We study the triangular lattice optical Su-Schrieffer-Heeger (SSH) model using determinant quantum Monte Carlo. By varying the model's carrier concentration, electron-phonon coupling strength, and phonon energy $Ω$, we identify two doping regimes of interest. At one-quarter filling ($\langle n\rangle = 0.5$), corresponding to the case of a circular noninteracting Fermi surface, we find evidence for a metal to insulating bond-order-wave (BOW) phase transition that breaks a local $C_6$ rotational symmetry. Conversely, at three-quarters filling ($\langle n\rangle = 1.5$), corresponding to a hexagonal Fermi surface, we find evidence for transitions to another BOW phase for small $Ω$ and an $s$-wave superconducting phase for sufficiently large $Ω$. This tendency toward pairing appears to be associated with the possibility of a sign change in the effective intersite hopping, which can occur for sufficiently large lattice displacements. We also find no evidence for enhanced magnetic correlations in the model, contrary to what has been reported for square lattice SSH models.

We present a Gaussian-process (GP) emulator for the monopole of the redshift-space halo power spectrum in $Λ$CDM cosmologies with massive neutrinos. The emulator is trained on 1000 COLA simulations distributed in a Latin-hypercube design over the six-dimensional cosmological parameter space $\{Ω_m h^2,Ω_b h^2,Ω_νh^2,σ_8,h,n_s\}$, with outputs at 11 snapshots spanning $0.5 \le z \le 2.0$. From redshift-space halo catalogues we measure shot-noise-subtracted monopole spectra over $0.01 \le k \le 0.50\,h\,\mathrm{Mpc}^{-1}$. We also generate 1000 fixed-cosmology realizations to estimate the covariance matrix and to construct synthetic data vectors for likelihood tests. On held-out cosmologies, the emulator reproduces the simulated spectra to typically better than $2\%$ across the scales and redshifts considered. Combined with its GP-based estimate of interpolation uncertainty, this speed and accuracy make the emulator well suited to repeated likelihood evaluations in Markov Chain Monte Carlo analyses. The resulting framework provides an efficient route toward neutrino-mass inference from DESI-motivated redshift-space clustering measurements.

The minimal network problem is a classical topic in geometric measure theory and the calculus of variations, which aims to find networks of minimal length connecting given points. Most classical results are established in the Euclidean plane, while a complete theory for constant-curvature Riemannian manifolds remains to be developed. In this paper, we locally extend the theory of minimal networks and the calibration method from the Euclidean plane to the standard unit sphere \(S^2\). We redefine \(\mathbb{R}^2\)-valued co-vectors, differential forms, currents, and calibrations adapted to spherical geometry. Using exponential maps and local metric perturbation estimates, we prove that spherical minimal networks composed of great-circle arcs with \(120^\circ\) triple junctions are \textbf{locally length-minimizing only within sufficiently small geodesic balls} on \(S^2\), without obtaining global minimality results. Our work partially enriches the theory of minimal networks on constant-curvature spaces, and provides a theoretical reference and technical basis for future research on extending such results to higher-dimensional Riemannian manifolds and more general surfaces.

We consider causal discovery in structural causal models driven by heavy-tailed noise, where extremes carry important information about causal direction. We introduce the Heavy-Tailed Homogeneous Structural Causal Model (HT-HSCM), a unified framework that generalizes heavy-tailed linear and max-linear models. We demonstrate that causal tail coefficients identify the complete ancestral partial order of the underlying directed acyclic graph. We also formulate a recursive algorithm for recovering quantities associated with the model called ancestral impulse-responses from the causal tail coefficients. Our results provide a general and theoretically justified framework for causal discovery in heavy-tailed systems.

The electrification and ongoing energy transition lead to systematic changes in electricity loading and variability in power systems. Distribution systems were designed for regular operating patterns, assuming constant low loading. Now, operators need to assess whether their assets can withstand more, as well as time-varying loading. Operating the system at or near its ampacity potentially accelerates thermal ageing, so the question arises: 'how much can one operate at the limits while keeping maintenance and failures low?' This paper introduces a novel approach that derives a time-varying Weibull approximation of failure rates using thermal models and provides a shortcut method to quantify maintenance implications under time-varying loading for heterogeneous MV cable populations. The case studies investigate a dataset from Denmark and the Oberrhein Medium Voltage (MV) system in Germany, studying ageing assets and the interplay with loading, and replacement paradigms of two different cable insulation types. The studies demonstrate that a small fraction of 25% of old, low-quality cables leads to 82% of failures, and 1.4% of the time of highest loading can cause 46% of cable ageing. The case studies also demonstrate that maintenance needs may be between 10-300 times higher under future loading conditions associated with the energy transition, specifically in networks that have older PILC cables. This paper provides a new tool for operators to plan maintenance under more realistic, future operating conditions.

A Gallai $k$-colouring of a graph $G$ is a colouring of $E(G)$ with $k$ colours that induces no rainbow triangles, that is, a triangle with edges of 3 different colours. We give a first step towards estimating the number of Gallai colourings of the Erdős-Rényi random graph, by proving that for every $δ> 0$ there are $c$ and $C$ such that with high probability the number of Gallai 3-colourings of $G(n,p)$ is at least $3^{(1-δ)\binom{n}{2}p}$ for $p \leq cn^{-1/2}$, and at most $2^{(1+δ)\binom{n}{2}p}$ for $p \geq Cn^{-1/2}$.

We discuss the finite-temperature properties of low-dimensional bosons with three-body interactions described by a Feshbach-resonance-like two-channel model. In particular, by using the approximate consideration that collects ring-like Feynman diagrams for the grand potential and resembles the three-body $t$-matrix approximation, we have computed the third virial coefficient, an equation of state, and the temperature depletion of the average number of closed-channel trimers. The calculated heat capacity demonstrates a non-monotonic temperature behavior, which is unusual for a low-dimensional Bose gas.

We present the first calculation of tensor and axial-tensor mesons with total spin $J\geq2$ within the Covariant Spectator Theory. We employ a refined quark-antiquark interaction kernel that incorporates the momentum dependence of the strong coupling, replacing the previously used constant term of the kernel. Global least-squares fits to the masses of experimentally established heavy and heavy-light meson states yield an excellent description of the mass spectrum for $J^P=0^\pm, 1^\pm, 2^\pm$, and $3^\pm$ using only eight adjustable parameters.

This is the Replicated Computational Results (RCR) Report for the paper C2|Q>: A Robust Framework for Bridging Classical and Quantum Software Development. The paper introduces a modular, hardware-agnostic framework that translates classical problem specifications - Python code or structured JSON - into executable quantum programs across ten problem families and multiple hardware backends. We release the framework source code on GitHub at https://github.com/C2-Q/C2Q, a pretrained parser model on Zenodo at https://zenodo.org/records/19061125, evaluation data in a separate Zenodo record at https://zenodo.org/records/17071667, and a PyPI package at https://pypi.org/project/c2q-framework/ for lightweight CLI and API use. Experiment 1 is supported through a released pretrained model and training notebook, while Experiments 2 and 3 are directly executable via documented make targets. This report describes the artifact structure, setup instructions, and the mapping from each execution route to the corresponding experiment.

Hot subdwarf (sdB) stars in binary systems with main-sequence (MS) companions provide valuable insights into mass transfer and envelope ejection processes in binary evolution. Their mass ratios, orbital periods, and stellar properties encode key information about their evolutionary histories. In this work, we analyze a sample of 123 composite-spectrum sdB+MS binaries identified from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope Low-Resolution Survey (LAMOST-LRS) Data Release (DR) 8. We adopt atmospheric parameters from spectral decomposition and estimate stellar masses and radii using theoretical evolutionary tracks. Radial velocities for both the hot subdwarfs and cool companions are measured independently through cross-correlation with synthetic templates. Orbital periods are statistically estimated using single-epoch RV separations and a Monte Carlo method that accounts for random inclination and orbital phase. We find that sdB masses are narrowly distributed around 0.5 Msun, consistent with expectations for core helium-burning stars, while MS companion masses span 0.6-1.9 Msun, with most falling between 1.0 and 1.4 Msun. The inferred orbital-period distribution shows a clear concentration toward long periods, broadly consistent with expectations for binaries formed through stable Roche-lobe overflow. Given that our sample consists of composite-spectrum sdB binaries, mainly sdB+FGK systems, the prevalence of long periods is largely driven by observational selection effects rather than the intrinsic period distribution of the sdB binary population. This study provides one of the largest uniform catalogs of composite spectrum sdB binaries to date, offering new observational constraints on their physical properties and formation channels.

There has been widespread global increasing use of renewable energy sources, which are usually connected to the electricity grids via power electronic inverters. Traditionally, these inverter-based resources operate in either grid-forming (GFM) or grid-following (GFL) mode. But more recently, the need of switching between these two modes are glowingly required because of the complex operation scenarios of systems such as source-side limitations, grid-side services, fault disturbances, etc. However, due to the differences between GFM and GFL modes, a direct switching between them would lead to large oscillations or even instability of inverters. Therefore, in this paper, a method called state mapping method for analyzing the switching transient and designing the switching control is proposed. Based on this method, an ideally-smooth transition between GFM and GFL can be achieved. The effectiveness of the proposed method is verified by both the theoretical analysis and experiment tests.

A two dimensional ferromagnetic XY model with its bound vortex-antivortex dominated quasi long range ordered phase at low temperatures is a long standing as well as well studied problem of interest in the field of condensed matter. We conduct a detailed Monte Carlo study of such model with rather unexplored extensions where additional anisotropic exchange coupling and Dzyaloshinskii-Moriya interactions (DMI) together affect the Kosterlitz-Thoulass (KT) transition in presence/absence of symmetry breaking fields. Without DMI, the exchange term promotes collinear (ferromagnetic) order, whereas the DMI term induces spin cantings. By tuning anisotropy upto Ising limit, we document energy, specific-heat, magnetizations as well as helicity modulus and vortex densities for different tempeatures and DMI strength. We also compute the 2nd moment of correlation lengths in order to probe the spatial correlation of the spins. Furthermore, the effect of U(1) symmetry breaking 4-fold and 8-fold symmetric h4 and h8 fields are explored which shows how the double-peaked specific heat profiles changes in presence of DMI. Overall, our findings append many important updates in the low temperature phases of a topological XY ferromagnet when additional DMI and isotropy-breaking exchange and/or field terms are considered and thus providing a practical blueprint for suitably engineering topological spin systems.

Developers utilize third-party libraries to improve productivity, which also introduces potential security risks. Existing approaches generate tests for public functions to trigger library vulnerabilities from client programs, yet they depend on proof-of-concepts (PoCs), which are often unavailable. In this paper, we propose a new approach, LiveFuzz, based on directed greybox fuzzing (DGF) to detect the exploitability of library vulnerabilities from client programs without PoCs. LiveFuzz exploits a target tuple to extend existing DGF techniques to cross-program scenarios. Based on the target tuple, LiveFuzz introduces a novel Abstract Path Mapping mechanism to project execution paths, mitigating the preference for shorter paths. LiveFuzz also proposes a risk-based adaptive mutation to mitigate excessive mutation. To evaluate LiveFuzz, we construct a new dataset including 61 cases of library vulnerabilities exploited from client programs. Results show that LiveFuzz increases the number of target-reachable paths compared with all baselines and improves the average speed of vulnerability exposure. Three vulnerabilities are triggered exclusively by LiveFuzz.

We study higher-order small-noise fluctuation expansions for the overdamped Langevin dynamics in a quartic double-well potential. Assuming that the initial data admits a suitable expansion structure, we obtain a strong dynamical expansion of the trajectories, as well as an expansion of the laws with respect to smooth observables. We then investigate the long-time behavior of the expansion coefficients. In the scalar case $d=1$, each coefficient converges exponentially fast to a finite limit as $t\to\infty$. In contrast, for $d\ge 2$, the fluctuation expansion coefficients reflect the degeneracy of the manifold of minima, which in general prevents the existence of a finite long-time limit. Furthermore, by combining a multi-level induction with combinatorial arguments, we derive a recursive formula for the fluctuation expansion coefficients. This recursion shows that the long-time limits of these dynamical expansion coefficients coincide with those arising from the corresponding equilibrium expansions.

Large language models (LLMs) are effective for automated program repair, but plausible patches that pass the full test suite often rewrite more code than necessary, increasing review and maintenance costs. This over-editing is common because most bugs are localized, while standard supervised fine-tuning provides no explicit signal about which tokens should be preserved and which should be changed. We propose PAFT, a preservation-aware fine-tuning method for minimal-edit program repair. PAFT derives token-level preservation signals by aligning buggy and fixed code, combines them with full-sequence masking, and applies an edit-difficulty curriculum. Across Defects4J and HumanEval-Java, PAFT improves pass@1 by up to 65.6% over standard supervised fine-tuning (StdFT) while reducing average edit distance (AED) by up to 32.6%. On Defects4J with DeepSeek-Coder-6.7B, PAFT also outperforms AdaPatcher, a strong preference-based repair baseline, improving pass@1 from 5.9% to 10.1% while reducing median AED from 61.0 to 42.0. Overall, PAFT preserves stable context and concentrates edits on faulty regions, yielding smaller, more localized, plausible patches without inference-time search, reranking, or post-processing.

We construct a stratification of the punctual Hilbert scheme of points on a non-reduced and nodal plane curve, $x^uy^v=0$. Each stratum is indexed by a new combinatorial object we define: a weak diagonal partition. The approach is based on introducing filtrations on ideals, together with a valuation adapted to the non-reduced structure, which allows us to analyze generators and their degrees of freedom in a systematic way. In particular, each stratum is affine when $u=1,2$; and each stratum is isomorphic to an algebraic torus times an affine space, $(\mathbb{C}^*)^{m_1} \times \mathbb{C}^{m_2}$, when $u=v,v-1,v-2$. We consequently compute the Poincaré polynomials of the punctual Hilbert scheme of points on curves $x^uy^v=0$ when $u=1,2,v-2,v-1,v$. As an application, we prove the colored Oblomkov-Rasmussen-Shende conjecture for the Hopf link for $u=1, v$ arbitrary, showing that the Poincaré polynomial is the row-colored link homology up to change of variables.

We study the spin excitation spectra in magnetically ordered phases proximate to the Kitaev quantum spin liquid (KQSL). Although the low-energy universal features should be governed by the magnetic orders, the $\textit{non-universal}$ high-energy features of the KQSL and adjacent phases can be remarkably similar. Therefore, we study the extended Kitaev model within a Stoner-like theory using Majorana partons, and compute the inelastic neutron scattering (INS) intensities in the random phase approximation. First, we benchmark against the antiferromagnetic (AFM) Heisenberg model and recover the AFM order with linear Goldstone modes. We then explore the phase diagram which agrees qualitatively with previous numerical results. In particular, the Majorana parton theory accurately captures Order-by-Disorder effects in the Kitaev-Heisenberg limit. We also find large INS intensities near the associated high-symmetry Brillouin zone (BZ) points of the magnetic orders. At intermediate and high energies, broad multi-spinon continua emerge across the BZ, providing a distinct mechanism for magnon decay and spectral broadening beyond the conventional multi-magnon decay scenario. Finally, we study the model Hamiltonian of candidate Kitaev material $α$-RuCl$_3$. The zigzag ground state agrees qualitatively with experiments, its stability under external magnetic field also exhibits strong anisotropy in the field directions, and broad scattering continua are recovered similar to those observed experimentally.

A hyperbolic observer canonical form (HOCF) for linear hyperbolic PDEs with boundary dynamics is presented. The transformation to the HOCF is based on a general procedure that uses so-called observability coordinates as an intermediate step. These coordinates are defined from an input-output relation given by a neutral functional differential equation (FDE), which, in the autonomous case, reduces to an autonomous FDE for the output. The HOCF coordinates are directly linked to this FDE, while the state transformation between the original coordinates and the observability coordinates is obtained by restricting the observability map to the interval corresponding to the maximal time shift appearing in the FDE. The proposed approach is illustrated on a string-mass-spring example.

We discuss spacetime singularities of a solution to the Schrödinger equation with a metric perturbation and a sublinear potential. The quasi-homogeneous wave front set, due to Lascar (1977), of a solution is characterized by that of the free solution, and a classical high-energy scattering data. In the one-dimensional case, it further reduces to the homogeneous wave front set, due to Nakamura (2005), of the initial time-slice. For the proof of the former result we implement an idea inspired by Nakamura (2009), which was originally devised for spatial singularities of the Schrödinger equation. As for the latter result, we use an exact Egorov-type formula for the free propagator, and a special partition of unity conforming with the classical flow.

Particle number fluctuations $N(t)$, measured in virtual observation boxes of an image or a simulation, offer a way to quantify particle dynamics when particle tracking is impractical, such as in high-density systems. While traditionally limited to equilibrium diffusive systems, we extend this approach -- named ``Countoscope'' -- to out-of-equilibrium self-propelled particles: Active Brownian (ABPs), Run and Tumble (RTPs), and Active Ornstein-Uhlenbeck Particles (AOUPs). For AOUPs, we leverage their Gaussian statistics to derive a general formula applicable to any Gaussian system. For ABPs and RTPs, we derive the intermediate scattering function (ISF) -- and thus the correlations of $N(t)$ -- using an exact perturbative expansion over the probability density fields, revealing key physical features of the ISF and of the number correlations. Our theoretical predictions for the mean-squared number difference $\langle ΔN^2(t) \rangle = \langle (N(t) - N(0))^2 \rangle$ match stochastic simulations and exhibit three time-dependent scaling regimes: diffusive, advective, and long-time enhanced diffusive, reflecting the regimes of the mean squared particle displacement. We further uncover limiting laws in each of these regimes that are useful to quantify self-propulsion properties.

Public sector agencies perform the critical task of implementing the redistributive role of the State by acting as the leading provider of critical public services that many rely on. In recent years, public agencies have been increasingly adopting algorithmic prioritization tools to determine which individuals should be allocated scarce public resources. Prior work on these tools has largely focused on assessing and improving their fairness, accuracy, and validity. However, what remains understudied is how the structural design of prioritization itself shapes both the effectiveness of these tools and the experiences of those subject to them under realistic public sector conditions. In this study, we demonstrate the fallibility of adopting a prioritization approach in the public sector by showing how the underlying mechanisms of prioritization generate significant relative disparities between groups of intersectional identities as resources become increasingly scarce. We argue that despite prevailing arguments that prioritization of resources can lead to efficient allocation outcomes, prioritization can intensify perceptions of inequality for impacted individuals. We contend that efficiencies generated by algorithmic tools should not be conflated with the dominant rhetoric that efficiency necessarily entails "doing more with less" and we highlight the risks of overlooking resource constraints present in real-world implementation contexts.

This note is an addendum to the work initiated by Promyslov on the integro-differential equation arising in the ruin problem for annuity payment models. First, the existence of viscosity solutions is proved. Then the regularity of these solutions is established, showing that they are indeed classical solutions.

Crystal field (CF) excitations in the ground multiplet $^3H_6$ of Tm$^{3+}$ ions were investigated using terahertz transmission spectra of magnetoelectric TmAl$_3$(BO$_3$)$_4$ and Tm$_{0.05}$Yb$_{0.1}$Y$_{0.85}$Al$_3$(BO$_3$)$_4$. These excitations were identified as mainly magnetic dipole transitions from the ground singlet A$_1$ to the next excited doublet E, split by the crystal field of the D$_3$ symmetry. The fine structure of the modes was resolved at low temperatures. It manifested differently in lightly doped and in pure Tm borates, consistent with different distortions of the local crystal field with the D$_3$ symmetry. Strong natural optical activity was observed near the CF transitions resulting in a polarization plane rotation up to 25 degrees. The optical activity is quantitatively described by contributions of magnetic and electric dipole transitions to dynamic magnetoelectric susceptibility and taking into account the classification of local distortions.

Neural Radiance Fields (NeRF) enables 3D scene reconstruction from several 2D images but incurs high rendering latency via its point-sampling design. 3D Gaussian Splatting (3DGS) improves on NeRF with explicit scene representation and an optimized pipeline yet still fails to meet practical real-time demands. Existing acceleration works overlook the evolving Tensor Cores of modern GPUs because 3DGS pipeline lacks General Matrix Multiplication (GEMM) operations. This paper proposes GEMM-GS, an acceleration approach utilizing tensor cores on GPUs via GEMM-friendly blending transformation. It equivalently reformulates the 3DGS blending process into a GEMM-compatible form to utilize Tensor Cores. A high-performance CUDA kernel is designed, integrating a three-stage double-buffered pipeline that overlaps computation and memory access. Extensive experiments show that GEMM-GS achieves $1.42\times$ speedup over vanilla 3DGS and provides an additional $1.47\times$ speedup on average when combining with existing acceleration approaches. Code is released at https://github.com/shieldforever/GEMM-GS.

Building off work of Farenick and Rahaman, we extend the definition of the density space and the Bures metric to the setting of non-unital C*-algebras equipped with a faithful trace and prove that the Bures metric is also a metric in this case and show that its topology is weaker than the topology induced by the C*-norm. Furthermore, we prove a Heine-Borel type theorem for C*-algebras and the density space. In particular, we prove that for any C*-algebra (unital or non-unital) equipped with a faithful trace, the density space equipped with the Bures metric topology is not compact if and only if the C*-algebra is infinite dimensional. We also exhibit several examples of sequences that have no converging sequence in the unital and non-unital case including both commutative and noncommutative C*-algebras. Next, building off work from some of the authors, we extend the definition of the quantum metric on the density space to the non-unital C*-algebra case by introducing the notion of a quantum Lipschitz triple, which form a subclass of quantum locally compact metric spaces of Latrémolière that utilize Rieffel's notion of a quantum metric (we also introduce new classes of quantum locally compact metric spaces that include certain noncommutative homogeneous C*-algebras). Furthermore, we prove that this quantum metric topology is weaker than the topology of the one induced by the C*-norm and finish the article with an analysis of matrix-valued functions on the quantized interval, which provides commutative and noncommuataive examples where the quantum metric topology on the density space is not compact and is not uniformly equivalent to both the Bures metric and the metric induced by the C*-norm.

Speech-based depression detection has shown promise as an objective diagnostic tool, yet the cross-linguistic robustness of acoustic markers and their neurobiological underpinnings remain underexplored. This study extends Cross-Data Multilevel Attention (CDMA) framework, initially validated on Italian, to investigate these dimensions using a Chinese Mandarin dataset with Electroencephalography (EEG) recordings. We systematically fuse read speech with spontaneous speech across different emotional valences (positive, neutral, negative) to investigate whether emotional arousal is a more critical factor than valence polarity in enhancing detection performance in speech. Additionally, we establish the first neurophysiological validation for a speech-based depression model by correlating its predictions with neural oscillatory patterns during emotional face processing. Our results demonstrate strong cross-linguistic generalizability of the CDMA framework, achieving state-of-the-art performance (F1-score up to 89.6%) on the Chinese dataset, which is comparable to the previous Italian validation. Critically, emotionally valenced speech (both positive and negative) significantly outperformed neutral speech. This comparable performance between positive and negative tasks supports the emotional arousal hypothesis. Most importantly, EEG analysis revealed significant correlations between the model's speech-derived depression estimates and neural oscillatory patterns (theta and alpha bands), demonstrating alignment with established neural markers of emotional dysregulation in depression. This alignment, combined with the model's cross-linguistic robustness, not only supports that the CDMA framework's approach is a universally applicable and neurobiologically validated strategy but also establishes a novel paradigm for the neurophysiological validation of computational mental health models.

We show that, assuming NP $\not\subseteq$ $\cap_{δ> 0}$DTIME$\left(\exp{n^δ}\right)$, the shortest vector problem for lattices of rank $n$ in any finite $\ell_p$ norm is hard to approximate within a factor of $2^{(\log n)^{1 - o(1)}}$, via a deterministic reduction. Previously, for the Euclidean case $p=2$, even hardness of the exact shortest vector problem was not known under a deterministic reduction.

AMBRA combines the large cosmological volume and statistical power of ASTRID with the physically motivated gas-based black hole seeding models from BRAHMA. Motivated by JWST's discoveries of massive black holes (BHs) at $z\gtrsim 9$, AMBRA adopts a lenient heavy-seed prescription from the BRAHMA suite, allowing for the formation of $4\times 10^{4-5}\ M_{\odot}$ seeds in halos with star-forming, metal-poor gas. The seeding model is motivated by scenarios in which heavy seeds form through stellar collisions in star clusters or from the rapid growth of Population III remnants. The improved seeding model enables AMBRA to form BH seeds much earlier and more efficiently compared to ASTRID. This significantly enhances early BH growth, producing a $z=8$ BH number density more than an order of magnitude higher than that in ASTRID over the mass range $10^{5-7}\ M_{\odot}$. BHs reaching masses consistent with GN-z11 and CEERS-1019 typically originate in highly compact density peaks and undergo multiple early mergers. In these systems, $\sim50\%$ of BH masses by $z=11$ is from BH mergers, after which gas accretion becomes the dominant growth channel. Without this early merger-driven assembly, ASTRID cannot reproduce the high-mass BH detected by JWST. Our results indicate that abundant early seed formation combined with frequent mergers can explain several JWST massive BH candidates without requiring sustained super-Eddington accretion. As a testable prediction, AMBRA yields $\approx4$ LISA detectable BH merger events per year at $z\geq8$, which is three orders of magnitude higher than that in ASTRID.

Large Language Models (LLMs) are increasingly applied to automate software engineering tasks, including the generation of UML class diagrams from natural language descriptions. While prior work demonstrates that LLMs can produce syntactically valid diagrams, syntactic correctness alone does not guarantee meaningful design. This study investigates whether LLMs can move beyond diagram translation to perform design synthesis, and how reliably they maintain design-oriented reasoning under variation. We introduce a preference-based few-shot prompting approach that biases LLM outputs toward designs satisfying object-oriented principles and pattern-consistent structures. Two design-intent benchmarks, each with three domain-only, paraphrased prompts and 10 repeated runs, are used to evaluate three LLMs (ChatGPT 4o-mini, Claude 3.5 Sonnet, Gemini 2.5 Flash) across three modeling strategies: standard prompting, rule-injection prompting, and preference-based prompting, totaling 540 experiments (i.e. 2x3x10x3x3). Results indicate that while preference-based alignment improves adherence to design intent it does not eliminate non-determinism, and model-level behavior strongly influences design reliability. These findings highlight that achieving dependable LLM-assisted software design requires not only effective prompting but also careful consideration of model behavior and robustness.

High-dimensional statistical settings ($p \gg n$) pose fundamental challenges for classical inference, largely due to bias introduced by regularized estimators such as the LASSO. To address this, Javanmard and Montanari (2014) propose a debiased estimator that enables valid hypothesis testing and confidence interval construction. This report examines their debiased LASSO framework, which yields asymptotically normal estimators in high-dimensional settings. The key theoretical results underlying this approach are presented. Specifically, the construction of an optimized debiased estimator that restores asymptotic normality, which enables the computation of valid confidence intervals and $p$-values. To evaluate the claims of Javanmard and Montanari, a subset of the original simulation study and the real-data analysis is presented. The original empirical analysis is extended to the desparsified LASSO, which is referenced but not implemented in the original study. The results demonstrate that while the debiased LASSO achieves reliable coverage and controls Type I error, the LASSO projection estimator can offer improved power in idealized low-signal settings without compromising error rates. The results reveal a trade-off: the LASSO projection estimator performs well in low-signal settings, while Javanmard and Montanari's method is more robust to complex correlations, improving precision and signal detection in real data.