The large-scale integration of inverter-interfaced renewable energy sources presents significant challenges to maintaining power balance and nominal frequency in modern power systems. This paper studies grid-level coordinated control of grid-forming (GFM) and grid-following (GFL) inverter-based resources (IBRs) for scalable and optimal frequency control. We propose a fully distributed optimal frequency control algorithm based on the projected primal-dual gradient method and by leveraging the structure of the underlying physical system dynamics. The proposed algorithm i) restores the nominal system frequency while minimizing total control cost and enforcing IBR power capacity limits and line thermal constraints, and ii) operates in a distributed manner that only needs local measurements and neighbor-to-neighbor communication. In particular, when the line thermal constraints are disregarded, the proposed algorithm admits a fully local implementation that requires no communication, while still ensuring optimality and satisfying IBR power capacity limits. We establish the global asymptotic convergence of the algorithm using Lyapunov stability analysis. The effectiveness and optimality of the proposed algorithms are validated through high-fidelity, 100% inverter-based electromagnetic transient (EMT) simulations on the IEEE 39-bus system.

The growing reliance on software in road vehicles has led to the emergence of Software-Defined Vehicles (SDV). This work analyzes SDV security and privacy through a systematic literature review complemented by an industry questionnaire across the automotive supply chain. The analysis is structured as four research questions and results in a security framework serving as a roadmap for SDV protection. The findings emphasize addressing mixed-criticality architectural challenges, deploying layered security mechanisms, and integrating privacy-preserving techniques. The results highlight the need to harmonize in-vehicle and cloud-based defenses to strengthen cybersecurity and V2X resilience in Intelligent Transportation Systems (ITS).

Changepoint detection is commonly formulated by minimizing the sum of in-sample losses to quantify the model's overall fit. However, for flexible modeling procedures -- especially those involving high-dimensional parameter spaces or hyperparameter tuning -- this strategy can lead to inaccurate changepoint estimation due to over-adaptivity biases. To mitigate this issue, we propose a novel cross-fitting methodology based on out-of-sample loss evaluations, which decouples model fitting from changepoint search. We establish a general theoretical framework for consistent changepoint estimation under mild conditions, and further extend it to temporally dependent data. A key implication of the theory is that consistency depends primarily on the models' predictive accuracy over nearly homogeneous segments. Numerical experiments show that the proposed method substantially improves the reliability and adaptability of changepoint detection in complex scenarios.

One of the key features of hole-doped cuprates is the presence of an extended pseudogap phase, whose microscopic origin has been the subject of intense investigation since its discovery and is believed to be crucial for understanding high-temperature superconductivity. Various explanations have been proposed for the pseudogap, including links to symmetry-breaking orders such as stripes or pairing, and the emergence of novel fractionalized Fermi liquid (FL*) and orthogonal metal (OM) phases. The topological nature of FL* and OM phases has been identified as scenarios compatible with a small Fermi surface without symmetry breaking, as suggested experimentally. With recent experimental and numerical studies supporting an intricate relationship between stripe order and the pseudogap phase, we here propose an alternative scenario: an orthogonal metal with a geometric origin (GOM) driven by fluctuating domain walls. The essential mechanism behind our proposal is hidden order, where the proliferation of domain walls stabilized by charge fluctuations obscures the underlying long-range antiferromagnetic order in real-space, but order is preserved in the reference frame of the background spins. As a result, well-defined fermionic quasiparticles in the form of magnetic polarons exist, which couple to $\mathbb{Z}_2$ topological excitations of the domain wall string-net condensate in the ground state and constitute a small Fermi surface. At a critical doping value, we argue that hidden order is lost, driving a transition to a regular Fermi liquid at a hidden quantum critical point (hQCP) featuring quantum critical transport properties. Our GOM framework establishes a deep connection between the antiferromagnetic, stripe, and pseudogap phases, and suggests a possible unification of superconductivity in (electron and hole) doped cuprates and heavy fermion compounds.

We study how coordinated disinformation campaigns affect elections. We develop a constrained information design model in which a sender deploys uninformative messages that mimic voters' exogenous informative signals. Voters initially opposed to the sender's preferred outcome receive favourable messages, while those in favour are targeted with unfavourable messages to dilute adverse information. The sender's ability to manipulate political outcomes increases with greater precision of voters' independent signals, but decreases with polarisation. When messaging is costly, the sender may stop targeting marginally opposing voters while moderating message extremism among supporters.

We propose a novel method for estimating nonseparable selection models. We show that, for a given selection function, the potential outcome distributions are nonparametrically identified from the selected outcome distributions and can be recovered using a simple iterative algorithm based on a contraction mapping. This result enables a full-information approach to estimating selection models without imposing parametric or separability assumptions on the outcome equation. We propose a two-step estimation strategy for the potential outcome distributions and the parameters of the selection function and establish the consistency and asymptotic normality of the resulting estimators. Monte Carlo simulations demonstrate that our approach performs well in finite samples. The method is applicable to a wide range of empirical settings, including consumer demand models with only transaction prices, auctions with incomplete bid data, and Roy models with data on accepted wages.

We develop a unified estimation and inference framework for dyadic network formation with individual fixed effects, covering both transferable-utility (TU) and nontransferable-utility (NTU) links under general link functions. Under NTU, bilateral consent makes the fixed effects non-additive and the log-likelihood non-concave in the high-dimensional fixed effects, so differencing and profile-likelihood methods fail. We combine a joint method-of-moments initial estimator, a Le Cam one-step refinement, and a split-network jackknife bagging step that removes the incidental parameter bias without inflating variance. The resulting homophily estimator is asymptotically normal, unbiased, and attains the Cramér--Rao lower bound without requiring the log-likelihood to be concave in the fixed effects; we extend the theory to average partial effects and establish robustness to link-function misspecification. Simulations under both TU and NTU designs confirm these predictions. Applied to Thai village networks (TU), kinship and wealth differences both increase linking; in the Nyakatoke risk-sharing network (NTU), wealth differences have no significant effect, mirroring the two regimes' distinct logics.

We develop resonance-based low-regularity numerical integrators for stochastic Schr"odinger equations with additive $Q$-Wiener noise, covering both the linear equation with rough potential and the cubic nonlinear case. For the linear problem, we prove strong and almost sure convergence, achieving first-order accuracy in $H^σ$ for solutions in $H^{σ+1}$, improving the classical $H^{σ+2}$ requirement. In a regime of $O(\varepsilon^2)$ potentials and $O(\varepsilon)$ noise, we establish uniform moment bounds up to times $O(\varepsilon^{-2})$ and construct a non-resonant scheme with long-time error $O(\varepsilon^2τ)$. For the cubic case, we derive analogous pathwise convergence results at low regularity. In the weakly nonlinear stochastic regime, we obtain long-time pathwise errors of size $O(\varepsilon^2τ^δ)$, for any $δ<1$, up to times $O(\varepsilon^{-2})$. The analysis relies on a novel extension of the regularity-compensation oscillation (RCO) technique to the stochastic setting, overcoming the loss of temporal regularity induced by stochastic convolutions and yielding an $O(\varepsilon^2)$ improvement in long-time error bounds. To the best of our knowledge, this is the first work establishing long-time error bounds for low-regularity integrators for stochastic dispersive equations. Numerical experiments support the theory.

I study a principal-agent model in which a principal hires an agent to collect information about an unknown continuous state. The agent acquires a signal whose distribution is centered around the state, controlling the signal's precision at a cost. The principal observes neither the precision nor the signal, but rather, using transfers that can depend on the state, incentivizes the agent to choose high precision and report the signal truthfully. I identify a sufficient and necessary condition on the agent's information structure which ensures that there exists an optimal transfer with a simple cutoff structure: the agent receives a fixed prize when his prediction is close enough to the state and receives nothing otherwise. This condition is mild and applies to all signal distributions commonly used in the literature.

This article extends the study of the dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although the map features six parameters, we demonstrate that only two are irreducible: the linearized rotation number at the fixed point and a nonlinear parameter representing the ratio of terms in the biquadratic invariant. Through a detailed analysis, we classify regimes of stable motion, provide exact solutions to the mapping equations, and derive a canonical set of action-angle variables, offering analytical expressions for the rotation number and nonlinear tune shift. We further establish connections between general standard-form mappings and the symmetric McMillan map, using the area-preserving Hénon map and accelerator lattices with thin sextupole magnet as representative case studies. Our results show that, despite being a second-order approximation, the symmetric McMillan map provides a highly accurate depiction of dynamics across a wide range of system parameters, demonstrating its practical relevance in both theoretical and applied contexts.

In this paper, we study the problem of energy equality for weak solutions of the 3D incompressible non-Newtonian fluid equations with initial value conditions. We derive new sufficient conditions via Sobolev multiplier spaces that guarantee the validity of the energy equality. Moreover, the aforementioned equations are often associated with the uniqueness problem of weak solutions for non-Newtonian fluids, which, in a certain sense, constitutes the positive counterpart of Onsager's conclusion for non-Newtonian fluids.

We investigate the Hilbert scheme of points on a smooth threefold. We introduce a notion of broken Gorenstein structure for finite schemes, and show that its existence guarantees smoothness on the Hilbert scheme. Moreover, we conjecture that it is exhaustive: every smooth point admits a broken Gorenstein structure. We give an explicit characterization of the smooth points on the Hilbert scheme of A^3 corresponding to monomial ideals. We investigate the nature of the singular points, and prove several conjectures by Hu. Along the way, we obtain a number of additional results, related to linkage classes, nested Hilbert schemes, and a bundle on the Hilbert scheme of a surface.

The particle filter (PF), also known as sequential Monte Carlo (SMC), approximates high-dimensional probability distributions and their normalizing constants in the discrete-time setting. To reduce the variance of the Monte Carlo approximation, various twisted particle filters (TPFs) have been proposed, in which a twisting function is chosen or learned to modify the Markov transition kernel. Guided by existing control-based importance sampling algorithms in the continuous-time setting, we propose a novel algorithm called the ``Twisted-Path Particle Filter'' (TPPF), in which the twisting function is parameterized by a neural network and trained to minimize a specific KL-divergence between path measures. Numerical experiments illustrate the capability of the proposed algorithm.

We explore a bond percolation model on slabs $\mathbb{S}^+_k=\mathbb{Z}_+\times \mathbb{Z}_+\times\{0,\dots,k\}$ featuring one-dimensional inhomogeneities. In this context, a vertical column on the slab comprises the set of vertical edges projecting to the same vertex on $\mathbb{Z}_+\times\{0,\dots,k\}$. Columns are chosen based on the arrivals of a renewal process, where the tail distributions of inter-arrival times follow a power law with exponent $ϕ>1$. Inhomogeneities are introduced as follows: vertical edges on selected columns are open (closed) with probability $q$ (respectively $1-q$), independently. Conversely, vertical edges within unselected columns and all horizontal edges are open (closed) with probability $p$ (respectively $1-p$). We prove that for all sufficiently large $ϕ$ (depending solely on $k$), the following assertion holds: if $q>p_c(\mathbb{S}^+_k)$, then $p$ can be taken strictly smaller than $p_c(\mathbb{S}^+_k)$ in a manner that percolation still occurs.

Let $G$ be a group. Associate a directed graph $\vec{E}(G)$ (called the Engel digraph of $G$) with $G$ whose vertex set is $G$, with an arc $(x,y)$ if $[y, {}_k x]=1$ for some positive integer $k$, where $[y,{}_kx]$ is the iterated commutator $[y,x,x,\ldots,x]$, with $k$ terms $x$ in the expression. From this we define the Engel graph $E(G)$ by ignoring directions; the co-Engel graph $E_c(G)$ is its complement. The co-Engel graph, under the name ``Engel graph'', was introduced by Abdollahi. However, the name we use is more natural. We begin with some general results about the Engel digraph and graph, before turning our attention to the co-Engel graph. Among other things, we show that the undirected Engel graph does not determine the directed version up to isomorphism, though counterexamples seem to be fairly rare: there are just two orders less than $100$ for which this happens. We also prove a universality theorem: every finite digraph is an induced sub-digraph of the Engel digraph of a finite group. The isolated vertices of $E_c(G)$ form the Fitting subgroup $F(G)$ of $G$. In this paper, we realize the induced subgraph of co-Engel graphs of certain finite non-Engel groups $G$ induced by $G \setminus F(G)$. We write $E_c^-(G)$ to denote the subgraph of $E_c(G)$ induced by $G \setminus F(G)$. We also compute genus, various spectra, energies and Zagreb indices of $E_c^-(G)$ for those groups. As a consequence, we determine (up to isomorphism) all finite non-Engel group $G$ such that the clique number of $E_c^-(G)$ is at most $4$ and $E_c^-(G)$ is toroidal or projective. Further, we show that $E_c^-(G)$ is ALQ-integral and satisfies the E-LE conjecture and the Hansen-Vuki{č}evi{ć} conjecture for the groups considered in this paper.

We study Hölder continuity, $p^\mathrm{th}$-variation function and Riesz variation of Weierstrass-type functions along the sequence of $b$-adic partitions, where $b>1$ is an integer. By a Weierstrass-type function, we mean that in the definition of the well-known Weierstrass function, the power function is replaced by a submultiplicative function, and the Lipschitz continuous cosine and sine functions are replaced by a general periodic Hölder continuous function.

For a polarized family of complex projective manifolds, we identify the algebraic obstructions that govern the existence of approximate solutions to the Wess-Zumino-Witten equation. When this is specialized to the fibration associated with a projectivization of a vector bundle, we recover a version of Kobayashi-Hitchin correspondence. More broadly, we demonstrate that a certain auxiliary Monge-Ampère type equation, generalizing the Wess-Zumino-Witten equation by taking into account the weighted Bergman kernel associated with the Harder-Narasimhan filtrations of direct image sheaves, admits approximate solutions over any polarized family. These approximate solutions are shown to be the closest counterparts to true solutions of the Wess-Zumino-Witten equation whenever the latter do not exist, as they minimize the associated Yang-Mills functional. As an application, in a fibered setting, we prove an asymptotic converse to the Andreotti-Grauert theorem conjectured by Demailly.

We give a new proof of a slightly modified version of a result of Queffelec--Rose, by constructing a linear basis for the $\mathrm{SL}(n)$ skein algebra of the twice punctured sphere for any non-zero complex number $q$, excluding finitely many roots of unity of small order. In particular, the skein algebra is a commutative polynomial algebra in $n-1$ generators, where each generator is represented by an explicit $\mathrm{SL}(n)$ web, without crossings, on the surface. This includes the case $q=1$, where the skein algebra is identified with the coordinate ring of the $\mathrm{SL}(n)$ character variety of the twice punctured sphere. The proof of both the spanning and linear independence properties of the basis depends on the so-called $\mathrm{SL}(n)$ quantum trace map, due originally to Bonahon--Wong in the case $n=2$. Two consequences of our method are that the quantum trace map and the so-called splitting map embed the polynomial algebra into the Fock--Goncharov quantum higher Teichmüller space and the Lê--Sikora stated skein algebra, respectively, of the annulus. We end by discussing the relationship with Fock--Goncharov duality.

Gateable semiconductor quantum dots (QDs) provide a versatile platform for analog quantum simulations of electronic many-body systems. In particular, QD arrays offer a natural representation of the interacting $π$-electron system of small hydrocarbons. Here we investigate the prospects for extending QD simulators to encompass also the nuclear degrees of freedom. We represent the molecular vibrational modes by single-mode microwave resonators coupled capacitively to the QDs and study the gate-tunable energy transfer from a voltage-biased triple quantum dot (TQD) system to a single damped resonator mode. We determine the QD population inversions, the corresponding charge and energy currents as well as the resonator photon number, using Lindblad master equations and lowest-order perturbation theory within Keldysh Green function formalism. Along the way, we discuss the merits and shortcomings of the two methods.A central result is the interrelation of a pronounced minimum in the charge current with a maximum in energy transfer, arising from a gate-tunable interference effect in the molecular orbitals of the TQD electron system.

The longstanding cusp-core problem--the discrepancy between the steep central density cusps predicted by cold dark matter (DM) simulations and certain shallow cores observed in dwarf galaxies, in particular the associated diversity of inner profiles--remains hotly debated despite decades of study. Building on a new interpretation of fermionic isothermal halos, we identify a physical mechanism--degeneracy-induced depletion--in which degenerate inner cores of fermionic DM suppress the surrounding density over large scales. This effect persists even in dense baryonic environments. Within the framework of hierarchical structure formation, degeneracies developed in the smallest constituent subhalos induce low-density regions that collectively configure into a King-type core of the host DM halo, with a core density-radius relation consistent with observations. This scenario accounts for the diversity of DM inner profiles through variation in the average degeneracy of constituent subhalos, and suggests a connection between this diversity and the halo formation history. Thus, the cusp-core problem may be reconciled within the standard "cold" DM paradigm without invoking strong baryonic feedback, instead pointing to the fermionic nature of DM.

The next generation of rare-event searches, such as those aimed at determining the nature of particle dark matter or in measuring fundamental neutrino properties, will benefit from particle detectors with thresholds at the meV scale, 100-1000x lower than currently available. Quantum parity detectors (QPDs) are a class of proposed quantum devices, extending recent work on superconducting qubit sensors, that exploit the fingerprints of single quasiparticle tunneling across a coherent weak-link as their detection concept. As envisioned, phonons generated by particle interactions within a crystalline substrate cause an eventual quasiparticle cascade within a surface-patterned superconducting qubit element. This process alters the fundamental charge parity of the device in a binary manner, which can be used to deduce the initial properties of the energy deposition. This work lays out multiple resonator coupled readout schemes depending on qubit architecture, provides an analytic formulation for reconstructing sensor energies, and details strategies for multiplexing large arrays of sensors. We further compute the sensitivity of QPDs and detail an R&D pathway to demonstrating sub-eV energy deposit thresholds.

We prove that Hamiltonicity in maximum-degree-3 grid graphs (directed or undirected) is ASP-complete, i.e., it has a parsimonious reduction from every NP search problem (including a polynomial-time bijection between solutions). As a consequence, given k Hamiltonian cycles, it is NP-complete to find another; and counting Hamiltonian cycles is #P-complete. If we require the grid graph's vertices to form a full $m \times n$ rectangle, then we show that Hamiltonicity remains ASP-complete if the edges are directed or if we allow removing some edges (whereas including all undirected edges is known to be easy). These results enable us to develop a stronger "T-metacell" framework for proving ASP-completeness of rectangular puzzles, which requires building just a single gadget representing a degree-3 grid-graph vertex. We apply this general theory to prove ASP-completeness of 38 pencil-and-paper puzzles where the goal is to draw a loop subject to given constraints: Slalom, Onsen-meguri, Mejilink, Detour, Tapa-Like Loop, Kouchoku, Icelom; Masyu, Yajilin, Nagareru, Castle Wall, Moon or Sun, Country Road, Geradeweg, Maxi Loop, Mid-loop, Balance Loop, Simple Loop, Haisu, Reflect Link, Linesweeper; Vertex/Touch Slitherlink, Dotchi-Loop, Ovotovata, Building Walk, Rail Pool, Disorderly Loop, Ant Mill, Koburin, Mukkonn Enn, Rassi Silai, (Crossing) Ichimaga, Tapa, Canal View, Aqre, and Paintarea. The last 14 of these puzzles were not even known to be NP-hard. Along the way, we prove ASP-completeness of some simple forms of Tree-Residue Vertex-Breaking (TRVB), including planar multigraphs with degree-6 breakable vertices, or with degree-4 breakable and degree-1 unbreakable vertices.

We analyse the effect of agent-dependent heavy-tailed waiting times in the voter model on the complete graph with $N$ vertices. We derive a novel scaling limit and show the existence of a limiting infinite voter model on the slowest updating sites. We further derive the consensus probabilities in the limit model explicitly. In the mean-field setting, the limit is determined by the extreme-value landscape of the waiting times and depends only on the tail index. To obtain these results, we study the coalescing system of random walks that is dual to the limit voter model and prove, among other auxiliary results, that it comes down from infinity.

In the first part of the paper, we formulate several arithmetic transfer conjectures, which are variants of the arithmetic fundamental lemma conjecture in the presence of ramification. The ramification comes from the choice of non-hyperspecial parahoric level structure. We prove a graph version of these arithmetic transfer conjectures, by relating it to the quasi-canonical arithmetic fundamental lemma, which we also establish. We relate some of the arithmetic transfer conjectures to the arithmetic fundamental lemma conjecture for the whole Hecke algebra in our recent paper arXiv:2305.14465. As a consequence, we prove these conjectures in some simple cases. In the second part of the paper, we elucidate the structure of an integral model of a certain member of the almost selfdual Rapoport-Zink tower, thereby proving conjectures of Kudla and the second author. This result allows us verify the hypotheses of the graph version of the arithmetic transfer conjectures in a particular case.

This paper studies the matrix Moment-SOS hierarchy for solving polynomial matrix optimization. Our first result is to show the finite convergence of this hierarchy, if the nondegeneracy condition, strict complementarity condition and second order sufficient condition hold at every minimizer, under the Archimedean property. A useful criterion for detecting the finite convergence is the flat truncation. Our second result is to show that every minimizer of the moment relaxation must have a flat truncation when the relaxation order is big enough, under the above mentioned optimality conditions. These results give connections between nonlinear semidefinite optimization theory and Moment-SOS methods for solving polynomial matrix optimization.

Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to develop a general approach to the dynamics of quantum/classical hybrid systems. By using two coupled stochastic differential equations, we can describe a classical component and a quantum one which have their own intrinsic dynamics and which interact with each other. A mathematically rigorous construction is given, under the restriction of having a Markovian joint dynamics and of involving only bounded operators on the Hilbert space of the quantum component. An important feature is that, if the interaction allows for a flow of information from the quantum component to the classical one, necessarily the dynamics is dissipative. We show also how this theory is connected to a suitable hybrid dynamical semigroup, which reduces to a quantum dynamical semigroup in the purely quantum case and includes Liouville and Kolmogorov-Fokker-Plank equations in the purely classical case. Moreover, this semigroup allows to compare the proposed stochastic dynamics with various other proposals based on hybrid master equations. Some simple examples are constructed in order to show the variety of physical behaviours which can be described; in particular, a model presenting hidden entanglement is introduced.

The theory of entire functions and its applications were at the center of Ostrovskii's research interests throughout his entire career. He made lasting contributions to several aspects of this theory, and many of his works had a significant influence on subsequent research. In this note, we describe some of this work.

Recently, the TRIUMF Storage Ring (TRISR), a storage ring for the existing Isotope Separator and Accelerator-I (ISAC-I) radioactive ion beam facility at TRIUMF, was proposed. It may be possible to directly measure neutron-induced radiative capture reactions in inverse kinematics by combining the ring with a high-flux neutron generator as the neutron target. Herein, we present the conceptual design of a low-energy ion storage ring as well as a fusion product extraction system with a Wien filter and recoil separator for detecting neutron capture products based on ion optical calculations and particle-tracking simulations.

Let $\lfloor t\rfloor$ denote the integer part of $t\in\mathbb{R}$ and $\|x\|$ the distance from $x$ to the nearest integer. Suppose that $1/2<γ_2<γ_1<1$ are two fixed constants. In this paper, it is proved that, whenever $α$ is an irrational number and $β$ is any real number, there exist infinitely many prime numbers $p$ in the intersection of two Piatetski--Shapiro sets, i.e., $p=\lfloor n_1^{1/γ_1}\rfloor=\lfloor n_2^{1/γ_2}\rfloor$, such that \begin{equation*} \|αp^2+β\|<p^{-\frac{14(γ_1+γ_2)-27}{43}+\varepsilon}, \end{equation*} provided that $27/14<γ_1+γ_2<2$. This result constitutes an generalization upon the previous result of Dimitrov [4].

Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been proposed. Meanwhile, motivated by realistic applications, the minimum spanning tree problem in stochastic network has attracted considerable attention of researchers, with respect to which stochastic and robust spanning tree models and related algorithms have been continuingly developed. However, all of them would be either too restricted by the types of the edge weight random variables or computationally intractable, especially in large-scale networks. In this paper, we introduce a target-based distributionally robust optimization framework to solve the minimum spanning tree problem in stochastic graphs where the probability distribution function of the edge weight is unknown but some statistical information could be utilized to prevent the optimal solution from being too conservative. We propose two exact algorithms to solve it, based on Benders decomposition framework and a modified classical greedy algorithm of MST problem (Prim algorithm),respectively. Compared with the NP-hard stochastic and robust spanning tree problems,The proposed target-based distributionally robust minimum spanning tree problem enjoys more satisfactory algorithmic aspect and robustness, when faced with uncertainty in input data.