Hyper-Ramsey protocols have been successfully implemented on ultra-narrow optical clock transitions to reduce systematic frequency-shifts induced by AC-Stark shift and amplitude pulse variation. However, the compensation remains imperfect against laser probe intensity fluctuation, decoherence and unsuited for external quasi-static or low frequency noise perturbations. Here, we address these limitations by employing dynamical-decoupling methods composed by multiple rotary Hahn-echo pulses toggling probe frequency detunings between opposite signs during interrogating laser pulses. Time-optimized Uhrig sequences of refocusing pulses produce highly contrasted and robust hyper-Ramsey interferences against low-frequency noise distortions caused by environmental factors and imperfections in the probe parameters. Dynamically-decoupled SU(2) hyper-clocks pave the way to universal noise-resilient quantum sensors, unveiling fault-tolerant quantum metrology to track fundamental symmetries and search for new physics beyond the Standard Model.

Model Soups, extending Stochastic Weights Averaging (SWA), combine models fine-tuned with different hyperparameters. Yet, their adoption is hindered by computational challenges due to subset selection issues. In this paper, we propose to speed up model soups by approximating soups performance using averaged ensemble logits performances. Theoretical insights validate the congruence between ensemble logits and weight averaging soups across any mixing ratios. Our Resource ADjusted soups craftINg (RADIN) procedure stands out by allowing flexible evaluation budgets, enabling users to adjust his budget of exploration adapted to his resources while increasing performance at lower budget compared to previous greedy approach (up to 4% on ImageNet).

We present GLOD, a transformer-first architecture for object detection in high-resolution satellite imagery. GLOD replaces CNN backbones with a Swin Transformer for end-to-end feature extraction, combined with novel UpConvMixer blocks for robust upsampling and Fusion Blocks for multi-scale feature integration. Our approach achieves 32.95\% on xView, outperforming SOTA methods by 11.46\%. Key innovations include asymmetric fusion with CBAM attention and a multi-path head design capturing objects across scales. The architecture is optimized for satellite imagery challenges, leveraging spatial priors while maintaining computational efficiency.

This paper presents Bundle Network, a learning-based algorithm inspired by the Bundle Method for convex non-smooth minimization problems. Unlike classical approaches that rely on heuristic tuning of a regularization parameter, our method automatically learns to adjust it from data. Furthermore, we replace the iterative resolution of the optimization problem that provides the search direction-traditionally computed as a convex combination of gradients at visited points-with a recurrent neural model equipped with an attention mechanism. By leveraging the unrolled graph of computation, our Bundle Network can be trained end-to-end via automatic differentiation. Experiments on Lagrangian dual relaxations of the Multi-Commodity Network Design and Generalized Assignment problems demonstrate that our approach consistently outperforms traditional methods relying on grid search for parameter tuning, while generalizing effectively across datasets.

This paper presents variable bitrate lossy image compression using a VAE-based neural network. An adaptable image quality adjustment strategy is proposed. The key innovation involves adeptly adjusting the input scale exclusively during the inference process, resulting in an exceptionally efficient rate-distortion mechanism. Through extensive experimentation, across diverse VAE-based compression architectures (CNN, ViT) and training methodologies (MSE, SSIM), our approach exhibits remarkable universality. This success is attributed to the inherent generalization capacity of neural networks. Unlike methods that adjust model architecture or loss functions, our approach emphasizes simplicity, reducing computational complexity and memory requirements. The experiments not only highlight the effectiveness of our approach but also indicate its potential to drive advancements in variable-rate neural network lossy image compression methodologies.

Several methods of triclustering of three dimensional data require the specification of the cluster size in each dimension. This introduces a certain degree of arbitrariness. To address this issue, we propose a new method, namely the multi-slice clustering (MSC) for a 3-order tensor data set. We analyse, in each dimension or tensor mode, the spectral decomposition of each tensor slice, i.e. a matrix. Thus, we define a similarity measure between matrix slices up to a threshold (precision) parameter, and from that, identify a cluster. The intersection of all partial clusters provides the desired triclustering. The effectiveness of our algorithm is shown on both synthetic and real-world data sets.

The Unified Modeling Language (UML) is a standard for modeling dynamic systems. UML behavioral state machines are used for modeling the dynamic behavior of object-oriented designs. The UML specification, maintained by the Object Management Group (OMG), is documented in natural language (in contrast to formal language). The inherent ambiguity of natural languages may introduce inconsistencies in the resulting state machine model. Formalizing UML state machine specification aims at solving the ambiguity problem and at providing a uniform view to software designers and developers. Such a formalization also aims at providing a foundation for automatic verification of UML state machine models, which can help to find software design vulnerabilities at an early stage and reduce the development cost. We provide here a comprehensive survey of existing work from 1997 to 2021 related to formalizing UML state machine semantics for the purpose of conducting model checking at the design stage.

Model Soups, extending Stochastic Weights Averaging (SWA), combine models fine-tuned with different hyperparameters. Yet, their adoption is hindered by computational challenges due to subset selection issues. In this paper, we propose to speed up model soups by approximating soups performance using averaged ensemble logits performances. Theoretical insights validate the congruence between ensemble logits and weight averaging soups across any mixing ratios. Our Resource ADjusted soups craftINg (RADIN) procedure stands out by allowing flexible evaluation budgets, enabling users to adjust his budget of exploration adapted to his resources while increasing performance at lower budget compared to previous greedy approach (up to 4% on ImageNet).

Finding the failure scenarios of a system is a very complex problem in the field of Probabilistic Safety Assessment (PSA). In order to solve this problem we will use the Hidden Quantum Markov Models (HQMMs) to create a generative model. Therefore, in this paper, we will study and compare the results of HQMMs and classical Hidden Markov Models HMM on a real datasets generated from real small systems in the field of PSA. As a quality metric we will use Description accuracy DA and we will show that the quantum approach gives better results compared with the classical approach, and we will give a strategy to identify the probable and no-probable failure scenarios of a system.

Parametric timed automata are a powerful formalism for reasoning on concurrent real-time systems with unknown or uncertain timing constants. Reducing their state space is a significant way to reduce the inherently large analysis times. We present here different merging reduction techniques based on convex union of constraints (parametric zones), allowing to decrease the number of states while preserving the correctness of verification and synthesis results. We perform extensive experiments, and identify the best heuristics in practice, bringing a significant decrease in the computation time on a benchmarks library.

We improve and refine a method for certifying that the values' sizes computed by an imperative program will be bounded by polynomials in the program's inputs' sizes. Our work ''tames'' the non-determinism of the original analysis, and offers an innovative way of completing the analysis when a non-polynomial growth is found. We furthermore enrich the analyzed language by adding function definitions and calls, allowing to compose the analysis of different libraries and offering generally more modularity. The implementation of our improved method, discussed in a tool paper (this https URL), also required to reason about the efficiency of some of the needed operations on the matrices produced by the analysis. It is our hope that this work will enable and facilitate static analysis of source code to guarantee its correctness with respect to resource usages.

The fluid flow transport and hydrodynamic problems often take the form of hyperbolic systems of conservation laws. In this work we will present a new scheme of finite volume methods for solving these evolution equations. It is a family of finite volume Eulerian-Lagrangian methods for the solution of non-linear problems in two space dimensions on unstructured triangular meshes. The proposed approach belongs to the class of predictor-corrector procedures where the numerical fluxes are reconstructed using the method of characteristics, while an Eulerian method is used to discretize the conservation equation in a finite volume framework. The scheme is accurate, conservative and it combines advantages of the modified method of characteristics to accurately solve the non-linear conservation laws with a finite volume method to discretize the equations. The proposed Finite Volume Characteristics (FVC) scheme is also non-oscillatory and avoids the need to solve a Riemann problem. Several test examples will be presented for the shallow water equations. The results will be compared to those obtained with the Roe.

Ensuring the correctness of critical real-time systems, involving concurrent behaviours and timing requirements, is crucial. Timed automata extend finite-state automata with clocks, compared in guards and invariants with integer constants. Parametric timed automata (PTAs) extend timed automata with timing parameters. Parameter synthesis aims at computing dense sets of valuations for the timing parameters, guaranteeing a good behaviour. However, in most cases, the emptiness problem for reachability (i.e., the emptiness of the parameter valuations set for which some location is reachable) is undecidable for PTAs and, as a consequence, synthesis procedures do not terminate in general, even for bounded parameters. In this paper, we introduce a parametric extrapolation, that allows us to derive an underapproximation in the form of symbolic sets of valuations containing not only all the integer points ensuring reachability, but also all the (non-necessarily integer) convex combinations of these integer points, for general PTAs with a bounded parameter domain. We also propose two further algorithms synthesizing parameter valuations guaranteeing unavoidability, and preservation of the untimed behaviour w.r.t. a reference parameter valuation, respectively. Our algorithms terminate and can output sets of valuations arbitrarily close to the complete result. We demonstrate their applicability and efficiency using the tools Roméo and IMITATOR on several benchmarks.

Compression experiments are widely used to study the mechanical properties of materials at micro- and nanoscale. However, the conventional engineering stress measurement method used in these experiments neglects to account for the alterations in the material's shape during loading. This can lead to inaccurate stress values and potentially misleading conclusions about the material's mechanical behavior especially in the case of localized deformation. To address this issue, we present a method for calculating true stress in cases of localized plastic deformation commonly encountered in experimental settings: (i) a single band and (ii) two bands oriented in arbitrary directions with respect to the vertical axis of the pillar (either in the same or opposite directions). Our simple analytic formulas can be applied to homogeneous and isotropic materials and crystals, requiring only standard data (displacement-force curve, aspect ratio, shear band angle and elastic strain limit) obtained from experimental results and eliminating the need for finite element computations. Our approach provides a more precise interpretation of experimental results and can serve as a valuable and simple tool in material design and characterization.

This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are constructed and their theoretical performance is assessed through convergence rates over Sobolev and Hölder smoothness classes. Numerical experiments on simulated and real datasets illustrate the practical relevance of the methodology.

In this paper we prove the soliton resolution conjecture for all times, for all solutions in the energy space, of the co-rotational wave map equation. To our knowledge this is the first such result for all initial data in the energy space for a wave-type equation. We also prove the corresponding results for radial solutions, which remain bounded in the energy norm, of the cubic (energy-critical) nonlinear wave equation in space dimension 4.

We propose a new method for obtaining complete asymptotic expansions in a systematic manner, which is suitable for counting sequences of various graph families in dense regime. The core idea is to encode the two-dimensional array of expansion coefficients into a special bivariate generating function, which we call a coefficient generating function. We show that coefficient generating functions possess certain general properties that make it possible to express asymptotics in a short closed form. Also, in most scenarios, we indicate a combinatorial meaning of the involved coefficients. Applications of our method include asymptotics of connected graphs, irreducible tournaments, strongly connected digraphs, 2-SAT formulae and contradictory strongly connected implication digraphs. Moreover, due to its flexibility, the method allows to treat a wide range of structural variations, including fixing the numbers of connected, irreducible, strongly connected and contradictory components, as well as source-like, sink-like and isolated ones, or adding weights and marking variables.

We show that the Word Problem in finitely generated subgroups of $\textsf{GL}_d(\mathbb{Z})$ can be solved in linear average-case complexity. This is done under the bit-complexity model, which accounts for the fact that large integers are handled, and under the assumption that the input words are chosen uniformly at random among the words of a given length. Our result generalizes to matrices in $\textsf{GL}_d(R)$, where $R$ is a subring of $\mathbb{C}$, of finite rank over $\mathbb{Z}$.

The binary branching Brownian motion in the boundary case is a particle system on the real line behaving as follows. It starts with a unique particle positioned at the origin at time $0$. The particle moves according to a Brownian motion with drift $\mu = 2$ and diffusion coefficient $\sigma^2 = 2$, until an independent exponential time of parameter $1$. At that time, the particle dies giving birth to two children who then start independent copies of the same process from their birth place. It is well-known that in this system, the cloud of particles eventually drifts to $\infty$. The aim of this note is to provide a precise estimate for the total number of particles that were born on the negative half-line, investigating in particular the tail decay of this random variable.

We show the vanishing of higher extension groups and torsion groups between linearisation of additive functors from a semi-additive category satisfying some conditions to a category of vector spaces. In particular, we apply our results to the category of correspondences functors of Bouc-Thévenaz.