For a half-unknotted implanted barbell $β$, we construct two specific pseudo-isotopies, both resulting in that barbell diffeomorphism, and compute the Hatcher-Wagoner invariants for both. We further generalize the results to half-unknotted immersed barbell diffeomorphisms and prove that for every $σ\in π_2 M,γ\in π_1 M$, there is a half-unknotted immersed barbell diffeomorphism $ϕ_β$ with the second induced Hatcher-Wagoner invariant $Θ(ϕ_β)=(0,σ)\cdot [γ]$.

We consider an optimal control problem for infinite horizon systems governed by coupled forward-backward stochastic Volterra integral equations with delay. Using Hida-Malliavin calculus, we prove both sufficient and necessary maximum principles for optimal control of such systems. We establish existence and uniqueness results for a class of infinite horizon backward stochastic Volterra integral equations (BSVIEs).

Continuous integration and delivery (CI/CD) pipelines are critical for sustaining the evolution of large software systems. In regulated industries with legacy technologies, however, pipelines themselves can become a source of technical debt. This paper presents an industrial case study of Bankdata, a cooperative IT provider for Danish banks, where a Jenkins-based COBOL CI/CD pipeline had grown fragile, slow, and tightly coupled to platform-specific logic. The original architecture relied on Groovy scripts spread across four repositories with runtime dependency installation, leading to long execution times, high maintenance costs, and vendor lock-in. We report on the migration to a containerized architecture featuring an abstraction layer for platform logic, simplified repository structure, and a pre-built OCI-compliant image containing COBOL tools and dependencies. The new design achieved an 82% runtime reduction. Our experience highlights lessons on abstraction, containerization, and organizational adoption, offering guidance for modernizing pipelines in legacy, high-security environments.

This paper develops a parametric Koopman operator framework for Stochastic Model Predictive Control (SMPC), where the Koopman operator is parametrized by Polynomial Chaos Expansions (PCEs). The model is learned from data using the Extended Dynamic Mode Decomposition -- Dictionary Learning (EDMD-DL) method, which preserves the convex least-squares structure for the PCE coefficients of the EDMD matrix. Unlike conventional stochastic Galerkin projection approaches, we derive a condensed deterministic reformulation of the SMPC problem whose dimension scales only with the control horizon and input dimension, and is independent of both the lifted state dimension and the number of retained PCE terms. Our framework, therefore, enables efficient nonlinear SMPC problems with expectation and second-order moment constraints with standard convex optimization solvers. Numerical examples demonstrate the efficacy of our framework for uncertainty-aware SMPC of nonlinear systems.

This paper asks what Brouwer might have replied to Dummett's interpretation of intuitionism. Complementing earlier literature, it treats Dummett's rejection of the ontological approach; the charge of psychologism and solipsism; indefinite extensibility; and predicativity. It is argued that Dummett's direct arguments against Brouwerian intuitionism do not settle the matter, and that, on the latter two themes,Dummett's position comes closer to Brouwer's than his own account suggests. The remaining philosophical distance, however, is substantial.

We introduce and analyze a class of valid inequalities for nonconvex quadratically constrained optimization problems (QCQPs) which we call Eigen-CG inequalities. These inequalities are obtained by applying a Chvátal-Gomory (CG) rounding to the well-known eigenvector inequalities for QCQPs, and transferring binary-valid inequalities to the continuous setting via a result of Burer and Letchford (2009). We define three nested subfamilies and prove that they are strictly contained in one another. However, we show that the convex conic closure of two of these subfamilies is equal and, in fact, coincides with the Boros-Hammer inequalities -- a powerful family of inequalities that include, in particular, the triangle and McCormick inequalities. Using this CG perspective, we also prove that dense Eigen-CG inequalities are ineffective when used with the standard SDP+McCormick relaxation. This provides a complementary perspective on what is observed in practice: that sparse inequalities are impactful. Finally, based on these insights, we develop a computational strategy to find sparse Eigen-CG cuts and verify their effectiveness in nonconvex QCQP instances. Our results confirm that density quickly degrades effectiveness, but that including sparse inequalities beyond triangle inequalities can provide significant improvements in dual bounds.

The phase transition in the Vicsek model is widely believed to be associated with spontaneous symmetry breaking of the two-dimensional rotational symmetry $O (2)$. In this paper, we revisit the original Vicsek model introduced in [Phys. Rev. Lett. 75, 1226] and demonstrate that the model lacks $O (2)$ symmetry. As a consequence, we numerically demonstrate that the phase transition reported in the original paper vanishes when the global phase is adaptively chosen.

In the context of finite Abelian groups two problems are presented and solved using quantum computing techniques. The first is the well--known Hidden Subgroup Problem, originally solved by Simon in a landmark work. The second is the Fully Balanced Image Problem, originally introduced by the authors (joint with J. Ossorio--Castillo), which is related to a certain class of mappings (which contains strictly, for instance, the family of group morphisms). Both problems are tackled using a combination of two techniques: first, a conversion into Boolean objects, better suited for quantum computing arguments, and subsequently a custom--tailored algorithm which takes advantage of the Generalised Phase--Kick Back technique.

Renewable energy (RE) generation exhibits pronounced seasonality and variability, and neglecting these features can lead to significant underestimation of long-term power system risks in power supply. While long-term dispatch strategies are essential for evaluating and mitigating tail risks, they are often excluded from existing models due to their complexity. This paper proposes a long-term tail risk assessment and mitigation framework for renewable power systems, explicitly embedding dispatch strategies. A representative scenario generation method is designed, combining multi-timescale Copula modeling to capture RE's long-range variability and correlation. Building on these scenarios, an evolution-based risk assessment model is established, where Conditional Value-at-Risk (CVaR) is employed as a robust metric to quantify tail risks. Finally, a controlled evolution-based risk mitigation scheme is introduced to refine long-term dispatch strategies for mitigating tail risks. Case studies on a modified IEEE-39 bus system incorporating real-world data substantiate the efficacy of the proposed method.

We establish a connection between the superconformal index of $\mathcal{N}=4$ $U(N)$ SYM and the elliptic Ruijsenaars-Schneider integrable system. The index admits an expression in terms of elliptic Macdonald polynomials, which leads to a compact summation over generalized partitions involving the structure constants $B_λ(p,q,t)$ and normalization constants $\mathcal{N}_λ(p,q,t)$. By solving the elliptic Ruijsenaars-Schneider model perturbatively in the elliptic parameter $p$, a systematic expansion of the index in powers of $p$ is obtained. We check that in various limits, namely a deformed 1/2 BPS limit and the large $N$ limit, our formalism reduces to previously known results.

We investigated the nonreciprocal spin-wave properties, including the frequency shift, of a helical equilibrium state in a versatile CoFeB/NiFe bilayer. Through an extension of the dynamic matrix formalism (developed in this work) to an arbitrary non-collinear configuration along a heterostructured multilayered system thickness, we explained the frequency shift via differences in the dynamic dipolar and interlayer exchange interactions arising from the distinct spin-wave mode profiles across the bilayer thickness for counterpropagating modes at the same wave vector. In contrast to recent literature wherein the frequency shift is attributed solely to the dipolar interaction, our results and explanations hereby presented involve a starring role of the interlayer exchange interaction not accounted in current literature. Furthermore, we also found a combination of large frequency shift values and sub-100 nm spin wave wavelengths that can be tuned or even enhanced with the twisting degree of the helical magnetization state by the application of the external field, and with the thickness of the NiFe sublayer, which might be highly relevant for magnonic applications. We validated our model and the physical mechanism that explains the frequency shift using recent simulations and experimental results.

We derive exact tail asymptotics of the Parisian ruin probability for Gaussian risk models driven by locally self-similar Gaussian processes with a power-type deterministic trend. The considered setting includes non-stationary Gaussian processes whose local correlation structure is governed by a self-similar limiting process, extending classical fractional Brownian motion models. The asymptotic behaviour is shown to depend on the interplay between the local variance decay, the self-similarity index, and the trend exponent, leading to several distinct regimes. In each regime, the ruin probability admits an explicit asymptotic representation involving Parisian Pickands-type constants. The analysis relies on a uniform Pickands lemma allowing for families of limiting Gaussian fields, extending existing double-sum techniques and enabling the treatment of locally self-similar Gaussian risk models.

Interior eigenvalue problems for large-scale sparse Hermitian matrices are fundamental in computational science. We propose an adaptive polynomial filtering strategy based on Chebyshev expansion of a step function, integrated into a filtered subspace iteration framework. We establish pointwise convergence bounds in both undamped and damped settings and incorporate an enhanced spurious eigenvalue detection technique to improve efficiency and robustness. At the implementation level, we employ MaSpMM to accelerate the polynomial filtering step. Numerical results demonstrate the efficiency and robustness of the proposed method compared with classical approaches.

We construct and analyze a class of one-dimensional boundary Hamiltonians arising from two-dimensional symmetry-protected topological phases with $\mathbb{Z}_N^{\times 3}$ symmetry on a triangular lattice. Using a cohomology-based transformation, the lattice models for the edge modes are explicitly obtained, and their structure is shown to be governed by the arithmetic properties of $N$. For prime $N$, the boundary theory admits a formulation in terms of mutually commuting Temperley-Lieb algebras. For the composite values of $N$, the models exhibit hierarchical or factorized structures. We demonstrate that all phases can be understood in terms of primary models augmented by local defect degrees of freedom that partition the system into independent segments. Finally, the global symmetry is realized on the boundary in a non-on-site and anomalous manner via a projective representation, directly realizing the corresponding 't Hooft anomaly.

We study continuous time quantum walk on a random comb graph with infinite teeth. Due to localization effects along the spine, the walk cannot go to infinity in the spine direction, while it can escape to infinity along the teeth of the comb. Starting from an initial vertex the walk has a nonzero probability to stay trapped in a finite region. These results are obtained by studying the spectrum and eigenstates of the random Hamiltonian for the graph and analysing its properties. We use both analytic and numerical methods many of which come from the theory of Anderson localization in one dimension.

Hydrogen is widely regarded as a cornerstone of future low-carbon energy technologies, yet the lack of safe, efficient, and reversible solid-state storage materials remains a major barrier to its large-scale deployment. Although porous frameworks and metal hydrides have been extensively explored, far less is known about the ability of dense molecular solids to stabilize hydrogen at near-ambient pressure. Here we show that fully crystalline cubic ice, despite its non-porous nature, can retain molecular hydrogen as an interstitial guest following controlled decompression from a high-pressure hydrogen hydrate precursor. Using synchrotron X-ray diffraction, neutron diffraction, and Raman spectroscopy, we demonstrate that hydrogen is retained within the ice structure up to about 130 K, producing reproducible lattice expansion and distinct spectroscopic signatures. We further show that pure cubic ice can be partially refilled with hydrogen at 0.18 GPa and 130 K, while fully hydrogen-filled cubic structure can be preserved at the same pressure up to 90 K. The retained hydrogen content reaches several percent of the parent hydrate composition, corresponding to gravimetric and volumetric storage densities comparable to those of interstitial hydrogen in metals. These results reveal an unexpected ability of a dense hydrogen-bonded crystal structure to host molecular hydrogen without permanent porosity or chemical bonding, establishing cubic ice as a minimal model for hydrogen-lattice interactions. More broadly, our findings identify dense hydrogen-bonded solids as an unexplored class of materials for hydrogen storage physics, with implications extending from energy materials to planetary and astrophysical ice environments.

Both ILC detector concepts, ILD and SiD, are very complex machines, the assembly and installation of which in the experimental cavern at the ILC interaction point will be complicated endeavours. These procedures require careful planning and logistics, taking into account numerous constraints and boundary conditions. Some of these are described in this document. Especially ILD has already invested significant effort into elaborate installation plans, which will be briefly described in this document. However, with the ILC not being a secured project and a final interaction point not chosen, all these plans have to be considered preliminary and need to be further detailed, taking into account the concrete site-specific and project-specific conditions.

We study top-antitop pair production in proton-proton collisions within the Standard Model Effective Field Theory (SMEFT) at dimension 6. We focus on the top chromomagnetic operator $C_{tG}$ together with the four-quark operators relevant for unpolarized $t{\bar t}$ production. We analyze the top-quark single-differential transverse-momentum ($p_T$) and rapidity ($y$) distributions and the double-differential distributions in $p_T$ and $y$ ($p_T\times y$) at 13~TeV, and we present projections for 13.6~TeV using the same binning. Our highest-order setup combines next-to-next-to-leading-order (NNLO) Standard Model (SM) predictions with approximate NNLO (aNNLO) SM--SMEFT interference corrections. We find that higher-order QCD effects are essential for a stable SMEFT interpretation, yielding substantially more robust bounds and milder parameter degeneracies. The strongest sensitivity is obtained for $C_{tG}$. In the combined highest-order analysis of the 13-TeV results and 13.6-TeV projections, we obtain sensitivity to effective scales up to 3.9~TeV. Our results show that higher-order differential top-pair production provides a precise and theoretically controlled probe of the top chromomagnetic interaction.

We consider data-based predictive control based on behavioral systems theory. In the linear setting this means that a system is described as a subspace of trajectories, and predictive control can be formulated using a projection onto the intersection of this behavior and a constraint set. Instead of learning the model, or subspace, we focus on determining this projection from data. Motivated by the use of regularization in data-enabled predictive control (DeePC), we introduce the use of soft projections, which approximate the true projector onto the behavior from noisy data. In the simplest case, these are equivalent to known regularized DeePC schemes, but they exhibit a number of benefits. First, we provide a bound on the approximation error consisting of a bias and a variance term that can be traded-off by the regularization weight. The derived bound is independent of the true system order, highlighting the benefit of soft projections compared to low-dimensional subspace estimates. Moreover, soft projections allow for intuitive generalizations, one of which we show has superior performance on a case study. Finally, we provide update formulas for soft projectors enabling the efficient adaptation of the proposed data-driven control methods in the case of streaming data.

We provide a complete characterization of those graphons $W$ for which the inhomogeneous random graph $G(n,W)$ is asymptotically almost surely Hamiltonian. The characterization involves three conditions. Two of them constitute the characterization of $G(n,W)$ being a.a.s. connected, as was shown recently by Hladký and Viswanathan. The third condition captures a geometric obstacle which prevents $G(n,W)$ from having perfect fractional matchings.

We present an approach to enumerate graphs whose automorphism group has exactly two orbits. Our method exploits the observation that we can enumerate all graphs whose automorphism group contains a given this permutation group. We obtain the relevant groups via Goursat's lemma. In order to scale the enumeration, we employ additional optimizations that prune irrelevant groups. In total, we enumerate, for the first time, all connected two-orbit graphs of up to 27 vertices, totaling 10,094,721 graphs, pushing the state of the art well beyond what direct enumeration methods can achieve.

Introduction High performance gradients poses a promise for breast diffusion weighted imaging (DWI) but are restricted by physiological limits in whole body scanners. While local nonlinear coils offer higher amplitudes, they often suffer from severe gradient reduction near the chest wall. Methods We introduced an optimization framework incorporating a constraint to control anterior posterior gradient variation. A width based figure of merit was defined to evaluate performance regarding coil efficiency and minimum wire width. A prototype was constructed to validate the design methodology. Results The optimized coil achieved a 2.35 fold efficiency increase over standard linear coils. Compared to previous nonlinear designs, the new constraint reduced spatial variation by 35.7% and improved minimum efficiency near the chest wall by 2.6 fold. Experimental field maps matched simulations with errors under 8%. Discussion The proposed method effectively mitigates the trade-off between gradient strength and spatial uniformity along anterior posterior direction. By enhancing performance in the posterior breast region, the design addresses a critical limitation of previous local coils. Conclusion This framework enables the development of high performance, robust local gradient coils, facilitating the clinical implementation of advanced DWI protocols for breast cancer screening.

We investigate the spectral properties of the Su-Schrieffer-Heeger (SSH) model with sublattice-dependent onsite nonlinearity. Two complementary approaches are employed in our studies. First, Bloch state solutions under periodic boundary conditions are assumed to enable semi-analytical treatment, which allows us to obtain the system's energy band structure and further derive a general expression of the Zak phase that incorporates nonlinearity-induced correction (referred to as nonlinear Zak phase). This analysis reveals that, at sufficiently high nonlinearities, a nonlinearity-induced topological phase transition occurs, marked by a discontinuity in the nonlinear Zak phase. The second approach amounts to numerically obtaining other (non-Bloch) solutions under open boundary conditions, employing the Self-Consistent Field Iterative Method. Its main results include the observation of an edge state's energy that is independent of a nonlinear parameter, a persisting band touching point that only shifts in the presence of perturbations reminiscent of Weyl points in a Weyl semimetal, as well as delocalized solutions that persist even at extreme nonlinearity strengths. These findings illuminate the rich interplay between topology and nonlinearity in lattice models with potential realization in optical/acoustic waveguide settings.

We present the MultiWave C++-framework for adaptive numerical methods approximating hyperbolic balance laws. MultiWave has been designed as a computational laboratory where new mathematical concepts can be quickly implemented and tested. We demonstrate the realisation of an adaptive perturbation discontinuous Galerkin method starting with the mathematical background and proceed to the low-level implementation details. We elaborate on the design choices made in particular regarding the modularity that allows one to extend the code reusing existing infrastructure.

Many problems are known to be solvable in subexponential parameterized time when the input graph is planar. The bidimensionality framework of Demaine, Fomin, Hajiaghay, and Thilikos [JACM'05] and the treewidth-pattern-covering approach by Fomin, Lokshtanov, Marx, Pilipczuk, Pilipczuk, and Saurabh [SICOMP'22] give robust tools for designing such algorithms. However, there are still many problems for which we do not know whether subexponential parameterized algorithms exist. The bidimensionality framework is not able to handle weights or directed graphs and the treewidth-pattern-covering approach only works for finding connected solutions. Building on a result by Nederlof [STOC'20], we provide a framework that is able to solve a variety of problems in planar graphs in subexponential parameterized time for which this was previously not known (where the polynomial part of the running time is usually $O(n^{2.49})$). Our framework can handle weights, does not require solutions to contain only few connected components, and applies to cases where the number of potential patterns of a solution is exponential in the parameter. We then use the framework to show that various weighted problems like Weighted Partial Vertex Cover, Maximum-Weight Induced Forest, Minimum-Weight Rooted Simple Minor, and Maximum-Weight Rooted Parallel Induced Minor allow for subexponential parameterized algorithms. This was previously not known for any of them. Moreover, we present a very easy-to-use fragment of our framework. This fragment allows for significantly simpler proofs in the case of Maximum-Weight Independent Set and Maximum $(k, n-k)$-Cut and is able to show a subexponential parameterized algorithm for weighted versions of Densest $k$-Subgraph. Even the unweighted version was not known before and is stated as an open problem in the existing literature.

In this paper, we present a systematic study on the ground state computation of quantum droplets in homonuclear Bose-Bose mixtures, governed by the extended Gross-Pitaevskii equations (eGPEs) with Lee-Huang-Yang (LHY) corrections. This model captures the formation of self-bound droplets stabilized by the delicate balance between the attractive mean-field interaction and the repulsive quantum fluctuations. We formulate dimensionless energy functionals for both the general two-component system and the reduced single-component density-locked model. To compute the ground states efficiently, we adapt and benchmark various gradient flow discretization schemes, identifying a backward-forward sine-pseudospectral scheme based on the gradient flow with Lagrange multiplier method (GFLM-BFSP) as the robust solver for our simulations. Utilizing this method, we report three main numerical observations: (i) the density-locked model is quantitatively validated as a reliable approximation for ground state properties; (ii) the dimension-dependent convergence rates of the Thomas-Fermi approximation are established in the strong-coupling regime; and (iii) the critical particle number for self-binding in free space is numerically determined, providing a precise correction to the analytical prediction by Petrov [Phys. Rev. Lett. 115, 155302 (2015)].

The non-Hermitian skin effect (NHSE), characterized by extensive boundary accumulation of eigenstates under open boundary conditions, has emerged as a central phenomenon in non-Hermitian physics. Conventionally, the NHSE arises from either non-reciprocal couplings or onsite gain and loss combined with synthetic gauge fields. Existing studies, however, have been largely confined to frameworks with Abelian-coupling, leaving the role of non-Abelian couplings essentially unexplored. Here, we demonstrate that non-Abelian-couplings can generate the NHSE, giving rise to a time-reversal-symmetry-protected Z2 skin effect with pseudospin-dependent boundary localization and dynamical pseudospin separation. Experimentally, we implement a representative four-level model using a programmable topolectrical circuit and directly observe both the predicted NHSE and the boundary-induced pseudospin-inversion reflection. Our work establishes a fundamental link between non-Abelian coupling and non-Hermitian topology, opening new avenues for realizing non-reciprocity-free topological materials and devices.

Java static analysis frameworks are commonly compared under the assumption that analysis algorithms and configurations compose monotonically and yield semantically comparable results across tools. In this work, we show that this assumption is fundamentally flawed. We present a large-scale empirical study of semantic consistency within and across four widely used Java static analysis frameworks: Soot, SootUp, WALA, and Doop. Using precision partial orders over analysis algorithms and configurations, we systematically identify violations where increased precision introduces new call-graph edges or amplifies inconsistencies. Our results reveal three key findings. First, algorithmic precision orders frequently break within frameworks due to modern language features such as lambdas, reflection, and native modeling. Second, configuration choices strongly interact with analysis algorithms, producing synergistic failures that exceed the effects of algorithm or configuration changes alone. Third, cross-framework comparisons expose irreconcilable semantic gaps, demonstrating that different frameworks operate over incompatible notions of call-graph ground truth. These findings challenge prevailing evaluation practices in static analysis and highlight the need to reason jointly about algorithms, configurations, and framework semantics when assessing precision and soundness.

We present a comprehensive, two-decade, multiwavelength variability study of the blazar PKS 1510-089, one of the most prominent and extensively monitored flat-spectrum radio quasars. Using Fermi-LAT $γ$-ray data together with Swift-XRT and UVOT observations spanning 2005-2024, we trace the long-term evolution of its flux, interband correlations, and spectral behaviour across the optical, X-ray, and $γ$-ray bands. We find that the HE $γ$-ray and X-ray flux distributions are log-normal, while the optical distributions are compatible with double-log-normal functions. The latter may be due to contributions from the accretion disk. The range of fluxes in a given band, as well as the fractional variability values are in-line with the expectations that high-energy parts of a given spectral component are more variable than low-energy parts. No obvious cross-correlations exist between the bands over the 20 years of observations. The X-ray and $γ$-ray spectra are variable, but do not show any trend with flux. These results are suggestive of different zones being active in the jet of PKS 1510-089 at any given time. In a previous paper, we used the same techniques to study the high-frequency-peaked BL Lac object PKS 2155-304. Both sources follow the aforementioned trend on the energy-dependent variability of the spectral components, as well as the lack of significant cross-correlations between the studied bands. While PKS 2155-304 exhibits a harder-when-brighter behaviour in its high-energy part of the synchrotron component, no such behaviour could be found in PKS 1510-089. Both sources show orphan flares, which can seemingly happen in any band. In summary, the long-term studies of these two sources reveal that the underlying physics is similar in these apparently different source classes, even though variability patterns keep changing and remain unpredictable.

In this paper, we perform a detailed study of the thermodynamic properties of a charged black hole in bumblebee gravity in the presence of a global monopole. We also analyze the optical characteristics of this black hole solution, highlighting the influence of Lorentz symmetry violation and the global monopole on the black hole shadow. Furthermore, we examine the trajectories of both photons and test particles in this spacetime, showing how the geometric parameters alter their paths. Moreover, we study the dynamics of neutral test particles, with particular attention to the location of the innermost stable circular orbits (ISCOs). Finally, we investigate massless scalar perturbations and derive bounds on the greybody factors, illustrating how the black hole's geometric parameters affect field propagation, energy emission, and radiation sparsity in this background.