Python's dynamic nature complicates testing and increases the possibility that some defects evade detection, so an effective fault prediction becomes essential. We examine whether post-release faults can be predicted using modern ML and DL. Using a balanced dataset of over 4,000 labeled faults with 83 product, process, statistical, and Python-specific metrics plus normalized code representations, we conduct cross-project experiments. LLMs and unsupervised models fail to distinguish residual from non-residual faults, while supervised metric-based models (RandomForest, XGBoost, CatBoost) perform far better, yielding a 0.85-0.9 recall and cutting false negatives by an order of magnitude. Process metrics, especially age, churn, and developer-activity, alongside class and file size, consistently prove most predictive. Notably, the Principal Component Analysis shows that metrics and code embeddings occupy distinct regions of the representation space, suggesting that they capture complementary rather than redundant information.

Deep learning compilers and vendor libraries deliver strong baseline performance but are bounded by finite, engineer-curated catalogs. When these omit needed optimizations, practitioners substitute hand-written CUDA or CUTLASS, demanding expertise in GPU microarchitecture and C++ template metaprogramming. Recent LLM-based agents target kernel generation in raw CUDA, forcing rediscovery of optimizations already encoded in mature libraries. We present FACT (Framework for Agentic CUTLASS Transpilation), a framework that employs a three-stage, agent-driven workflow optimizing PyTorch modules through multi-pattern composition while grounding synthesis in CUTLASS C++. (1) Pattern discovery: an LLM agent inspects the traced graph, matches subgraphs to optimization rules, retrieves vetted examples from an architecture-specific index, and outputs prioritized patterns. (2) Pattern realization: each pattern is implemented as a CUTLASS kernel wrapped in a PyTorch extension, verified, and auto-tuned by sweeping parameters inferred from the CUTLASS hierarchy. (3) Pattern composition: extensions are loaded together into a single composed module for end-to-end benchmarking. We evaluate the workflow using KernelBench's evaluation framework and provided modules on an NVIDIA A100. On Level 1, we apply the workflow to three GEMM workloads (square matrix multiply, batched matrix multiply, and large-$K$ matrix multiply). Auto-tuned CUTLASS kernels improve over PyTorch cuBLAS baseline by $1.06\times$--$1.18\times$. On Level 3 MiniGPT block, composing fused multi-head attention with fused MLP GEMM+GELU yields $2.79\times$ end-to-end speedup. Our work couples agentic graph-level pattern discovery with auto-tuning and a dynamic pattern table, offering a practical path from traced PyTorch to deployable kernels by automating CUTLASS kernel synthesis and auto-tuning.

The intrinsic anomalous Hall effect (IAHE) provides a powerful transport fingerprint of quantum magnets, with its linear and second-order responses distinguishing ferromagnets and $\mathcal{P}\mathcal{T}$-symmetric antiferromagnets, respectively. Altermagnets, as an emergent class of quantum magnets, have recently been shown to host a third-order extrinsic anomalous Hall effect, raising a question of whether an \textit{intrinsic} counterpart can serve as a diagnostic of altermagnetic order. Based on spin-group symmetry analysis, we demonstrate that the third-order IAHE is generically allowed in the ten spin Laue groups relevant to altermagnets when spin-orbit coupling (SOC) is taken into account. By combining these symmetry constraints with the anomalous velocity induced by the second-order Berry curvature, we uncover a resonant third-order IAHE arising near the altermagnetic band crossings at generic momenta in both the Lieb-lattice altermagnet and the experimentally realized altermagnet V$_2$Se$_2$O. Notably, we identify the Berry curvature quadrupole, encoded in the second-order Berry curvature and activated by finite SOC, as the microscopic quantum geometric origin of this resonance. Our results establish the third-order IAHE as an intrinsic quantum geometric transport fingerprint of altermagnets and extend the hierarchy of IAHE across collinear quantum magnets.

Compiling time-evolution operators of the form $U(t)=e^{-iHt}$ into hardware-native gate sequences is a central bottleneck for digital quantum simulation on noisy intermediate-scale quantum (NISQ) devices. Generic transpilation treats $U(t)$ as an arbitrary unitary, discarding the structure of Hamiltonian dynamics and producing circuits whose depth exceeds hardware coherence limits. We introduce a structure-aware compilation framework that treats product-formula decompositions as synthesis primitives rather than simulation approximations. The method combines (i) native placement of Hamiltonian terms onto the hardware coupling map, (ii) adaptive selection of Trotter blocks via a greedy discretization procedure, and (iii) variational refinement using a Trotter-initialized ansatz. Across Heisenberg, Ising, and XY models with $n=3$--$8$ qubits, the compiled circuits achieve fidelities $F>0.996$ with approximately linear scaling in the number of entangling gates, while generic synthesis produces circuits that are orders of magnitude deeper. On IBM Torino hardware, we observe a regime in which shorter approximate circuits outperform deeper exact decompositions: a 27-CX circuit achieves higher hardware fidelity ($F_{\mathrm{hw}}=0.987$) than a 187-CX exact circuit. These results demonstrate that, in the NISQ regime, structure-aware approximate compilation can outperform exact structure-agnostic synthesis, providing a practical pathway for executing Hamiltonian dynamics without requiring pulse-level control.

Let $\mathcal{OP}_n$ be the monoid of all orientation-preserving full transformations on $X_n=\{1,\dots, n\}$ with the natural order. For $α\in \mathcal{OP}_n$, let $F(α)=\{y\in X_n: yα=y\}$ and $F(n,m)=|\{α:|F(α)|=m\}|$. Umar posed the question about the number $F(n,m)$ of elements of $\mathcal{OP}_n$ with $m$ fixed points. In this paper, we show that the number $F(n,m)$ of $\mathcal{OP}_n$ is $\binom{2n}{n-m}$ for $2\leqslant m\leqslant n$ and get the expectation and probability distribution of the cardinality of fixed-point set $F(α)$ for $α\in\mathcal{OP}_n$.

We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum mixture theory. It adopts a mass-averaged (barycentric) velocity so that the two-phase flow is quasi-incompressible: the velocity is no longer divergence-free, and the pressure enters the equation of the chemical potential. For the initial-boundary value problem in $\mathbb{T}^3$ with a class of physically relevant singular free energy densities, we prove the existence of global-in-time weak solutions. The proof relies on a suitable reduction of the original system to a Korteweg-type fluid model combined with a two-layer approximation, together with delicate estimates for the mass density and the phase-field variable inspired by the celebrated Bresch-Desjardins entropy. A key observation is that capillarity at the free interface provides a damping effect on the density evolution. For the limiting procedure, we derive delicate tail estimates to exclude possible concentrations of the singular potential, since no integrability of the pressure is available \textit{a priori}. This work appears to be the first existence result for the Navier-Stokes/Cahn-Hilliard type system with unmatched densities and mass-averaged velocity without spatial regularization.

In this paper we improve the previously achieved upper bound on the corank of an equivariantly stable singularity for a group of prime order. We also prove that the maximal corank of a simple $\mathbb{Z}_p$-invariant germ tends to infinity as $p$ increases.

Proton therapy has been rapidly advancing due to its excellent conformal index, but its relatively low relative biological effect (RBE) has somewhat limited its therapeutic efficacy for certain tumors. To address this, we previously proposed a nitrogen-targeting Proton-Carbon-Alpha-Therapy (Proton-CAT) enhancement method. In this letter, we present combined multi-scale DNA damage simulations and in vitro cell experiments, further investigating the mechanism of the Proton-CAT. It has been show that $^{15}$N enrichment significantly enhances complex DNA damage induced by high linear energy transfer(LET) particles within tumor regions. Under 30\% $^{15}$N conditions, $α$ and $^{12}$C particle induced DSB++ increased by 175.19\% and 52.94\%, respectively. Furthermore, in vitro cell experiments using $^{15}$N-glutamine ($^{15}$N-Glu) as the $^{15}$N carrier indicated that high concentrations of $^{15}$N-Glu did not bring about significant cytotoxicity. Following 2 Gy irradiation, the cell viability in the 500 $μ$g/mL $^{15}$N-Glu treated group exhibited a net reduction of about 15.41\% compared to the control group.This indicates that the enhanced effect of Proton-CAT primarily stems from increased complex DNA damage. This work provides a theoretical basis and multi-scale research framework for the development of the Proton-CAT.

The rise of machine learning and additive manufacturing has enabled the design of architected materials with tailored properties that surpass those of natural materials. Inverse design offers a data-efficient alternative to trial-and-error methods, yet most existing approaches depend on either large datasets or scarce high-fidelity data from simulations and experiments. These requirements pose a particular challenge for architected materials with nonlinear mechanical responses, where capturing complex deformation modes requires expensive evaluations. To address this, a Multi-Fidelity Bayesian Optimisation (MFBO) framework for the inverse design of cellular composites that directly targets their full nonlinear response is introduced. By integrating information from multiple fidelity sources and scalarising the response using a similarity score, the framework enables efficient exploration of the design space while reducing reliance on costly evaluations. As a proof of concept, the method is applied to spinodoid cellular composites using finite element models, validated with compression tests on short carbon-fibre reinforced PET-G composites. Four target responses were considered, with three multi-fidelity strategies benchmarked against a standard single-fidelity approach. Across all cases, MFBO achieved higher similarity scores and consistently recovered the targeted responses, outperforming the single-fidelity baseline under the same evaluation budget, while also successfully recovering all targeted responses. These results demonstrate the effectiveness of MFBO for inverse design of stochastic architected materials, where high-quality data is scarce but lower-cost proxies exist. By efficiently navigating complex design spaces, MFBO enables the creation of cellular composites with precisely tailored nonlinear mechanical behaviour.

In the rapidly evolving field of software engineering, the skills required of graduates entering the job market are constantly changing. Several studies have identified a gap between the skills taught in university curricula and those demanded by the software engineering industry. This chapter investigates the technical skill and expertise gap between higher education institutions (HEIs) and the UK software engineering industry by mapping job descriptions to the skills included in computer science degree programmes. A custom web scraping and text analysis tool, utilising fuzzy matching, was developed to extract and categorise skills from 300 job postings and undergraduate curricula from 30 UK universities. The analysis showed that the curricula place a strong emphasis on Programming Languages (18%) and Database Management (12.83%). In contrast, the industry s most frequently requested skill category is Software Design and Planning, which appears in approximately 88.68% of job descriptions, highlighting its critical importance. General Programming Language and System Structures also show strong demand, present in over 78.30% and 66.04% of postings, respectively. The mapping indicates that areas such as System Structures and Software Domains are significantly underrepresented in curricula, while Database Management and Compiler Design may be overemphasised. These insights can support HEIs in aligning their programmes with industry needs, supporting the preparation of graduates for dynamic careers in software engineering.

This paper presents an application of the biologically realistic JASTAP neural network model to classification tasks. The JASTAP neural network model is presented as an alternative to the basic multi-layer perceptron model. An evolutionary procedure previously applied to the simultaneous solution of feature selection and neural network training on standard multi-layer perceptrons is extended with JASTAP model. Preliminary results on IRIS standard data set give evidence that this extension allows the use of smaller neural networks that can handle noisier data without any degradation in classification accuracy.

Training trustworthy agentic LLMs requires data that shows the grounded reasoning process, not just the final answer. Existing datasets fall short: question-answering data is outcome-only, chain-of-thought data is not tied to specific documents, and web-agent datasets track interface actions rather than the core retrieval and synthesis steps of a RAG workflow. We introduce AgentSim, an open-source platform for simulating RAG agents. It generates verifiable, stepwise traces of agent reasoning over any document collection. AgentSim uses a policy to ensure the agent widely explores the document set. It combines a multi-model validation pipeline with an active human-in-the-loop process. This approach focuses human effort on difficult steps where models disagree. Using AgentSim, we construct and release the Agent-Trace Corpus (ATC), a large collection of grounded reasoning trajectories spanning three established IR benchmarks. We make three contributions: (1) the AgentSim platform with two mechanisms, Corpus-Aware Seeding and Active Validation, that improve trace diversity and quality; (2) the Agent-Trace Corpus (ATC), over 103,000 verifiable reasoning steps spanning three IR benchmarks, with 100% grounding rate on substantive answers; and (3) a comparative behavioral analysis revealing systematic differences in how state-of-the-art models approach information seeking. Platform, toolkit, and corpus are publicly available.

Hoehler noted that resonance poles obtained from different partial waves in $πN$ scattering appear to bunch together near a small set of common complex energies, and suggested that this could indicate mixing between angular momenta. Here, we examine whether at least part of this pattern could arise effectively from the extraction procedure itself. Exact partial-wave unitarity preserves the separation of angular momenta in the infinite problem, whereas practical pole extraction from bilinear observables requires truncation of the partial-wave series. Combined with the truncation-induced mixing mechanism established in Ref.~\cite{Svarc2026}, this provides a natural source by which fitted partial-wave coefficients can inherit overlapping pole-bearing content, thereby offering a plausible contribution to Hoehler-type clustering.

Let $\mathcal{PO}_n$ be the monoid of all order-preserving partial transformations on $X_n=\{1,\dots, n\}$ with the natural order, and let $\mathcal{O}_n$ and $\mathcal{POI}_n$ denote its submonoids of order-preserving full and injective partial transformations, respectively. For each transformation $α\in\mathcal{PO}_n$, write the random variables $Y(α)=|{\im}α|$ and $Y_r(α)=|{\im}α|$ given that $|{\dom}α|=r$ for $0 \leqslant r \leqslant n$. We determine the probability distribution, expectation and variance of $Y_r$ and $Y$ for $\mathcal{PO}_n$ and $\mathcal{POI}_n$. In particular, $Y_r(α)$ follows a hypergeometric distribution $H(n+r-1,n,r)$ for $α\in \mathcal{PO}_n$, while $Y_r(α)$ is degenerate and $Y(α)$ follows a hypergeometric distribution $H(2n,n,n)$ for $α\in \mathcal{POI}_n$.

In this note we survey some of our results on the Lagrangian reduction of discrete-time mechanical systems (DMSs). It is intended as an introduction to the general ideas that we used in the reduction of DMSs with nonholonomic constraints, DMSs with external forcing, as well as a theory of reduction by stages for such systems. This line of work was inspired by the paper and the monograph written by H. Cendra, J. Marsden and T. Ratiu in 2001.

Quantum state discrimination is a fundamental information processing task that serves as a building block for numerous applications and provides implications at the foundational level. In this work, we consider minimum error discrimination of multi-copy states, where instead of preparing a single system we assume that multiple instances of the same state are prepared. Now the discrimination allows for measurements from multiple parties with different measurement strategies varying from global measurement strategy to ones restricted to different forms of local operations and classical communication strategies. By comparing the average success probabilities in quantum and classical cases, we find a qubit strategy that outperforms all the bit strategies. However, we find that there are other bit-like operational theories which can outperform the best qubit strategies even with a classical measurement strategy and we are able to identify instances of different theories where different measurement strategies are optimal. In this way, we are able to find instances of nonlocality without entanglement as well as provide general bounds for bit-like operational theories.

Low-frequency turbulence in the solar chromosphere remains poorly understood. We address 1) the sources of low-frequency turbulence that potentially heat the chromosphere, and 2) how turbulence is transported and dissipated throughout the chromosphere and lower corona. We use particle-in-cell simulations to investigate mixed polarity magnetic fields corresponding to emergent magnetic carpet field in coronal holes or quiet Sun regions for strong (imbalanced) and weak (balanced) guide magnetic fields. The initial mixed polarity magnetic field transitions rapidly to a turbulent state dominated by advected small-scale nonlinear structures, with a minority slab turbulence population and the emergent field is largely annihilated. Turbulence is anisotropic for imbalanced magnetic field and more isotropic for balanced cases. We develop a transport model for turbulence advected and dissipated throughout the chromosphere by randomly distributed energy-containing scale dynamical flows described by log-normal statistics. We compute the expectations for the total energy per unit volume <y>(h) J m^{-3}, the Elsasser specific energy <Z^{\infty 2}>(h) m^2 s^{-2}, the heating rate <\cdot{H}>(h) J m^{-3} s^{-1}, and the correlation length <λ>(h) km as functions of height h above the photosphere. Turbulent energy is injected into the low corona by a random "patchwork" of sites across the transition region surface. The expected energy injection rates <\cdot{S}> J m^{-2} s^{-1} for the chromosphere and at the base of the corona exceed the estimated energy requirements needed to heat both the chromosphere and corona. Similarly, we show that spicules can be heated gradually with increasing height by entrained magnetic carpet and photospheric turbulence.

Moiré superlattices based on rhombohedral multilayer graphene have emerged as a highly tunable platform for engineering correlated topological phases. Here, we systematically investigate the transport properties of the hole-doped side in rhombohedral tetralayer graphene/ hexagonal boron nitride (hBN) moiré superlattices across a range of twist angles and alignment orientations. Notably, we observed multiple high-Chern-number Chern insulators, including the previously reported integer Chern insulator with Chern number C = -4 at moiré filling factor v = -1 and newly discovered symmetry-broken Chern insulating states with C = +3, $\pm$2, $\pm$1 at fractional moiré fillings of v = -2.5 or -2.6. These Chern insulating states emerge in both hBN alignment, but exhibit a sensitive moiré wavelength dependence. Our findings demonstrate the exceptional tunability of these high-Chern-number states via moiré wavelength, displacement electric field and external magnetic field, underscoring the distinct topological landscape realized in hole-doped RTG/hBN moiré superlattices.

We formulate a variational principle for non-relativistic quantum mechanics inspired by Gauss's principle of least constraint. We define a quantum constraint functional as the probability-weighted square deviation between the actual motion and the unconstrained motion that would arise from external forces alone. In this functional, the quantum potential plays the role of an intrinsic constraint that modifies the acceleration. Minimizing this quantum constraint functional with respect to the acceleration field yields the quantum Euler equations, which together with the continuity equation are equivalent to the Schrödinger equation. The principle is instantaneous and provides a differential characterization of quantum evolution. We demonstrate that this formulation is not a mere rewriting of existing dynamics: it provides a unified and technically economical treatment of geometric constraints and velocity-dependent dissipative forces, neither of which admits a straightforward global variational formulation. Potential applications to a broad range of quantum phenomena are also indicated.

We show that the associativity condition of the universal symmetric 2-algebraic 2-valued group defined by the Buchstaber polynomial admits several mutually equivalent interpretations from the viewpoints of the Chazy equation, Gauss-Manin connections, Dubrovin-Frobenius structures, and the quantum Yang-Baxter equation. These results place the universal 2-valued law in a unified framework linking geometry, algebraic topology, group theory, and mathematical physics.

Penning traps, renowned for their unparalleled precision in determining fundamental properties such as mass and magnetic moments, are cornerstone instruments in modern physics. Their applications span from nuclear structure studies to stringent tests of quantum electrodynamics and CPT invariance. Although Penning traps have been demonstrated for fundamental studies, often employing superconducting magnets, their high cost and operational complexity remain challenges. In this work, we report the development of a compact cryogenic Penning trap that utilizes a permanent magnet to provide a confining magnetic field, offering a more economical and flexible alternative. We have successfully demonstrated all core functionalities of this system, including ion generation, transport, confinement, manipulation, and signal detection. This compact trap not only serves as a vital technical testbed for the development of the Shanghai Penning Trap, but also establishes a cryogenic Penning-trap experiment platform for ion trapping and cooling applications as well as envisaged spectroscopic studies applications.

There exists a geometric phase for a quantum state during the adiabatic evolution of the system. If the adiabatic procedure happens between the system and the environment interacting with it similar to Born-Oppenheimer (BO) approximation, we can introduce a temperature into the environment, which can be regarded as in an equilibrium state. Then a temperature-dependent geometric phase can be obtained for the system, which originates from the Abelian gauge potential induced by the BO approximation. This gauge potential contributes to the effective potential of the system, which is temperature dependent, too. Finally, we demonstrate them using an example of H_2^+ ion system.

We present a genuinely non-radial quantum-mechanical route by which $π$ emerges from equatorial localization on the sphere. For the highest-weight branch of spherical harmonics, this localization is captured by a natural geometric rigidity index, whose exact finite-quantum-number value is a Wallis partial product. The mechanism is realized in two settings: the standard rigid rotor and the surface sector of a thin spherical shell, where radial freezing reduces the dynamics to the same angular problem. In the large-quantum-number limit, the probability cloud collapses toward the equator, the rigidity index approaches its classical value, and the Wallis formula is recovered through the correspondence principle. The result shows that Wallis-type structures in quantum mechanics can arise as exact signatures of semiclassical localization encoded by a simple geometric observable.

We design the Arboretum$.$hs package for symbolic computations with algebras of trees and more general graphs in Haskell. Thanks to the declarative nature of functional programming, the package's implementation closely follows mathematical definitions, making the code intuitive and transparent for users working with algebraic and combinatorial structures. To assist with current mathematical research, Arboretum$.$hs supports experimentation by facilitating the introduction of new algebraic operations, as well as providing functionality for rendering trees and forests through LaTeX integration. Compared to recent imperative implementations in languages such as Julia or Python, Arboretum$.$hs offers greater flexibility for manipulating and extending tree-based structures. Its use of Haskell enables safe programming and strong compile-time guarantees, serving both as a practical computational tool and a foundation for further research in algebraic combinatorics, beyond the setting of trees usually considered in the implementation of Butcher series, which are a fundamental tool for the analysis of numerical integrators.

I perform a model-independent reconstruction of the background pre-recombination expansion history of the Universe. I find that purely early-time resolutions to the Hubble tension, satisfying the geometric CMB constraints, exist at the background level. This class of solutions requires a smooth transition around matter-radiation equality, characterized by a $\simeq 15\%$ expansion rate enhancement prior to recombination. This result serves as a blueprint for future model-building approaches, providing a background stress-test for Hubble tension proposals.

Generative search engines increasingly determine whether online information is merely discoverable, cited as a source, or actually absorbed into generated answers. This paper proposes a two-stage measurement framework for Generative Engine Optimization (GEO): citation selection, where a platform triggers search and chooses sources, and citation absorption, where a cited page contributes language, evidence, structure, or factual support to the final answer. We analyze the public geo-citation-lab dataset covering 602 controlled prompts across ChatGPT, Google AI Overview/Gemini, and Perplexity; 21,143 valid search-layer citations; 23,745 citation-level feature records; 18,151 successfully fetched pages; and 72 extracted features. The central descriptive finding is that citation breadth and citation depth diverge. Perplexity and Google cite more sources on average, while ChatGPT cites fewer sources but shows substantially higher average citation influence among fetched pages. High-influence pages tend to be longer, more structured, semantically aligned, and richer in extractable evidence such as definitions, numerical facts, comparisons, and procedural steps. The results suggest that GEO should be measured beyond citation counts, with answer-level absorption treated as a separate outcome.

To meet the growing demand for nanoscale surface analysis, nitrogen-vacancy (NV) centers offer a high-sensitivity alternative by leveraging their ability to operate in immediate proximity to the sample. In this work, we propose a quantum control protocol designed to overcome the inherent challenges of solid-state environments, specifically by mitigating anisotropy and strong dipole-dipole interactions to enable the detection of isotropic chemical shifts at the nanoscale. To achieve this, our scheme synchronizes a slowly rotating magnetic field with tailored RF decoupling and MW control of the NV sensors. We provide an analytical mapping that explicitly links the measured spectrum to the control sequence features and the underlying system parameters, enabling a straightforward characterization of the sample.

Epsilon-near-zero (ENZ) photonic media exhibit extreme optical dispersion that enables unconventional light-matter interactions and enhanced optical nonlinearities. Recent studies suggested that thermo-optic effects, traditionally regarded as slow and secondary, can be strongly modified under the ENZ condition. Here we establish thermo-optic reconfiguration of effective media as a unified physical framework to describe both static and transient thermo-optic phenomena in ENZ systems. Using a CMOS-compatible effective medium operating in the visible spectral range, we experimentally demonstrate that temperature variation, whether under thermal equilibrium or transient excitation, reconfigures the constitutive parameters defining the ENZ condition, giving rise to pronounced linear and nonlinear optical responses. At thermal equilibrium, this reconfiguration manifests itself as static ENZ wavelength shift with an unprecedentedly large thermal-spectral modulation rate and an effective thermo-optic coefficient on the order of $10^{-1}$ K$^{-1}$. Under ultrafast excitation, we observe a picosecond-scale thermo-optic nonlinear response induced by transient heating. This response can be consistently interpreted as a time-dependent reconfiguration of the effective ENZ medium, corresponding to a transient evolution of its optical parameters. By reframing thermo-optic effects as a process of static and dynamic reconfiguration of effective media, this work provides a unified perspective that bridges thermo-optic physics, effective-medium theory, and time-varying photonics.

We investigate the role of hierarchical assembly in the angular momentum (AM) evolution of galaxies using a sample of 471 Milky Way-mass galaxies from the TNG-50 simulation. While galaxy orientation is often attributed to tidal torques and the cooling of gas within halos, we demonstrate that galaxy reorientation (tilting) is a common consequence of satellite accretion. Specifically, 80+/-2% of galaxies show alignment between their present-day AM and the orbital AM of their most massive (dominant) merger progenitor. This reorientation typically results in changes of around 50% in the galaxies' specific AM, with the most significant shifts occurring in galaxies that were initially highly misaligned. We find only a weak influence from the second most massive merger, and negligible impacts from surviving satellites. We show that accreted stellar halos encode the history of this reorientation. Driven by the same accretion event, the main bodies of galaxies and their stellar halos tend to co-align, with 81+/-2% of TNG-50 stellar halos showing prograde rotation relative to the galaxy. This signature will be detectable through major-axis kinematics with 30-meter class telescopes for Milky Way mass galaxies, offering a valuable observational test of this picture. While halo rotation directly constrains the specific AM of mergers within the last ~7 Gyr, this kinematic `memory' is largely erased for older and more radial events. Consequently, the Milky Way itself appears to be a notable exception to the general merger-driven trend: TNG-50 analogs with early, radial, and low angular momentum dominant mergers affect present-day disk orientation minimally. The current MW disk orientation may instead reflect the accumulated influences of gas accretion or dark matter torques.

This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system of equations, including the slope coefficients, to be unknown. For this reason, we describe the linear system as having unknown (as opposed to known) coefficients. This hypothesis testing problem arises naturally when constructing confidence sets for possibly partially identified parameters in the analysis of nonparametric instrumental variables models, treatment effect models, and random coefficient models, among other settings. To rule out certain instances in which the testing problem is impossible, in the sense that the power of any test will be bounded by its size, we begin our analysis by characterizing the closure of the null hypothesis with respect to the total variation distance. We then use this characterization to develop novel testing procedures based on sample-splitting. We establish the validity of our testing procedures under weak and interpretable conditions on the linear system. An important feature of these conditions is that they permit the dimensionality of the problem to grow rapidly with the sample size. A further attractive property of our tests is that they do not require simulation to compute suitable critical values. We illustrate the practical relevance of our theoretical results in a simulation study.