Papers

Proposals for international agreements that limit frontier AI development depend on verification, and a central challenge is detecting undeclared compute facilities used to evade restrictions. Underwater data centers (UDCs) have been suggested as one such evasion vector, but their feasibility at frontier scale and their detectability have not been seriously assessed. We examine current UDC deployments, evaluate construction and maintenance complexity relative to land-based facilities, and analyse the feasibility of a 100,000 H100-equivalent training run underwater. We find that power delivery and cooling are tractable, but interconnect and the hands-on maintenance that large training runs require are severe obstacles - surmountable only by a well-resourced state actor accepting large cost and schedule penalties, and only where concealment, rather than efficiency, is the objective. We then assess detectability through thermal, acoustic, optical and synthetic-aperture-radar (SAR) surveillance. Thermal detection of an operational pod is unlikely outside shallow, calm water; acoustic detection is marginally more effective, but faces limitations in attribution; and optical/SAR monitoring is most powerful during construction and maintenance, when the pressure-vessel fabrication base and the cable-laying fleet create distinctive signatures for AIS-tracking. We conclude that UDCs are a comparatively unlikely evasion route relative to underground or industrially disguised land-based facilities, but the residual risk is non-zero and warrants operationalising the detection modalities discussed.

How do VLMs map from pixels to semantics? To understand this general question, we focus on a narrow one: studying how VLMs perform optical character recognition (OCR). Across four models, we identify attention heads causally necessary for OCR, and discover that these are in fact general-purpose heads that output interpretable semantic features across all image tokens. For example, pointing these heads at an image token containing the word "bike" causes Qwen3-VL-8B to output "bike," but pointing them at a bird wing causes the model to output the token "feathers." We collapse these heads' attention weights into a single verbalization lens transformation that reveals interpretable semantic features in hidden states across all layers. When combined with projection to vocabulary space, we can obtain interpretable labels starting from layer 0, showing that image representations are in fact aligned with language in early layers. We find that we can also use the inverse of this transformation to edit non-word concepts, e.g., replacing a tractor with a revolver in a naturalistic image, providing causal evidence that this subspace is useful for more than just OCR. Our results are an example of how the study of specific mechanisms can shed light on broader interpretability problems.

A sizable literature studies content moderation locally, at the level of individual moderation decisions, for example by measuring or predicting the effects of specific interventions. However, the problem of how such decisions should be combined into effective platform-level moderation strategies is comparatively unexplored. We address this latter problem by formulating content moderation as a global, adaptive, and sequential decision process in which heterogeneous interventions must jointly balance multiple competing objectives. Drawing on feedback control, we introduce a general control-theoretic framework for composing moderation actions according to their expected effects on an evolving platform. We instantiate the framework in large-scale, empirically grounded simulations and compare two control-theoretic moderators against several baselines and local strategies. When moderation aims to maintain competing platform-level properties around desired conditions, the control-theoretic approaches achieve the best overall performance. They also use severe interventions more selectively and recover more effectively after external surges of harmfulness. These results demonstrate the advantages of studying content moderation as a global, adaptive, and sequential decision problem.

Although a large number of cosmological simulations are now publicly available, their spatial and mass resolutions remain insufficient to accurately follow the dynamics of compact stellar systems and black holes. A complementary approach is therefore required to exploit the cosmological assembly histories encoded in these simulations without rerunning them. We present CosmoDyn, an open-source Python framework that reconstructs time-dependent galactic environments from any cosmological simulations and explicitly follows unresolved compact objects within them. A distinctive feature of CosmoDyn is that it models not only the main host galaxy but also its accreted satellites via moving gravitational potentials. The framework can therefore account simultaneously for the delivery of ex-situ populations and for the dynamical influence of satellites on in-situ population already present in the host. The modular pipeline comprises four main stages: reconstructing the evolving host and satellite potentials; generating in-situ and ex-situ populations of compact objects; integrating their orbits with configurable prescriptions for dynamical friction, and mass loss; and modeling tidal streams. Once reconstructed, the same cosmological environment can be reused to explore different objects, initial conditions, and physical prescriptions at low computational cost. CosmoDyn thus enables rapid parameter exploration and applications to statistically significant galaxy samples, while its modular architecture is designed to incorporate progressively more realistic potentials, and formation models.

Agentic workflows now make consequential decisions in regulated settings, and the governance placed around them is almost entirely step-scoped: input-output classifiers, per turn rails, and span-level evaluators. The policies organizations actually hold, such as referral thresholds, authority limits, and review requirements, are properties of the whole execution rather than of any one step. This mismatch admits a failure mode we call a Compositional Policy Violation (CPV): every individual step passes its own check while the composed execution violates the governing policy. A predicate over a single step cannot evaluate a property that step does not determine, so no improvement in the accuracy of the step-scoped monitors detects this class. We define CPVs as the failure of step-level compliance to compose, and present a taxonomy of four types: Authority Creep, Threshold Laundering, Cumulative Sum Violation, and Context Collapse. We show that the correct repair for each class is dictated by where the guarded quantity mutates. We then introduce a provenance-aware runtime architecture that evaluates policies over complete execution traces, recomputing guarded quantities from raw provenance rather than the pipeline's derived representation.

We propose SEAM, a LiDAR-based lifelong mapping framework. Instead of relying on a single anchor spanning the entire session, SEAM generates evidence based on a trajectory optimized with submap-level anchors, and performs dynamic object removal and change detection. Through submap-level reprojection, the generated evidence remains usable even if the trajectory is subsequently modified by a new session, eliminating the need to recompute the entire process from scratch. SEAM suppresses geometrically unreliable inter-session loop edges using a DOP-based confidence measure. Suppressing unreliable loop edges prevents alignment errors. SEAM also uses a directional voxel-wise evidence model. The model accounts for occupancy patterns that vary with ray direction. Direction-aware evidence separates dynamic objects from environmental changes more precisely. Experiments on a real construction-site dataset and a long-term multi-session dataset show that SEAM achieves higher accuracy and faster processing than existing methods.

We prove $L^p$ bounds for multilinear multipliers whose symbols are singular along degenerate subspaces. When the singularity has a sufficiently mild degeneracy, we show that the wavepacket analysis of the nondegenerate theory can be adapted to this setting. The admissible range of exponents depends on the geometry of the singularity.

Physics Education has played a prominent role in advancing physics education research since its establishment in 1966. However, a comprehensive investigation of its publication trends, impact, and thematic evolution over six decades remains limited. This study examines the journal development through a bibliometric analysis of publications over six decades. Following a PRISMA-based screening process, 6,311 documents were retained from an initial dataset of 7,709 records. Publication trends, citation impact, leading countries and institutions, topic modeling, and topic evolution were analyzed to examine the journal's development and thematic structure. The results indicate sustained growth in publication output, significantly after the digital and information era. The UK and the US emerged as the most productive contributors and accumulated the highest total citations, whereas Germany and Norway achieved the highest citation impact in terms of citations per paper. This pattern was further reinforced by increasing contributions from countries in Asia and the Global South, reflecting the growing internationalization of the journal. Major research themes include force and motion experiments, energy and light experiments, laboratory-based learning, conceptual understanding, and physics teacher education. Topic prevalence analysis indicates that, while experimental and laboratory-based studies have remained a defining feature of Physics Education, increasing attention has been devoted to conceptual understanding, assessment, technology-supported instruction, and pedagogical innovation in recent decades. Overall, Physics Education has evolved from a journal primarily centered on laboratory experiments and instructional demonstrations into a multidisciplinary venue emphasizing conceptual understanding, educational technology, and contemporary innovations in physics teaching and learning.

A hypergraph is said to be integral if all of its adjacency eigenvalues are integers. Recently, Portugal and Del-Vecchio in [Appl. Math. Comput. 504: 129507 (2025)] studied the integral hypergraphs and gave a characterization of integral hypercycles in three particular cases: $3$-uniform, $4$-uniform and $5$-uniform hypercycles. In the same article, they conjectured that the $k$-uniform hypercycle on $n$ vertices $\Cnk$ is never integral for $k<n-1$, when $n>6$. In this article, we confirm this conjecture and prove that for $2\le k\le n-1$, $\Cnk$ is integral if and only if $k=n-1$ or $(n,k)\in\{(4,2),(6,2),(6,3),(6,4)\}$. The proof begins with computing the complete adjacency spectrum of $\Cnk$ and then uses Niven's theorem, a cyclotomic-unit lemma, an elementary property of Euler's totient function, and the Galois symmetry of cyclotomic fields to complete it. Our result gives a complete characterization of $k$-uniform integral hypercycles on $n$ vertices.

It is known that a major difficulty in proving Hölder regularity for solutions to quasilinear singular parabolic equations of $p$-Laplace type via the method of intrinsic scaling is to establish the decay estimate of the space-time measure of level sets. In this paper, we consider an inhomogeneous singular parabolic $p$-Laplace equation with nonnegative time-independent forcing and Dirichlet data. By combining a time-rescaling argument with $L^\infty$ comparison estimates, we derive Lipschitz regularity in time after any fixed positive elapsed time, which reduces the problem to an elliptic-type decay estimate for the spatial measure of level sets that is essentially uniform in time. This reduction enables us to address the above obstacle.

We examine the inverse problem of recovering the potential term of an n-dimensional heat equation from a single time solution profile. We show that it is possible to uniquely determine this potential term via a stability inequality using solution measurements taken at a fixed time, assuming the potential is known within an arbitrary subdomain. The approach is based on the Carleman estimate. Additionally, we discuss the optimality of this type of observation.

Multi-robot task and motion planning (MR-TAMP) requires jointly reasoning about discrete task decisions and continuous collision-free motions of multiple interacting robots. Although asymptotically optimal algorithms have been developed for task and motion planning, extending these guarantees to the multi-robot setting introduces an important challenge: different task transitions may involve different subsets of robots and therefore impose constraints of different dimensions on the composite configuration space. Consequently, an asymptotically optimal planner must not only optimize motion within each task mode, but also ensure sufficient exploration of the different types of transitions connecting them. We characterize this transition structure and establish sufficient conditions for global asymptotic optimality in MR-TAMP, requiring persistent coverage of relevant transitions and asymptotically improving motion planning within connected feasible regions. Based on these conditions, we develop an efficient asymptotically optimal MR-TAMP algorithm that combines evolving individual-robot roadmaps with implicit tensor-product search, avoiding explicit construction of the composite roadmap. The planner further employs conditional transition sampling, lazy collision checking, and mode- and solution-level guidance to improve finite-time planning efficiency while retaining persistent exploration. The resulting framework provides asymptotic optimality guarantees for multi-robot manipulation while efficiently exploiting the structure of individual-robot motion planning.

Time-series language models provide a shared natural-language interface across temporal tasks, but plausible text does not guarantee reliable task outputs. Responses may appear reasonable while hallucinating the required object: numerical sequences can violate shape, scale, channel order, or temporal alignment, and textual decisions can fall outside the legal label space. We formulate reliable time-series language modeling, separating task-object reliability from predictive quality. We introduce ExecTS-QA, a contract-grounded benchmark spanning forecasting, imputation, classification, anomaly detection, and waveform analysis. We further propose WaveTLM, a unified compiler-executor model whose task compiler transforms user requests, visible arguments, and wave-grounded evidence into typed task states, while task-native executors construct numerical tensors, legal decisions, or structured records. On ExecTS-QA, a single WaveTLM checkpoint achieves 99.40% contract-valid coverage, compared with 37.83% for the strongest evaluated string-first baseline, while retaining balanced predictive performance across all five task families. Evaluations on SciTS, TSQA, IRTS-ToolBench, and ARFBench provide additional evidence of transfer. The code, construction scripts, and ExecTS-QA dataset will be publicly released upon publication. These results show that task compilation can convert plausible language generation into reliable time-series outputs.

Anonymous credentials (ACs) are fundamental to privacy-preserving authentication, allowing users to prove possession of attributes without revealing their identities. State-of-the-art ACs distribute credential issuance across multiple authorities, typically employing techniques such as Shamir's secret sharing or aggregate signatures. While this approach enhances system robustness and eliminates a single point of failure, it treats all authorities equally in the credential issuance phase. This uniform treatment disregards the varying levels of trustworthiness or stake held by different authorities. Such a limitation has become particularly problematic in modern decentralized systems like Proof-of-Stake networks, where the inherent trust differentiation among nodes cannot be leveraged in the credential issuance process. To address this limitation, we propose the notion of Multi-Authority Anonymous Credentials with Epoch-Based Weights (MA-ACEW), the first Multi-Authority Anonymous Credential (MA-AC) model that considers authorities' weight distribution in credential issuance. Crucially, MA-ACEW enables efficient credential updates when authority weight distributions change across epochs. The core of MA-ACEW is our novel Epoch-Bound Pointcheval-Sanders Signature (EB-PS) primitive, which binds signatures to specific time epochs. This temporal binding enables both weight-based credential issuance within epochs and efficient non-interactive credential updates across epochs. We formalize the EUF-eCMA unforgeability requirement for EB-PS and prove our construction satisfies it under a novel STB-GPS assumption. We then prove that our MA-ACEW construction achieves unforgeability, anonymity, and blindness. Finally, we present benchmarks demonstrating the efficiency of EB-PS and MA-ACEW. Remarkably, presenting a credential aggregated from 128 partial ones takes only 10.68 ms on average.

In this paper, we introduce a novel multi-fluid approximation scheme for the one-dimensional Vlasov-Poisson system, that is relevant for arbitrarily long time intervals. For low regularity solutions, we establish an error estimate in the Wasserstein-1 distance, obtaining a convergence rate of order $O(h^{\frac{2}{3}})$, where h denotes the velocity grid size. This establishes the consistency, as the grid size tends to zero, between the pressureless Euler-Poisson and the Vlasov-Poisson systems. Numerical illustrations are given to illustrate the efficiency of our approach.

We establish an integral Harnack inequality and expansion of positivity for solutions to fractional porous medium-type equations in the fast diffusion regime, under optimal tail assumptions.

We prove that strong solutions to the incompressible, homogeneous Navier-Stokes system on $\mathbb{R}^3$ are global in time for initial data in the Sobolev space $H^1_\sigma(\mathbb{R}^3)$. The central ingredient of the proof is a new energy estimate that rules out finite-time blow-up in $L^r(\mathbb{R}^3)$ for $r = 2 + 2 / \sqrt{3}$. This estimate is based crucially on properties of the material derivative in combination with the divergence-free constraint, together with an intricate estimate that harnesses the delicate interplay between the viscous coercivity of the new energy functional and the control of a perturbing pressure term. Notably, the estimate does not carry over to systems that merely share the standard energy structure, such as T. Tao's averaged Navier-Stokes system. As a consequence of the new energy estimate, every Leray-Hopf weak solution $u$ to the homogeneous Navier-Stokes system is globally unique whenever the initial value $u(0, \cdot)$ belongs to $L^2_\sigma(\mathbb{R}^3) \cap L^3(\mathbb{R}^3)$. Even for $u(0, \cdot) \in L^2_\sigma(\mathbb{R}^3)$, the only possible non-uniqueness in the class of Leray-Hopf weak solutions is initial branching, and every such solution is $C^\infty$-smooth on $\left( 0, \infty \right) \times \mathbb{R}^3$. Moreover, if $u(0, \cdot)$ is smooth with derivatives of all orders decaying rapidly at infinity, we show that $u$ is in fact $C^\infty$-smooth on all of $\left[ 0, \infty \right) \times \mathbb{R}^3$.

Minimum-cost spanning tree game (MSTG) is a cooperative game played on an undirected edge-weighted graph $(G,w)$ representing the network, where each vertex corresponds to a player and each edge has an associated cost~$w$. A distinguished vertex $s \in V(G)$ represents the supply or source. For any coalition of players $S$, the characteristic cost function $c(S)$ is defined as the minimum cost of a spanning tree with respect to $w$, connecting exactly the vertices in $S \cup \{s\}$. In this paper we study the computational complexity of deciding core membership for MSTG. In general, deciding whether a given allocation is in the core is coNP-hard~(Faigle et al.,International Journal of Game Theory,1997). We study the core recognition problem under the name MSTG Core Non-Membership. We extend the hardness to graphs which are very close to being planar. On the positive side, we present several algorithmic results within the framework of parameterized complexity. We show that MSTG Core Non-Membership is fixed-parameter tractable when parameterized by the support size of the allocation. Turning into structural parameters of graphs, we show that the problem admits an FPT algorithm parameterized by treewidth and signed neighborhood diversity. Last but not least, we investigate kernelization. While in general graphs, under standard complexity-theoretical assumptions, MSTG Core Non-Membership does not admit a polynomial kernel parameterized by the vertex cover number, we design a cubic kernel in planar graphs. Furthermore, in general graphs, we obtain quadratic kernel for signed neighborhood diversity and linear kernel for the parameter feedback edge number.

Higher-order time-convolutionless (TCL) master equations provide systematic corrections for non-Markovian dynamics in open quantum systems, but their time-ordered integrals become increasingly costly to evaluate. Direct quadrature of the Hadamard-reduced sixth-order (TCL6) generator at all $N_t$ sampled times requires $O(N_t^3)$ operations at fixed system dimension. We derive an exact reduction for a finite-dimensional system coupled through one Hermitian operator to a stationary centered Gaussian bath. By separating operator coefficients from scalar time-dependent spectral densities, the complete TCL6 time series is reduced to cumulative sums and first-order recurrences, one-dimensional causal convolutions, and an exact dyadic recursion for interlocked sums. With the algorithm, evaluating the complete TCL6 time series requires $O(N_t\log^2N_t)$ operations. These reductions enable fast, practical simulations of non-Markovian dynamics involving multiphonon and multiphoton processes in open quantum systems.

Coding agents are typically evaluated with desired behavior specified through issues or instructions. In practical web development, however, agents may need to infer behavior from working software and implement it in an incomplete application. We introduce ProgramDistill, a benchmark evaluating coding agents on features discovered through interaction with fully functional reference applications. We build ProgramDistill by factorizing applications into features of different granularities, each associated with replayable behaviors executable via its gold patch. Our pipeline, mine-craft-patch, discovers 1,975 replay-verified behaviors across 26 applications and constructs 4,063 tasks without human intervention. Across nine frontier coding agents, GPT-6 Astra and Claude Opus 5 achieve 49.2% and 28.8% success on cumulative workflows in full-application reconstruction. In partial-application reconstruction, success falls from 100% to 64.0% and from 96% to 32% as restoration depth increases from 1 to 8. ProgramDistill thus provides a scalable benchmark with controlled difficulty for evaluating and diagnosing coding agents, and a natural basis for future curriculum-based training.

Identifying technological trends is a core scientometric task, yet traditional frequency-based approaches struggle to capture substantial meaning shifts of domain-specific terms. We hypothesise that contextual embeddings can complement frequency dynamics to effectively track diachronic semantic change. We compare frequency and embedding-based approaches across Astrophysics and NLP corpora spanning from 2010 to 2024. Candidate terms are extracted using KeyBERT (utilizing SciBERT as its underlying language model) and filtered for significant frequency increases using Fisher's exact test. These terms are then evaluated for genuine semantic shift by domain experts to establish ground-truth labels. To quantify semantic drift, each term's contextual embedding ”clouds” from the two discrete periods are compared using multiple metrics: cosine distance, average pairwise distance, Hotelling-type T 2 , and maximum mean discrepancy. Results indicate that frequency-based methods align slightly better with human judgments of ”trend-related terms” than semantic metrics (Precision@50 of 0.62 vs 0.60 in Astrophysics). The two signals show a correlation of around 0.6. Several terms identified exclusively by embedding metrics (e.g., ”primordial black holes”) represent critical conceptual developments invisible to pure frequency analysis. These findings indicate that semantic metrics may capture complementary information, highlighting the value of integrating contextual embeddings into scientometric trend analysis.

This work studies the placement of an entanglement source along a communication line formed by two noisy qubit channels. Recent work argued, on analytical and numerical grounds, that midpoint placement should be at least as favorable as endpoint placement. Here it is shown that, for arbitrary qubit channels, if a sequential composition can preserve entanglement, then the corresponding parallel action cannot annihilate all entanglement. The proof uses the transpose-factorization criterion introduced in that recent work. Quantum Sinkhorn scaling converts every strictly positive qubit channel into a unital representative, and the special normal form of unital qubit channels then yields the required factorization of the transposed map through the original channel. Depolarizing regularization and the closedness of the set of entanglement-breaking channels extend the result to arbitrary channels. Consequently, $\Lambda_1 \otimes \Lambda_2 \in \mathrm{EA}$ implies $\Lambda_2 \circ \Lambda_1 \in \mathrm{EB}$, and, by exchanging the two channels, the same holds for the opposite composition order. This proves the recent conjecture that midpoint placement is optimal for all qubit channels, in the feasibility sense in which that optimality was originally defined.

We study Transient Multiagent Pathfinding, a variant of the classical Multi-Agent Pathfinding problem in which a set of agents must be routed without collisions from designated start vertices to designated destination vertices in a graph. We analyze the problem within the above-and-below-guarantee paradigm of parameterized complexity. In particular, we consider the natural upper bound \(L\), given by the sum of the shortest-path distances between pairs of agents' terminals (corresponding to sequential routing of the agents). The parameterization is given by the gap \(\zeta = L - \lambda\) between this bound and the target makespan \(\lambda\), together with the number \(k\) of agents. Our main result establishes fixed-parameter tractability for the combined parameter \(k + \zeta\). Matching lower bounds show that parameterization by \(k\) alone is W[1]-hard, and that parameterization by \(\zeta\) alone is W[1]-hard when terminals are not required to be distinct. On the positive side, if all terminals are distinct, the problem becomes fixed-parameter tractable when parameterized solely by \(\zeta\). Finally, we show that Transient Multiagent Pathfinding is unlikely to admit a polynomial kernel when parameterized by \(k + \zeta\). Together, our results provide an almost complete characterization of the parameterized complexity landscape of the problem for the considered parameters.

To manage the complexity of smart cities, a variety of smart city platforms (SCPs), both proprietary and open-source, have been proposed. Typically acting as middleware between IoT devices at a lower layer and smart services at a higher layer, these platforms simplify the management of smart cities by reifying a variety of requirements common to different municipalities. Open-source software (OSS) is typically free of charge, making open-source SCPs an attractive option for municipalities with smaller budgets that still wish to improve efficiency and quality of life for residents and visitors. Furthermore, using an OSS SCP promotes digital sovereignty, since municipalities can control where the data will reside and will be less prone to vendor lock-in. A lack of support for OSS hinders its adoption by municipalities' IT teams, often with scarce technical resources. An active (aka "healthy") ecosystem, including well-orchestrated developers and users, the availability of installation and user manuals, non-vulnerable and documented code, test batteries, and other artifacts, is an important decision factor before adopting an OSS SCP. In this paper, we evaluate different open-source SCPs using the concept of "OSS health", covering several of the aforementioned characteristics.

Recent quantum gas cavity-QED experiments demonstrated simultaneous coupling of photons to single atom transitions as well as correlated pairs of ultracold fermions trapped inside optical cavities. This enables simultaneous control over density ordering and pairing. Using extensive numerical simulations, we show that in a transversely driven, two-component degenerate Fermi gas, the interplay of cavity-induced and bare atom–atom interactions controls not only the power threshold for self-organization, but also the type of spatial ordering in the $\mathbb Z_2$-symmetry-broken superradiant state. In the repulsive interaction regime, unpaired or weakly paired fermions first self-organize through a charge-density-wave instability, and finite-momentum pairing only occurs at much stronger pump strengths. In contrast, an attractive superfluid undergoes a joint density–pairing instability, directly entering into intertwined phase with charge-density-wave and pair-density-wave orders. At strong pumping the photon-enhanced pair interaction generates localized density and pairing order even when the bare contact interaction is repulsive. In this cavity-dominated regime strong spatial localization suppresses the long range superfluid coherence. Our results identify the role of cavity-induced atomic interactions in supporting intertwined fermionic orders and pave the way for exploring exotic states with multiple orders in highly controlled hybrid light-matter systems.

For sixty years, the Sun served neutrino physics more than the reverse: its neutrinos established oscillations rather than probing the star itself. That is now changing. Reactor antineutrinos have pinned down the oscillation parameters governing solar-neutrino flavour conversion so precisely that the propagation-related uncertainty is becoming negligible – closing the first of two abysses. Solar neutrinos can, at last, be turned on the Sun. Yet a second abyss remains: today's solar-neutrino detection falls an order of magnitude short of the precision the Standard Solar Model already predicts for the dominant pp flux ($>\,$90$\%$) – a gap no reactor experiment can close. The intrinsic $^{14}\mathrm{C}$ background walls off the pp region; only new detection techniques can breach it. Bridging this second abyss demands a revolution, not an increment. Combined with helioseismology's complementary reading of the Sun's mechanical structure, precision neutrino measurements of the nuclear source terms would enable a multi-messenger heliotomography of the solar interior – reading our star from both sides at once. A new age of solar discoveries may follow, on one condition: that the field builds the instruments equal to the task.

We study the geography of surfaces of general type with extremal cotangent dimension, in other words surfaces which have either no global holomorphic symmetric differentials at all or the maximal asymptotic growth of their number, i.e. big cotangent bundle. We are mainly interested in surfaces with low slope K^2 /$\chi$, which, as far as maximal cotangent dimension is concerned, were out of reach of previous methods. We prove vanishing theorems for symmetric logarithmic differentials on minimal rational surfaces and for differentials on their double covers and extend a bigness criterion of Sakai to fibrations of general type in the sense of Campana. As a consequence, we prove, on the one hand that generic Horikawa surfaces have no nontrivial symmetric differentials and on the other hand that there exist Horikawa surfaces with big cotangent bundle.

Quantum Key Distribution (QKD) in optical networks can provide information-theoretic security but is limited by its operability range, thereby requiring repeater nodes for extended coverage. Existing works typically assume that all repeater nodes and their associated key management systems are fully trusted, overlooking the risks posed by software exploits and insider threats. To address this, in this work, we propose a Bayesian fusion-based model to quantify the trustworthiness of each node. We have formulated a reliability-guided Trusted Repeater Node (TRN) selection framework for metro optical networks, where each node is assigned a trust score. We have subsequently mapped this trust score to link weights, which in turn has been used for reliable path computation for TRN selection, using the Dijkstra algorithm. We have also ranked the nodes using a composite score combining eigenvector and betweenness centrality, to capture their topographical relevance in the network. Simulation results on a reference topology demonstrate that the proposed method achieves approximately 8.93% higher path coverage than traditional centrality-based approaches like degree centrality, using the same number (around ten) of TRNs, thereby supporting reliable and resilient TRN selection for QKD-enabled optical networks.

Applying the BBDJS minimal model to the derived symplectification of a $-1$-shifted contact derived Artin stack and descending algebraically along the structural free $\mathbb{G}_m$-action, we construct an $\ell$-adic perverse sheaf on any oriented such stack, and use Verdier's specialization equivalence for monodromic sheaves to equip it with a tame twisted monodromy operator $\theta$. We show that the local fundamental class of a Legendrian $L$ satisfies $\theta \circ \mu_L = (-1)^{\mathrm{vdim} L}\mu_L$, so that on Legendrians of odd virtual dimension, the class vanishes due to $\theta$-invariance. Moreover, both parities occur already on the $A_1$ chart while an odd Legendrian can carry a nonzero local class. We further formulate a contact analogue of Joyce's conjecture for a graded orientation, in which the orientation datum is twisted by the parity of the virtual dimension. Under the assumption of a monodromic refinement of the symplectic conjecture, we construct the categorified Legendrian 2-categories $\mathfrak{L}\mathcal{F}_c(X)$ and $LLeg_0$ via $\ell$-adic pull-push functors. Finally, we show that the contact Behrend function is identically $1$, so that the associated Donaldson-Thomas invariant is the compactly supported étale Euler characteristic of the classical truncation, and that the higher traces of $\theta$ recover the singularity type that the first trace discards. As an application, we show that the symplectic invariant of a derived intersection of conic Lagrangians in a cotangent bundle vanishes identically, while the contact invariant computes the Euler characteristic of the projectivized intersection, with an explicit formula for conormal bundles.

We consider solutions of space-periodic reaction-diffusion-advection equations in the whole space R^N, with general unbounded initial support. We show the existence of spreading sets for the solutions at large time, and variational formulas for the spreading speeds. The location of the upper-level sets of a solution with unbounded initial support is estimated in terms of that initial support and the spreading set for the solutions with bounded initial supports. The results hold for the standard classes of Fisher-KPP, ignition, or bistable reactions. The general results apply to the cases of V-shaped and Lambda-shaped initial supports. The proofs rely in particular on upper estimates of what we call retracting solutions.