Branch-and-bound algorithms (B&B) and polynomial-time approximation schemes (PTAS) are two seemingly distant areas of combinatorial optimization. We intend to (partially) bridge the gap between them while expanding the boundary of theoretical knowledge on the B\&B framework. Branch-and-bound algorithms typically guarantee that an optimal solution is eventually found. However, we show that the standard implementation of branch-and-bound for certain knapsack and scheduling problems also exhibits PTAS-like behavior, yielding increasingly better solutions within polynomial time. Our findings are supported by computational experiments and comparisons with benchmark methods. This paper is an extended version of a paper accepted at ICALP 2025

In typical rare-earth lanthanide compounds, the localized 4\textit{f}-electrons have a weak effect on the electrical conduction, limiting their influence on the Berry curvature and, hence, the intrinsic anomalous Hall effect. A comprehensive study of the magnetic, thermodynamic, and transport properties of single-crystalline NdGaSi, guided by first-principles calculations, reveals a ferromagnetic ground state that induces a splitting of quasi-flat 4\textit{f} electronic bands and positions them near the Fermi energy. The observation of an extraordinarily large intrinsic anomalous Hall conductivity of 1165 $Ω^{-1}$ cm$^{-1}$ implies the direct involvement of localized states in the generation of non-trivial band crossings around the Fermi energy. The angle-resolved photoemission spectroscopy measurements provide direct evidence of non-trivial crossing of the 4\textit{f}-bands with dispersive bands. These results are remarkable when compared to ferrimagnetic NdAlSi, which differs only in a non-magnetic atom (a change in the principal quantum number \textit{n} of the outer \textit{p }orbital) with the same number of valence electrons and does not exhibit any measurable anomalous Hall conductivity.

For any given positive definite binary quadratic form $Q$ with integer coefficients, we establish two results on Diophantine approximation with integers represented by $Q$. Firstly, we show that for every irrational number $α$, there exist infinitely many positive integers $n$ represented by $Q$ and satisfying $||αn||<n^{-(1/2-\varepsilon)}$ for any fixed but arbitrarily small $\varepsilon>0$. This is an easy consequence of a result by Cook on small fractional parts of diagonal quadratic forms. Secondly, we give a quantitative version with a lower bound of this result when the exponent $1/2-\varepsilon$ is replaced by any fixed $γ<3/7$. To this end, we use the Voronoi summation formula and a bound for bilinear forms with Kloosterman sums to fixed moduli by Kerr, Shparlinski, Wu and Xi.

The fact that no Hawking radiation from the final stages of evaporating primordial black holes (PBHs) has yet been observed places stringent bounds on their allowed contribution to dark matter. Concretely, for Schwarzschild PBHs, i.e., uncharged and non-rotating black holes, this rules out black hole masses of less than $10^{-15} M_{\odot}$. In this article, we propose that by including an additional 'dark' $U(1)$ charge one can significantly lower the PBHs' Hawking temperature, slowing down their evaporation process and significantly extending their lifetimes. With this, PBHs again become a viable option for dark matter candidates over a large mass range. We will explore in detail the effects of varying the dark electron (lightest dark charged fermion) mass and charge on the evaporation dynamics. For instance, we will show that by allowing the dark electron to have a sufficiently high mass and/or low charge, our approach suppresses both Hawking radiation and the Schwinger effect, effectively extending even the lifespan of PBHs with masses smaller than $10^{-15} M_{\odot}$ beyond the current age of the universe. We will finally present a new lower bound on the allowed mass range for dark-charged PBHs as a function of the dark electron charge and mass, showing that the PBHs' mass can get to at least as low as $10^{-24}M_\odot$ depending on the dark electron properties. This demonstrates that the phenomenology of the evaporation of PBHs is ill-served by a focus solely on Schwarzschild black holes.

A module $M$ is {called} stable if it has no nonzero projective direct summand. For a ring $ R $, we study conditions under which $R$-modules from certain classes decompose as a direct sum of a projective submodule and a stable submodule. Over {an arbitrary} ring, modules of finite uniform dimension or finite hollow dimension can be decomposed as a direct sum of a projective submodule and a stable submodule. By using the Auslander-Bridger transpose of finitely presented modules, we prove that every finitely presented right $R$-module over a left semihereditary ring $R$ has such a decomposition. Our main focus in this article is to give examples where such a decomposition fails. We give some ring examples over which there exists an infinitely generated or finitely generated or finitely presented module where such a decomposition fails. Our main example is a cyclically presented module $M$ over a commutative ring such that~$M$ has no such decomposition and $M$ is not projectively equivalent to a stable module.

We compute the K-theory of a collection of C*-algebras, which we refer to as boundary C*-algebras, arising as the crossed product C*-algebras of lattice actions on the maximal Furstenberg boundaries of symmetric spaces of noncompact type. As a result, we add new examples to the collection of known isomorphic boundary C*-algebras which are not spatially isomorphic.

The Kirkwood-Dirac (KD) quasiprobability distribution is known for its role in quantum metrology, thermodynamics, as well as quantum foundations. In this work we classify unitary evolutions that preserve KD positivity. We identify conditions under which positivity preservation is equivalent to $l_1$-norm preservation, and exhibit unitaries that preserve positivity on KD-positive distributions while failing to preserve the $l_1$-norm of non-positive ones. We further prove that unitaries inducing stochastic updates of KD quasiprobabilities form a strict subset of the positivity-preserving unitaries. By adapting the classical sampling algorithm of Pashayan et al. [Phys. Rev. Lett. 115, 070501], we obtain efficient simulation methods for all identified classes of positivity-preserving unitaries. Our classification is complete for distributions defined on Fourier-conjugate bases in dimensions $d = p^k$ and $d = pq$, where $p, q$ are distinct primes, as well as for generic randomly chosen bases. As a consequence, no resource theory in the Fourier-conjugate $d=pq$ setting can simultaneously regard KD non-positivity as a monotone and include all efficiently simulable positivity-preserving unitaries among its free operations.

In this paper, we present a unified approach to establish the uniqueness of generalized conformal restriction measures with central charge $c \in (0, 1]$ in both chordal and radial cases, by relating these measures to the Brownian loop soup. Our method also applies to the uniqueness of the Malliavin-Kontsevich-Suhov loop measures for $c \in (0,1]$, which was recently obtained in [Baverez-Jego, arXiv:2407.09080] for all $c \leq 1$ from a CFT framework of SLE loop measures. In contrast, though only valid for $c \in (0,1]$, our approach provides additional probabilistic insights, as it directly links natural quantities of MKS measures to loop-soup observables.

We present new convergence analyses for parallel subspace correction methods for unconstrained semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to a class of nonlinear problems. Our results demonstrate that the elegant theoretical framework developed for singular and nearly singular linear problems can be extended to unconstrained semicoercive and nearly semicoercive convex optimization problems. For semicoercive problems, we show that the convergence rate can be estimated in terms of a seminorm stable decomposition over the subspaces and the kernel of the problem, aligning with the theory for singular linear problems. For nearly semicoercive problems, we establish a parameter-independent convergence rate, assuming the kernel of the semicoercive part can be decomposed into a sum of local kernels, which aligns with the theory for nearly singular problems. To demonstrate the applicability of our results, we provide convergence analyses of two-level additive Schwarz methods for solving certain nonlinear partial differential equations with Neumann boundary conditions, within the proposed abstract framework.

Functional Principal Components Analysis (FPCA) is a widely used analytic tool for dimension reduction of functional data. Traditional implementations of FPCA estimate the principal components from the data, then treat these estimates as fixed in subsequent analyses. To account for the uncertainty of PC estimates, we propose FAST, a fully-Bayesian FPCA with three core components: (1) projection of eigenfunctions onto an orthonormal spline basis; (2) efficient sampling of the orthonormal spline coefficient matrix using a parameter expansion scheme based on polar decomposition; and (3) ordering eigenvalues during sampling. Extensive simulation studies show that FAST is very stable and performs better compared to existing methods. FAST is motivated by and applied to a study of the variability in mealtime glucose from the Dietary Approaches to Stop Hypertension for Diabetes Continuous Glucose Monitoring (DASH4D CGM) study. All relevant STAN code and simulation routines are available as supplementary material.

Ab initio techniques have revolutionised the way in which theory can help practitioners to explore critical mechanisms that govern reactions or properties, and to develop new strategies for materials discovery and design. Yet, their application to electrochemical systems is still limited, due to the challenges electronic structure calculations face in achieving a realistic description of electrified solid/liquid interfaces including, e.g., potential and pH control or free energies of barrier configurations. A well-known example of how novel concepts can extend the scope of simulations is the development of thermostats, which introduced temperature control to electronic structure Density Functional Theory (DFT) calculations. The analogous technique for modelling electrochemical systems - potential control, inherent to most electrochemical experiments - is just emerging. In this review, we critically discuss state-of-the-art approaches to describe electrified interfaces between a solid electrode and a liquid electrolyte in realistic environments. By exchanging energy, electronic charge and ions with their environment, electrochemical interfaces are thermodynamically open systems. In addition, large fluctuations of the electrostatic potential and field occur on the time and length scales relevant to chemical reactions. We systematically discuss the key challenges in incorporating these features into realistic ab initio simulations, as well as the available techniques and approaches to overcome them, in order to facilitate the development and use of these novel techniques by the wider community. These methodological developments provide researchers with a new level of realism to explore fundamental electrochemical mechanisms and reactions from first principles.

We propose an analytical thermodynamic model for describing defect phase transformations, which we term the statistical phase evaluation approach (SPEA). The SPEA model assumes a Boltzmann distribution of finite size phase fractions and calculates their statistical average. To benchmark the performance of the model, we apply it to construct binary surface phase diagrams of metal alloys. Two alloy systems are considered: a Mg surface with Ca substitutions and a Ni surface with Nb substitutions. To construct a firm basis against which the performance of the analytical model can be leveled, we first perform Monte Carlo (MC) simulations coupled with cluster expansion of density functional theory dataset. We then demonstrate the SPEA model to reproduce the MC results accurately. Specifically, it correctly predicts the surface order-disorder transitions as well as the coexistence of the 1/3 ordered phase and the disordered phase. Finally, we compare the SPEA method to the sublattice model commonly used in the CALPHAD approach to describe ordered and random solution phases and their transitions. The proposed SPEA model provides a highly efficient approach for modeling defect phase transformations.

The distance of a stabilizer quantum code is a very important feature since it determines the number of errors that can be detected and corrected. We present three new fast algorithms and implementations for computing the symplectic distance of the associated classical code. Our new algorithms are based on the Brouwer-Zimmermann algorithm. Our experimental study shows that these new implementations are much faster than current state-of-the-art licensed implementations on single-core processors, multicore processors, and shared-memory multiprocessors. In the most computationally-demanding cases, the performance gain in the computational time can be larger than one order of magnitude. The experimental study also shows a good scalability on shared-memory parallel architectures.

Despite the central importance of quantum entanglement in quantum technologies, the understanding of the optimal ways to exploit it is still beyond our reach, and even measuring entanglement in an operationally meaningful way is prohibitively difficult. Here we study two fundamental tasks in the processing of entanglement: entanglement testing, which is a quantum state discrimination problem concerned with entanglement detection in the many-copy regime, and entanglement distillation, concerned with purifying entanglement from noisy entangled states. We introduce a way of benchmarking the performance of distillation that focuses on the best achievable error rather than its yield in the asymptotic limit. When the underlying set of operations used for entanglement distillation is the axiomatic class of non-entangling operations, we show that the two figures of merit for entanglement testing and distillation coincide. We solve both problems by proving a generalised quantum Sanov's theorem, enabling the exact evaluation of asymptotic error rates of composite quantum hypothesis testing. We show in particular that the asymptotic figure of merit is given by the reverse relative entropy of entanglement, a single-letter quantity that can be evaluated using only a single copy of a quantum state -- a distinct feature among measures of entanglement that quantify the optimal performance of information-theoretic tasks.

The combined structural and electronic complexity of iron oxides poses many challenges to atomistic modeling. To leverage limitations in terms of the accessible length and time scales, one requires a physically justified interatomic potential which is accurate to correctly account for the complexity of iron-oxygen systems. Such a potential is not yet available in the literature. In this work, we propose a machine-learning potential based on the Atomic Cluster Expansion for modeling the iron-oxygen system, which explicitly accounts for magnetism. We test the potential on a wide range of properties of iron and its oxides, and demonstrate its ability to describe the thermodynamics of systems spanning the whole range of oxygen content and including magnetic degrees of freedom.

Aqueous metal corrosion is a major economic concern in modern society. A phenomenon that has puzzled generations of scientists in this field is the so-called anomalous hydrogen evolution: the violent dissolution of magnesium under electron-rich (anodic) conditions, accompanied by strong hydrogen evolution, and a key mechanism hampering Mg technology. Experimental studies have indicated the presence of univalent Mg$^+$ in solution, but these findings have been largely ignored because they defy our common chemical understanding and evaded direct experimental observation. Using recent advances in the \emph{ab initio} description of solid-liquid electrochemical interfaces under controlled potential conditions, we described the full reaction path of Mg atom dissolution from a kinked Mg surface under anodic conditions. Our study reveals the formation of a solvated [Mg$^{2+}$(OH)$^-$]$^+$ ion complex, challenging the conventional assumption of Mg$^{2+}$ ion. This insight provides an intuitive explanation for the postulated presence of (coulombically) univalent Mg$^+$ ions and the absence of protective oxide/hydroxide layers normally formed under anodic/oxidizing conditions. The discovery of this unexpected and unconventional reaction mechanism is crucial for identifying new strategies for corrosion prevention and can be transferred to other metals.

Quantum steering is an asymmetric form of quantum nonlocality where one can detect whether a measurement on one system can steer or change another distant system. It is well-known that there are quantum states that are entangled but unsteerable in the standard quantum steering scenario. Consequently, a long-standing open problem in this regard is whether the steerability of every entangled state can be activated in some way. In this work, we consider quantum networks and focus on the swap-steering scenario without inputs and find linear witnesses of network steerability corresponding to any negative partial transpose (NPT) bipartite state and a large class of bipartite states that violate the computable cross-norm (CCN) criterion. Furthermore, by considering that the trusted party can perform tomography of the incoming subsystems, we construct linear inequalities to witness swap-steerability of every bipartite entangled state. Consequently, for every bipartite entangled state one can now observe a form of quantum steering.

Postprandial glucose collected through continuous glucose monitoring (CGM) provides critical information for assessing metabolic capacity and guiding dietary recommendations. Traditional approaches summarize these data into scalar measures, such as 2-hour AUC or peak glucose, potentially overlooking temporal dynamics. We propose analyzing entire CGM trajectories using multilevel functional data analysis (FDA), which accounts for the smooth, hierarchical nature of glucose responses. Applying these methods to AEGIS study participants without diabetes, we illustrate how FDA characterizes variability in postprandial responses and links dietary/patient characteristics to glucose dynamics. We further extend the r-square metric to hierarchical functional models to quantify explanatory power. Our results show that dietary effects vary across the 6-hour postprandial window-for example, fiber blunts responses after 90 minutes, while fats reduce early rises within 50 minutes. Moreover, metabolic responses differ between normoglycemic and prediabetic individuals. These findings demonstrate that functional approaches reveal temporal and stratified insights into postprandial glucose regulation that scalar methods cannot capture.

With reference to a binary outcome and a binary mediator, we derive identification bounds for natural effects under a reduced set of assumptions. Specifically, no assumptions about confounding are made that involve the outcome; we only assume no unobserved exposure-mediator confounding as well as a condition termed partially constant cross-world dependence (PC-CWD), which poses fewer constraints on the counterfactual probabilities than the usual cross-world independence assumption. The proposed strategy can be used also to achieve interval identification of the total effect, which is no longer point identified under the considered set of assumptions. Our derivations are based on postulating a logistic regression model for the mediator as well as for the outcome. However, in both cases the functional form governing the dependence on the explanatory variables is allowed to be arbitrary, thereby resulting in a semi-parametric approach. To account for sampling variability, we provide delta-method approximations of standard errors in order to build uncertainty intervals from identification bounds. The proposed method is applied to a dataset gathered from a Spanish prospective cohort study. The aim is to evaluate whether the effect of smoking on lung cancer risk is mediated by the onset of pulmonary emphysema.

We review the condensation completion of a modular tensor category $\mathcal{C}$, which yields a fusion 2-category $Σ\mathcal{C}$ of separable algebras, bimodules over algebras and bimodule maps in $\mathcal{C}$. Physically, $Σ\mathcal{C}$ is the fusion 2-category of codimension-1 defects, codimension-2 defects and instantons in the $2+1$D topological order $\mathcal{C}$. We realize the rough-rough wall and $e$-$m$ exchange wall in Toric Code model on the lattice by deforming the Hamiltonian based on the corresponding algebraic data. We apply condensation completion to Toric Code, $3\mathbf{F}$, two-laryer semion and $\mathbb{Z}_4$ topological orders, and explicitly enumerate their $1$d and $0$d defects along with fusion rules. We also mention other applications of condensation completion: alternative interpretations of condensation completion of a braided fusion category; condensation completion of the category of symmetry charges and its correspondence to gapped phases with symmetry; for a topological order $\mathcal{C}$, one can find all gapped boundaries of the stacking of $\mathcal{C}$ with its time-reversal conjugate through computing the condensation completion of $\mathcal{C}$.

In this paper we investigate the degrees of irrationality of degenerations of $ε$-lc Fano varieties of arbitrary dimensions. We show that given a generically $ε$-lc klt Fano fibration $X\to Z$ of dimension $d$ over a smooth curve $Z$ such that $(X, t F)$ is lc for a positive real number $t$ where $F$ is the reduction of an irreducible central fibre of $X$ over a closed point $z\in Z$, then $F$ admits a rational dominant map $π\colon F\dashrightarrow C$ to a smooth projective variety $C$ with bounded degree of irrationality depending only on $ε, d, t$ such that the general fibres of $π$ are irreducible and rational. This proves the generically bounded case of a conjecture proposed by the first author and Loginov for log Fano fibrations of dimensions greater than three. One of the key ingredients in our proof is to modify the generically $ε$-lc klt Fano fibration $X\to Z$ to a toroidal morphism of toroidal embeddings with bounded general fibres.

We present an algorithm for efficiently exploring inequivalent Calabi-Yau threefold hypersurfaces in toric varieties. A direct enumeration of fine, regular, star triangulations (FRSTs) of polytopes in the Kreuzer-Skarke database is foreseeably impossible due to the large count of distinct FRSTs. Moreover, such an enumeration is needlessly redundant because many such triangulations have the same restrictions to 2-faces and hence, by Wall's theorem, lead to equivalent Calabi-Yau threefolds. We show that this redundancy can be circumvented by finding a height vector in the strict interior of the intersection of the secondary cones associated with each 2-face triangulation. We demonstrate that such triangulations are generated with orders of magnitude fewer operations than the naive approach of generating all FRSTs and selecting only those differing on 2-faces. Similar methods are also presented to directly generate (the support of) the secondary subfan of all fine triangulations, relevant for random sampling of FRSTs.

The ability to detect quantum superpositions lies at the heart of fundamental and applied aspects of quantum mechanics. The time-frequency degree of freedom of light enables encoding and transmitting quantum information in a multi-dimensional fashion compatible with fiber and integrated platforms. However, the ability to efficiently detect time-frequency superpositions is not yet available. Here we show, that multidimensional time-bin superpositions can be detected using a single time-resolved photon detector. Our approach uses off-the shelf components and is based on the temporal Talbot effect -- a time-frequency counterpart of the well-know near field diffraction effect. We provide experimental results and discuss the possible applications in quantum communication, quantum information processing, and time-frequency quantum state tomography.

Segregation and dissolution behavior of Mg alloyed with Ca and Al are studied by performing density functional theory calculations considering an extensive set of surface structures and compositions. Combining ab initio surface science approaches with cluster expansion for ordered surface structures we construct surface phase diagrams for these alloys. We utilize these diagrams to study segregation phenomena and chemical trends for surfaces in contact with a dry environment or with an aqueous electrolyte. We show that the presence of water dramatically impacts the stability and chemical composition of the considered metallic surfaces. We furthermore find that the two alloying elements behave qualitatively different: whereas Ca strongly segregates to the surface and becomes dissolved upon exposure of the surface to water, Al shows an anti-segregation behavior, i.e., it remains in Mg bulk. These findings provide an explanation for the experimentally observed increase/decrease in corrosion rates when alloying Mg with Al/Ca.

For a connected graph $G$, the average hitting time $α(G)$ and the Kemeny's constant $κ(G)$ are two similar quantities, both measuring the time for the random walk on $G$ to travel between two randomly chosen vertices. We prove that, among all weighted trees whose edge weights form a fixed multiset, $α$ is maximized by a special type of ``polarized'' paths and is minimized by a unique weighted star graph. We also obtain a similar characterization of the $κ$-maximizing and $κ$-minimizing elements among such a collection of weighted trees. Our proofs are based on the forest formulas for $α$ and $κ$.

We consider the approximability of constraint satisfaction problems in the streaming setting. For every constraint satisfaction problem (CSP) on $n$ variables taking values in $\{0,\ldots,q-1\}$, we prove that improving over the trivial approximability by a factor of $q$ requires $Ω(n)$ space even on instances with $O(n)$ constraints. We also identify a broad subclass of problems for which any improvement over the trivial approximability requires $Ω(n)$ space. The key technical core is an optimal, $q^{-(k-1)}$-inapproximability for the Max $k$-LIN-$\bmod\; q$ problem, which is the Max CSP problem where every constraint is given by a system of $k-1$ linear equations $\bmod\; q$ over $k$ variables. Our work builds on and extends the breakthrough work of Kapralov and Krachun (Proc. STOC 2019) who showed a linear lower bound on any non-trivial approximation of the MaxCut problem in graphs. MaxCut corresponds roughly to the case of Max $k$-LIN-$\bmod\; q$ with ${k=q=2}$. For general CSPs in the streaming setting, prior results only yielded $Ω(\sqrt{n})$ space bounds. In particular no linear space lower bound was known for an approximation factor less than $1/2$ for any CSP. Extending the work of Kapralov and Krachun to Max $k$-LIN-$\bmod\; q$ to $k>2$ and $q>2$ (while getting optimal hardness results) is the main technical contribution of this work. Each one of these extensions provides non-trivial technical challenges that we overcome in this work.

Guided mode resonance (GMR), the resonant coupling of free-space light into leaky waveguide modes, is traditionally achieved with periodic patterned structures. However, this approach makes its key properties such as quality factor (Q-factor) fabrication-dependent and non-tunable. Here, we introduce a time grating platform, i.e., a homogeneous waveguide whose refractive index is modulated periodically in time, that allows tunable GMRs through temporal modulation engineering rather than spatial structural redesign. We show that the Q-factors of these GMRs diverge as the modulation depth vanishes. Furthermore, unconstrained by energy conservation, the resonances exhibit near-unity reflection for fundamental harmonics and values exceeding 40 for first-order harmonics. Our findings not only apply to yield a giant Goos-Hänchen shift over 103 times wavelength without sacrificing the reflection magnitude, but also open new avenues for related phenomena such as bound states in the continuum, unidirectional GMRs and beyond.

Almost every numerical task can be cast as extrapolation with respect to the fidelity or tolerance parameters of a consistent numerical method. This perspective enables probabilistic uncertainty quantification and optimal experimental design functionality to be deployed, and also unlocks the potential for the convergence of numerical methods to be accelerated. Recent work established Probabilistic Richardson Extrapolation as a proof-of-concept, demonstrating how parallel multi-fidelity simulation can be used to accelerate simulation from a whole-heart model. However, the number of simulations was required to increase super-exponentially in $d$, the number of tolerance parameters appearing in the numerical method. This paper develops a refined notion of 'extrapolation dimension', drastically reducing this simulation requirement when multiple tolerance parameters feature in the numerical method. Sparsity-exploiting methodology is developed that is simultaneously simpler and more powerful compared to earlier work, and this is accompanied by sharp theoretical guarantees and substantial empirical support.

We demonstrate the stray-field-mediated skyrmion stabilizing capabilities of ultrathin exchange-decoupled antisymmetric ferromagnetic bilayers based on conventional transition metal materials. Using an asymptotically exact micromagnetic model valid in the ultrathin film limit, we show that the antisymmetric tailoring of the bilayer allows the Dzyaloshinskii-Moriya interaction and the dipolar interaction to act synergistically to stabilize skyrmions, in contrast to the monolayer case, in which these energies compete. To obtain optimal stability of these skyrmions against collapse and bursting -- the two fundamental processes determining skyrmion lifetime, we carry out an asymptotic analysis of the saddle point solution that separates the skyrmion from the demagnetized state. The result is an optimal stability line for compact skyrmions in the non-dimensional parameter space of the effective Dzyaloshinskii-Moriya interaction strength and the effective film thickness. Our predictions are confirmed by extensive micromagnetic simulations of antisymmetric bilayers, using magnetic parameters of the conventional Pt/Co/AlO$_x$ systems. Our results provide a new pathway for experimental observations of 10 nm radius zero-field skyrmions with lifetimes compatible with information technology applications.

Lasso problems arise in many areas, including signal processing, machine learning, and control, and are closely connected to sparse coding mechanisms observed in neuroscience. A continuous-time ordinary differential equation (ODE) representation of the Lasso problem not only enables its solution on analog computers but also provides a framework for interpreting neurophysiological phenomena. This article proposes a fixed-time-stable ODE representation of the Lasso problem by first transforming it into a smooth nonnegative quadratic program (QP) and then designing a projection-free Newton-based ODE representation of the Lasso problem by first transforming it into a smooth nonnegative quadratic program (QP) and then designing a projection-free Newton-based fixed-time-stable ODE system for solving the corresponding Karush-Kuhn-Tucker (KKT) conditions. Moreover, the settling time of the ODE is independent of the problem data and can be arbitrarily prescribed. Numerical experiments verify that the trajectory reaches the optimal solution within the prescribed time.