Papers

Tool observations dominate the context of software-engineering agents, making long interaction histories costly to maintain. Existing context compression methods can discard information needed by later actions, while adapting agents to soft-token representations can compromise their original behavior. To reduce context while preserving action-critical information and agent behavior, we combine Latent Observations, Hard Actions (LOHA), a context layout that separates compressed history from text needed for exact reference, with Anchored Context Distillation (ACD), a training method that enables latent reading while constraining behavioral drift. LOHA compresses older tool observations into soft tokens while retaining the agent's own turns and the last K observations in text, providing compact access to historical information and exact access to recent content. To enable the agent to use this representation, ACD distills the base model's full-text predictions into the latent view while anchoring its behavior on plain-text inputs to the same base model. On SWE-bench Verified, K=3 reduces context per call by 43% for Qwen3-4B and 57% for SWE-Master-4B-RL, with resolve rates of 12.1% and 21.8% versus 14.5% and 27.5% for their uncompressed bases. A single-run recency sweep reaches 14.4% and 23.0% at K=8, with larger windows generally favoring task performance over compression. Under a 32K-token limit, Qwen3 with K=3 resolves 21.1% of a 199-instance subset versus 11.1% for the same adapted agent using full text. In concurrent single-GPU serving, it achieves 1.9 times that full-text agent's instance throughput.

Cooperative perception can expose object state beyond a vehicle's onboard sensors, but sensing occlusion can still leave a local safety application without the objects its collision computation needs. To tackle this challenge, we present the ITS Fairy, an infrastructure-side Server Local Dynamic Map (S-LDM) service whose decision unit is the pair (recipient, missing conflict-relevant object): among objects absent from a recipient's CPM-derived reported awareness, it sends only those relevant to a Time of Closest Approach (TCA) conflict test. Comparable services predict what a vehicle can perceive; the ITS Fairy instead reads what it has already reported. The recipient inserts the selected state into its local LDM and uses its unchanged collision-avoidance controller. We evaluate this application-level mechanism in SUMO–ms-van3t–S-LDM emulation, since extended as VaN3Twin, using a sensing-occluded lane merge and four-way intersection scenario. At every main-sweep speed, the smallest assisted per-encounter minimum TCA exceeds the largest local-only value in the archived data. Additionally, assisted medians remain in the multi-second range where local-only operation repeatedly approaches zero. In the lane-merge robustness data, the median benefit persists at 80% configured assistance omission with 10 and 5 Hz analysis, but largely disappears at 100-120 km/h when 80% omission is combined with 1 Hz analysis. These results demonstrate the application-level value of supplying object state selected against what a recipient has itself reported. They are not a vehicular wireless-channel evaluation, and they do not quantify what selectivity saves relative to forwarding every nearby object.

Multimodal inference in safety-critical applications, such as autonomous driving and robot navigation, requires heterogeneous sensor observations to reach an edge server within a task-prescribed temporal window. Referenced to the event or state being inferred, this window ends at the latest time an observation remains useful for the current decision. Since sensor readiness times, data volumes, wireless channel conditions, and task relevance vary across sensors, maximising network throughput does not necessarily minimise the fused prediction error when the window closes. We cast multimodal uplink scheduling as sequential wireless evidence acquisition and, for a linear minimum mean-square error (LMMSE) fusion model, derive a conditional evidence gain metric from the reduction in residual-error volume. Defined through second-order statistics, this metric applies beyond Gaussian models and coincides with conditional mutual information when the target and prediction errors are jointly Gaussian. We then develop MIRA, a greedy task-driven maximum information-rate allocation policy that combines conditional evidence gain with each sensor's channel state information and remaining data volume, while updating sensor relevance as evidence is acquired. Experiments on synthetic classification, human activity recognition, and vehicle-trajectory regression show that MIRA outperforms both relevance-only and channel-only scheduling. Relative to the former, MIRA improves classification accuracy by up to 70% and reduces regression mean-square error (MSE) by up to 5.5%. Relative to the latter, it requires 58% less acquisition time to attain an 80% target accuracy, while achieving up to 95% higher accuracy and 9% lower regression MSE. These gains are achieved without maximising received-data volume.

This paper explores variations of vertex-coloring problems defined on graph visibility properties. It introduces and studies the dual, outer, and total mutual-visibility chromatic numbers, which partition the vertex set of a graph into color classes that preserve specific mutual-visibility conditions called dual, outer or total. The work provides structural conditions under which these chromatic parameters are finite or infinite, and establishes that deciding whether a graph admits a dual, outer, or total mutual-visibility coloring using a given number of colors is NP-complete, even when restricted to two colors. Exact formulas and tight bounds for these chromatic parameters are established across several fundamental graph classes. For block graphs, complete characterizations are provided for the outer and dual mutual-visibility chromatic numbers based on structural invariants such as cut vertices and specific forbidden subgraph structures. On Hamming graphs, the dual and total mutual-visibility chromatic numbers are shown to equal the smaller dimension of the factors, while the outer mutual-visibility chromatic number is proven to equal the star arboricity of a corresponding complete bipartite graph. Finally, the paper examines strong grid graphs, determining exact values for their total, outer, and dual mutual-visibility chromatic numbers. These results demonstrate how the parameter behaviors range from finite constants to infinity depending on the grid dimensions.

We investigate two late-time cosmological models generated by Kruglov's nonadditive entropy at the apparent horizon. Model I, originally derived by Kruglov, follows the Cai–Kim thermodynamic construction and leads to an implicit modified Friedmann equation, whereas Model II, proposed and derived in this work, is obtained from an entropy-integral prescription and contains an effective vacuum contribution. We formulate both models in terms of the dimensionless Hubble parameter, include radiation, impose exact present-day closure, and evolve the physical branch using analytic derivatives of the implicit Friedmann equations. We constrain the models with DESI DR2 baryon acoustic oscillations and a compressed CMB likelihood, with and without DES-Y5 Type-Ia supernovae. Model I is driven to a markedly lower Hubble constant, $H_0\simeq62.4,\mathrm{km,s^{-1},Mpc^{-1}}$ for the combined data, and remains non-phantom with $w_{\rm DE,0}\simeq-0.814$; it is strongly disfavoured relative to flat $\Lambda$CDM. Model II stays close to $\Lambda$CDM in the standard cosmological parameters and gives $w_{\rm DE,0}\simeq-1.003$, while its two entropy-sector parameters remain strongly degenerate. Its best-fit likelihood is comparable to $\Lambda$CDM, but the additional parameters are not supported by information criteria. These results show that the two thermodynamic realizations of the same nonadditive entropy have sharply different phenomenological consequences at the homogeneous-background level. In summary, the observational plausibility of entropy-based cosmology hinges critically on how the generalized horizon entropy is incorporated into the Friedmann dynamics.

Top-quark pair production at the LHC provides a bipartite spin system whose correlations are imprinted in the angular distributions of the decay products and can be studied with quantum-information tools. We investigate whether this spin structure can be used to probe invisible new physics in $pp\to t\bar t+X$, where $X$ is a spin-0 or spin-1 mediator motivated by top-philic simplified dark-matter models. Focusing on the dileptonic channel at the High-Luminosity LHC, we compare the sensitivity of the inclusive event yield, the visible invariant-mass distribution, an event-level estimator of the entanglement marker $D$, and the fiducial spin correlation $\mathcal{D}$ measured as a function of the visible invariant mass. We find that observables retaining spin information improve the expected exclusion sensitivity with respect to rate and kinematic information alone, with $\mathcal{D}(M_{t\bar t}^{\rm vis})$ providing the strongest reach for both mediator spins. The same observables also enhance the discrimination between scalar and pseudoscalar couplings of the spin-zero mediator, with $\mathcal{D}(M_{t\bar t}^{\rm vis})$ again providing the strongest sensitivity, particularly at larger mediator masses. These results show that quantum-information-motivated observables of the $t\bar t$ system can be efficient tools to probe both the presence of invisible new physics and the structure of its couplings to top quarks.

The edge radial electric ($E_r$) in the Tokamak à Configuration Variable (TCV) is compared in matched L-mode discharges with opposite ion magnetic drift directions (favorable versus unfavorable $B \! \times \! \nabla B$ configurations). As previously reported on the WEST and AUG tokamaks, the $E_r$ profile—measured by Doppler backscattering (DBS)—exhibits a "well" just inside the separatrix in the favorable drift case, which is absent or less pronounced in the unfavorable counterpart. This observation holds over a broad range of plasma conditions, notably also in Ohmic discharges with nearly identical edge density and temperature profiles. Density fluctuation characteristics inferred from DBS are not drastically different: Under Ohmic heating, edge fluctuation levels tend to be higher in the favorable configuration, while radial correlation lengths are similar. The edge $E_r$ difference appears uncorrelated with carbon toroidal rotation behavior. Reducing density, or increasing auxiliary heating power tends to accentuate the edge $E_r$ disparity. Plasma current has little impact on both favorable and unfavorable $E_r$ profiles—in contrast to results from WEST. Approaching the L-H transition via auxiliary heating, edge $E_r \times B$ shear and pressure grow more readily in the favorable configuration, and DBS fluctuation levels are reduced relative to the unfavorable case. Overall, our results confirm that the edge $E_r$ sensitivity to magnetic drift configuration is a robust, multi-machine phenomenon, with a plausible connection to confinement level and H-mode access.

Let $p>3$ be a prime, and let $b,c$ be integers with $p\nmid b+2c$. We obtain an explicit congruence modulo $p^2$ for the sum of $\binom{2k}{k}T_{2k}(b,c^2)/(4^k(k+1)(b+2c)^{2k})$ from $k=0$ to $(p-1)/2$, where $T_n(b,c)$ denotes the generalized central trinomial coefficient. This gives a parametric formula for the sum considered in a question of Wang and Cui. The proof uses a constant term representation and a logarithmic generating function to reduce the sum to two coefficients of an algebraic generating function. A differential identity and a coefficientwise polynomial congruence then yield the desired evaluation. The formula also applies when $p$ divides $b$ or $b-2c$.

Large language model-based multi-agent debate (MAD) systems are being increasingly used as complex decision pipelines in distributed processes. However, their final synthesis phase still remains inadequately controlled. Even with detailed debate logs, summarizing models are prone to fabricating smoothly written debate consensus that is not grounded in the debate's history. To address this safety gap, this paper presents empirical research and studies if the introduction of active post-debate verification can mitigate the production of such factually unsupported summaries, while still providing valuable information. Furthermore, it is examined whether explicitly signalling divergence is preferable in the absence of a reliable compromise. The Active Provenance Gate (APG) is introduced as a post-debate verification layer that treats the source as a hard constraint, analysing the debate logs, auditing each claim, and applying self-correction. In crisis simulations, the self-healing mechanism more than doubles the average data Provenance Fidelity in difficult condition scenarios, before the strict gate blocks unsupported claims and generates divergence reports. In the human study, a vast majority of the users (over 75%) preferred a report explicitly stating failure in critical scenarios, despite most of them perceiving fabricated consensus from the baseline system as more fluent. Our main contribution is the transition of data origin tracing from passive logging to active conditional blocking before publication.

A smooth complete intersection $X\subset\mathbb{P}^{n+2}_{\mathbb{C}}$ of two quadrics admits an interpretation as a moduli space of bundles. For $n=2$, it parametrizes stable rank $2$ parabolic bundles on $\mathbb{P}^1$ with five marked points, while for $n=3$ it parametrizes stable rank $2$ bundles of odd degree with fixed determinant on a genus $2$ curve. For general $n$, it can be interpreted as a moduli space of semistable twisted $\mathrm{Spin}$-bundles. We study $X\setminus W$, where $W$ is the wobbly locus, consisting of bundles that admit a nonzero nilpotent Higgs field. We prove that $W$ is an irreducible divisor for $n\geq 3$ and compute $H_1(X\setminus W,\mathbb{Z})$. Using a root-stack description, we identify $\pi_1(X\setminus W)$ with the kernel of a monodromy homomorphism from an orbifold mixed braid group. The Reidemeister-Schreier method then yields an explicit presentation in every dimension. For $n=2$, where $X$ is a degree $4$ del Pezzo surface and $W$ is the union of its sixteen $(-1)$-curves, we obtain a presentation with $10$ generators and $25$ relators and prove that both numbers are minimal among all finite presentations. For $n=3$, we show that $\pi_1(X\setminus W)$ admits a presentation with $4$ generators and $78$ relators.

Manufacturing firms face uncertainty in both supply and demand. They implement process flexibility, enabling plants to produce multiple products, to hedge against supply–demand mismatches. Assigning more products to a plant results in efficiency losses at the plant, whereas limited flexibility may improve efficiency because of the specialization effect. Furthermore, the flexibility design determines the sourcing locations of products, thereby affecting demand due to the country-of-origin effect and exposure to tariffs. We incorporate these mechanisms into the supply network flexibility design problem by modeling supply and demand uncertainties as endogenous, that is, as functions of the first-stage design decisions. We propose a two-stage stochastic program and solve it via a decomposition scheme that relies on distribution-specific optimality cuts. To avoid exhaustive enumeration of all distributions, we derive distribution-free formulations that are valid for all distributions and for subsets of supply and demand distributions. Through extensive computational experiments, we demonstrate the superior performance of our solution approach and distribution-free formulations relative to exhaustive distribution enumeration and state-of-the-art inequalities, respectively. Moreover, we explain how the problem structure affects the effectiveness of the proposed formulations. From a managerial perspective, we show the trade-offs between endogenous effects and how they affect the optimal flexibility design.

We analyze a general class of difference operators $H_\varepsilon = T_\varepsilon + V_\varepsilon$ on $\ell^2(\varepsilon\mathbb{Z}^d)$, where $V_\varepsilon$ is a multi-well potential and $\varepsilon$ is a small parameter. We construct approximate eigenfunctions in neighbourhoods of the different wells and give weighted $\ell^2$-estimates for the difference of these and the exact eigenfunctions of the associated Dirichlet-operators.

A photorealistic 3D view tells a teleoperator where a robot is, but not what the scene contains, how well each object has been observed, or how to turn pointing and speech into robot action. CognitiveReality turns a robot's RGB-D stream into a live, semantically indexed Gaussian-TSDF map shared by an operator in virtual reality and a tool-using language agent. One mapper binary serves any platform through configuration alone: it ingests poses from robot SLAM, joint kinematics, motion capture or an inline visual tracker, bridges localization outages with a shadow tracker and keyframe-anchored PnP, and maintains open-vocabulary instance identities with per-object quality at 2 Hz. Speech and controller rays are grounded against persistent scene objects through validated typed tools and operator-confirmed robot actions. In the controlled agent evaluation, the deployed local Qwen3-VL-8B router reaches 81.24% tool exact match, while merge-aware replay correctly redirects 101 absorbed object identifiers. On robot data CognitiveReality exceeds a Gaussian-plus-SDF baseline by 2-8 dB; pose error through 5-40 s SLAM outages stays within 1-8 cm. Deployed live on two quadrupeds, the agent executed 26 of 30 navigation requests and 20 of 20 re-observation requests, raising object quality by 2-5 dB.

For any finite-dimensional algebra $A$ over an algebraically closed field, we prove that if $A$ is $E$-infinite, then the Second brick-Brauer-Thrall Conjecture holds for $A$. In fact, we show that if there is a rational ray outside the $\tau$-tilting fan of $A$, then $A$ admits an infinite family of $\theta$-stable bricks of dimension $d$, for some positive integer $d$ and weight $\theta$. To show our main result, from any $\tau$-regular component of $A$ with no dense orbit, we obtain a brick component that also has no dense orbit and whose points in general position are $\theta$-stable modules for a given weight $\theta$. As an important consequence, we conclude that $A$ is stably-discrete (also called multiplicity-free) if and only if $A$ is $E$-finite. Moreover, we prove that Demonet's (lattice point) Conjecture implies the stable Second brick-Brauer-Thrall Conjecture. For $E$-infinite algebras, our results settle several open conjectures. Together with our earlier work and recent developments, this leads to important reductions in the study of some challenging open problems.

This paper presents mathematically principled filters for multiple-model systems with states of different dimensionality, specifically the variable-dimension interacting multiple model (VD-IMM) filter and the variable-dimension generalised pseudo-Bayesian filter of order 2 (VD-GPB2). To do so, we first provide a Bayesian modelling of a variable dimensional dynamic system, and its measurements. Then, for variable dimensional linear Gaussian dynamic and measurement models, the VD-IMM filter is derived by assuming a posterior that has a Gaussian density for each mode, and then performing a Kullback-Leibler Divergence (KLD) minimisation after each prediction step to keep the Gaussian density form for each mode. Subsequently, the Bayesian update step is performed, keeping a Gaussian density for each mode. The VD-GPB2 filter considers the same model as the VD-IMM filter and also assumes that the posterior for each mode is Gaussian. In contrast, the VD-GPB2 filter propagates a Gaussian mixture for each mode in the prediction step. In the update step, the VD-GPB2 filter performs a KLD minimisation to have a Gaussian density for each mode. Simulation results show the benefits of the VD-IMM and VD-GPB2 filters compared to previous alternatives.

Position-independent KV cache reuse aims to reduce latency in retrieval-augmented generation by reusing chunk-level KV caches across prompts. We show that current evaluations of KV cache reuse techniques rely on measurements that fail to faithfully capture the loss of accuracy attributable to reuse, often artificially inflating the reported effectiveness. We also show that existing datasets do not exhibit the reuse dynamics needed to thoroughly evaluate such techniques. To address these issues, we propose an evaluation methodology that measures this accuracy loss without ambiguity and we introduce Boxoffice, a tool that programmatically generates evaluation datasets that exercise challenging KV cache reuse patterns.

Linear dynamics of the small amplitude perturbations in the antiferromagnetic multiferroics is analytically considered. Equilibrium state in the considered regime is assumed to be cycloidal structure both for the antiferromagnetic vector and the nonzero magnetization vector (presence of weak ferromagnetism in the system is included). The electric polarization of spin origin related to the "noncollinear" spins is considered and its influence on the spin dynamics is included. The dynamical electric susceptibility tensor is obtained to demonstrate response of the multiferroics on the alternating electric field. Existence of two polarization projections is found, response of each of them on two projections of the electric field perpendicular to the cycloid direction is presented. Different roles of the in plane and out of plane electric perturbations is demonstrated analytically. Essential role of the low frequency gapless spin wave in the dielectric response is described. Contributions of the spiral structure and the weak ferromagnetism in the dielectric response are specified.

Let $X=\mathbb{P}^n$, where $p=n+1$ is prime. Consider the orbit of the standard numerical exceptional basis in $K_0(X)$ under mutations, sign changes, and isometries of the Euler form. We construct an invariant of this orbit: for every basis from the orbit, the square of rank of all basic vectors art congruent to $1$ modulo $p$. For $\mathbb{P}^4$ and $\mathbb{P}^6$, we present explicit numerical exceptional bases violating this congruence; hence the action is not transitive. We also establish a stronger obstruction modulo $p^2$ and use Polishchuk's theorem to show that no vector of the constructed bases is the class of an exceptional object. Finally, we prove that for every prime $p$, the category $D^b(\operatorname{Coh}\mathbb{P}^{p-1}_{\mathbb C})$ does not contain a pair of mutually orthogonal exceptional objects.

We present the dynamic rotation-stacked visibility graph (dRVG), an online motion planner that guides polygonal robots to specified goals in initially unknown, static environ- ments. It merges local roadmaps from successive observations to plan collision-free translations and rotations without a uniform position grid. A spatial quadtree schedules sensing goals across regions to reduce repeated visits while retaining all orientation configurations for routing. Under exact sensing and geometric computation and star-shaped robot and envelope assumptions, dRVG with center scans is resolution-complete relative to full- map RVG at the same angular resolution. In experiments using footprint scans, dRVG solves all 140 cases across 20 difficult maps and seven angular resolutions within a 20 s planning budget, with a median planning time of 1.18 s at 360 orientation layers. Six microMVP demonstrations illustrate the complete online planning loop on a physical robot.

HfO$_2$-based ferroelectric tunnel junctions (FTJs) are promising candidates for scalable non-volatile memory, but simultaneously achieving a high tunneling electro-resistance ratio (TER) and a low resistance-area (RA) product remains challenging. To address this challenge, this work introduces non-uniform quantum well (QW) and barrier thickness engineering in HfO$_2$-based multi-QW FTJs using a self-consistent Preisach-based ferroelectric (FE) model integrated with the coherent and inelastic non-equilibrium Green's function (NEGF) formalism. The non-uniform well and barrier configuration produces a wide range of FTJ design landscapes due to closely spaced, broad resonant states in the low resistance state (LRS) and a larger separation in the high resistance state (HRS), resulting in strong polarization-dependent resonant transmission with TER reaching the order of $\mathbf{1\times10^{8}\%}$ and an LRS RA product as low as $\mathbf{1~\Omega\cdot\mathrm{cm}^{2}}$ at read bias and in the presence of scattering. By incorporating self-consistent elastic scattering into the NEGF framework, we also show that elastic scattering can positively influence the TER and RA performance of non-uniform FTJs by progressively increasing the overlap of the closely spaced resonances. Overall, the results establish non-uniform QW and barrier thickness as an effective and robust design parameter for controlling resonant-state alignment and achieving a favorable combination of high TER and low RA in HfO$_2$-based multi-QW FTJs.

This proof-of-concept paper demonstrates how the Kalman filter, as a brain imaging method, can be enhanced by incorporating raw diffusion tensor imaging (DTI) data without tractography, in addition to EEG recordings. An efficient algorithm is designed to streamline the otherwise tedious process of inferring connectivity between brain regions from DTI data. The DTI-based evolution model is applied to the Kalman filter and the Standardized Kalman filter, and these are compared with their conventional counterparts using the random walk evolution model. The numerical experiments use synthetic somatosensory and auditory evoked potentials. The results show that the DTI-modelled Kalman filter can obtain deep activity in the brainstem and thalamus. Moreover, the connection model limits the estimated spreads to the correct or nearest anatomical brain region.

Third-party libraries (TPLs) are widely used in Android apps, but their reuse can introduce security risks and interfere with downstream program analyses. Existing Android TPL detection approaches face two key limitations: their hand-crafted features are fragile under aggressive code transformations, and their whole-library matching strategies are ineffective when apps retain only part of a TPL. In this paper, we propose LibFan, a learning-based Android TPL detection approach based on context-aware functional modeling. It realizes this modeling through two complementary components: context-aware contrastive learning at the method level and functional partitioning at the library level. At the method level, it learns semantic representations through contrastive training while incorporating outgoing call relationships and class-level context, improving robustness to obfuscation, shrinking, and optimization. At the library level, it partitions each TPL into functionally coherent units and determines library presence using the best-matching partition, thereby accommodating partial library reuse. To evaluate LibFan, we construct a new benchmark comprising 200 apps and 46 vulnerable TPLs, with each app compiled under four transformation configurations. Under the most challenging R8 full mode, LibFan achieves F1 scores of 81.3% at the library level and 47.6% at the version level, representing relative improvements of 64.9% and 35.6% over the state of the art, respectively.

We construct an exact static, magnetically charged solution of four-dimensional Einstein–Maxwell–dilaton theory that generalizes the centered Reissner–Nordström black hole in a Bertotti–Robinson magnetic background. Its pure-background limit is the magnetic EMD deformation of Bertotti–Robinson spacetime. Using the Emparan–Teo solution-generating technique, the charged construction reduces in canonical Weyl coordinates to replacing the Schwarzschild horizon rod by the Reissner–Nordström rod of half-length $\sigma=\sqrt{m^2-e^2}$ and integrating the resulting nonlinear background–rod interaction. This yields a completely explicit solution for arbitrary dilaton coupling $\alpha$, with the expected special limits and numerical verification of the full field equations. The horizon exhibits a coupled mechanical, electromagnetic and intrinsic response to the monopole–background interaction. The residual conical stress is tied to north–south magnetic polarization; increasing the background field produces the ordered reversal scales $B_{\rm pole}<B_{\rm crit}<B_{\rm eq}$, independent of $\alpha$ at fixed seed parameters $(m,e)$, while Gauss–Bonnet identifies the conical stress with the integrated distributional Gaussian-curvature contribution at the singular pole. Along the fixed-$(m,B,\alpha,C)$ near-extremal path considered here, every $\alpha>0$ gives vanishing horizon area and divergent curvature, whereas a correlated near-extremal strong-field limit yields a universal magnetic-reversal law.

The number of unlabeled regular graphs can be expressed as an average of fixed-point counts over vertex permutations, but evaluating each fixed-point count still requires the degree constraints to be enforced. We give an exact recurrence that processes one complete permutation cycle at a time and records the remaining cycles only by their lengths and residual degrees. The recurrence combines internal edge orbits with orbits joining distinct cycles, while binomial and multinomial coefficients retain the multiplicities of choices that lead to the same remaining state. We prove that this state description is sufficient under complete-cycle elimination and derive bounds on the number of states and transitions. For every fixed degree, the resulting algorithm has an $\exp(O(\sqrt n))$ upper bound in the number of vertices, including integer-arithmetic costs. The quartic case requires only four positive residual-degree classes for each cycle length. Small-instance comparisons with a separately implemented, vertex-indexed edge-orbit calculation verify both regular and nonuniform residual-degree inputs. The quartic calculation gives unrestricted and connected counts through order 50, including 22 orders beyond the corresponding reference tables through order 28. Connected counts are recovered by the inverse Euler transform, and all 22 identity-permutation contributions for orders 29–50 agree with the published labeled counts. The nonidentity fixed-point terms at these orders have not been independently recomputed.

This work presents an analytical, parameter-free derivation of the lepton mixing matrix and active neutrino mass spectrum from an icosahedral $A_5$ flavor manifold coupled to the three-generation Iwahori-Hecke algebra $H_3(q)$. Partitioning the icosahedral vertex curvature across the six fundamental Weyl chambers of $H_3(q)$ fixes an elementary angular defect $\Delta_{AD} = \pi/18$, unifying ultra-high-energy mass generation and low-energy flavor mixing as dual realizations of a single geometric invariant. At the topological braiding threshold $\mu \sim M_0$, the right-handed Majorana scale $M_0$ breaks scale invariance and drives the five-dimensional Temperley-Lieb quotient into its hyperbolic regime with loop modulus $d'_{AD} = 2\cosh\Delta_{AD}$, where Quantum Yang-Baxter Baxterization projects the algebraic roots onto a hierarchical heavy spectrum $M_1 > M_2 > M_3 > 0$. Integrating out and inverting these states via a flavor-isotropic Seesaw mechanism Type-I locks in the normal mass hierarchy with $m_1 \approx 3.64$ meV, $\sum_i m_i \approx 63.5$ meV, and $m_\beta \approx 9.45$ meV. Simultaneously, probability conservation requires analytic continuation onto the compact unitary circle, factorizing the mixing matrix into the $A_5$ Golden Ratio baseline, a unitary boundary twist generated by the longest Coxeter involution, and a discrete Majorana parity matrix. This geometry yields $\theta_{13} = 8.49^\circ$, $\theta_{12} = 32.11^\circ$, $\theta_{23} = 45^\circ$, and maximal Dirac CP violation, $\delta_{CP} = \pm \pi/2$, while discrete $SO(3)$ parities quantize the relative Majorana phases, $\alpha_{13} = -\pi, \alpha_{23} = 0$, preventing $0\nu\beta\beta$ decay cancellation, $m_{\beta\beta} \approx 1.14$ meV, and suppressing renormalization group drift to $\dot{\theta}_{ij} \sim 10^{-7}$ rad.

This work explores interference coordination techniques (inter-cell interference coordination, ICIC) based on fractional frequency reuse (FFR) as a solution for a multi-cellular scenario with user concentration varying over time. Initially, we present the problem of high user concentration along with their consequences. Next, the use of multiple-input multiple-output (MIMO) and small cells are discussed as classic solutions to the problem, leading to the introduction of fractional frequency reuse and existing ICIC techniques that use FFR. An exploratory analysis is presented in order to demonstrate the effectiveness of ICIC techniques in reducing co-channel interference, as well as to compare different techniques. A statistical study was conducted using one of the techniques from the first analysis in order to identify which of its parameters are relevant to the system performance. Additionally, another study is presented to highlight the impact of high user concentration in the proposed scenario. Because of the dynamic aspect of the system, this work proposes a solution based on machine learning. It consists of changing the ICIC parameters automatically to maintain the best possible signal-to-interference-plus-noise ratio (SINR) in a scenario with hotspots appearing over time. All investigations are based on ns-3 simulator prototyping. The results show that the proposed Q-Learning algorithm increases the average SINR from all users and hotspot users when compared with a scenario without Q-Learning. The SINR from hotspot users is increased by 11.2% in the worst case scenario and by 180% in the best case

This paper investigates the periodic homogenization of a two-phase elasto-plastic material in the framework of $\Gamma$-convergence. It establishes the link between the homogenized functional and that which was previously obtained in [12] in the context of two-scale convergence. Although there is no gap between the two formulations and that involving two-scale has the hallmark of a (two-scale) elasto-plastic problem, we are unable to positively ascertain the elasto-plastic character of the homogenized energy except in a one-dimensional setting.

Vision-language models (VLMs), despite their success in optical character recognition (OCR) tasks, are vulnerable to typographic attacks and have a fragile structure for images with multiple text layers. In this study, the DecoyBench dataset was created using the Decoy Font method. The dataset consists of 300 images, each containing text with sharp contour lines superimposed on another text with soft shading. Six recent closed-source models from three different model families were evaluated using this dataset under two different prompting conditions (naive and guided) and at two different resolutions ($512\times512$ and $64\times64$). A validation study showed that human participants could read both text layers with high accuracy. In contrast, the models, with most variants and both prompting methods, read the contour text with near-human accuracy at high resolution, but almost never fully extracted the shading text. At low resolution, the contour text could not be read by either the models or humans, while the shading text could be extracted with high accuracy. The findings indicate that the evaluated VLMs exhibit a consistent behavioral limitation when processing typographic structures containing multiple spatial frequency layers.

Auditory Attention Detection (AAD) utilizes electroencephalographic (EEG) signals to identify a target speaker in a multi-speaker environment. Despite considerable progress, existing deep learning architectures often lack explicit mechanisms for handling noisy EEG data. To address this limitation, we propose Auditory Focus Attention Networks (AFA-Net), a machine learning framework that replaces vanilla attention with a simple yet flexible differential attention mechanism to help focus on task-relevant neural activity. AFA-Net achieves an upward accuracy of 96.8% at the 2s decision window, while using substantially fewer parameters than most existing methods. To the best of our knowledge, AFA-Net is among the first frameworks to explicitly try to combat EEG noise to improve AAD.

Prior work established that a probe can decode an in-context binding on model errors and that probe-guided steering can repair some of them. We follow probe accuracy, model output, and steering response across public pretraining and post-training checkpoints. Probe accuracy rises during Pythia pretraining, while probe-guided steering moves from negligible all-trial benefit to a larger benefit at two model sizes. Saved scores distinguish probe-correct errors with low and above-uniform model probability for the correct candidate. Oracle-target steering already repairs many early errors, but saved aggregates cannot separate target quality from intervention sensitivity. A held-out comparison of decoders trained on the final state or candidate logits finds no detected final-state advantage on late-checkpoint model errors. An information-theoretic counterexample explains why decodability on errors alone cannot establish discarded output information. The connection to downstream omissions remains open.