Blazars are conventionally classified into BL Lac objects and flat-spectrum radio quasars (FSRQs), commonly associated with radiatively inefficient and efficient accretion onto supermassive black holes, respectively. Increasing evidence, however, suggests that this division is not strictly discrete, with several sources occupying intermediate or transition-like spectral states. Since the photon index traces the evolution of the non-thermal emission spectrum, it provides a useful probe of jet energetics, particle acceleration, and radiative processes across blazar populations. Using multi-mission observations from Swift-XRT, Swift-BAT, NuSTAR, ROSAT, Chandra, XMM-Newton, NICER, AstroSat, TeVcat, and archival VizieR compilations, we investigate the distribution and long-term evolution of X-ray and TeV photon indices across multiple blazar subclasses. We identify broad overlap regions in photon-index space linking EHBL, HBL, IBL, LBL, and FSRQ-like populations, suggesting a continuous rather than sharply separated spectral distribution. Across X-ray instruments, the intermediate regime is concentrated near $Γ_{\mathrm{X}} \approx 2$, typically spanning $Γ_{\mathrm{X}} \sim 1.5$--$2.2$. Multi-epoch observations reveal substantial intra-source spectral evolution, including stochastic variability in Mrk~421 and state-dependent transitions in OJ~287. Several sources exhibit spectral-index changes of $ΔΓ_{\mathrm{X}} > 0.5$, while occupancy of the intermediate regime reaches $\sim22$--$43%$ depending on instrument. Multiple objects repeatedly traverse spectral regions connecting traditionally distinct subclasses, supporting their interpretation as candidate transition-like blazars. Overall, the results favor a framework in which blazar subclasses represent overlapping and evolving spectral populations driven by long-term changes in jet emission and radiative processes.

The growing adoption of edge computing has created an increasing need for workloads capable of operating under strict resource and energy constraints. Neuromorphic computing, and spiking neural networks (SNNs) in particular, offers an energy-efficient alternative to conventional machine learning through event-driven computation. However, how SNN workloads behave when deployed within modern container orchestration frameworks, especially in edge environments, remains largely unexplored. This paper investigates the feasibility of deploying and orchestrating SNN workloads in a virtual edge environment using Kubernetes, focusing on end-to-end latency, throughput, classification accuracy, infrastructure overhead, and runtime behavior under concurrent load. Experiments were conducted on a single-node K3d cluster running on a Windows 11 host with WSL2 and Docker Desktop. The results show that SNN workloads are highly sensitive to resource availability. Restricting CPU to 0.5 cores increased median latency by 47.6x and reduced throughput by 49x, while the most constrained configuration failed due to insufficient memory. Classification accuracy remained stable across all working configurations. From an orchestration perspective, K3d successfully deployed and scaled SNN workloads, though its default round-robin routing policy introduced significant tail latency under replica scaling, highlighting a mismatch between stateless load-balancing assumptions and long-running inference workloads. Overall, this study provides a baseline for deploying neuromorphic workloads in containerized edge environments and highlights the importance of resource provisioning and orchestration configuration. Future work should explore improved routing strategies, memory optimization, and validation on physical edge hardware.

Large Language Models (LLMs) have shown increasing potential in automating model-driven software engineering tasks, particularly in generating models conforming to Domain Specific Languages (DSLs) from natural language. While most existing approaches rely on large proprietary models, their high cost and limited deployability hinder broader adoption. In this paper, we evaluate whether open-source LLMs of varying sizes (0.5B to 32B parameters) can generate DSL-conformant models using only few-shot prompting, without any fine-tuning. Our evaluation focuses on key model-driven engineering (MDE) requirements, including syntactic validity, semantic completeness, and inter-model reference consistency. We extend our prior work by moving from generating user interface models (referred to as "UI models" in this paper) over fixed, predefined data schemas ("data models") to generating both the UI and data models entirely from scratch. This shift serves two purposes: first, it highlights the LLM's ability to infer domain-specific relationships and maintain consistency across multiple interconnected models; second, it allows us to generalize earlier findings by testing DSL generation across models of different natures and structural roles. Our structured evaluation combines automatic parsing and expert feedback across 39 LLMs, revealing that several compact models (e.g., \texttt{gemma3:12b}, \texttt{mistral:7b-instruct}) approach or match the quality of much larger models. These findings demonstrate the feasibility of using smaller, open-source LLMs for grammar-conformant DSL generation in MDE workflows, offering a cost-effective and deployable alternative to closed LLMs.

Non-Hermitian physics enables novel control over open quantum and wave systems, but selectively isolating individual modes without delicate balancing of gain and loss remains challenging. Here we introduce a gauge-engineering method in directed-graph networks that support geometry-protected pure decay modes-eigenstates exhibiting smooth exponential amplitude decay along directed paths. In fully connected configurations, a single dominant mode naturally emerges with a large, tunable energy gap from the rest. By adding synthetic gauge fields via phase-compensated non-reciprocal hopping, we can promote any desired pure decay mode to the dominant position, while preserving its amplitude profile. The approach extends to simultaneous selection of paired modes in half-connected graphs and customizable multi-mode distributions in higher dimensions via orthogonal folding. Our method enables robust, loss/gain-free control over mode profiles, advancing applications in single-mode lasers, sensors, and quantum processing.

We consider a class of C*-algebras C(X) associated with quantum spaces such as spheres, projective spaces, and lens spaces. We introduce a non-self-adjoint operator algebra A together with an explicit functor from the category of representations of A to that of C(X). We then construct explicitly a family of one-dimensional representations of A that parametrise the entire spectrum of C(X).

Cross-fitting is a key ingredient in many semiparametric estimation procedures, such as double/debiased machine learning (DML), enabling valid estimation of low-dimensional targets in the presence of high-dimensional nuisance functions by enforcing out-of-sample use of nuisance predictions. crossfit is an R package that provides a general-purpose, estimator-agnostic cross-fitting engine. Users specify (i) a target functional and (ii) a directed acyclic graph (DAG) of nuisance models, with node-specific training fold widths and target-specific evaluation windows. The engine executes a reproducible schedule over folds, panels, and repetitions, returning either a scalar estimate (mode="estimate") or a cross-fitted predictor function for application to new data (mode="predict"). Beyond standard cross-fitting, crossfit implements fold-allocation modes that control how training data are shared across nuisance components, including disjoint and independence-enforcing allocations that duplicate reused nodes to reduce dependence between nuisance branches. The implementation targets simulation-heavy benchmarking and method development, with explicit and auditable schedules, defensive validation of specifications and nuisance dependencies, reuse-aware caching to avoid redundant refits, and failure isolation policies for large experiment grids. The crossfit package is available on CRAN, openly developed on GitHub under GPL-3, and is intended as a lightweight, tested foundation to prototype and empirically evaluate cross-fitted estimators with explicit control over fold geometry, dependence, and computation.

In recent years, the performance of automatic speech recognition (ASR) systems has made considerable progress. Unfortunately, for people with speech impairments, such as people treated for oral cancer (OC), ASR performance is still lagging behind. The scarcity and variability of OC speech data makes development of ASR models for this type of speech difficult. In this work, we use data augmentation and large language model (LLM) error correction to mitigate this problem. We apply various augmentation techniques on a corpus of Dutch oral cancer speech to create synthetic data, and evaluate their effect on ASR performance. We finetune Whisper and Massively Multilingual Speech (MMS) models for each augmentation technique and observe, on average, an 8% relative decrease in Word Error Rate (WER) when including data created using text-to-speech (TTS). When employing LLMs for error correction, we see a further 21.4-26.2% relative decrease in WER for finetuned ASR models and a 10.0% relative decrease for non-finetuned models. Overall, we achieve a 40% relative WER decrease for Whisper and a 50% relative WER decrease for MMS, indicating that a combination of data augmentation and LLM correction is a viable strategy for the recognition of OC speech.

Double parton scattering provides a sensitive probe of multi parton correlations inside hadrons. In this work we present a numerical study of unintegrated double parton distribution functions constructed from non-factorized collinear DPDFs. As input we use the GS09 DPDFs and evolve them to unequal scales with a numerical double DGLAP evolution framework, which is validated through the corresponding momentum sum rule. We investigate MRW-inspired prescriptions for generating transverse momentum dependence in the double parton case. In particular, we study the double modified KMRW approach (DMKMRW), the double virtuality ordered MRW (DVO-MRW) model, and a normalization-matched version of the latter. These prescriptions can be applied directly to the full collinear DPDF, including its non-homogeneous component, and avoid the piecewise treatment required in the conventional LO-MRW construction. We analyze the normalization, transverse momentum dependence, flavor dependence, and sensitivity to longitudinal DPDF correlations of the resulting distributions. The DMKMRW model is normalization preserving by construction, while the DVO-MRW model shows nontrivial normalization deviations that are removed in the matched version. Non-factorized effects are strongly channel dependent: in DMKMRW they enter mainly through longitudinal DPDF correlations, whereas in the virtuality ordered models they also modify the transverse momentum shape. The largest deviations occur near the double parton kinematic boundary and in channels affected by valence-number and quark-antiquark correlations.

This paper presents a data-driven framework for uncertainty propagation under unmeasured or statistically unmodeled (unstructured) disturbances. We consider residual disturbances, which consolidate all unstructured disturbances into a single quantity that can be estimated from data. Under mild assumptions, the resulting stochastic predictor is causal and distributionally consistent, enabling efficient uncertainty quantification through polynomial chaos expansions and higher-order Chebyshev inequalities. The proposed method is validated using experimental data from a smart home in Norway.

In this paper, we introduce a symmetrization technique for the distributional gradient of a function of bounded variation in the anisotropic setting. This generalizes the result obtained in the Euclidean case in [Amato-Gentile-Nitsch-Trombetti, 2024] by separating the absolutely continuous part of the anisotropic gradient from its singular part. Our main result is an $L^1$ comparison between the function and its anisotropic symmetrization. Moreover, as an application, we derive isoperimetric inequalities for some geometric functionals related to the torsional rigidity.

The distance dependent Chinese Restaurant Process (ddCRP) provides a flexible prior distribution for clustering observations, incorporating covariate information through pairwise distances and accommodating a rich variety of cluster structures. When cluster parameters are conjugate to the likelihood, Bayesian inference is straightforward. In the non-conjugate setting, however, inference becomes substantially more challenging due to the trans-dimensional parameter spaces that arise as cluster assignments change. We develop a reversible jump Markov chain Monte Carlo (RJMCMC) framework to address this challenge, targeting the dimension-changing nature of cluster parameter vectors when observation assignments are updated. We introduce and compare several proposal strategies for birth and death moves, including prior-based, independence, and data-driven moment-matching proposals that target regions of high posterior density. For fixed-dimensional moves, we propose a posterior resampling strategy that improves acceptance rates while maintaining computational efficiency. Through a simulation study and an application to Old Faithful eruption durations, we demonstrate moment-matched proposals offer a principled, data-driven alternative to prior-based proposals. The resulting methodology provides a general RJMCMC framework for ddCRP models with non-conjugate likelihoods, demonstrated here on both discrete and continuous observation models.

In this study, we develop an interface-contact simulation framework based on physical criteria and machine-learning-assisted classification to describe coalescence and bouncing within a unified formulation. The framework realizes interfacial coalescence and bouncing through the fusion and generation of multiple volume-of-fluid fields. When adjacent interfaces are predicted to coalesce, multiple VOF fields are collapsed into a single VoF field. When approaching interfaces are predicted to bounce, a single VOF field is regenerated into multiple VOF fields, allowing the interfaces to continue evolving independently. With this treatment, the difficulties associated with topological transition, regime-map identification, increasing computational demand, and stochastic behavior during interfacial approach are separated from the interface-tracking procedure. These decisions are instead assigned to a physics-guided machine-learning model with strong adaptability. This strategy avoids the direct resolution of an ultrathin gas film and reduces the dependence on empirical molecular-force parameters. Simulations of droplet--droplet collisions show that the proposed framework can reproduce both coalescence and bouncing over different impact conditions. By further introducing a drainage-time criterion, the framework is extended to the simulation of droplet impact on a liquid surface. For this problem, the numerical results agree well with both previous experimental observations and the present experiments. Moreover, the framework captures the complete sequence of bouncing followed by subsequent coalescence within a single simulation, These results demonstrate that the proposed framework has strong adaptability for interfacial contact problems and provides a unified modeling route for droplet coalescence, bouncing.

The semiconductor industry is foundational to modern technology, yet its complex global multi-relational firm network remains poorly understood, posing challenges to scientists, firms, and policymakers. Traditional analysis relies on proprietary databases that are often expensive, incomplete, and slowly updated, limiting their ability to capture rapidly evolving dependencies. Here, we demonstrate that a novel, generalizable methodology combining Large Language Models (LLMs) with open web data can reconstruct this network and its structural dynamics at scale. We identify and classify supply-chain, partnership, and ownership links from 170 million semiconductor firm webpages, yielding a temporal network of over 1,300 linked firms. We validate link-extraction quality (Precision: 0.884; F1-score: 0.784), network overlap and complementarity with a proprietary database, and consistency with aggregate economic data. Our network reveals a temporary 9% decline in edges during the 2022 chip shortage, rapid increases in the centrality of AI supply-chain bottleneck firms such as NVIDIA, and geographic realignment of interfirm relations amid geopolitical turbulence. This generalizable framework overcomes barriers to transparency and provides essential, up-to-date maps for assessing resilience and informing policy across strategically relevant sectors.

Wegner's $\mathbb{Z}_2$ gauge model is the earliest formulation of pure lattice gauge theory and predicts the topological nature of the confinement-deconfinement transition. In three dimensions ($D=3$), the equilibrium critical behavior of the model is understood in terms of geometrically defined objects, namely loop excitations and Fortuin-Kasteleyn (FK) clusters. This work investigates the critical quench dynamics of this model from a geometric perspective, following quenches from both a high-temperature percolation phase and the zero-temperature ground state. Using time-dependent finite-size scaling analysis, we find that the critical non-equilibrium relaxation of the percolation order parameter is governed by a dynamical exponent $z_{\rm p} \simeq 2.6$, consistent with that associated with the energy density, $z_{\rm c}$. Importantly, the value of $z_{\rm p}$ is robust with respect to the initial quench condition and the choice of geometrical objects. Furthermore, we provide a detailed characterization of the kinetics of different geometrical objects during the evolution from the percolation phase. Notably, we observe that the quench dynamics obeys dynamic scaling in terms of a growing lengthscale, $ξ_{\rm p}(t) \sim t^{1/z_{\rm p}}$, despite the absence of a local order parameter.

We investigate the fluorescence and relaxation dynamics of Cs atoms embedded in a cryogenic argon matrix using spectroscopy measurements combined with diatomic-in-molecule (DIM) simulations. The data reveal complex emission spectra, large Stokes shifts, and slow relaxation effects, indicating strong host-guest interactions and substantial lattice reorganization. Although the spectra are superimposed on a broad background, possibly due to low-symmetry, defect-related, or grain-boundary trapping sites, the main spectral structure is consistent with two dominant trapping environments that give rise to two triplet absorption features with distinct fluorescence behavior of the doublet and singlet components. Polarization measurements further suggest that these sites may differ in symmetry, although a unique structural assignment remains difficult

Turing patterns are a cornerstone of biological self-organization, yet their emergence typically requires finely tuned parameters occupying narrow regions of high-dimensional space. This poses a fundamental challenge: how can evolving biological systems reliably find and exploit such rare conditions? In this work, we propose that common biochemical limit cycles, such as those arising from genetic feedback loops, can act as natural explorers of Turing space. By coupling a reaction-diffusion system to an orbit that modulates some of its parameters, we show that the system can dynamically sweep through Turing-permissive regimes and generate transient spatial patterns. We use an entropy-based measure in Fourier space to quantify pattern formation and demonstrate how cycles enhance the detectability and robustness of Turing islands. We further explore how coupling to positional gradients increases reproducibility, suggesting a route from oscillatory dynamics to stable developmental programs. Our results highlight a powerful mechanism by which nature might bootstrap complex spatial structure from simple temporal motifs.

We address the problem of computing stationary points for non-smooth, non-convex optimization problems. While this topic is well studied in the smooth setting, fewer algorithmic and theoretical results exist for the non-smooth case. Within Difference-of-Convex functions (DC) programming, the well-known DC Algorithm (DCA) is a standard method for computing critical points, whose definition depends on the chosen DC decomposition. More recently, some works have focused on computing directional stationary points - a stronger notion that does not depend on any particular DC decomposition - for specific non-smooth DC programs, where the second DC component is the pointwise maximum of finitely many smooth convex functions. In this contribution, we propose a new and unified approach for identifying directional stationary points of non-smooth DC programs, where both DC components may be non-smooth. Our framework generalizes both the classical DCA and the above recent approaches. It applies when the second DC component is the pointwise maximum of a continuous family of smooth convex functions, and more generally, to any continuous convex function on the whole space. We also establish strong convergence results. Specifically, when the second DC component is the pointwise maximum of finitely many $C^{1,1}$ - smooth convex functions, we prove under the Łojasiewicz inequality that the entire sequence generated by our algorithm converges. This extends previous results requiring global $C^{1,1}$ - smoothness. Finally, we introduce a randomized (stochastic) variant of our method and prove its almost sure convergence, thereby extending our deterministic results to the randomized setting.

We prove a large-data $L^2$-decay estimate for nonlinear dissipative Schrödinger equations with attractive-dissipative power nonlinearity. The main difficulty is the lack of sign definiteness of the standard energy when $\Reλ<0$, which prevents the usual energy argument from directly yielding a uniform gradient bound. We introduce an augmented energy, obtained by adding a suitable multiple of the decreasing $L^2$-norm to the standard energy. This produces an additional dissipative term and gives a direct uniform-in-time $H^1$ bound without the iteration argument used in previous works. Consequently, for arbitrary initial data in the weighted energy space $Σ= H^1 \cap \mathcal{F}H^1$, we obtain the decay rate previously known under the strong dissipative condition throughout the sharp decay range $1<p\le 1+2/d$. This removes the remaining restriction $p\le 1+4/(3d)$ in the attractive-dissipative case.

We show theoretically that a superconducting critical temperature can be effectively increased in a high-entropy mixture of electrons belonging to conduction and valence bands. In order to employ the entropy of mixing into the superconducting phase dynamics, we suggest to use a metallic trap that removes quasiparticle excitations from the superconductor. This makes the concentration of Cooper pairs a dynamic variable of the entropy of mixing, and thus affects the Ginzburg-Landau functional of the superconductor effectively reducing the first expansion coefficient or, in other words, increasing the critical temperature.

We study the Temporal Exploration problem, where an agent must visit all vertices of a temporal graph while traversing at most one available edge per time step. Unlike static graphs, which can be explored in linear time, temporal constraints can substantially increase exploration time even when every snapshot of the graph is connected. To better understand the source of this complexity, we focus on a near-static setting and consider always-connected $k$-edge-deficient temporal graphs, in which each snapshot is connected and differs from a fixed underlying $n$-vertex graph by at most $k$ edges. Although such graphs are structurally close to static graphs, they can still exhibit non-trivial temporal behaviour. Prior work showed that these graphs can be explored in $O(kn \log n)$ time steps and established a lower bound of $Ω(n \log k)$, leaving open whether linear-time exploration in $n$ is possible. We resolve this question by showing that any always-connected $k$-edge-deficient temporal graph admits an exploration schedule of length $O(nk \log k)$. Moreover, given such a temporal graph, the corresponding exploration schedule can be computed in polynomial time. The obtained bound is linear in the number of vertices up to a factor depending only on $k$, removes the extraneous logarithmic dependence on $n$, and is nearly optimal. In particular, for constant $k$, our result yields an order-optimal $Θ(n)$ exploration time, showing that temporal exploration in this near-static regime essentially retains the linear-time character of static graph traversal.

The aim of this paper is to provide a different perspective in the study of the rate of convergence of the chaos game algorithm to the attractor of an iterated function system. We prove that for any function $ψ$ with $\lim\limits_{\ve\to 0}ψ(\ve)=\infty$, a typical (in the sense of the Baire category) driver yields a rate of recovery comparable to $ψ$. This result extends the main theorem from Leśniak et al. (Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 157, 2024). Moreover, thanks to the change of perspective, we are able to prove that a typical driver gives arbitrarily slow rate of recovery.

Caesar is a deductive verifier for probabilistic programs. At its core lies HeyVL, a quantitative intermediate verification language based on the real-valued logic HeyLo. HeyVL allows users to express a probabilistic program, its specifications, and proof rules in a programming-language style, so that new proof rules can be easily integrated into the verifier. Caesar translates HeyVL programs into verification conditions, which are then checked using the Z3 SMT solver. It also includes a backend based on probabilistic model checking for a subset of HeyVL. We report on the results of five years of development of Caesar, highlighting its main features and architecture. In particular, we describe recent improvements such as additional proof rules, a model-checking backend, and better diagnostics.

We investigate the propagation of fronts in an inhomogeneous medium within the framework of the $ϕ^4$ model. The inhomogeneity is modeled either as an interface separating regions with different dissipation or as a finite layer with modified dissipation. The propagating front is described in two ways: as a kink solution in an effectively unbounded domain, and as a half-kink in a finite system. The half-kink represents the decay of the unstable state $ϕ=0$ toward the true vacuum. We show that while the effective description based on the kink provides accurate results, applying a similar approach to the half-kink leads to significant deviations from the predictions of the field model. We then demonstrate that a consistent description does exist and propose a modified effective model which reproduces the field-theory results over a relatively broad range of parameters.

Researchers and practitioners in the field of reliability engineering and optimization frequently use active redundancy techniques to intensify the performance of systems. In this article, we study allocation strategies of non-matching active redundancies (spares) in coherent systems consisting of possibly dependent and identical components for achieving better system reliability. The dependence of the components is modeled through copulas using the distortion function. Sufficient conditions are derived to establish optimal allocation strategies for two heterogeneous active redundancies at the component or system levels. Moreover, the results are true for the component lifetimes following a general family of parametric distributions. The results guarantee the likelihood ratio (reversed hazard) ordering between the coherent systems at the component level (system level) active redundancies. Some aging properties are also established in this endeavor. Several examples are provided to demonstrate the theoretical results.

We propose a near-cutoff parallel-plate waveguide haloscope for sub-meV dark matter. The concept retains the large-area openness of a dish antenna while providing cavity-like field enhancement through slow-wave response and coherent accumulation, without relying on a closed standing-wave resonance. For a copper waveguide, the projected dark photon sensitivity reaches $\varepsilon\simeq2.1\times10^{-15}$ near $m_{A'}\simeq 0.1\,\mathrm{meV}$. With an external magnetic field, the same transducer can approach QCD axion parameter space. The waveguide haloscope highlights a sensitive and scalable route toward future sub-meV bosonic dark matter searches.

We study the relations between the triviality of the tangent bundle $TM$ and the generalized tangent bundle $\mathbb{T}M = TM\oplus T^*M$ of a manifold. We show that the generalized tangent bundle of a paralellizable manifold is trivial. We also prove that the converse implication does not hold, by studying the cases of the Möbius strip, spheres and projective spaces. Finally, we relate the triviality of the generalized tangent bundle to generalized geometric structures.

Understanding how travelers form overall evaluations of public transport journeys is critical for improving travel satisfaction and encouraging sustainable mode choice. While travel satisfaction is discussed to influence attitudes and future behavior, the cognitive rules by which moment-to-moment experiences are aggregated into retrospective evaluations remain poorly understood in transport research. Drawing on psychological theories of experienced and remembered utility, this study investigates which temporal aggregation heuristics best predict post-trip travel satisfaction. Using a smartphone-based experience sampling approach, we collected high-frequency on-trip experience ratings and post-trip evaluations for 2576 real-world public transport trips across three German cities. Travel experience was assessed every five minutes during trips using a multi-item scale, allowing direct comparison of competing aggregation rules, including mean experience, peak-end, minimum-end, final moment, and trip duration. Multilevel regression models were estimated to evaluate the explanatory power of each heuristic. Results show that retrospective travel satisfaction is best predicted by a Minimum-End heuristic, combining the most negative moment of the journey and the final experience. Models based on mean experience, peak-end rules, final moment alone, or trip duration performed substantially worse. This pattern indicates that both negative extremes and the final phase of a journey independently contribute to remembered evaluations, rather than overall satisfaction reflecting an average of momentary experiences. The results have important implications for theory and practice, suggesting that targeted interventions at critical negative moments and at trip endings may yield substantial improvements in remembered satisfaction and, ultimately, support shifts toward sustainable mobility.

Suppose we have an observed path from a point process counting event occurrences in a large population. Based on the observed path, we would like to test the null hypothesis that the conditional intensity of the point process belongs to a particular parametric family. We propose a novel approach to conducting such goodness-of-fit tests. The idea is to construct a unitary transformation of a natural parametric testing process such that it converges weakly to a ``standard'' target process, independent of the particular parametric form assumed under the null hypothesis. This transformation therefore paves the way for asymptotically distribution-free goodness-of-fit testing of parametric point processes. We demonstrate the good finite-sample performance of our approach through Monte Carlo simulations of Aalen-type survival processes, without and with censoring, mixture cure models, and software reliability models, and we illustrate its applicability with observed human lifetimes as well as real software failures.

The Nakanishi Fujii Todo (NFT) algorithm, also known as Rotosolve, implements Sequential Minimal Optimization for Variational Quantum Eigensolvers (SMO-VQE) by exploiting the trigonometric dependence of the energy on individual circuit parameters. This enables analytical one-dimensional minimization using only a few , typically two, energy evaluations, but introduces bias in the estimated energy. Although performing additional measurements every few tens of iterations can mitigate bias accumulation, we find that such corrections often degrade optimization performance. In this paper, we analyze the origin and accumulation of bias during the SMO-VQE process. Specifically, we show that the bias can be accurately estimated without additional measurements. Furthermore, we find that bias correction destabilizes optimization along directions with small curvature, whereas the original biased estimator implicitly acts as a regularizer. Based on these insights, we propose a simple regularization method that implements error accumulation while maintaining unbiased energy estimation. The resulting algorithm consistently improves performance across different system sizes, circuit depths, target Hamiltonians, and measurement shots, with minimal hyperparameter tuning.

We investigate completeness for modal Gödel logics with respect to finite Gödel-Kripke models, along with related aspects. It is well known that the logics studied in [4, 11] fail to be complete with respect to finite Gödel-Kripke models. We show that the natural candidate axiomatic extensions do not restore completeness, thereby resolving a 15 year open problem posed in the aforementioned works. We then provide new axiomatizations that are complete for finite models and characterize intermediate witnessing conditions that hold for the basic logics.