Rare $b\to s\ell^+\ell^-$ decays provide some of the most sensitive tests of the Standard Model and require precise and systematically improvable hadronic input from lattice QCD. For the phenomenologically important channel $B\to K^*\ell^+\ell^-$ this entails a first-principles treatment of a resonant $Kπ$ final state together with controlled heavy-quark dynamics. We present the status of a new exploratory lattice calculation that combines a variational determination of finite-volume $Kπ$ states with the $1+J\to2$ finite-volume formalism to access the relevant matrix elements. The computation is carried out on an RBC/UKQCD domain-wall fermion ensemble with $a^{-1} \approx 2.7\,\mathrm{GeV}$ and employs a dual heavy-quark strategy, using both a relativistic heavy-quark action tuned to the physical $b$ mass and domain-wall heavy masses extrapolating from charm. All correlation functions are computed using (stochastic) distillation, providing a versatile setup that supports a broad range of heavy-to-light transitions into resonant final states. We show first two-point results for the $K^*\leftrightarrow Kπ$ system and discuss the accessible kinematic region, which allows for a controlled study at high $q^2$. The outlook for extending the calculation to lower $q^2$ and for incorporating effects from charmonium resonances is outlined.

We characterize the optimal tax policy in an economy with human manual and cognitive labor, physical capital, and artificial intelligence (AI). Extending the dynamic taxation setup of Slavik and Yazici (2014), we find that it is optimal to start taxing AI when cognitive workers start to consider switching to manual jobs. This threshold may be crossed once AI becomes sufficiently capable in substituting humans across cognitive tasks.

We study the secure domination number of the Mycielskian graph of a simple, connected, undirected graph. We give generally applicable bounds, compute secure domination numbers for Mycielskians of important families of graphs, and construct families of graphs realizing particular values of (secure) domination parameters.

Feedback control plays a central role in active matter, yet it is inevitably accompanied by noise and finite perception--action delays. This Perspective reviews recent advances on active systems with delayed interactions, showing how time delay can induce activity, chirality, transport, and collective pattern formation, and can act as an effective control parameter for switching between dynamical states. We discuss representative single-particle and many-body systems, highlight key experimental realizations, and argue that time delay constitutes an underexplored dimension of morphological intelligence--where intrinsic response dynamics, rather than explicit sensors or computation, enable functional behavior in active matter.

The deep locus of a cluster variety is defined to be the set of its points that do not belong to any cluster torus. We show that, if the cluster variety has a seed whose mutable part is a tree without multiple edges, then the deep locus can be characterized as the set of points whose stabilizer under a certain group action is nontrivial. Deep points without a stabilizer are called mysterious. We establish that many other classes of acyclic quivers (including keys) often have mysterious points. This refutes Conjecture 1.1 of arXiv:2402.16970, but establishes it in many important cases.

In the first part of the paper we show that every closed subspace of $JT$ or $JT^*$ contains $\ell_2$ complemented in $JT$ or $JT^*$ respectively, and $JT$ contains uncomplemented copies of $\ell_2$. As a result, the predual $\B$ of $JT$, as well as the spaces $JT$ and $JT^*$, are subprojective and superprojective. In the second part, we prove that every weakly Cauchy sequence that is not weakly convergent in $JT$ has a subsequence equivalent to the basis of $J$. Hence, every non-reflexive subspace of $JT$ contains an isomorphic copy of $J$, and every Schauder basic sequence in $JT$ has a subsequence which is equivalent either to the basis of $\ell_2$ or to the basis of $J$. Moreover these subspaces may be selected to be complemented in $JT$.

Ionization is critical in the formation and evolution of plasma dynamics; collisional ionization, in particular, is an often overlooked source of electrons when dealing with laser-plasma interactions. Ionization plays a crucial role in understanding the complex plasma kinetics, ranging from cold and sparse astrophysical settings to hot and dense fusion systems. In this paper, we describe the underlying theory for and development, validation, and verification of an extension to the standard particle-in-cell method to include a deterministic algorithm for collisional ionization physics. This algorithm offers improved accuracy, achieving up to two orders of magnitude decrease in the error of the ionization rate calculations, scales linearly in execution time with the number of macro-particles per cell, has been tested for physical correctness and benchmarked against several codes.

As hardware serves as the root of trust in modern computing systems, Hardware Reverse Engineering (HRE) is foundational for security assurance. In practice, HRE enables critical security applications, including design verification, supply-chain assurance, and vulnerability discovery. Over the past two decades, academic research on Integrated Circuit (IC), Field-Programmable Gate Array (FPGA), and netlist reverse engineering has steadily grown. However, knowledge remains fragmented across domains and communities, which complicates assessing the state of the art and hampers identifying shared research challenges. In this paper, we present a systematization of knowledge based on an in-depth analysis of 187 peer-reviewed publications. Using this corpus, we characterize technical methods across the HRE workflow and identify technical and organizational challenges that impede research progress. We analyze all 30 artifacts from our corpus using established artifact evaluation practices. Key results could be reproduced for only seven publications (4%). Based on our findings, we derive stakeholder-centric recommendations for academia, industry, and government to enable more coordinated and reproducible HRE research. These recommendations target three cross-cutting opportunities: (i) improving reproducibility and reuse via artifact-centric practices, (ii) enabling rigorous comparability through standardized benchmarks and evaluation metrics, and (iii) improving legal clarity for public HRE research.

The CD index is a widely used measure of disruptive inventions. Most studies compute it using USPTO data. This creates a puzzle because the US appears less disruptive than European and Asian countries. We show that this largely stems from missing international citations. Using a global citation network, we quantify and correct this bias. The disruptiveness advantage of non-US inventors drops by 64% to 148% of the US baseline mean. The US emerges as a disruption leader over Europe, with Asia's advantage substantially reduced. Globally integrated citation data are essential for credible measurement of disruptive innovation in international contexts.

While the Open Radio Access Network Alliance (O-RAN) architecture enables third-party applications to optimize radio access networks at multiple timescales, real-time distributed applications (dApps) that demand low latency, high performance, and strong isolation remain underexplored. Existing approaches propose colocating a new RAN Intelligent Controller (RIC) at the edge, or deploying dApps in bare metal along with RAN functions. While the former approach increases network complexity and requires additional edge computing resources, the latter raises serious security concerns due to the lack of native mechanisms to isolate dApps and RAN functions. Meanwhile, WebAssembly (Wasm) has emerged as a lightweight, fast technology for robust execution of external, untrusted code. In this work, we propose a new approach to executing dApps using Wasm to isolate applications in real-time in O-RAN. Results show that our lightweight and robust approach ensures predictable, deterministic performance, strong isolation, and low latency, enabling real-time control loops.

Recent evidence from Parker Solar Probe on the suprathermal electrons with Kappa-type velocity distributions in the outer corona has revived interest in the kinetic-based macro-modelling of the solar (SW), aiming to explain its properties. Invoked in kinetic modelling of nonequilibrium plasmas, standard Kappa distributions (SKDs) have been adjusted to the regularized Kappa distributions (RKDs) to fix the inconsistencies of SKD and develop consistent fluid modelling of space plasmas. We propose a new analysis of these properties at large heliocentric distances based on the existence of RKD electrons at the exobase. This new semi-analytic formalism is inspired by the methodology proposed initially by Meyer-Vernet and Issautier (1998), https://doi.org/10.1029/98ja02853. Compared to SKDs, the results for RKDs have extended applicability, since all moments can be defined and calculated consistently for all values of the $κ$ parameter, even lower than the critical ones (e.g., $κ_c=3/2$ imposed to the second-order moment) of SKDs. However, the excess energy of the more energetic suprathermal electrons associated with low values of $κ\lesssim 3/2$, is regulated by the RKD-specific cutoff parameter $α< 1$. The estimates for, e.g., the temperature and bulk velocity of the SW, remain at realistic values even for small $3/2 < κ\lesssim 2$, which would otherwise exceed specific observations. One can thus model a higher abundance of suprathermal electrons at the exobase (e.g., $κ\leqslant 3/2$), which is plausible for the sources of energetic events (flares and coronal mass ejections), and also in the astrospheres of stars with coronas hotter than the Sun's.

We employ a novel real-time formulation of the functional renormalization group (FRG) to compute universal scaling functions of the thermal diffusivity and the shear viscosity in the vicinity of the liquid-gas critical point, i.e., for the dynamic universality class of Model H from the Halperin-Hohenberg classification. We map out the universal dependence of the transport coefficients on temperature, external magnetic field, and wavenumber, and provide a detailed comparison with the Kawasaki approximation, which is here obtained from a perturbative one-loop approximation to our real-time FRG flow. In contrast to the Kawasaki approximation, the non-perturbative scaling functions from the full real-time FRG flow show a mild dependence on the thermodynamic path towards the critical point. We further compare our FRG results for the universal wavenumber and temperature dependence of the thermal diffusivity with experimental data from critical fluids.

I introduce a new analytical framework for estimating critical temperatures in interacting many-body systems, focusing on the Ising model. Combining the Bethe cluster setting, the Metropolis update, and the Galam Majority Model developed in sociophysics, I build a two stroke pumping technique (TSP). Applied to the Ising model in dimensions d=2, 3, 4, TSP yields values of T_c which are all at an excess of +0.03 from exact estimates. At d=1 the exact value T_c=0 is obtained. In addition, TSP indicates analytically the practical impossibility to reach full symmetry breaking at T=0. The results are thus found in good agreement with numerical findings while requiring significantly fewer computational resources than Monte Carlo sampling. Calculations are computationally efficient and transparent. The framework is general and can be extended to a broad class of discrete spin models. This positions TSP as an intermediate yet scalable tool for studying cooperative behavior in many body interacting systems.

In this paper the notion of a quadratic (left) Bol algebra is discussed. Several examples of quadratic Bol algebras are given and it is observed that the only two-dimensional quadratic real Bol algebras are quadratic Lie triple systems. Dual representations of Bol algebras are investigated with a particular emphasis on coadjoint representations for quadratic Bol algebras. The notion of T*-extension of a quadratic Bol algebra is introduced.

For $n \ge 2$, Gamburd, Jakobson, and Sarnak [J. Eur. Math. Soc. 1, 51-85 (1999)] conjectured that almost every $n$-tuple in $\mathrm{SU}(2)$ has a spectral gap. Toward this conjecture, Fisher [Int. Math. Res. Not. (2006)] established a zero-one law for $n \ge 3$, but obtained only a partial result for $n=2$. In this paper, we prove that the zero-one law also holds for $n=2$. We also remark that a Baire categorical analogue of this result holds.

Metal chalcogenides are promising layered topological materials, yet their electronic performance is often limited by parasitic bulk conduction arising from defects that introduce excess carriers and shift the Fermi level out of the topological regime. Controlling early-stage growth and defect formation is therefore essential for suppressing bulk transport and enhancing surface-state conduction. Here we investigate ultrathin Bi2Te3 films grown by pulsed laser deposition on substrates spanning van der Waals, lattice-matched, and amorphous regimes to determine how substrate-dependent nucleation pathways influence defect formation and electronic transport. Phase-pure, c-axis-oriented Bi2Te3 forms on all substrates, but the growth morphology varies strongly. Layered growth with well-defined quintuple-layer terraces is governed primarily by substrate roughness rather than lattice match: atomically smooth mica and step-terraced SrTiO3 yield continuous terraces, whereas rougher BaF2 and amorphous Si3N4 produce island-structured films. Between the two smooth substrates, the higher surface energy of SrTiO3 enhances adatom adsorption and nucleation density, promoting rapid vertical growth and early Te depletion. Transport measurements reveal n-type conduction with carrier densities of 10e19-10e20 cm-3. The highest carrier density occurs for films on SrTiO3, consistent with defect formation during high-density nucleation, whereas mobility correlates with structural coherence and terrace formation. Weak anti-localization signatures confirm phase-coherent transport in films on mica and SrTiO3. These results show that substrate roughness and nucleation density provide key levers for controlling defect formation and strengthening topological surface transport in Bi2Te3 thin films.

We study analogs of planar-quadrilateral meshes in Laguerre sphere geometry and the approximation of smooth surfaces by them. These new Laguerre meshes can be viewed as watertight surfaces formed by planar quadrilaterals (corresponding to the vertices of a mesh), strips of right circular cones (representing the edges), and spherical faces. In the smooth limit, we get an analog of conjugate nets in Laguerre geometry, which we call Laguerre conjugate nets with respect to an attached sphere congruence. We introduce the notion of Laguerre conjugate directions, provide a method for computing them, and apply them to approximate surfaces by L-meshes with prescribed radii of spherical faces.

Detection of minimal residual disease (MRD) in cancer patients after surgery can provide an early marker for disease recurrence and guide subsequent treatment decisions. Accurate and sensitive estimation of tumour burden after cancer surgery may be obtained through liq- uid biopsies, measuring circulating tumour DNA (ctDNA) using, for example, mutation-based Variant Allele Frequency (VAF) values. However, to be applicable to all patients this ei- ther requires tumour-informed, patient-specific mutation panels or sensitive, tumour-agnostic genome-wide measurements. We propose a solution that accounts for patient-specific charac- teristics in genome-wide screens. For that, we introduce a bivariate deconvolution model to estimate tumour proportion from circulating cell-free DNA (cfDNA) methylation profiles of patients before and after surgery. The observations are modelled as a convolution of two bivariate latent variables, corresponding to tumour and background signals, mixed by the tumour proportion at each measurement. This bivariate approach links pre- and post-surgery measurements improving estimation of the tumour proportion after surgery, when the tumour signal is potentially very weak, or absent. We approximate likelihood of the convolution through a discretisation of the bivariate density for each latent variable into a two-dimensional grid for each pair of observations which allows for fast maximum likelihood estimation. We evaluate the predictive performance of the estimated post-surgery tumour proportions based on cfDNA methylation against available mutation-based VAF values in one-year recurrence-free survival.

We study one-sided matchings with endowments in the absence of money. It is well-known that a competitive equilibrium may not always exist and that the strong core may be empty in this setting [Hylland and Zeckhauser, 1979]. We propose a generalization of competitive equilibria that associates each item with a multi-dimensional price. We show that this solution concept always exists and resides within the rejective core [Konovalov, 2005]. Rejective core stability is strictly stronger than weak core stability: allocations in the rejective core are elements of the weak core, but the opposite is not true. Moreover, we show that the rejective core always converges to the set of competitive equilibria with multi-dimensional prices as the economy grows, demonstrating core convergence in a setting without non-satiation.

We develop a transport-entropy framework for Gaussian concentration inequalities on the infinite product space $S^{\mathbb Z^d}$, where $S$ is a finite set, in which sensitivity is measured by the $\ell^2$-norm of local oscillations. We show that the associated transportation costs cannot be induced by any metric or cost function on the configuration space, due to a structural lack of extensivity in infinite product spaces. Our main result proves that the associated integral probability metric and coupling functional coincide in finite volume, yielding a duality extending the classical Kantorovich-Rubinstein theorem beyond the metric setting. As a consequence, Marton's coupling inequality in all finite volumes is equivalent to Gaussian concentration, yielding a new characterization in the infinite-product setting. In the translation-invariant setting, the corresponding metrics converge in the thermodynamic limit to the $\bar d$-metric. We further introduce a thermodynamic Gaussian concentration bound and prove its equivalence with a transport-entropy inequality involving the relative entropy density.

We establish existence of probabilistically strong solutions and pathwise uniqueness for a class of quasilinear stochastic evolution equations on bounded domains. Our results combine recent weak existence results for quasilinear stochastic evolution equations in an $L^p$-setting (with $p > 2$) with Yamada--Watanabe theory. To establish pathwise uniqueness, we rely on an $L^1$-contraction argument.

Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars. We introduce a numerical bootstrap framework which casts the problem of tensor-network contractions into a convex optimization problem, thereby yielding certified lower and upper bounds on expectation values of physical observables. As a proof-of-principle, we construct such constraints explicitly for translationally invariant matrix product states and demonstrate that, assuming a canonical form, second-order-cone relaxation can provide tight bounds on the contraction result. We further demonstrate that when the requirement on canonical form is lifted, a more general semidefinite-programming approach could yield similar tight bounds at higher but still polynomial computational cost. Our work suggests numerical bootstrap could be a possible way forward for the rigorous contractions of tensor networks.

Quantum spin rings represent an intriguing platform for studying unconventional magnetic order and exotic quantum phases, and they are also promising materials for emerging quantum technologies. Conventional spin systems consist of a set of weakly interacting localized spins that are well described by the Heisenberg spin models. Here, we demonstrate that strong interactions between radical centers in macrocycles of different sizes lead to fluctuations in the total number of unpaired electrons and to non-trivial antiferromagnetic order that extends beyond the Heisenberg picture. We demonstrate that the electronic structure of these spin rings is governed by the concept of 4n/4n+2 Hückel (anti)aromaticity for even-membered rings, whereas odd-membered rings possess a highly degenerate frustrated magnetic ground state. The strongly coupled spin rings are experimentally realized through the on-surface synthesis of π-magnetic carbon-based macrocycles, which consist of [2]triangulene units. The close correlation between the electronic structure and the Hückel aromaticity rule is revealed by scanning tunneling spectroscopy and multireference calculations. This work establishes a novel design principle employing the concept of Hückel aromaticity for quantum spin macrocycles.

We introduce generalizations of global equivariant spectra which encode globally equivariant cohomology theories equipped with additional transfers, such as the deflation maps present in equivariant topological $K$-theory. We call these $\mathcal{Q}$-ambidextrous global spectra, where $\mathcal{Q}$ is a parameter encoding which additional transfers one allows. As our main example, we prove that the tempered cohomology theory associated with an oriented $\mathbf{P}$-divisible group, constructed by Lurie, is represented by a $π$-ambidextrous global $\mathbf{E}_\infty$ ring spectrum, encoding transfers along all relatively $π$-finite maps of global spaces. This is established by means of a general parametrized decategorification process, perhaps of independent interest, that produces $\mathcal{Q}$-ambidextrous global spectra from suitable global families of stable $\infty$-categories. By allowing $\mathcal{Q}$ to vary, we are able to coherently encode the fact that non-invertible morphisms of oriented $\mathbf{P}$-divisible groups induce maps of tempered theories that only commute with certain transfers. With these $π$-ambidextrous enhancements in hand, we explore the fundamental properties of tempered theories as equivariant stable homotopy types. We construct a well-behaved $F$-global homology theory for any $π$-finite space $F$, with good base change properties. Taking $F = \mathbf{B} H$ for a finite group $H$, this establishes general base change results for the geometric fixed points of tempered theories. We use this to compute the $H$-geometric fixed points of tempered theories, showing that they vanish for $H$ nonabelian and admit a simple algebro-geometric model when $H$ is abelian, with identifiable blueshift properties.

We study coarse separation in one-ended hyperbolic groups from a quantitative point of view, focusing on the volume growth of separating subsets. We prove that a one-ended hyperbolic group that is not virtually a surface group is coarsely separable by a subset of subexponential growth if and only if it splits over a virtually cyclic subgroup. To do so, we show that sufficiently large thickened spheres are hard to cut, in the sense that their cut-sets have exponential size, a result of independent interest. As an application, we obtain a polynomial lower bound on the separation profile of one-ended hyperbolic groups that do not split over a two-ended subgroup. We also apply our criterion to graph products of finite groups, giving a combinatorial characterisation of when such graph products are coarsely separable by a subset of subexponential growth.

We prove a splitting result in global equivariant homotopy theory that is a simultaneous refinement of the Segal--Becker splitting and its `Real' and equivariant generalizations, and of the explicit Brauer induction of Boltje and Symonds. We show that the morphism of ultra-commutative Real-global ring spectra from $Σ^\infty_+ B_{\text{gl}}U(1)$ to the Real-global K-theory spectrum that classifies the tautological Real $U(1)$-representation admits a section on underlying Real-global infinite loop spaces. We prove that this global Segal--Becker splitting induces the classical Segal--Becker splittings on equivariant cohomology theories, and that it induces the Boltje--Symonds explicit Brauer induction on equivariant homotopy groups. As an application we rigidify the unstable Adams operations in Real-equivariant K-theory to global self-maps of the Real-global space $\mathbf{BUP}$.

Fourier representations play a central role in operator learning methods for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT), particularly in its Cooley--Tukey decomposition, exhibits a structure that naturally matches continuous-variable quantum circuits. This correspondence establishes a direct structural isomorphism between the Cooley-Tukey butterfly network and Gaussian photonic gates, enabling the FFT to be realized as a native optical computation in continuous-variable quantum computing. Building on this observation, we introduce a continuous-variable Quantum Fourier Layer (CV--QFL) based on a bipartite Gaussian encoding and a Cooley-Tukey quantum Fourier transform, enabling exact two-dimensional spectral processing within a Gaussian photonic circuit. We test the CV--QFL on two representative tasks: spectral low-pass filtering and Fourier-domain integration of the heat equation. In both cases, the results match the classical reference to machine precision. Beyond these examples, our method naturally extends to optical-input settings in which the signal is already available as a Gaussian optical field. In such scenarios, coherent light coupled into single-mode waveguides can be processed directly by the CV--QFL, bypassing the need for an explicit classical-to-quantum encoding stage. This enables native spectral processing of light and lays the groundwork for new approaches to quantum scientific machine learning, in particular for future neural operator architectures within the CV framework.

AgSbTe2 is a well-known thermoelectric material with a high Seebeck coefficient and intrinsically low thermal conductivity, but its behavior under pressure remains largely unexplored. Here we report a systematic investigation of the structural, electronic, and transport properties of non-stoichiometric AgSbTe2 under high pressure. At ambient pressure, the material can be described as having a cubic crystal structure that remains stable up to 21.7 GPa beyond which it loses long-range structural order, while its crystal system fully recovers upon decompression. Remarkably, superconductivity emerges at a very low pressure of 0.38 GPa with an onset superconducting critical temperature (Tc) of 3.2 K. Tc increases with increasing pressure, reaching 6.9 K at 31.9 GPa, and peaks at 7.4 K during decompression. Magnetic-field-dependent transport measurements and electronic structure calculations reveal an evolution of the superconducting state driven by an enhanced electronic density of states at the Fermi level under compression. Our findings uncover pressure-induced superconductivity in AgSbTe2 and demonstrate that pressure can effectively tune the electronic ground state of thermoelectric materials, extending their functionality beyond thermoelectric energy conversion.

We derive an exact uncertainty relation for arbitrary quantum states of finite-dimensional Hilbert spaces. For any given $k$-partition of a $d$-dimensional multipartite system, we introduce the total uncertainty as the sum of the uncertainties associated with all possible tensor products of local $\mathrm{SU}(N)$ observables, where each observable acts on the corresponding subsystem. We show that the total uncertainty exactly equals the algebraic sum of the global state purity and the purities of all possible state reductions. For systems containing at least one single-qubit subsystem, this equality implies saturation of the Robertson-Schrödinger uncertainty inequality, with the missing term needed for saturation equal to the bipartite qubit-environment entanglement for a pure global state, or to the qubit two-Rényi entropy for a mixed global state. Leveraging on these results, we show how for any finite-dimensional multipartite system the Hilbert-Schmidt squared norm of the correlation matrix $t$ can be expressed exclusively in terms of the global and reduced state purities. We then derive a correlation matrix-based necessary condition for $k$-separability of arbitrary finite-dimensional quantum states and show, in the case of $n$ qubits, how it is related to a necessary criterion for Bell nonlocality in scenarios with two dichotomic measurements per party. For sufficiently large systems the purity-based formulation of the $k$-separability criterion always yields an exponential advantage over the direct evaluation of the $t$-matrix norm, allowing for a more efficient practical verification of multipartite entanglement and nonlocality via simple experimental schemes based on purity measurements. Our results shed some further light on the intimate and intricate relation between correlations, entropies, uncertainties, and the entanglement certification and detection problem.

We provide a method to design adaptive controllers for nonlinear systems using model predictive control (MPC). By combining a certainty-equivalent MPC formulation with least-mean-square parameter adaptation, we obtain an adaptive controller with strong robust performance guarantees: The cumulative tracking error and violation of state constraints scale linearly with noise energy, disturbance energy, and path length of parameter variation. A key technical contribution is developing the underlying certainty-equivalent MPC that tracks output references, accounts for actuator limitations and desired state constraints, requires no system-specific offline design, and provides strong inherent robustness properties. This is achieved by leveraging finite-horizon rollouts, artificial references, recent analysis techniques for optimization-based controllers, and soft state constraints. For open-loop stable systems, we derive a semi-global result that applies to arbitrarily large measurement noise, disturbances, and parametric uncertainty. For stabilizable systems, we derive a regional result that is valid within a given region of attraction and for sufficiently small uncertainty. Applicability and benefits are demonstrated with numerical simulations involving systems with large parametric uncertainty: a linear stable chain of mass-spring-dampers and a nonlinear unstable quadrotor navigating obstacles.