurements, indicating that the main physics is captured and such simple models are helpful tools for investigating ice clouds.

A growing body of theoretical and experimental evidence strongly supports the existence of a second liquid-liquid critical point (LLCP) in deeply supercooled water leading to the co-existence of two phases: a high-and low-density liquid (HDL and LDL). While the thermodynamics associated with this putative LLCP has been well characterised through numerical simulations, the dynamical properties of these two phases close to the critical point remain much less understood. In this work, we investigate their dynamical and spectroscopic features using machine-learning interatomic potentials (MLIPs). Dynamical analyses using the van-Hove correlation function, reveal that LDL exhibits very sluggish and heterogeneous molecular mobility, in contrast to the faster and more homogeneous dynamics of HDL. Infrared absorption (IR) spectra further show clear vibrational distinctions between LDL and HDL, in particular in the far IR region between 400 - 1000 cm-1. Together, these findings provide new dynamical fingerprints that clarify the microscopic behavior of supercooled water and offer valuable guidance for experimental efforts aimed at detecting the long-sought liquid-liquid transition.

This paper studies a robust utility maximization problem for intractable claims under distributional ambiguity, where the distribution of the claim cannot be inferred from market information and its dependence with tradable assets is largely unknown. We extend the existing framework for intractable claims in two directions. First, we allow the marginal distribution of the claim to vary within a $φ$-divergence ambiguity set, capturing statistical uncertainty in its estimation. Second, we consider a general (possibly non-additive) bivariate utility function, which enables more flexible interactions between the decision and the claim beyond the classical additive specification. To analyze this problem, we adopt a random distributionally robust optimization (RDRO) formulation, which lifts the optimization to the space of joint distributions and provides a convenient representation of the coupling between the decision and the uncertain claim. We establish the existence of optimal decisions using tools from optimal transport and develop a Legendre-Fenchel duality framework that links the constrained and penalized formulations, leading to uniqueness results and tractable reformulations. Finally, we propose a numerical algorithm based on unbalanced optimal transport scaling combined with projected gradient methods, and illustrate the relationship between the parameters in the constrained and penalized formulations.

Given a finitely generated amenable group $H$ satisfying some mild assumptions, we relate isoperimetric profiles of the lampshuffler group $\mathsf{Shuffler}(H)=\mathsf{FSym}(H)\rtimes H$ to those of $H$. Our results are sharp for all exponential growth groups for which isoperimetric profiles are known, including Brieussel-Zheng groups. This refines previous estimates obtained by Erschler and Zheng and by Saloff-Coste and Zheng. The most difficult part is to find an optimal upper bound, and our strategy consists in finding suitable lamplighter subgraphs in lampshufflers. This novelty applies more generally for many examples of halo products, a class of groups introduced recently by Genevois and Tessera as a natural generalisation of wreath products. Lastly, we also give applications of our estimates on isoperimetric profiles to the existence problem of regular maps between such groups.

A dominating set of a graph $G$ is a set $D \subseteq V(G)$ such that every vertex in $V(G) \setminus D$ is adjacent to at least one vertex in $D$. A set $L\subseteq V(G)$ is a locating set of $G$ if every vertex in $V(G) \setminus L$ has pairwise distinct open neighborhoods in $L$. A set $D\subseteq V(G)$ is a locating-dominating set of $G$ if $D$ is a dominating set and a locating set of $G$. The location-domination number of $G$, denoted by $γ_{LD}(G)$, is the minimum cardinality among all locating-dominating sets of $G$. A well-known conjecture in the study of locating-dominating sets is that if $G$ is an isolate-free and twin-free graph of order $n$, then $γ_{LD}(G)\le \frac{n}{2}$. Recently, Bousquet et al. [Discrete Math. 348 (2025), 114297] proved that if $G$ is an isolate-free and twin-free graph of order $n$, then $γ_{LD}(G)\le \lceil\frac{5n}{8}\rceil$ and posed the question whether the vertex set of such a graph can be partitioned into two locating sets. We answer this question affirmatively for twin-free distance-hereditary graphs, maximal outerplanar graphs, split graphs, and co-bipartite graphs. In fact, we prove a stronger result that for any graph $G$ without isolated vertices and twin vertices, if $G$ is a distance-hereditary graph or a maximal outerplanar graph or a split graph or a co-bipartite graph, then the vertex set of $G$ can be partitioned into two locating-dominating sets. Consequently, this also confirms the original conjecture for these graph classes.

In this paper, we show how factorisation with respect to nonlocal pseudosymmetries allows one to obtain Bäcklund transformations, interpreted as nonlocal $\mathcal{C}$-morphisms of differential equations. According to this approach, which is illustrated through several examples, the Bäcklund transformations are determined by basic invariants of the exploited nonlocal pseudosymmetries.

In this work, we investigate the influence of a perfectly conducting plate on the Uehling potential of Quantum Electrodynamics (QED), corresponding to the first loop correction to the classical Coulomb potential in that situation. We use the method of images adapted to the photon propagator, extending the method beyond the standard (classical) tree level calculation. We show that the effect of the plate on the quantum correction is much stronger than the expectation from a naive application of the method of images.

We develop an estimator-based stochastic fixed-point framework for approximately computing the 2-Wasserstein barycenter of continuous, non-parametric probability measures. Notably, we provide the first rigorous convergence analysis for implementable estimator-based stochastic extensions of the fixed-point iterative scheme proposed by Álvarez-Esteban, del Barrio, Cuesta-Albertos, and Matrán (2016). In particular, we establish almost sure convergence, and identify sufficient conditions for geometric rates of convergence under controlled errors in optimal transport (OT) map estimation. We subsequently propose a concrete, provably convergent, and computationally tractable stochastic algorithm that accommodates input measures satisfying Caffarelli-type regularity conditions, which form a dense subset of the Wasserstein space. This algorithm leverages a modified entropic OT map estimator to enable efficient and scalable implementation. To facilitate quantitative evaluation, we further propose a novel and efficient procedure for synthetically generating benchmark instances, in which the input measures exhibit non-trivial features and the corresponding barycenters are approximately known. Numerical experiments on both synthetic and real-world datasets demonstrate the strong computational efficiency, estimation accuracy, and sampling flexibility of our approach.