Papers

We study a generalized vanishing discount problem for Hamilton–Jacobi equations without assuming monotonicity either pointwise or in the averaged sense with respect to all Mather measures. Specifically, we consider \[ \lambda a(x)u(x)+H\big(x,Du(x)\big)=c_0, \] and assume that, for every sufficiently small $\lambda>0$, this equation admits a strict subsolution bounded from below uniformly with respect to $\lambda$. We prove that, under a smallness assumption on the Mather quotient, the maximal viscosity solution converges uniformly as $\lambda\to 0^+$ under a sign condition on the discount coefficient $a(x)$ determined by a prescribed part of the Aubry set. The limit is characterized explicitly in terms of the Peierls barrier and the selected Mather measures. As an application, the elementary solution of the critical Hamilton–Jacobi equation \[ H\big(x,Du(x)\big)=c_0 \] associated with any isolated static class can be realized as the vanishing discount limit. This provides the first mechanism for selecting multiple critical solutions in vanishing discount problems beyond the classical monotonicity framework, showing that different families of Mather measures yield different limiting critical solutions. We finally propose a variant of the discounted problems for which the strict subsolution hypothesis is automatically verified and hence applies to more general Hamiltonians $H$ and functions $a$.

In recent years, pre-training has become fundamental to learning effective video representations, enabling strong transfer to downstream tasks. A popular framework in pre-training involves aligning features of a video encoder with that of another modality, for example, language or audio. We introduce Video-STLayout pre-training, a novel strategy for obtaining rich video representations informed by spatio-temporal layout of object bounding boxes. Object layouts can easily be obtained by applying an off-the-shelf object detector on the video frames. Our method uses a contrastive loss to align video features with the layout features from a trained layout encoder. We show the effectiveness of our approach in the task of activity recognition in complex scenes.

In this short note, we establish dimension-free $\ell^p(\mathbb Z^d)$ bounds, for all $p\in(1,\infty]$, for the discrete Hardy–Littlewood maximal functions associated with cubes in $\mathbb Z^d$, answering a question that had been open for a while. The key idea is to prove dimension-free bounds for the $\ell^p(\mathbb Z^d)$ norms of the differences of the corresponding averages. This follows from an ad hoc interpretation of the associated discrete multipliers as a special continuous family of multipliers to which basic fractional integration and complex interpolation can be applied. The same method also yields an elementary proof of Bourgain's dimension-free $L^p(\mathbb R^d)$ bounds for the Hardy–Littlewood maximal function associated with cubes in $\mathbb R^d$.

Light-induced forces and torques offer a versatile strategy for remotely actuating microscopic objects, enabling breakthroughs including optical trapping and light-driven nanomachines. Extending such optical actuation to sustained cyclic motion, however, requires fundamentally distinct designs and, in particular, forces capable of delivering nonzero mechanical work over repeated cycles. Here, we demonstrate via simulations a nanoscale stator-rotor architecture, which achieves persistent orbital motion of a spherical rotor under circularly polarized plane-wave illumination. An off-center rotor displacement defines a stator-rotor structural polarity. Optical helicity coupled to this polarity generates a tangential force perpendicular to the instantaneous stator-rotor direction; as the rotor moves around the stator, the force direction rotates with it. Electrodynamic symmetry analysis identifies this response as arising from antisymmetric, nonconservative forces that produce nonzero closed-cycle work, whereas linear polarization yields symmetric, conservative responses with zero closed-cycle work. Material screening and Bayesian optimization identify an Ag-nanoshell design region, while Pareto analysis balances tangential actuation and radial confinement. A balanced candidate is predicted to lower the maximum steady-state temperature rise from 56.2 to 20.9 K relative to Au at the same light intensity. Brownian-dynamics simulations further show confined, helicity-defined orbital motion, with all 32 trajectories retaining the same circulation direction. These results establish a symmetry-guided route toward sustained cyclic optical actuation at the nanoscale.

Generating coherent meta-reviews from multiple peer reviews is challenging when reviewer evidence conflicts and varies in reliability. Existing approaches typically formulate meta-review generation as a multi-document summarization task and aggregate reviewer feedback uniformly, making it difficult to determine which opinions should be prioritized under disagreement. In this paper, we study meta-review generation through reliability-aware evidence aggregation. Our framework first extracts aspect-level opinions from peer reviews and identifies conflicting evidence within each aspect. It then estimates opinion-level support and review-level quality to measure evidence reliability. Based on these signals, the framework assigns reliability-aware weights to reviewer feedback, enabling the generator to prioritize better-supported arguments while preserving diverse perspectives. Experiments demonstrate that our method consistently improves meta-review generation over strong baselines on both automatic and human evaluations, with clear gains in conflict recognition and resolution under high-conflict review scenarios. The code and implementation details are publicly available at https://github.com/Wangxz729/reliability-aware-meta-review.

The focus of this paper is the curve shortening flow for closed spacelike curves in pseudo-Euclidean spaces, which has very few results so far. Will they produce singularities where certain tangent line tends to light cone? If not, will such a curve shrink to a circular point? To answer these questions, we establish a dichotomy for planar weighted normalized curve shortening flow with uniformly positive and bounded weights. Applying to closed smooth spacelike curves in pseudo-Euclidean spaces that admit a one-to-one convex projection onto a spacelike plane, at their finite maximal time we will see: either the curve shrinks to a point and becomes asymptotically circular, or the tangent directions subsequentially approach the null cone. Both alternatives occur. In the first case, this proves our previous conjecture that a strong spacelike curve in $\mathbb{R}^{2,q}$ with index 1 will converge to a circular point under the usual CSF. In the latter case, a monotone area-bivector defect is found in $\mathbb R^{2,1}$, which gives a quantitative obstruction to point collapse. Explicit examples of spacelike curves with lightlike tangent limit are given.

In this paper, we investigate the limitations of fixed, hand-crafted connectors in hierarchical semantic representations for open-vocabulary object detection. Existing methods establish semantic relationships between base categories and unseen novel categories by placing a fixed connector between adjacent super-/sub-categories. However, such fixed connectors may not optimally capture the relationships within a semantic hierarchy. To address this limitation, we propose interconnected hierarchical semantic representations (InterHier), which utilize a prepended learnable context to globally guide the interpretation of prompts containing hierarchical relationships. InterHier operates in two main stages. First, it constructs a hierarchy-aware prompt by integrating super-/sub-categories and prepending a learnable context. Second, it optimizes this learnable context to align visual region embeddings and textual embeddings. InterHier consistently improves performance over methods that rely on fixed connectors and can be seamlessly integrated into existing open-vocabulary object detection models. Experiments on open-vocabulary object detection benchmarks demonstrate that InterHier achieves competitive performance against state-of-the-art methods.

We present a method for synthesizing reactive character behaviors for continuous games as compact, human-readable programs. Game AI practice still relies heavily on manually authored behavior trees, state machines, and scripts, while academic reinforcement learning typically produces opaque neural controllers that are expensive to train and difficult to edit. Our approach bridges this gap by searching directly over a domain-specific language for continuous-space game policies. The language is designed around reactive geometric decisions and includes higher-order constructs such as direction maximization. These constructs help discretize a continuous behavior space into enumerable program structures. To make program search practical, we introduce a large set of synthesis antipatterns that remove redundant program forms while preserving behavioral coverage. We further combine bottom-up symbolic enumeration with top-down guidance from a coding agent. Our resulting method, agentic sketching, has the agent propose high-level policy structure and call an enumerator to complete local program slots. We evaluate the method on a benchmark of 14 continuous games, ranging from classic control tasks to multi-agent football. We find that pure enumeration is often more efficient than using a coding agent alone, while the combined method substantially outperforms both. Our results suggest that programmatic policy search can be a practical authoring tool for game AI: designers specify reward functions, and the system discovers editable behaviors that are effective, portable, and often surprising.

Let $k\geq 3$ and $\alpha\in[0,1)$, and let $\lambda_k(\alpha)$ denote the $\alpha$-spectral radius of a $k$-uniform loose cycle. Lu and Man classified all connected $k$-uniform hypergraphs with adjacency spectral radius at most $\lambda_k(0)$. In this paper, we extend their classification to the $\alpha$-spectral setting. In particular, for every $k\geq 3$ and $0<\alpha<1$, we prove that $\lambda_k(\alpha)$ is the smallest limit point of the $\alpha$-spectral radii of connected $k$-uniform hypergraphs. Moreover, we give a complete comparison between the $\alpha$-spectral radius of an arbitrary finite connected $k$-uniform hypergraph $H$ and that of a loose cycle by determining the sign of $\rho_\alpha(H)-\lambda_k(\alpha)$. As a consequence, for each fixed $0<\alpha<1$, we classify all finite connected $k$-uniform hypergraphs with $\alpha$-spectral radius at most $\lambda_k(\alpha)$.

In this paper, within the framework of real infinitesimal free probability introduced by Cébron and the second author, we compute the real infinitesimal free cumulants of independent complex Wigner matrices. Our approach relies on establishing a combinatorial relation between annular non-crossing partitions and families of directed graphs. As a consequence, we demonstrate that independent complex Wigner matrices are asymptotically real infinitesimally free. In particular, we show (under mild conditions) that a complex Wigner matrix is asymptotically infinitesimally free from its transpose.

We investigate the phenomenological consequences of a genuine three-body holonomy in a relativistic Dirac system in one spatial dimension. After removing the center-of-mass coordinate, the triple-coincidence point punctures the two-dimensional relative configuration space and permits a nontrivial $U(1)$ winding phase, whereas the pairwise Sakamoto–Munakata–Ino contact interactions give trivial net matching around this point. At fixed intrinsic parity, the six particle-ordering sectors reduce to a three-dimensional cyclic space. A Hermitian $C_3$-invariant effective mass operator admits a Peierls-type realization in which the gauge-invariant phase around the three links equals the three-body holonomy $\theta_3$. Its eigenvalues are $$ M^{[k]}=M_0+2\Delta\cos\!\left(\frac{\theta_3+2\pi k}{3}\right), \qquad k=0,1,2. $$ The holonomy lifts the conjugate-channel degeneracy and can generate a parametrically light branch through cancellation between the common mass and the holonomy-induced shift. We further allow cyclic-symmetry breaking and consider a general Hermitian three-state mass matrix. Exact elimination of two heavy states by the Schur complement yields a low-energy correction containing the rephasing-invariant loop product $\mathrm{Re}(t_{12}t_{23}t_{31})\propto\cos\theta_3$. Thus, even when only one branch is kinematically accessible, its effective mass can retain finite memory of the complete three-state loop. The complementary invariant $\mathrm{Im}(t_{12}t_{23}t_{31})\propto\sin\theta_3$ is phase sensitive but does not alone imply CP violation. The construction provides a low-dimensional phenomenological proof of concept for family-like triplication, mass hierarchy, and infrared memory, rather than a microscopic theory of Standard Model fermion generations.

Neural operators are data-driven models that learn mappings from inputs that parameterize partial differential equations, such as spatially varying coefficients, initial conditions, forcing terms, boundary conditions, or geometries, to solution fields or quantities of interest. Once trained, they can serve as surrogates for classical numerical solvers in many-query settings that require repeated evaluations for varying inputs. We address the question of when, and then why, neural operator surrogates outperform classical numerical solvers, in terms of cost for a given accuracy. We focus on the post-training, many-query limit, in which data-acquisition and training costs are treated as fixed and fully amortized. Even in this deliberately favorable regime for neural operators, there are regimes in which classical solvers outperform the surrogate models. We compare the cost-accuracy performance of neural operator surrogates and classical numerical solvers through a reproducible benchmark study comparing neural operators with problem-matched classical solvers on representative problems in computational science and engineering, focusing on prediction error, per-query floating-point cost, and wall-clock runtime. Neural operators are most competitive at low-to-moderate accuracy requirements. Their floating-point cost advantage depends strongly on the problem structure, arising when they avoid temporal or nonlinear iterations or predict a reduced quantity of interest rather than a full solution field. Additional wall-clock speedups result from dense tensor operations that are well suited to modern hardware. As the target accuracy is tightened, achieving the required accuracy with neural operators becomes increasingly challenging, and classical solvers outperform surrogates in this regime; thus classical solvers will remain important for verification and high-accuracy computation.

This paper provides a theoretical framework to evaluate the trade-off between the self-regulated peer review system and independent government inspection (PCAOB) in the auditing profession. We model the peer review system as a Judgment Regime, where a stakeholder utilizes professional expertise, captured as a private signal, to make ex-post decisions on verifying audit failures. In contrast, PCAOB inspection is modeled as a Commitment Regime, where the stakeholder lacks private information but can commit ex-ante to a predetermined level of verification. We find that the Judgment Regime benefits from a resource-allocation effect and a deterrence effect driven by informed verification, whereas the Commitment Regime deters audit failures through the first-mover advantage of ex-ante commitment. Our analysis demonstrates that the stakeholder prefers the peer review system if and only if the private signal is sufficiently informative. Furthermore, comparative statics reveal that higher verification costs or stronger audit incentives shift the stakeholder's preference toward PCAOB inspection.

The quantity $q(A\circ A^{-1})$, the minimum modulus of the eigenvalues of $A\circ A^{-1}$, arises naturally in connection with positive diagonal symmetrizability. For an invertible $\mathbf{M}$-matrix $A$ of order $n$, the classical bounds $\frac{2}{n}\leq q(A\circ A^{-1})\leq 1$ are known. We discuss the sharpness of the lower bound $\frac{2}{n}$ and investigate the converse of a related result involving the Jacobi iteration matrix. In particular, we show that $\rho(J_{A_k})\to 1$ does not, in general, imply $q(A_k\circ A_k^{-1})\to \frac{2}{n}$, and identify a class for which this implication holds. We then turn to invertible $\mathbf{H}$-matrices, a broader class that contains invertible $\mathbf{M}$-matrices. We show that $A\circ A^{-1}$ is an invertible $\mathbf{H}$-matrix whenever $A$ is an invertible $\mathbf{H}$-matrix. In contrast to the $\mathbf{M}$-matrix setting, $q(A\circ A^{-1})$ can be arbitrarily close to zero. However, replacing $A^{-1}$ by the inverse of the comparison matrix restores the classical lower bound: we prove that $q(A\circ\mathcal{M}(A)^{-1})\geq \frac{2}{n}$ and obtain further bounds involving the Jacobi iteration matrix of $\mathcal{M}(A)$. Finally, for positive diagonally symmetrizable invertible $\mathbf{H}$-matrices, we establish the upper bound $q(A\circ A^{-1})\leq1$ and, in the irreducible case, characterize when equality occurs.

Asynchronous Byzantine Reliable Broadcast (BRB) is a fundamental primitive that guarantees agreement and validity in distributed systems subject to Byzantine faults, but it lacks ordering guarantees. In this paper, we address Byzantine Causal Reliable Broadcast (BCRB), which builds on BRB to enforce causal message ordering. We present a novel BCRB protocol that decouples causal ordering from the BRB layer, achieving constant-size $\mathcal{O}(1)$ message metadata overhead and $\mathcal{O}(n^2)$ communication word complexity as against $\mathcal{O}(n^3)$ communication word complexity of existing protocols; here $n$ is the number of processes. We present two variants of our protocol: a cryptographic version using a threshold encryption scheme and sequence gating, and its non-cryptographic version. In the cryptographic version, senders broadcast ciphertexts immediately, and decryption shares are piggybacked on out-of-band ACKs, preventing early decryption and front-running. In both versions, causal safety is achieved probabilistically. We evaluate the probability of causal safety violations using a random variable path analysis under independent exponential link delay distributions. We show that both variants satisfy liveness and the probability of weak safety violation is bounded by $\mathcal{O}(f^{-3}\cdot\ln^3 f)$, where $f$ is the upper bound on the number of Byzantine processes, and $f < n/3$ and $f=\mathcal{O}(n)$. Further, for the crypto version, we show that the probability of strong safety violation is bounded by $\mathcal{O}(f^{-1} \cdot \ln^2 f)$. We also show how to modify our two protocols to guarantee 100% weak safety keeping $\mathcal{O}(1)$ message space overhead but with $\mathcal{O}(n^3)$ messages and $\mathcal{O}(n^3)$ communication word complexity.

We generalize square-root procedure to non-Hermitian systems with finite lattices, providing a spectral operation scheme applicable to arbitrary tight-binding models. Via this generalized square-root approach, we construct novel chiral-symmetric higher-order exceptional points (EPs) with multiple spectral responses. By taking square-root of a parent Hamiltonian hosting an $n$th-order EP (EP$_n$), an EP$_{2n+1}$ chiral-symmetric square-root system is obtained, whose lattice sites are inherited from both the parent system and an auxiliary residual system. The chiral-symmetry-induced structure of the generalized eigenspace enables onsite and coupling perturbations to selectively generate spectral responses of different orders. The proposed scheme is universal, applicable to any existing tight-binding EP system and iterable to generate EPs of arbitrarily high order. With enriched ultrasensitive spectral responses, the chiral-symmetric higher-order EP system provides a promising platform for signal amplification, detection and non-Hermitian control.

Commercial large language models are increasingly deployed across African fintech infrastructure for fraud detection and customer communication, yet no Nigerian or African continental regulatory instrument specifies what pre-deployment evaluation such systems must undergo before procurement. This paper reviews African fintech AI governance across global, continental, and Nigerian instruments, and shows that safety is affirmed as a principle while pre-deployment evaluation is operationally unspecified. Generic safety benchmarks cannot surface the failure modes most relevant to this domain, since none contain Nigerian institutional content or test for false positive misclassification of legitimate financial communications. These claims are demonstrated using SafeAlert, a purpose-built evaluation kit applied to six commercial models across three system prompt conditions. Results show that models resisting generic harmful content requests still produce complete fraud scripts under specific framing, and that several models misclassify most legitimate Nigerian bank communications as suspicious or fraudulent, a failure invisible to standard safety evaluation. The paper concludes with a regulatory framework proposing pre-deployment evaluation requirements for the CBN, NITDA, SEC, and the AU, arguing that the identified gap reflects an absence of regulatory specification, not a shortage of technical or financial resources.

We present a scalable electron-counting current cell based on a floating gate architecture operated as a Multiple Electron Transport device (MET). The system enables controlled injection, transport, and precise quantification of discrete charge packets using the sensor non-destructive multiple readout capability. We repurposed the charge-injection technique, jointly with the electron-resolution capability, for a controlled generation of quantized charge packets for an electron-traceable current source. Scalable architectures based on parallel and series multi-amplifier configurations are explored. Experimental results confirm noise reduction following the square root of the number of independent measurements and demonstrate stable, programmable output current. This approach provides a compact and scalable platform for electron-counting current sources and precision quantum metrology applications.

Reliable quality control (QC) of magnetic resonance imaging (MRI) is essential for reliable diagnostic neuroimaging, yet standard manual assessment is subjective and time-consuming. MRIQC has established standardized automated extraction of image-quality metrics (IQMs), but its reliance on local computational imaging skills and capacity including high-performance computing, limits its adoption in resource-constrained settings (RCS). We present WebMRIQC (webmriqc.mailab.io), an open-source browser-based platform that wraps the validated MRIQC engine behind a zero-installation web interface. WebMRIQC automates the DICOM-to-BIDS conversion of de-identified MRI scans, executes the unmodified containerized MRIQC pipeline on a shared compute node governed by a fair-share job queue, and returns an interactive in-browser dashboard. The dashboard grounds every IQM in published quality thresholds, benchmarks each scan against the normative distribution of high-resource open datasets, and supports cross-site multicentre implementation of optimized scan protocols in RCS.We describe the system architecture and a validation framework establishing measurement equivalence between WebMRIQC and native MRIQC across thirteen IQMs on the BraTS-Africa and BraTS 2021 datasets. Preliminary results indicate strong agreement for contrast-, signal and noise-based metrics, demonstrating that web-based implementation lowers the barrier to standardized MRI QC and provides a foundation for harmonized, regionally adapted quality benchmarks across RCS imaging sites. The code is publicly available here https://github.com/CAMERA-MRI/WebMRIqc.

Let $D$ be an irreducible bounded symmetric domain of complex dimension at least two. We study local holomorphic maps from $D$ into products of irreducible bounded symmetric domains satisfying a metric identity with positive and negative conformal factors. Under a noncancellation condition on these factors, we prove that every nonconstant component extends to a holomorphic isometric embedding up to a positive integer factor. This proves a componentwise rigidity conjecture formulated by Cheng–Hao–Yuan–Zhang.

Validation of generative social simulators often stops at face validity: emergent network structure is compared descriptively, without quantified parameter uncertainty or an adequacy check. We present an adequacy-aware calibration protocol that couples amortized posterior estimation with a synthetic identifiability assessment, a matched-sample-size adequacy check (prior-predictive reachability plus per-statistic posterior-predictive localization), a diagnosis-guided repair, and a statistic-held-out audit. We demonstrate it on a real second-hand luxury resale market with four channel-by-residency cells, each a bipartite buyer-brand network, using a forward model built from persona profiles elicited once, offline, by a language model. The behavioural parameters are recoverable in all four cells, though calibration is approximate and overconfident for one parameter. The observed summary falls outside the simulator's reachability reference in every cell, with the mean purchased tier as the pervasive discrepancy. The repair meets the value-block criterion in two of four cells but does not restore adequacy, and the held-out audit surfaces a buyer-breadth-dispersion miss no earlier diagnostic detected. A profile-source ablation finds the language-model profiles beat a flat rule baseline in all four cells, yet within-category brand relabelling causes no consistent degradation, so the profiles are a partially validated input whose value rests on structure, not brand identity. Making no causal claim, we conclude that an independent-aggregation account, without agent interaction or a buyer-breadth mechanism, cannot jointly reproduce the market's purchased-tier level, head-brand concentration, community structure and buyer-breadth heterogeneity.

In this paper, we study the Rochet-Choné model of monopolist pricing in the seller's market limit. We introduce a monotonicity formula which yields an asymptotic description of solutions, and prove that the proportion of consumers priced out of the market vanishes as overall consumer demand increases, providing a counterpoint to Armstrong's desirability of exclusion.

Common-envelope evolution (CEE) is a key process in the evolution of close binary systems. Many important astrophysical objects and evolutionary stages are closely related to CEE, including white dwarf binaries, hot subdwarfs, and gravitational wave mergers. In the standard energy formalism of CEE, the binding energy of the donor envelope plays a crucial role, as it directly affects the final orbital period after CEE and serves as a key physical parameter in binary population synthesis studies. However, the currently adopted binding energy suffers from large uncertainties, mainly because the envelope binding energy of giant-branch stars varies strongly near the helium-core boundary. In addition, the expansion of the star during CEE can also affect the binding energy. To address these issues, we introduce an improved binding energy for the envelope mass residual. Based on adiabatic mass loss models, we recalculate the distribution of the CEE binding-energy parameter lambda for stars with different masses and at different evolutionary stages, and we analyse the effects of envelope mass residual and adiabatic expansion. Due to the envelope mass residual, the lambdas of some donors can increase by one to two orders of magnitude at the late red giant branch and asymptotic giant branch stages. Furthermore, we provide interpolation grids and fitting formulae for these results, which can be readily applied to various binary population synthesis codes.

We study simultaneous vanishing discount and viscosity limits for mechanical Hamilton–Jacobi equations on the $n$-dimensional torus. In the critical regime, we explicitly identify the selected limit in terms of the critical Mañé potential and the quadratic behavior of the potential near its wells. We also obtain quantitative and sharp convergence estimates in the subcritical regime. In the supercritical regime, we prove convergence when the local harmonic ground-state energy of the potential has a unique minimizer among the wells. Finally, we establish a concentration phenomenon of the associated Gibbs measures.

Let $\varrho\neq -1$ be a complex number with modulus $|\varrho|=1$ and $K(x,y)=P_1(x)+P_2(y)$ for two polynomials $P_1$ and $P_2$. We consider the non-oscillatory solutions such that $\lambda(f)<\infty$ of the generalized Hill equation $f''-K(e^z,e^{-\varrho z})f=0$ ($\sharp$). When $\varrho=1$, the Hill equation $f''-K(e^z,e^{-z})f=0$ ($\dag$) is also written as $x^2u''-[K(x,x^{-1})-1/4]u=0$ ($\ddag$). We point out that there is a full correspondence between the non-oscillatory solutions of equation ($\dag$) and the Liouvillian solutions of equation ($\ddag$). Then this paper has two purposes. First, we show that if equation ($\sharp$) has a nonzero non-oscillatory solution, then $\varrho=1$. To this end, we solve entire solutions of a general Tumura–Clunie type differential equation. Second, for the particular Hill equation $f''-(e^{\mathbf{k}z}+b_{\mathbf{s}}e^{\mathbf{s}z}+b_0)f=0$, where $\mathbf{k}>\mathbf{s}\geq 1$ are integers and $b_{\mathbf{s}}\not=0$, we use Kovacic's algorithms to determine the non-oscillatory solutions with relatively few zeros.

Let \(A\) be a finite-dimensional quantum complete intersection over an arbitrary field. We prove that a finite-dimensional left \(A\)-module \(M\) is projective whenever \(\Ext_A^1(M,M)=\Ext_A^2(M,M)=0\), with no restriction on the multiplicative orders of the commutation parameters. Consequently, \(A\) satisfies the Auslander–Reiten conjecture and Tachikawa's second conjecture. The proof combines the gradability of rigid modules with successive graded twists and the self-extension criterion of Avramov and Buchweitz for commutative complete intersections. We derive a formula comparing ordinary self-extension groups under graded twisting, apply the resulting criterion to the Liu–Schulz algebras, and describe the successive twists explicitly in the four-generator case.

In dynamic epistemic logic, the four notions of success, self-refutation, true lies, and impossible lies have been discussed in the context of public announcements. In this paper, we introduce eventual and strong eventual versions of these notions, as well as their transfinite versions, which allow transfinite iteration of announcements. We also introduce the notions of always informativeness when true or false. For example, a formula is eventually self-refuting if, whenever initially true, it eventually becomes false at some finite stage under iterated announcements, and strong eventual self-refutation further requires the formula to remain false at all sufficiently late stages. There are two main results. The first result gives the relationship among strong eventual notions, eventual notions, and several other conditions including conditions on the limit of the truth values of the announced formula, the uniform bound condition, and the fixed-point views of the Moore sentence and the self-fulfilling sentence. The second result gives the relationship among finite and transfinite versions of the eventual and strong eventual notions and the fixed-point views.

AT2019aalc is considered a repeating tidal disruption event (TDE) candidate occurring in an active galactic nucleus (AGN). In this paper, we highlight previously unnoticed but intriguing features that include a brief optical dimming prior to the rise of the main flare and a significantly lower post-flare luminosity compared to the pre-flare level. By applying a time-dependent obscured TDE model to AT2019aalc, we successfully reproduce its light curves with the tidal disruption of a $1.122_{-0.176}^{+0.246}\rm M_\odot$ main-sequence star by a $1.862_{-0.259}^{+0.255} \times 10^7{\rm M_\odot}$ supermassive black hole (SMBH). Both the pre-flare dimming and the reduced post-flare luminosity are attributed to obscuration of the intrinsic AGN emission. The total energy of the event derived from our fit is $1.24\times10^{51}$ ergs and about 0.2 ${\rm M_\odot}$ of debris mass is accreted by the SMBH. In addition, the $g-r$ color of the net flare in AT2019aalc exhibits a continuous reddening trend during the first flare, consistent with a gradual increase in $E(B-V)$ predicted by the obscured TDE model. These results suggest that AT2019aalc can be considered a second member of the recently proposed class of obscured TDE candidates hosted in AGNs. } \keywords{galaxies: active-galaxies: nuclei-quasars: supermassive black holes-quasars: individual (AT2019aalc)-transients: tidal disruption events.

Understanding the relationship between gene expression and protein abundance is central to molecular and systems biology. While gene expression reflects transcriptional activity, proteins are the functional molecules that determine cellular phenotypes. However, numerous post-transcriptional and translational regulatory layers complicate this relationship, and prior studies have reported only weak to moderate correlations between RNA and protein levels. Predicting protein abundance from transcriptomic data remains challenging, but it is a valuable goal for biological insight, especially when proteomic data is limited or unavailable. In this study, we applied a large-scale, Ridge regression-based feature selection strategy to identify predictive gene expression features for each of 8,423 proteins across 940 cancer cell lines. To our knowledge, this is the first work to perform such comprehensive protein-wise feature selection at this scale. Our analysis revealed both globally predictive and context-specific gene features. These included biologically meaningful modules such as immune-related genes, HOX transcription factor targets, and cytoskeletal components. The models identified stable candidate gene-protein associations that remained interpretable at the level of individual proteins and recurrent transcriptomic predictor patterns. Our approach enables interpretable modeling of protein expression from transcriptomic data and provides insight into transcriptomic features associated with protein abundance. This framework may support hypothesis generation, protein imputation in incomplete datasets, and deeper understanding of post-transcriptional regulation in cancer biology.

Text-controlled time series generation aims to synthesize sequences that follow natural-language descriptions while remaining faithful to real data distributions. Existing paradigms often couple semantic understanding and sequence modeling in a single continuous latent space, lacking explicit local semantic anchors and separation between global continuous attributes and local discrete shapes. As a result, key local structures may be smoothed, missed, or misplaced. We propose Shape Lexicon (ShapeLex), which decouples text-to-sequence generation into discrete symbolization of local shapes and continuous modeling of global attributes. ShapeLex first induces a reusable vocabulary of discrete shape units, such as rises, spikes, and sharp drops, from training data, forming an interpretable symbolic space. An autoregressive generator then selects shapes according to the textual description, adjusts attributes such as position and duration, and composes them in temporal order into a shape skeleton. Finally, a mixture-density scale head models and samples the overall level and volatility to restore realistic global scale. Experiments on twelve public datasets, real user-written text, and downstream forecasting tasks show that ShapeLex generates series that better match real data distributions than existing methods. In addition, paired supervision is automatically synthesized from the learned vocabulary, avoiding annotation costs that grow with dataset size and improving scalability.