Papers

Discrete diffusion models now match autoregressive language models on several benchmarks, while the question of how best to train them has received far less attention: the optimizer is inherited from one paper to the next and never compared. New optimizers, meanwhile, are validated almost exclusively on autoregressive pretraining, a different objective on a different loss surface. We present a controlled optimizer benchmark across four diffusion formulations, to our knowledge the first for discrete diffusion: seven optimizers (AdamW, Lion, Muon, SOAP, MARS, MARS-M, Schedule-Free) on masked diffusion (text8), uniform diffusion (QM9, and LM1B through the Gaussian duality) and Gaussian diffusion on images (CelebA-64), each on a task with published reference values. Every optimizer receives the same search protocol, and every winner is retrained at the full budget with three seeds. AdamW is a strong default but not always the right choice: it is beaten by a resolved margin on two of the four tasks, and the winner changes with the formulation, so the optimizer deserves the same care as the rest of the training recipe. Notably, methods validated on autoregressive language model pretraining transfer well: Muon, MARS-M and SOAP each beat the tuned AdamW on at least one diffusion formulation. The benchmark, all runs and every figure are reproducible end to end from the released code at https://github.com/armanbolatov/diffusion-baselines.

The Time-Evolving Natural Gradient (TENG) method evolves neural approximations of time-dependent partial differential equations by projecting time-discrete target states onto the neural-network manifold through local natural-gradient iterations. For stiff diffusion-dominated problems, however, explicit Runge–Kutta methods face severe stability restrictions. High-frequency diffusive components can drive stage targets beyond the locally reachable region of the neural manifold, worsening the conditioning of local least-squares projections and destabilizing parameter updates. We propose TASE–TENG, which applies the highly stable explicit operator $T_p(hW_0)$ to each Runge–Kutta stage increment before projection, where $W_0$ approximates the dominant stiff diffusion operator. To construct this surrogate in a mesh-free setting, we develop a learnable operator whose local interaction coefficients are generated by a shared geometry-dependent neural rule. A structured factorization enforces discrete self-adjointness, dissipativity, and constant preservation. The operator is trained offline and remains fixed during online integration, where it is used only within the TASE stabilization operator. Numerical experiments on stiff diffusion and reaction–diffusion problems demonstrate improved stability and accuracy at the same time-step size, with reduced errors from high-frequency diffusive modes. The learned rule also allows the stabilization operator to be reconstructed at different spatial point resolutions without retraining.

A RAG system can hand you the right answer and cite a source it did not actually use. Models output these unfaithful citations via post-rationalization: they write the answer first and then attach a citation to whatever passage looks close enough. Search agents are now trained with reinforcement learning from verifiable rewards (RLVR), which pays them for getting the answer right. We asked whether that training also teaches them to cite honestly. Improving an existing methodology with a required control, we compared an instruction-tuned model against three RLVR agents trained from it, on four question-answering datasets, using only free-tier Kaggle GPUs. Post-rationalization is everywhere: on Wikipedia-based questions roughly one citation in seven is unfaithful. RLVR does not fix it. The agents post-rationalize at their base model's rate, and one lands slightly worse. Rewarding correct answers buys nothing in citation faithfulness, so faithfulness has to be trained and measured on its own terms.

Implicit neural video representation (NVR) encodes a video as the parameters of an overfitted neural network, where training and testing data are identical and the objective is instance-specific signal fitting. In this deterministic regime, optimization dynamics directly determine reconstruction quality under a fixed budget, yet existing methods universally adopt general-purpose optimizers designed for stochastic gradient training. Adam-family optimizers descend steadily but converge slowly, while Lion achieves faster early progress but oscillates markedly in later stages when gradient directions become unstable. We trace this instability to the insensitivity of the sign-based update to gradient–momentum alignment. To address this, we propose Direction-Aware Lion (DA-Lion), a task-driven optimizer tailored for NVR. DA-Lion introduces (i) a direction-consistency criterion that switches between sign update and momentum update based on gradient–momentum alignment, and (ii) a learning-rate-aware magnitude modulation that stabilizes effective step sizes across training phases. DA-Lion modifies only the parameter update rule, preserving model architecture, parameter count, FLOPs, and decoding throughput. Experiments on three datasets with four NeRV-family backbones show that DA-Lion improves convergence stability and boosts PSNR/MS-SSIM across all backbones. The source code will be made available at https://github.com/maoqingyu1996/DA-Lion.

We prove the local version of the Pólya–Szegö conjecture for the torsional rigidity of polygons: for every \(n\geq5\), the regular $n$-gon is a strict local maximizer of torsional rigidity among convex $n$-gons of prescribed area. Our proof is entirely analytic. It builds on a locally stable proportional triangular covering inspired by Solynin and Zalgaller and an associated weighted Voronoi-type partition, together with a quantitative asymptotic analysis of the loss produced by truncating the overlapping triangles to the partition cells. The result is then obtained by establishing two key ingredients: the optimality of isosceles triangles for mixed torsional rigidity at fixed area and vertex angle, and a strict concavity property of the mixed torsional rigidity of isosceles triangles.

We introduce the coherent memory Born machine (CoMB), an algorithm for quantum generative modeling on a register whose size does not depend on the dimension of the data. CoMB generates a sample one component per round. In each round, a work register is entangled with a memory register and measured, and the outcome gives one component. The memory is never measured and carries correlations between rounds. We show that the characteristic function of the generated distribution is a product of small matrices, one per round. This gives exact training, with maximum mean discrepancy losses and gradients costing time linear in the data dimension, without sampling or likelihood. We also compile every round onto one work qubit and evaluate device noise exactly. To isolate coherence, each CoMB is compared with its dephased twin and with equally trained classical hidden Markov models. We benchmark it on continuous data, $368$-cell calorimeter showers from five qubits, and on sequential data, handwritten digits from three qubits. The coherent memory provides a memory-dimension advantage. Four coherent levels do the work of about six classical states on both benchmarks, and of at least five with $95\%$ confidence on showers at every training budget, including convergence. On showers, removing their coherence raises the loss by $23$ to $31\%$. With eight levels, where all models approach a common floor, coherent and classical memories become indistinguishable with longer training. On an IBM Heron processor, the memory carries two thirds of the inter-round correlation through twelve mid-circuit measurements.

Large-scale scene reconstruction is a critical foundational technology in robotic autonomous systems such as 3D mapping and autonomous driving. In recent years, 3D Gaussian Splatting (3DGS) has demonstrated remarkable advantages in both visual quality and computational efficiency, making it a promising representation for large-scale scene reconstruction. However, it still faces challenges in large-scale scenes, including excessive memory consumption and uneven viewpoint coverage caused by UAV acquisition, limiting its real-world applications. To address this, we propose VDGS, a novel 3DGS framework that incorporates camera distribution into scene modeling. VDGS introduces visibility-driven statistics for scene anchors to quantify supervision strength. These statistics are further leveraged for scene partitioning and for gradient compensation in under-optimized regions, thereby promoting balanced optimization across different regions. Extensive experiments on multiple large-scale aerial scene datasets demonstrate that, under imbalanced viewpoint distributions, VDGS consistently outperforms existing methods, while maintaining competitive performance in scenarios with more uniform view distributions.

Compressed manipulation policies can pass offline evaluation while failing in closed-loop execution; this dissociation is established in prior work and is not our claim. We contribute a causal anatomy of one naturally occurring case. An 8-layer distillation of Octo-Base retains 86% of parameters, passes every offline check we applied (0.996 and 1.000 teacher-ratios on the family's own validation metrics), and collapses in closed loop: 0/72 vs. the teacher's 40/72 on a simulated WidowX pick-and-place task. The collapse is structured, not diffuse: early task stages degrade gradually (the student moves the object at 90% of the teacher's rate and grasps at 55%), while transport-to-target fails categorically, at 0% in every training variant. Paired action-trace forensics isolate the signature: a negative, late-heavy $z$ residual, roughly 10x its post-repair magnitude, and persistent across the base distillation and both continuation branches. Four standard therapies fail under matched controls: continued training and in-domain offline data leave success at zero, even though the latter measurably improves marginal action statistics; command-level compensation recovers nothing at any offset, although the same perturbations degrade healthy policies; clamping the symptom in the command channel preserves grasping, yet success stays at floor. A minimal-pair intervention that substitutes half of the training stream with deployment-distribution teacher rollouts, with every other setting held fixed, restores parity with the teacher (18/36 vs. 17/36 held-out), eliminates that signature, and recovers a teacher-like perturbation-response profile. We claim existence, not universality. Operationally, offline gates, including a family's own validation metrics, are insufficient acceptance tests for compressed policies; a few dozen closed-loop trials sufficed to find what they missed.

Quantum networks are usually framed by two hardware limits: how fast entanglement can be heralded, and how long a memory can hold it. We establish a third, geometric limit: entanglement decoheres while control information travels, so the distance to whoever allocates resources enters the fidelity budget directly. We develop a functional-graph abstraction weighting each link by its predicted multiplicative contribution to end-to-end fidelity, separating global but delayed state from local and immediate state, and compare centralized against local allocation in a replicated discrete-event model. Centralized delivery latency grows with network diameter while local latency is nearly scale invariant, differing up to twenty-fold for short-range traffic; the coherence threshold at which a global view outweighs a fresh one does not shift across the tested sizes; and as heralding accelerates, the dominant cost moves into the control plane. Slot synchronization instead obeys the product of slot rate and one-way link delay, so it is bounded by repeater spacing rather than diameter. Controller placement, decision locality, repeater spacing and slot rate are physical design parameters, not implementation details.

Quantum computing promises to outperform classical computing for certain computational tasks. One of the key concepts underlying this potential is universality. Universality has been extensively studied not only for qubits but also for higher-dimensional quantum systems, such as qutrits and qudits, which span Hilbert spaces of dimension greater than two. However, the concept of universality in Bose-Einstein condensates (BECs) qubit systems, which have been proposed relatively recently, remains insufficiently understood. In this work, we analyzed universality in BECs qubit systems. Our results clarify the theoretical aspects of universality in quantum computation within the class of ((N+1))-dimensional representations of SU(2), taking into account two distinct representations of the quantum states.

We establish the asymptotic-preserving property of the exponential Euler method for stochastic reaction-diffusion-advection equations in $\mathbb R^2$ under fast Hamiltonian advection with multiple critical points. In the fast-advection limit, the dynamics reduces to a stochastic partial differential equation on a noncompact metric graph. A key ingredient is the strong convergence analysis of the limiting exponential Euler scheme, which is complicated by the graph's noncompactness, its multiple edges and vertices, and the nonuniform ellipticity and vertex degeneracy of the graph operator. Using a weighted $L^2$ framework and analytic-semigroup smoothing estimates, we prove a temporal convergence order arbitrarily close to $1/2$ for weighted $L^2$ initial data and exactly $1/2$ under a half-order fractional-domain condition. Combining these estimates with the fast-advection limits yields the asymptotic-preserving property in the multiple-critical-point setting. Numerical experiments illustrate the asymptotic behavior and confirm the predicted temporal convergence rate.

It is well known that in (2+1)-dimensional general relativity, black hole solutions exist only in the anti-de Sitter case–the so-called Banados-Teitelboim-Zanelli (BTZ) black hole. In this letter, we construct, for the first time, three independent LQG-inspired frameworks for (2+1)-dimensional black holes: the $\bar{\mu}$-scheme holonomy corrections, the quantum Oppenheimer-Snyder collapse, and a covariant effective model. Remarkably, all three approaches yield the same qualitative picture: when LQG-inspired corrections are included, we find three distinct types of solutions corresponding to asymptotically flat, anti-de Sitter, and de Sitter geometries. Our results demonstrate that the asymmetry between classical (2+1)-dimensional and (3+1)-dimensional solutions is eliminated upon incorporating effective quantum gravity effects.

Large Language Models (LLMs) enable open-ended dialogue in interactive games, but their non-deterministic outputs make it difficult to preserve authorial control, factual consistency, and the intended sequence of information disclosure. These challenges are particularly significant in detective games, where premature revelation or fabricated details can undermine the logic of player progression. We present a Structured Knowledge Tree architecture coupled with a tri-agent LLM pipeline for controlling dialogue in an open-ended interrogation game. The system separates knowledge retrieval, dialogue generation, and response verification to ensure that the virtual suspect reveals only information permitted by the current narrative state. We evaluate the approach through The Interrogation of Adrian Gale, a playable detective-game testbed, and a formal user study examining hallucination reduction, adherence to authored disclosure sequences, and perceived logical progression. Our results demonstrate that the structured architecture reduces critical hallucinations by 64.78% and entirely prevents premature narrative disclosure. While the strict mechanical constraints introduced usability trade-offs regarding forced conversational reveals, the system successfully enforces rigorous epistemic pacing and provides players with a clear, subjective sense of progression toward solving the case.

Pre-deployment secret scanning operates only on source code, never on what a production application serves. We document two exploitation chains in which Azure AD client credentials and APIM subscription keys from production JavaScript bundles enabled account takeover and mass data exposure. An authorized engagement covered approximately 2,000 enterprise web assets in one organization; 113 (5.65%) served live credentials. To quantify the shift-right gap, we built an independent Ground Truth (GT-194) of 194 secret-grade credentials through Claude Opus 4.7 extraction and manual analyst review, with the 247 LLM-extracted candidates independently validated by GPT-5.5 (Brennan-Prediger kappa = 0.676). The principal finding is structural: 13.9% of GT-194 (27 of 194) is surfaced only by manual analysis and recovered by none of the nine evaluated production scanners, a tool-agnostic blind spot the ground-truth model also misses. CryptoJS encrypted configuration separately defeats every static scanner: the credential exists only after decryption with a co-located key, reached only by runtime-aware detection. Combined coverage plateaus at 86.1%. Among the nine scanners, the best static scanner recovers 36.6% and the best runtime-aware scanner 77.8% (F1 = 0.818, McNemar p < 0.001); the ground-truth model is reported separately as a reference comparator, not an evaluated detector. On 63 of 86 secret-exposed applications (73.3%), the full Azure AD token-mint chain is co-located in one bundle, reachable from browser code. We characterize five paths by which credentials reach production undetected and present a layered runtime detection methodology and remediation framework. Recall is scoped to a single-organization Azure-heavy corpus.

It is argued that many real-valued constructions of quantum mechanics are only nominally real in that the operators and states are restricted to impose a complex structure on the Hilbert space. That is, complex algebra between pairs of elements representing complex numbers is preserved in these formulations. It is therefore mistaken to think of these constructions as being `real' as they are actually a representation of complex linear algebra. It is then shown that under the assumptions of state normalisation and strict energy conservation, this complex structure (at the very least) is required to allow for time evolution in quantum mechanics. This is only a minimum requirement, as our arguments do not preclude the formulation of quantum mechanics in terms of hyper-complex entities, such as quaternions.

We consider a nonlinear model motivated by polychromatic computed tomography (CT). Here, $W$ distinct $d$-dimensional signals $x^*_1, \ldots, x^*_W \in \mathbb{R}^d$ must be recovered from $n$ measurements $(a_i, y_i)_{i = 1}^n$ that obey the nonlinear model $\mathbb{E}[y_i|a_i] = h(\langle a_i, x^*_1 \rangle, \ldots, \langle a_i, x^*_W \rangle)$, where $h: \mathbb{R}^W \to \mathbb{R}$ is a known nonlinearity that models a certain type of exponential attenuation law. Even when there is no noise in the measurements, the sample size $n$ (for any measurement ensemble $\{a_i\}_{i = 1}^n$) must exceed the number of unknowns $Wd$ to guarantee that the underlying signals are identifiable. We construct a measurement ensemble that ensures perfect signal recovery almost surely provided $n \geq Wd + W - 1$, thereby isolating the injectivity threshold up to an additive factor $W - 1$. We also study computational complexity of signal recovery in this model with a general measurement ensemble $\{a_i\}$. We show that if $W \geq 2$, then there is a measurement ensemble for which deciding whether there exist signals consistent with the measurements is NP-hard. In particular, this implies that polychromatic, multimaterial CT reconstruction is NP-hard in general. This finding stands in sharp contrast to the single-material setting, for which a polynomial-time algorithm can provably perform signal recovery for any measurement ensemble.

LLM-based AI systems answer political questions for hundreds of millions of people. Current audits measure what they say to an average user, but their behavior is dynamic. I argue that their political behavior is a set of policies over whom to answer, what to say, and whether to engage at all, conditional on the topic and what the system knows about the user. I call these policies the system's speech regime, which is how a developer settles the tradeoff between answering, accommodating the user, and refusing, each of which carries a cost that varies by topic. I derive a typology of five regimes from two dimensions, engagement and stance. I test six AI systems (OpenAI, Anthropic, xAI, Google, Mistral, DeepSeek) in a preregistered experiment of 7,500 multi-turn conversations that randomly assign the user's political identity across five topics: abortion, Catalan independence, climate change, Nazism, and a zero-stakes control (pineapple on pizza). Two LLM judges from different developers score every answer, validated against human coding, and refusal is treated as an outcome rather than missing data. Every system accommodates the user on the control topic, showing that political restraint is a policy. On contested topics the systems fall into different regimes: on abortion, GPT engages and mirrors every user, Gemma refuses everyone, Claude answers strongly conservative users 35 percent of the time and almost no one else, and Grok accommodates conservatives only. On settled topics such as climate change and Nazism, five systems hold firm for every user. The systems also infer the user's overall ideology, so accommodation can spill over to topics not yet discussed. A comparison of two Grok releases shows the regime changing between versions in a way current audits miss. Speech regimes matter for alignment research and for polarization, political knowledge, and the quality of democracy.

Spatial reasoning is essential for vision-language models (VLMs) to understand and act in the physical world. Reasoning in dynamic environments requires VLMs to perceive local state transitions caused by object motion and viewpoint changes and integrate them over long trajectories to maintain an updated spatial state, yet existing VLMs remain limited in both capabilities. Current spatial training primarily focuses on static questions about object attributes and spatial relations, providing limited direct supervision for state transitions; in contrast, interaction trajectories naturally connect a preceding observation, an action, and a subsequent observation, offering direct supervision for local state transitions, while complete trajectories reveal dependencies among consecutive transitions. We therefore introduce Spatial-Interactor, a framework that trains VLMs to model physical-world state transitions through interaction, organizing this learning process into a three-level curriculum covering L1 passive world-state transitions, L2 active self-state transitions, and L3 long-horizon interaction trajectories. Accordingly, we construct the Learning from Spatial Interaction dataset (LSI-108K) from simulated and real interaction trajectories, with tasks aligned with the objective of each level. Our two-stage training strategy applies Supervised Fine-Tuning (SFT) to L1 and L2 for local transition modeling, and On-Policy Distillation (OPD) then uses privileged self-distillation: a teacher branch given segment-level transition descriptions supervises the student's on-policy CoT, helping the student learn to integrate consecutive transitions over L3 long trajectories. Experiments across multiple VLMs and spatial benchmarks show consistent gains in local transition modeling and long-horizon integration.

We present a fast numerical method for safe continuous-time motion planning under Temporal Logic (TL) specifications. The method generates smooth continuous trajectories that remain collision-free while robustly satisfying temporal and logical task requirements. A central component of our method is the formulation of nonconvex safety and logic constraints as unions of convex sets where associated discrete decisions are encoded in a joint feasibility graph. This graph representation allows Euclidean projection onto the feasible set and proximal robustness maximization to be reformulated as shortest- and widest-path problems, respectively. Building on this structure, we develop a nonconvex splitting method based on the Alternating Direction Method of Multipliers (ADMM), which decouples smooth spatio-temporal trajectory optimization from nonsmooth discrete constraint handling within the optimization. The resulting algorithm exhibits reliable convergence across benchmarks and scales to large-scale motion-planning problems, providing a 4.7x average speedup over the state of the art on discrete and continuous-time logic problems.

Approximate nearest neighbor search (ANNS) underpins large-scale vector retrieval in search, recommendation, and retrieval-augmented generation. Graph-based indexes have demonstrated state-of-the-art search performance for ANNS. They connect each corpus vector to a small set of nearby or navigationally useful vertices and answer queries by traversing the resulting graph. Because these edges are selected using construction-time distances, the graph index is tied to the embedding model. Re-encoding a corpus with a new model may change distances and neighborhoods of the vectors. Reconstructing the graph for the new embedding vectors incurs substantial construction cost and delays deployment. When the embedding model changes, we observe a phenomenon in the old graph index that we call residual reachability. Specifically, although derived from different models, the vectors describe the same underlying objects and often retain part of their similarity structure. These shared relations are reflected in the connectivity of the old graph index, leaving many exact new-model neighbors reachable within a few hops in the old graph index. Motivated by this observation, we develop an index-migration approach that utilize the residual reachability in the old graph index to faster construct the new graph index for the new embedding vectors. Our method, Drift-Guided Migration (DGM), provides two migration paths. DGM-Local performs parallel shallow expansion over the inherited graph index and screens second-hop candidates with packed position sign codes before exact evaluation. DGM-Search uses hop-bounded beam traversal to explore beyond shallow expansion. Across eight text and image migrations, our DGM methods can achieve up to 17.43 times speedup on constructing the new graph index than the fastest degree-matched reconstruction method while keeping competitive recalls.

We investigate the operator distance between the Identity and the Copson operator on the cone of nonnegative, nonincreasing sequences within the Lebesgue sequence spaces $\ell^p(\mathbb{N})$. By proving the exact value of this distance, we confirm a conjecture originally formulated by A. Ben Said, S. Boza, and J. Soria in “The norm of Hardy-type oscillation operators in the discrete and continuous settings” (Analysis and Applications, 2025).

In this paper, we investigate higher-order symmetries and non-geometric symmetries within the framework of $k$-cosymplectic Hamiltonian field theory. We introduce the concept of generalized infinitesimal symmetry, which relaxes the standard symmetry condition, and then define two new classes of symmetries: higher-order general infinitesimal Cartan symmetries and good non-geometric symmetries. For each of these symmetry classes, we establish a Noether-type theorem that provides explicit conserved quantities for exact $k$-cosymplectic Hamiltonian systems. These results extend and generalize previous work on standard Cartan symmetries in the $k$-cosymplectic setting. Furthermore, we extend all of these results in a parallel fashion to Hamiltonian systems on $k$-symplectic manifolds, demonstrating the unifying nature of our approach. Concrete examples are provided to illustrate the existence and applicability of the proposed symmetries. Our framework offers a systematic geometric treatment of generalized symmetries and their associated conservation laws in classical field theories.

Looped language models repeatedly apply a weight-shared block to increase effective depth without increasing parameter count, but the resulting T sequential recurrent-block calls per generated token substantially increase decoding latency. To address the issue, we introduce Wavefront Decoding (WFD), a training-free self-speculative decoding framework designed for looped language models. WFD exploits two properties of these architectures: intermediate recurrence outputs provide effective draft predictions, and weight sharing allows token states at different positions and recurrence depths to be processed in one batched recurrent-block call. WFD organizes these mixed-depth states into a diagonal wavefront, continuously drafting new positions at shallow depth while advancing earlier positions toward full-depth verification. Unlike the phase-separated draft-then-verify schedule, WFD therefore concurrently batches drafting and verification within the same recurrent calls, while rejected drafts are corrected using full-depth predictions. Across six Spec-Bench task categories, WFD achieves 2.42x speedup on Ouro-2.6B and 3.54x on Huginn-3.5B over autoregressive decoding, consistently outperforming draft-then-verify. Cross-recurrence KV sharing further reduces wavefront KV traffic and increases WFD's speedup to 4.81x on Huginn-3.5B. The code is available at https://github.com/summerbro-hhj/wavefront-decoding.

GQL (ISO/IEC 39075:2024) is the first international standard for a graph query language, and SQL/PGQ (ISO/IEC 9075-16:2023) embeds the same pattern-matching core, GPML, in SQL. Both fix a precise semantics for path patterns: four path modes, four selectors, quantified segments. What engines compute for those patterns has never been measured. Work on GQL is theoretical and runs no engine; cross-engine work measures performance and normalises the semantics away. We build an executable reference semantics for the GPML path core and gate it against the six worked answers printed in the standard's own reference exposition. We then run a 17-construct suite against six releases of five products - Kuzu, DuckPGQ, Neo4j at 5.26 and 2026.04, Memgraph, Apache AGE - scoring each cell as conforming, diverging, rejected, or inexpressible in that dialect. Nine of seventeen constructs draw more than one answer across the engines that accepted them. Of 26 disagreements, 15 are silent - the query runs, returns a different multiset, raises no error - a silence ratio of 0.58. Scoring each divergence against the path mode each engine's manual declares separates language from implementation: 9 of 15 are documented differences, 6 are departures from the standard the engine implements. A metamorphic layer needing no reference semantics finds 39 self-consistency violations, yielding two minimal defects. No engine we measured parses the order the standard's own examples are written in, except the authors' own, which added it after this suite reported the gap. Suite, semantics, reproducers and results are open source.

For two even integers $r_1\leq r_2$, a graph $G$ of even order is \emph{2-DCC edge $[r_1,r_2]$-bipancyclic} if for every ordered pair $(e,f)$ of independent edges and every even integer $\ell\in[r_1,r_2]$, there exist two vertex-disjoint cycles $C_1$ and $C_2$ with $V(C_1)\cup V(C_2)=V(G)$, $|C_1|=\ell$, $|C_2|=|V(G)|-\ell$, $e\in E(C_1)$, and $f\in E(C_2)$. We study this property for Cartesian products $G=H_1\square\cdots\square H_d$ with $d\geq2$, where each factor is $K_2$ or an even-order bipartite edge-Hamiltonian graph. We prove that $G$ is 2-DCC edge $[4,|V(G)|/2]$-bipancyclic whenever $d\geq4$, and also for $d\in\{2,3\}$ under explicit Hamiltonian-cycle conditions on $H_i$. Here $1\leq i\leq d$. As applications, we give sharp characterizations for undirected toroidal meshes, star-cube networks, and hyperstar networks.

Astrochemical processes involving sulfur are not yet well understood because cosmic sulfur reservoirs and the production pathways of sulfur-bearing species remain elusive. Addressing this, requires high-resolution interferometric observations capable of probing individual molecular cores. Following our previous study focused on early molecular cores, we are motivated to expand this investigation toward a sample of evolved cores to understand their chemical transition. We analyzed data from ALMA toward 16 molecular cores in massive star-forming regions associated with methanol masers, targeting the same six sulfur-bearing species studied in a previous work toward early molecular cores: SO, SO2, H2CS, SO+, NS, and 34SO. Column densities and abundances were derived assuming LTE, and temperatures were estimated from methanol transitions. Comparisons were made between the results obtained for the evolved cores and those previously obtained for the early ones. We find that the abundances of the sulfur-bearing molecules are higher in the evolved cores than in the early ones, confirming a general time-dependent enrichment of sulfur in the gas phase. While abundances increase within the 100-220 K range, their correlation with temperature weakens, suggesting that gas kinematics become increasingly more important in the sulfur chemistry. This evolutionary transition involves a chemical reorganization where SO2 becomes dominant. We confirm the validity of SO2/SO as a chemical clock, though chemical modeling reveals a discrepancy in sources with more pronounced kinematic processes, namely a steeper increase in the SO2/SO ratio. The line-width analysis of the molecular species indicates that core evolution and kinematics lead to a well-mixed gas, erasing the spatial stratification where different species trace distinct layers in the cores at earlier stages.

We investigate fermion production and its cosmological consequences in a warm inflationary scenario with a Yukawa interaction between the inflaton field and Dirac fermions. Treating the produced fermions as a thermalized relativistic fluid, we derive the coupled perturbation equations incorporating dissipative effects and thermal fluctuations. By solving the resulting system through Green's function methods, we identify distinct contributions from thermal noise, thermal-acoustic propagation, and higher-order scattering processes to the scalar perturbations. We show that acoustic propagation of fermionic fluctuations becomes significant in the relativistic regime, where the competition between gravitational attraction and Pauli degeneracy pressure allows collective fermionic modes to influence the primordial spectrum. Furthermore, we calculate the fermion number density and acoustic velocity, revealing that strong Yukawa interactions enhance non-adiabatic fermion production and modify the thermodynamic properties of the fermion bath. The sourced scalar and tensor perturbations are calculated, indicating that fermion production can substantially amplify primordial fluctuations, particularly in the strong-coupling regime. Since scalar perturbations receive more efficient enhancement than tensor modes, the tensor-to-scalar ratio is suppressed relative to the standard single-field warm inflation prediction. Our results show that thermalized fermions provide an additional mechanism for modifying primordial perturbations and offer new insights into the role of particle production in warm inflationary cosmology.

This paper concerns the variational inequality arising from a specific singular control problem: portfolio selection under proportional transaction costs. This variational inequality is a gradient-constrained partial differential equation (PDE). Generally, the literature only guarantees the W^{2, \infty} regularity of the solution to such a PDE, and counterexamples exist for higher regularity. In this paper, by exploiting the concavity of the value function, we connect this gradient-constrained problem to an obstacle problem, and finally show that the solution is C^{2,\alpha} except at the corner points where multiple gradient constraints bind. Especially, if there are two assets, then a global C^{2,\alpha} solution can be guaranteed.

3D Gaussian Splatting (3DGS) has become a practical scene representation for real-time novel-view rendering, compression, and immersive content delivery. However, its quality assessment still largely follows rendered-view proxy protocols that sample camera poses, render images or videos, and apply inherited image and video quality metrics. While convenient, this practice does not fully capture 3DGS-native degradations that originate from Gaussian primitive distributions, splatting and visibility behavior, and trajectory-dependent artifacts. This survey reviews recent 3DGS quality assessment studies from four perspectives, covering distortion characteristics, subjective benchmarks, objective metric reliability, and emerging directions for native 3DGS evaluation. Across the literature, we find that different benchmarks construct different notions of quality, and that metric effectiveness is highly protocol dependent, varying with distortion sources, stimulus formats, and view and trajectory sampling. Finally, we summarize open challenges and outline practical guidelines for building more comparable and representative 3DGS-QA evaluations.

Brain lesion segmentation is a fundamental task in medical image analysis, playing a critical role in diagnosis, treatment planning, and longitudinal disease monitoring. Yet existing models still struggle to meet the demands of real clinical use, where deployments contain data distribution shifts, arising from differences in scanner hardware, imaging protocol (varying MRI modality sets), and new pathologies. We present BrainIAC (Brain lesion Interactive Adaptive Continuously learning segmentation), a unified framework that integrates (i) a multi-modal backbone network trained to segment multiple types of brain lesions and handle heterogeneous sets of modalities via zero-filling and random modality dropping; (ii) 3D interactive segmentation with bounding-box and click prompts that preserves fully automatic prediction when no prompt is given; and (iii) an online adaptation mechanism combining Mid-Interaction adaptation and Post-Interaction adaptation, supervised by the network's own predictions as pseudo labels and guided by an extra Click-Centered Gaussian loss. To our knowledge, this is one of the first 3D online adaptation methods for interactive segmentation, and the first to combine handling of heterogeneous modality sets with online adaptation. Experiments across seven brain MRI datasets demonstrate that the proposed components provide complementary and synergistic benefits. The method consistently outperforms existing approaches and generalizes well across heterogeneous imaging modalities, including those unseen during training, as well as previously unseen brain pathology types. The code and a 3D Slicer plug-in will be released at https://github.com/WenTXuL/BrainIAC upon publication.