In the development and maintenance of Android apps, the quick and accurate reproduction of user-reported bugs is crucial to ensure application quality and improve user satisfaction. However, this process is often time-consuming and complex. Therefore, there is a need for an automated approach that can explore the Application Under Test (AUT) and identify the correct sequence of User Interface (UI) actions required to reproduce a bug, given only a complete bug report. Large Language Models (LLMs) have shown remarkable capabilities in understanding textual and visual semantics, making them a promising tool for planning UI actions. Nevertheless, our study shows that even when using state-of-the-art LLM-based approaches, these methods still struggle to follow detailed bug reproduction instructions and replan based on new information, due to their inability to accurately predict and interpret the visual effects of UI components. To address these limitations, we propose LTGDroid. Our insight is to execute all possible UI actions on the current UI page during exploration, record their corresponding visual effects, and leverage these visual cues to guide the LLM in selecting UI actions that are likely to reproduce the bug. We evaluated LTGDroid, instantiated with GPT-4.1, on a benchmark consisting of 75 bug reports from 45 popular Android apps. The results show that LTGDroid achieves a reproduction success rate of 87.51%, improving over the state-of-the-art baselines by 49.16% and 556.30%, while requiring an average of 20.45 minutes and approximately $0.27 to successfully reproduce a bug. The LTGDroid implementation is publicly available at https://github.com/N3onFlux/LTGDroid.

In this article, we solve the Stokes and Navier-Stokes equations with the deal$.$II finite-element library. In particular, we use its multigrid, adaptive-mesh, and matrix-free infrastructures to design efficient linear and nonlinear iterative solvers, respectively. We solve the stationary Stokes equations on hp-adaptive meshes with a hp-multigrid approach, the transient Stokes equations with space-time finite elements and space-time multigrid, and, finally, the stabilized incompressible Navier-Stokes equations on locally refined meshes with a monolithic multigrid solver. The selected examples underline the flexibility and modularity of the multigrid infrastructure of deal$.$II.

This is a survey highlighting several recent results concerning well/ill posedness of the Euler system of gas dynamics. Solutions of the system are identified as limits of consistent approximations generated either by physically more complex problems, notably the Navier- Stokes-Fourier system, or by the approximate schemes in numerical experiments. The role of the fundamental principles encoded in the First and Second law of thermodynamics in identifying a unique physically admissible solution is examined.

Orthogonal graph layout algorithms aim to produce clear, compact, and readable network diagrams by arranging nodes and edges along horizontal and vertical lines, while minimizing bends and crossings. Most existing orthogonal layout methods focus primarily on quality criteria such as area usage, total edge length, and bend minimization. Explicitly controlling the global aspect ratio (AR) of the resulting layout is as of now unexplored. Existing orthogonal layout methods offer no control over the resulting AR and their rigid geometric constraints make adaptation of finished layouts difficult. With the increasing variety of aspect ratios encountered in daily life, from wide monitors to tall mobile devices or fixed-size interface panels, there is a clear need for aspect ratio control in orthogonal layout methods. To tackle this issue, we introduce Aspect Ratio-Constrained Orthogonal Layout (ARCOL). Building upon the Human-like Orthogonal Layout Algorithm (HOLA)~\cite{Kieffer2016}, we integrate aspect ratio at two different stages: (1) into the stress minimization phase, as a soft constraint, allowing the layout algorithm to gently guide node positions toward a specified target AR, while preserving visual clarity and topological faithfulness; and (2) into the tree reattachment phase, where we modify the cost function to favor placements that improve the AR. We evaluate our approach through quantitative evaluation and a user study, as well as expert interviews. Our evaluations show that ARCOL produces balanced and space efficient orthogonal layouts across diverse aspect ratios.

Tumor growth beyond a critical size relies on the development of a functional vascular network, which ensures adequate oxygen and nutrient supply. In this work, we present a modeling framework based on an optimization-based 3D-1D coupling strategy to simulate perfusion in a tumoral tissue with growing mass, interacting with a dynamically evolving capillary network. The tumor is described as a multiphase system including tumor cells and interstitial fluid, governed by a non-linear PDE system for cell volume fraction, pressure, oxygen, and VEGF, and discretized via finite elements. Capillary growth is tackled using a continuous-discrete hybrid tip-tracking approach. The vascular geometry is updated over time according to angiogenic signals, and coupled to the tissue model through a constrained optimization formulation that enforces fluid and nutrient exchange via interface variables. A sensitivity analysis using the Morris elementary effect method identifies key parameters influencing system behavior. Results highlight the critical role of vascular development in regulating tissue perfusion and tumor progression. Overall, the proposed numerical approach provides a versatile tool for investigating tumor-vascular interactions and can support further quantitative analysis of angiogenesis and tumor perfusion dynamics.

In their seminal work, Fermi, Pasta, Ulam and Tsingou explored the connection between statistical mechanics and dynamical properties, such as chaos and ergodicity. Even today, seventy years later, the topic is not fully understood: while most results of statistical mechanics require the ergodic hypothesis to be rigorously proved, there are many indications that these predictions, both in and out of equilibrium, hold even in the absence of a rigorous form of ergodicity. Motivated by the above considerations, in this work we reconsider the point of view that the relevant ingredients for the validity of statistical mechanics are the large number of degrees of freedom and the choice of extensive observables, while the details of the dynamics do not play an essential role. This is the idea behind Khinchin's famous proof of the typicality of macroscopic observables at equilibrium. We extend this perspective to the context of non equilibrium, by investigating the thermalization properties of both harmonic (integrable) and nonharmonic (chaotic) oscillator chains initially prepared in out-of-equilibrium conditions. In integrable systems, thermalization occurs, or not, depending on the observable. In the chaotic regime, instead, thermalization is reached by any observable, although the relaxation timescale might be larger than the observation time.

The readout system with a high multiplexing ratio has become a bottleneck limiting the application of large-scale Transition Edge Sensor (TES) detector arrays. In recent years, the microwave superconducting quantum interference device (SQUID) multiplexer has emerged as a key technology for effectively reading large-scale cryogenic detector arrays. Currently, the microwave SQUID multiplexer is being adopted by an increasing number of experiments due to its capability of achieving a multiplexing ratio of 2000:1 within the readout bandwidth. In this study, we developed and fabricated a 32-channel microwave SQUID multiplexer prototype. And we measured 8 channels of the prototype. The measured equivalent noise current of the prototype reached 154 pA/$\sqrt{Hz}$.

We compare the spectrum and the localisation properties of the eigenmodes of the Laplacian and the adjacency matrix of 2D random geometric graphs, using numerical diagonalization of these matrices for different system sizes and connectivities. For sufficiently large ensembles of systems, we evaluate the spectrum, the probability distribution of the participation ratio and the relation between participation ratios and eigenvalues. While all eigenmodes of the adjacency matrix are localised for sufficiently large system sizes, the Laplacian matrix always leads to a small proportion of system-spanning modes due to a conservation law, and therefore to power-law tails in the probability distribution of the participation ratio and its relation to the eigenvalues. By disentangling the effects of finite system size, of mean degree, of component size distribution, and of network motifs, we provide a thorough understanding of the data.

Supersymmetric sectors of $\mathcal{N}=4$ super-Yang-Mills theory motivate the study of the partition function for the counting of gauge-invariant functions of $d=2,3$ matrices transforming under the adjoint action of $U(N)$. The partition function $ \mathcal{Z}_d ( x) $ in the large $N$ limit has a known Hagedorn phase transition at $ x = d^{-1} $ which provides a simple model for the phase structure of the thermal partition function of SYM. We study the all-orders asymptotic expansion of $ \mathcal{Z}_d(x)$ based on a geometric picture of concentric circles of poles in the complex plane accumulating in a natural boundary at $|x| =1$. We find that the order by order structure has a precise combinatorial interpretation organized in terms of increasing cycle size of permutations arising in the enumeration of the invariants. We refer to this organization as small-cycle dominance, and find that it extends to refined versions of the partition functions depending on several complex variables. An analysis of the coefficients in the asymptotic expansion of $ \mathcal{Z}_d(x) $ using the modular property of the Dedekind eta function reveals that the asymptotic expansion is actually convergent for $d\ge d_{ \rm crit } = 13$. A fermionic version of $\mathcal{Z}_d (x)$ has an analogous critical dimension of $ d_{ \rm crit} = 7$. This distinction indicates that the partition functions of the matrix models can be completely reconstructed from their high-energy (UV) limit for $d\ge d_{ \rm crit}$ whereas additional input is required to reconstruct the exact coefficients of the low-energy (IR) expansion for $2\le d \le d_{ \rm crit } -1 $.

Let $X$ and $Y$ be rational functions of degree at least two with complex coefficients such that $\mathbb{C}(X,Y)=\mathbb{C}(z)$. We study the problem of determining when the field extension $[\mathbb{C}(z):\mathbb{C}(X)\cap\mathbb{C}(Y)]$ is finite and attains the minimal possible degree ${\rm deg X}\cdot{\rm deg Y}$. We give a complete characterization in the case where $X$ is a Galois covering. We also establish several related results concerning the functional equation $A \circ X = Y \circ B$ in rational functions, in the case where one of the functions involved is a Galois covering. Finally, we consider an analogous problem for holomorphic maps between compact Riemann surfaces.

Saturated fusion systems are categories modeling properties of conjugacy of p-subgroups in finite groups. It was shown by Chermak that they correspond nicely to group-like structures called localities. In this paper we start to explore how concepts and results from a program of Meierfrankenfeld, Stellmacher and Stroth, aiming to reprove and generalize parts of the classification of the finite simple groups, translate to fusion systems and localities. Central in the program is the notion of a large $p$-subgroup. The presence of a large $p$-subgroup in a finite group turns out to be strong enough information to nearly classify the entire $p$-local structure, while also accommodating a very large class of groups of interest including many groups of Lie type in defining characteristic $p$. Utilizing the group-theoretical definition of a large $p$-subgroup as a blueprint, we define large subgroups of fusion systems and localities. We then analyze how the three definitions relate to each other, showing in particular that the newly defined notions behave well under the correspondence between saturated fusion systems and localities with certain properties. We further proceed with an example of how classification results from the program of Meierfrankenfeld et.al. translate to fusion systems and localities. In more detail, we give a new characterization of the $2$-fusion system of $\operatorname{Aut}(\operatorname{G}_2(3))$ following the strategy in a paper of Meierfrankenfeld and Stroth, where the group $\operatorname{Aut}(\operatorname{G}_2(3))$ is characterized in a similar fashion.

Suppose $R$ is a commutative ring and $G$ is a group acting on a set $W$. We consider the $RG$-module $RW$ in the case where $G$ is the automorphism group of an $ω$-categorical structure $M$ and $W$ is, for example, $M^n$ (for $n \in \mathbb{N}$). We develop methods which may provide information about two questions in the case where $R$ is a field $F$: whether $FW$ has a.c.c. on submodules; and in the case where $M$ is finitely homogeneous, whether $FW$ is of finite composition length. In the case where $M$ is a Ramsey structure and so $G$ is extremely amenable, we give a simple `decision procedure' for membership in a submodule of $RW$ specified by a given generating set. If $F$ is a field, we show that there is a duality between submodules of $FW$ and the topological $FG$-module of definable functions from $W$ to $F$.

A body moving in a wall-bounded flow often experiences a hydrodynamic lift force normal to the wall, which plays an important role in many fluid systems. In this study, we develop a framework for diagnosing steady inertial lift from the internal structure of the flow field. Based on the generalised reciprocal theorem for finite-Reynolds-number flows, the lift is expressed as a volume integral that identifies both the dominant contributions and the regions from which they arise. We apply this framework to numerically obtained steady flows of Newtonian and shear-thinning fluids between eccentric rotating cylinders, and analyse the lift acting on the inner cylinder undergoing rotation and orbital motion. In particular, we focus on lift reversal induced by increasing eccentricity in a Newtonian fluid and on lift reversal induced by stronger shear-thinning behaviour at high eccentricity. The volume-integral expression decomposes the lift into a vortex-force contribution associated with inertia and a viscous stress contribution associated with the non-uniform viscosity field, and shows that the former dominates over the parameter range considered here. As the eccentricity increases, negative relative vorticity, and in some cases tangential velocity, become stronger in the narrow-gap region, thereby enhancing the negative local vortex-force contribution and inducing lift reversal. Stronger shear-thinning behaviour, on the other hand, amplifies negative relative vorticity near the inner cylinder, thereby increasing the positive local vortex-force contribution and inducing lift reversal. These results demonstrate that the proposed framework is useful for diagnosing and interpreting steady inertial lift in wall-bounded flows.

The paper deals with the 3D Stokes problem with Navier-Tresca stick-slip boundary conditions. A weak formulation of this problem leads to a variational inequality of the second kind, coupled with an equality constraint. This problem is then approximated using the mixed finite element method, yielding a generalized equation, to the numerical solution of which we implement a variant of the SCD semismooth* Newton method. This includes also a globalization technique ensuring convergence for arbitrary starting points. Numerical experiments demonstrate the effeciency of this approach.

We study the superfluid response of a dilute bosonic fluid in the presence of two-dimensional composite potentials (such as triangular, Kagomé and quasiperiodic potentials, or superlattices), which may be obtained for example by superposing multiple laser beams. We first find a sufficient condition for the external potential to yield a fully isotropic superfluid response. Then, we derive analytical expressions for Leggett's upper and lower bounds to the superfluid fraction (valid in the perturbative regime) that allow us to find the optimal direction along which each bound should be measured. Finally, we solve the problem numerically, and we confirm our analytical findings.

The practical utility of a quantum network depends on its ability to establish entanglement between arbitrary node pairs with quality sufficient to execute entanglement enabled tasks. This capability can be assessed globally, through aggregate performance over all node pairs, as well as locally, at the level of individual nodes. Since entanglement-based connections form a layer above the underlying physical topology, quantum connectivity is not adequately captured by classical topological connectivity metrics. To enable characterisation of the quantum connectivity at the level of the network (or its subnetworks), we introduce the quantum connectivity measure (QCM), which quantifies the average connection quality between pairs of network nodes. Further, we describe two quantities, the quantum-connected fraction (QCF) and the quantum clustering coefficient (QCC), naturally derived from the QCM, which capture important features of the functional connectivity of the quantum network at the level of the network and an individual node, respectively. These metrics of quantum connectivity depend crucially on the entanglement distribution protocol and the quantum network parameters in addition to its physical topology. We demonstrate the crucial distinction between topological and quantum connectivity, showing that even a fully connected graph can be functionally disconnected for quantum tasks if average network edge-concurrence falls below a critical threshold. These quantum connectivity metrics thus provide important tools for the design, optimization, and benchmarking of future quantum networks.

We address Steinerberger's Wasserstein transport problem on the cube $Q=[0,1]^d$. For every $d\ge2$, we consider a dyadic digital sequence $(x_n)\subset Q$ and prove that every prefix $\{x_1,\dots,x_N\}$ admits an exact equal-mass transport partition at the optimal scale. More precisely, for every $N\in\mathbb{N}$, there exist pairwise disjoint Borel sets $A_1,\dots,A_N\subset Q$ such that \[ λ_d(A_n)=\frac1N,\qquad A_n\subset B(x_n,6\sqrt d\,N^{-1/d})\qquad(1\le n\le N), \] and $λ_d\!\bigl(Q\setminus\bigcup_{n=1}^N A_n\bigr)=0$. In other terms, every prefix of the sequence supports an exact transport allocation of Lebesgue mass to its points with uniformly controlled radius $O(N^{-1/d})$. By an elementary partition criterion, this yields \[ W_\infty\!\left(\frac1N\sum_{n=1}^Nδ_{x_n},\,λ_d\right)\le 6\sqrt d\,N^{-1/d} \qquad(N\in\mathbb{N}). \] The bound holds for every $1\le p\le\infty$. The exponent $1/d$ is optimal, so it gives the sharp uniform prefix rate on the cube. The result settles Steinerberger's problem for all $d\ge1$ and all $1\le p\le\infty$.

The low-energy spin- and charge-sensitive thermodynamic properties of a broad range of strongly correlated 4f-electron systems follow Kondo scaling, with a characteristic Kondo temperature, $T_K$. While the theory is known for thermodynamic properties and high-energy spectroscopies of Kondo materials, the surface sensitivity of electron spectroscopy limits the extent to which Kondo scaling can be quantitatively verified. In this study, bulk-sensitive photon-in photon-out temperature-dependent resonant inelastic X-ray scattering (RIXS), in combination with single-impurity Anderson model (SIAM) calculations, is used to provide quantitative evidence of low- and high-energy Kondo scaling in CeSi$_2$. RIXS Ce M$_5$-edge spectra show a clear decrease in the occupancy of the $f^0$ state as temperature increases accompanied by an increase of the spectral weight of the $f^1\underline L^1$ state, in good agreement with the SIAM calculations. The results demonstrate the breakdown of the Kondo singlet state, coupled with thermal occupation of the low-lying first-excited magnetic states. The RIXS data reveal a temperature evolution of the $f^n$ spectral weights, which is in stark contrast to that extracted from photoemission and inverse photoemission spectroscopies. This study provides an accurate spectroscopic method to determine the Kondo energy $k_B$$T_K$ that is consistent with thermodynamic measurements, and highlights soft X-ray RIXS as a quantitative bulk probe of low- and high-energy-scale hybridization effects in strongly correlated materials.

Compiling quantum circuits is a major bottleneck in quantum computing, and given the scale required in a few years, is likely to become infeasibly long. Techniques to reduce compilation time for quantum circuits are sorely needed. Furthermore, resources to test acceleration techniques are similarly lacking due to the limited scale of circuits in benchmark suites and mismatches in characteristics of these circuits and those produced by random circuit generators. This paper resolves the latter of these problems by describing a random circuit generator which allows control of circuit density, width and depth parameters. This is used to derive 8000 experimental large-scale circuits and test a novel approach to compiler parallelisation. This separates a circuit into sub-circuits which are compiled in parallel and recombined to produce a compiled circuit. When the parallel approach was tested using Qiskit, a peak speedup of 15.56 was achieved with corresponding overheads of less than 1%.

Reservoirs, typically implemented as recurrent neural networks with fixed random connection weights, can be combined with a simple trained readout layer to perform a wide range of computational tasks. However, increasing the magnitude of reservoir connection weights to exploit nonlinear dynamics can cause the network to develop strong spontaneous activity that drives neurons into saturation, dramatically degrading performance. In this work, we investigate two distinct countermeasures against such runaway excitation. The first approach introduces a subtle non-homogeneous structure into the matrix of connection weigths $w_{ij}$, without altering the overall probability distribution $p(w)$. We identify several favorable structuring principles, such as creating a small subset of neurons with weaker-than-average input connections. Even if the rest of the reservoir falls into runaway saturating behavior, this weakly coupled subset remains in a mildly nonlinear regime whose dynamics can still be exploited by the readout layer. The second approach implements a form of automatic gain control, in which a dedicated control unit dynamically regulates the reservoir's average global activation toward an optimal setpoint. Although the control unit modulates the excitability of the reservoir only via a global gain factor, this mechanism substantially enlarges the dynamical regime favorable for computation and renders performance largely independent of the underlying connection statistics.

To construct a curve with a monotonic curvature (spiral), and given tangents and curvatures at the ends, the author proposed the following method. From given boundary conditions, the values of two inverse invariants are determined. Then, on some base spiral (initially, a logarithmic spiral was chosen), an arc with the same invariant values is sought for. A linear-fractional map of the found arc solves the problem. It seems that choosing the involute of a circle as the base spiral yields the simplest solution, which we present here.

An insider is a team member who covertly deviates from the team's optimal collaborative strategy to pursue a private objective while still appearing cooperative. Such an insider may initially behave cooperatively but later switch to selfish or malicious actions, thereby degrading collective performance, threatening mission success, and compromising operational safety. In this paper, we study such insider threats within an insider-aware, game-theoretic formulation, where the insider interacts with a decision maker (DM) under a continuous-time switched system, with each time interval characterized by a distinct insider behavioral pattern or threat level. We develop a periodic off-policy mitigation scheme that enables the DM to learn optimal mitigation policies from online data when encountering different insider threats, without requiring a priori knowledge of insider intentions. By designing appropriate conditions on the inter-learning interval time, we establish convergence guarantees for both the learning process and the closed-loop system, and characterize the corresponding mitigation performance achieved by the DM.

The proliferation of diverse, high-leverage trading instruments in modern financial markets presents a complex, "noisy" environment, leading to a critical question: which trading strategies are evolutionarily viable? To investigate this, we construct a large-scale agent-based model, "MAS-Utopia," comprising 10,000 agents with five distinct archetypes. This society is immersed in five years of high-frequency data under a counterfactual baseline: zero transaction friction and a robust Unconditional Basic Income (UBI) safety net. The simulation reveals a powerful evolutionary convergence. Strategies that attempt to fight the market's current - namely Mean-Reversion ("buy-the-dip") - prove structurally fragile. In contrast, the Trend-Following archetype, which adapts to the market's flow, emerges as the dominant phenotype. Translating this finding, we architect an LLM-driven system that emulates this successful logic. Our findings offer profound implications, echoing the ancient wisdom of "Be Water": for investors, it demonstrates that survival is achieved not by rigid opposition, but by disciplined alignment with the prevailing current; for markets, it critiques tools that encourage contrarian gambling; for society, it underscores the stabilizing power of economic safety nets.

We provide polynomial completeness results for finite algebras in congruence permutable varieties. In 2001, Idziak and Słomczy{ń}ska introduced the completeness concept of being \emph{polynomially rich}: a finite algebra is polynomially rich if every function preserving congruences and the Tame Congruence Theory labelling of prime quotients in the congruence lattice is a polynomial function of the algebra. We call a finite algebra \emph{strictly polynomially rich} if every partial congruence and type preserving function is a polynomial function, and we describe strictly polynomially rich algebras in congruence permutable varieties.

Virtual Try-On is a promising research area with broad applications in e-commerce and everyday life, enabling users to visualize garments on themselves or others before purchase. Most existing methods depend on predefined or user-specified masks to guide garment placement, but their performance is highly sensitive to mask quality, often causing misalignment or artifacts, and introduces redundant steps for users. To overcome these limitations, we propose a mask-free virtual try-on framework that requires only minimal modifications to the underlying architecture while remaining compatible with common diffusion-based pipelines. To address the increased ambiguity in the absence of masks, we integrate an attention-based guidance mechanism that explicitly directs the model to focus on the target garment region and improves correspondence between the garment and the person. Additionally, we incorporate instruction prompts, allowing users to flexibly control garment categories and wearing styles, addressing the underutilization of prompts in prior work and improving interaction flexibility. Both qualitative and quantitative evaluations across multiple datasets demonstrate that our approach consistently outperforms existing methods, producing more accurate, robust, and user-friendly try-on results.

Optimal scheduling of batteries has significant potential to reduce electricity costs and to enhance grid resilience. However, effective battery scheduling must account for both physical constraints as well as uncertainties in consumption and generation of renewable energy sources. Instead of optimizing fixed battery power setpoints, we propose an approach that optimizes battery power intervals, allowing the optimization to explicitly account for uncertain consumption and generation as well as how the battery system should respond to them within its physical limits. Our method is based on mixed random variables, represented as mixtures of discrete and continuous probability distributions. Building on this representation, we develop an analytical stochastic formulation for minimizing electricity costs in a residential setting with load, photovoltaics, and battery storage. We demonstrate its effectiveness across real-world data from 15 residential buildings over five consecutive months. Compared with deterministic and probabilistic benchmark controllers, the proposed interval-based optimization achieves the lowest costs. These results show that mixed random variables are a practical and promising tool for decision-making under uncertainty.

The naming of astronomical objects has represented among the most significant challenges in the record-keeping of the field since the very beginning. Long and unwieldy coordinate names, uninformative and ambiguous internal names, and the sheer volume of aliases accumulated for some of the most studied objects conspire to complicate our study of the celestial sphere. This paper proposes StarHash, a reproducible, open-source astronomical naming scheme based on the terrestrial concept of geohashing, but re-implemented from the ground up for the rigorous demands of astronomy. Every 3.2 arcsec patch of sky now has three words associated with it, enabling the precise localisation of astronomical sources, and an easily communicable and memorable identifier. A carefully selected wordlist reduces ambiguity due to plurals and homophones, whilst the use of format-preserving encryption minimises residual spatial correlation in StarHash-derived identifiers. Pre-computed names for several existing catalogues are provided, alongside a Python reference implementation for validation and integration into databases, transient brokers, and other similar projects. Although not intended to be the final word in the naming of astronomical objects, StarHash humbly provides a memorable alternative to the status quo, and is intended to spark a discussion about this most foundational of issues in astronomy.

We study the dynamics of a lattice hard-core boson gas released from a domain wall initial state in the presence of two weak links (defects). When the two defects are separated by a finite distance, the resulting density profile exhibits clear deviations from the standard Euler-scale hydrodynamic description of the gas, due to genuine quantum interference effects between the two defects. By analyzing the exact fermionic propagators, we show that repeated reflections at the defects give rise to interference fringes and coherent patterns that are beyond the reach of the (generalized) hydrodynamic description. We derive a closed analytic expression for the density profile during the expansion, explicitly highlighting the role played by these interference processes.

The Weighted Tree Augmentation Problem (WTAP) is a fundamental network design problem where the goal is to find a minimum-cost set of additional edges (links) to make an input tree 2-edge-connected. While a 2-approximation is standard and the integrality gap of the classic Cut LP relaxation is known to be at least 1.5, achieving approximation factors significantly below 2 has proven challenging. Recent advances of Traub and Zenklusen using local search culminated in a ratio of $1.5+ε$, establishing the state-of-the-art. In this work, we present a randomized approximation algorithm for WTAP with an approximation ratio below 1.49. Our approach is based on designing and rounding a strong linear programming relaxation for WTAP which incorporates variables that represent subsets of edges and the links used to cover them, inspired by lift-and-project methods like Sherali-Adams.

Laser-cooled atoms are increasingly being used to realise practical quantum devices, motivating the development of compact and robust atom sources. Grating magneto-optical traps (gMOTs) simplify the cold-atom source architecture but are typically vapour-loaded and provide limited atomic flux. Here we explore the loading of gMOTs from cold-atom beams. We numerically simulate loading to show that unbalanced diffracted beams deflect incoming atoms away from the trap centre, thereby strongly constraining radial loading. In contrast, axial loading injects atoms directly into the trapping volume and largely avoids these effects. We experimentally demonstrate rapid axial loading of a gMOT, achieving loading rates of $2.1 \times 10^9$ atoms~s$^{-1}$ using a moving optical molasses to transfer atoms from a 2D MOT into the gMOT. These results establish axial loading as a robust route to high-flux gMOT operation for portable cold-atom systems.