We consider the problem of propagating the uncertainty from a possibly large number of random inputs through a computationally expensive model. Stratified sampling is a well-known variance reduction strategy, but its application, thus far, has focused on models with a limited number of inputs due to the challenges of creating uniform partitions in high dimensions. To overcome these challenges, we propose a simple methodology for constructing an effective stratification of the input domain that is adapted to the model response. Our approach leverages neural active manifolds, a recently introduced nonlinear dimensionality reduction technique based on neural networks that identifies a one-dimensional manifold capturing most of the model variability. The resulting one-dimensional latent space is mapped to the unit interval, where stratification is performed with respect to the uniform distribution. The corresponding strata in the original input space are then recovered through the neural active manifold, generating partitions that tend to follow the level sets of the model. We show that our approach is effective in high dimensions and can be used to further reduce the variance of multifidelity Monte Carlo estimators.

We prove the optimal $C^{1,1}$ regularity of the volume function on the big cone of a projective manifold, and investigate its regularity when restricted to segments moving in ample directions.

Light possesses both spin and orbital angular momentum, which can spontaneously couple in spatially asymmetric optical fields. This phenomenon is referred to as optical spin-orbit coupling. This coupling is pivotal in modern optics due to its broad applications in communications, sensing, and quantum control. A central challenge is to elucidate how spatial asymmetries in optical fields facilitate this coupling. Previous research has primarily addressed spatial asymmetry using materials and devices such as lenses, interfaces, inhomogeneous media, and metasurfaces. However, Maxwell's equations indicate that matter can also introduce temporal asymmetry to optical fields. For instance, magnetic ordering can break time-reversal symmetry via the magneto-optical effect, resulting in nonreciprocal optical phenomena. Despite its importance, the combined effects of spatial and temporal asymmetries in optical fields remain unexplored. This study demonstrates that breaking time-reversal symmetry via magnons and spatial symmetry via light focusing enables the nonreciprocal transformation of a Gaussian beam into an optical vortex beam. This effect is attributed to the interplay between magnon-induced Brillouin light scattering and optical spin-orbit coupling. The results indicate that total angular momentum, including contributions from both magnons and photons, is conserved, suggesting that magnons can control both the spin and orbital angular momentum of light.

Quantum simulation offers a powerful approach to studying quantum field theories, particularly (2+1)D quantum electrodynamics (QED$_3$) with Wilson fermions, which hosts a rich landscape of physical phenomena. A key challenge in lattice formulations is the proper realization of topological phases and the Chern-Simons terms, where fermion discretization plays a crucial role. In this work, we highlight the differences between staggered and Wilson fermions coupled to $\text{U}(1)$ gauge fields in the Hamiltonian formulation. We analyze why staggered fermions fail to induce (2+1)D topological phases, while Wilson fermions admit a variety of topological phases including Chern insulator and quantum spin Hall phases. Additionally, we uncover a rich phase diagram for the two-flavor Wilson fermion model in the presence of a chemical potential. Our findings resolve existing ambiguities in Hamiltonian formulations and provide a theoretical foundation for future quantum simulations of lattice field theories with topological phases. We further outline connections to experimental platforms, offering guidance for implementations on near-term quantum computing architectures. A complementary presentation of the analytical calculations, the identification of robust topological structure and response, and extensive numerical results is contained in a joint submission [1].

Stochastic Ising machines, sIMs, are highly promising accelerators for optimization and sampling of computational problems that can be formulated as an Ising model. Here we investigate the computational advantage of sIM for simulations of quantum magnets with neural-network quantum states (NQS), in which the quantum many-body wave function is mapped onto an Ising model. We study the sampling performance of sIM for NQS by comparing sampling on a software-emulated sIM with standard Metropolis-Hastings sampling for NQS. We quantify the sampling efficiency by the number of computational steps required to reach iso-accurate stochastic estimation of the variational energy and show that this is entirely determined by the autocorrelation time of the sampling. This enables predictions of sampling advantage without direct deployment on hardware. Although sampling of the quantum Heisenberg models studied exhibits much longer autocorrelation times on sIMs, the massively parallel sampling of hardware sIMs leads to a projected speed-up of 100 to 10000, suggesting great opportunities for studying complex quantum systems at larger scales.

Ensemble-based methods for data assimilation and emission inversions are a popular way to encode flow-dependency within the model error covariance. While most ensemble methods do not require the use of an adjoint model, the need to repeatedly run a geophysical model to generate the ensemble can be a significant computational burden. In this paper, we introduce EnsAI, a new AI-based ensemble generation system for atmospheric chemical constituents. When trained on an existing ensemble for ammonia generated by the GEM-MACH air quality model, it was shown that the ensembles produced by EnsAI can accurately reproduce the meteorology-dependent features of the original ensemble, while generating the ensemble 3,300 times faster than the original GEM-MACH ensemble. While EnsAI requires an upfront cost for generating an ensemble used for training, as well as the training itself, the long term computational savings can greatly exceed these initial computational costs. When used in an emissions inversion system, EnsAI produced similar inversion results to those in which the original GEM-MACH ensemble was used while using significantly less computational resources.

It is long known that quantum Calogero models feature intertwining operators, which increase or decrease the coupling constant by an integer amount, for any fixed number of particles. We name these as ``horizontal'' and construct new ``vertical'' intertwiners, which \emph{change the number of interacting particles} for a fixed but integer value of the coupling constant. The emerging structure of a grid of intertwiners exists only in the algebraically integrable situation (integer coupling) and allows one to obtain each Liouville charge from the free power sum in the particle momenta by iterated intertwining either horizontally or vertically. We present recursion formulæ for the intertwiners as a factorization problem for partial differential operators and prove their existence for small values of particle number and coupling. As a byproduct, a new basis of non-symmetric Liouville integrals appears, algebraically related to the standard symmetric one.

Dissipative processes have long been proposed as a means of performing computational tasks on quantum computers that may be intrinsically more robust to noise. In this work, we prove two main results concerning the error-resilience capabilities of two types of dissipative algorithms: dissipative ground state preparation in the form of the dissipative quantum eigensolver (DQE), and dissipative quantum computation (DQC). The first result is that under circuit-level depolarizing noise, a version of the DQE algorithm applied to the geometrically local, stabilizer-encoded Hamiltonians that arise naturally when fermionic Hamiltonians are represented in qubits, can suppress the additive error in the ground space overlap of the final output state exponentially in the code distance. This enables us to get closer to fault-tolerance for this task without the associated overhead. In contrast, for computation as opposed to ground state preparation, the second result proves that DQC is no more robust to noise than the standard quantum circuit model.

The physics of the SYK model at low temperatures is dominated by a soft mode governed by the Schwarzian action. In arXiv:1604.07818 the linearised action was derived from the soft mode contribution to the four-point function, and physical arguments were presented for its nonlinear completion to the Schwarzian. In this paper, we give two derivations of the full nonlinear effective action in the large $p$ limit, where $p$ is the number of fermions in the interaction terms of the Hamiltonian. The first derivation uses that the collective field action of the large-$p$ SYK model is Liouville theory with a non-conformal boundary condition that we study in conformal perturbation theory. This derivation can be viewed as an explicit version of the renormalisation group argument for the nonlinear soft mode action in arXiv:1711.08467. The second derivation uses an Ansatz for how the soft mode embeds into the microscopic configuration space of the collective fields. We generalise our results for the large-$p$ SYK chain and obtain a "Schwarzian chain" effective action for it. These derivations showcase that the large-$p$ SYK model is a rare system, in which there is sufficient control over the microscopic dynamics, so that an effective description can be derived for it without the need for extra assumptions or matching (in the effective field theory sense).

We study the computational power that oblivious robots operating in the plane have under sequential schedulers. We show that this power is much stronger than the obvious capacity these schedulers offer of breaking symmetry, and thus to create a leader. In fact, we prove that under any sequential scheduler, robots are capable of solving problems that are unsolvable even with a leader under the fully synchronous scheduler FSYNC. More precisely, we consider the class of pattern formation problems, and focus on the most general problem in this class, Universal Pattern Formation (UPF), which requires the robots to form every pattern given in input, starting from any initial configuration (where some robots may occupy the same point, hence forming a multiplicity). We first show that UPF is unsolvable under FSYNC, even if the robots are endowed with additional strong capabilities (multiplicity detection, rigid movement, agreement on coordinate systems, presence of a unique leader). On the other hand, we prove that, except for point formation (Gathering), UPF is solvable under any sequential scheduler without any additional assumptions. We then turn our attention to the Gathering problem, and prove that weak multiplicity detection (the ability to detect a multiplicity but not the exact number of robots forming it) is necessary and sufficient for solvability under sequential schedulers. The results obtained show that the computational power of the robots under FSYNC (where Gathering is solvable without any multiplicity detection) and that under sequential schedulers are orthogonal.

One Health issues, such as the spread of highly pathogenic avian influenza~(HPAI), present significant challenges at the human-animal-environmental interface. Recent H5N1 outbreaks underscore the need for comprehensive modeling efforts that capture the complex interactions between various entities in these interconnected ecosystems. To support such efforts, we develop a methodology to construct a synthetic spatiotemporal gridded dataset of livestock production and processing, human population, and wild birds for the contiguous United States, called a \emph{digital similar}. This representation is a result of fusing diverse datasets using statistical and optimization techniques, followed by extensive verification and validation. The livestock component includes farm-level representations of four major livestock types -- cattle, poultry, swine, and sheep -- including further categorization into subtypes such as dairy cows, beef cows, chickens, turkeys, ducks, etc. Weekly abundance data for wild bird species identified in the transmission of avian influenza are included. Gridded distributions of the human population, along with demographic and occupational features, capture the placement of agricultural workers and the general population. We demonstrate how the digital similar can be applied to evaluate spillover risk to dairy cows and poultry from wild bird population, then validate these results using historical H5N1 incidences. The resulting subtype-specific spatiotemporal risk maps identify hotspots of high risk from H5N1 infected wild bird population to dairy cattle and poultry operations, thus guiding surveillance efforts.

In this article we show that Maximum Partial List H-Coloring is polynomial-time solvable on P_5-free graphs for every fixed graph H. In particular, this implies that Maximum k-Colorable Subgraph is polynomial-time solvable on P_5-free graphs. This answers an open question from Agrawal, Lima, Lokshtanov, Saurabh & Sharma [SODA 2024]. This also improves the $n^{O(ω(G))}$-time algorithm for Maximum Partial H-Coloring by Chudnovsky, King, Pilipczuk, Rzążewski & Spirkl [SIDMA 2021] to polynomial-time algorithm.

Two-Time relativistic Bohmian Model (TTBM) is a theory in which the apparently paradoxical aspects of Quantum Mechanics are the effect of the existence of an extra unobservable time dimension. The hypothesis that matter is capable of motion with respect to an additional independent time (thus resulting instantaneous with respect to usual time) is capable of restoring determinism, explaining the Zitterbewegung without evoking virtual antimatter. The model also predicts a relativistic correction of the uncertainty principle. Here the model is first summarized (definition, salient properties and empiricism) and after applied to a generic spherical atomic orbit, obtaining electron oscillations in the new time dimension, tau, which demonstrate the static nature of the orbitals. Something very similar happens in the case of a particle in a box, where tau-oscillations cause the particle to spread out at steady states. Some astrophysical and about spin speculations follow. Finally, it is discussed how the model fits into the fundamental problem of the definition of time in Quantum Mechanics. Keywords: Quantum Mechanics Foundations; de Broglie-Bohm Theory; Zitterbewegung; Uncertainty principle verification; Extra dimensions; Atomic orbitals; Spin; Definition of time in Quantum Mechanics.

In this article we give an overview of the Plancherel theory for Riemannian symmetric spaces Z = G/K. In particular we illustrate recently developed methods in Plancherel theory for real spherical spaces by explicating them for Riemannian symmetric spaces, and we explain how Harish-Chandra's Plancherel theorem for Z can be proven from these methods.

Prompt fission neutron spectra produced up to 20 MeV. Simultaneous analysis of measured and calculated data for 233U(n, F), 235U(n, F) and 239Pu(n, F) maintains stronger justification for the predicted PFNS of 233U(n, F). For the latter the reliable measured PFNS data are available at Eth only. Pre-fission neutron spectra influence the partitioning of fission energy between excitation energy and total kinetic energy of fission fragments. For the reactions 233U (n, F) and 235U (n, F) we have shown that the shape of PFNS depends on the fissility of composite and residual nuclei. The correlation of these peculiarities with contributions of (n, xnf) to the (n, F) and competition of (n, ng) and (n, xn) is established. Exclusive neutron spectra (n, xnf) are consistent with cross sections of 235U(n, F), 234U(n, F), 233U(n, F) and 232U(n,F) reactions, as well as neutron emissive spectra of 235U(n,xn) at 14 MeV. Initial model parameters for 233U (n,F) PFNS are fixed by description of prompt fission neutron spectra of 233U (nth, F). We predict the 233U(n,xnf) exclusive pre-fission neutron spectra of 233U(n,xn) reactions, total kinetic energy TKE of fission fragments and products, partials of average PFNS and observed PFNS of 233U(n,F). PFNS of 233U (n, F) are harder than those of 235U(n, F) PFNS, but softer than those of 239Pu(n, F). Difference of average energies of PFNS of 233U (n, F) and 235U(n, F) amounts to 1-3 %. At incident energies higher than (n, 2nf) reaction threshold the observed PFNS may seem similar, though the partial contributions of 233U(n,xnf) and 235U(n,xnf) are quite different. PFNS of 233U(n,xnf) are obtained in the energy range up to 20 MeV.

It is well known that ordered exponential fields with a compatible non-trivial valuation cannot be spherically complete, but there are some that are ``complete enough''. This paper gives analogues of Kaplansky's theorem on maximally valued fields that hold for a suitable class of elementary extensions of some ordered exponential fields with a compatible valuation. More precisely it does so for models of any theory $T_{\text{convex}}$ given by the expansion of a fixed complete o-minimal theory of ordered fields $T$, by a predicate $\mathcal{O}$ for a non-trivial $T$-convex valuation ring. For $λ$ an uncountable cardinal, say that a unary type $p(x)$ over a model of $T_{\text{convex}}$ is \emph{$λ$-bounded weakly immediate} if its cut is defined by an empty intersection of fewer than $λ$ many nested valuation balls. Call an elementary extension \emph{$λ$-bounded wim-constructible} if it is obtained as a transfinite composition of extensions each generated by one element whose type is $λ$-bounded weakly immediate. I show that $λ$-bounded wim-constructible extensions do not extend the residue-field sort and that any two wim-constructible extensions can be amalgamated in an extension which is again $λ$-bounded wim-constructible over both. A consequence of this is that given an uncountable cardinal $λ$, every model of $T_{\text{convex}}$ has a unique-up-to-isomorphism $λ$-spherically complete $λ$-bounded wim-constructible extension providing an analogue of Kaplansky's theorem. I call this extension the $T$-$λ$-spherical completion. Another consequence is that $T_{\mathrm{convex}}$ is \emph{definably spherically complete}. When $T$ is power bounded wim-constructible extensions are just the immediate extensions. I discuss the example of power bounded theories expanded by $\exp$ (\emph{simply exponential} theories).

In a previous publication, we studied the parameter space of the phenomenological Minimal Supersymmetric Standard Model (pMSSM) with a light neutralino thermal dark matter ($M_{\tildeχ_1^0} \leq M_h/2$) and observed that the recent results from the dark matter and collider experiments put strong constraints on this scenario. In this work, we present in detail the arguments behind the robustness of this result against scanning over the large number of parameters in pMSSM. The Run-3 of LHC will be crucial in probing the surviving regions of the parameter space. We further investigate the impact of light staus on our parameter space and also provide benchmarks which can be interesting for Run-3 of LHC. We analyse these benchmarks at the LHC using the machine learning framework of \texttt{XGBOOST}. Finally, we also discuss the effect of non-standard cosmology on the parameter space.

I present an unbiased method of mapping particles to distribution functions and vice versa. This method alone defines the canonical formulation of statistical mechanics, since it can be used to derive the principle of maximum entropy in both Boltzmann's paradigm and Gibbs' paradigm. A rigorous definition of the macrostate enables application of this statistical mechanical theory to self-gravitating systems, by decoupling time-averages and ensemble averages. I compute two-point correlation functions for self-gravitating and electrostatic systems.

Skiplists are used in a variety of applications for storing data subject to order criteria. In this article we discuss the design, analysis and performance of a concurrent deterministic skiplist on many-core NUMA nodes. We also evaluate the performance of concurrent lock-free unbounded queue implementation and two concurrent multi-reader,multi-writer(MWMR) hash table implementations and compare them with those from Intel's Thread Building Blocks(TBB) library. We introduce strategies for memory management that reduce page faults and cache misses for the memory access patterns in these data structures. This paper proposes hierarchical usage of concurrent data structures in programs to improve memory latencies by reducing memory accesses from remote NUMA nodes.

We study the SHORTEST PATH problem with positive disjunctive constraints from the perspective of parameterized complexity. For positive disjunctive constraints, there are certain pair of edges such that any feasible solution must contain at least one edge from every such pair. In this paper, we initiate the study of SHORTEST PATH problem subject to some positive disjunctive constraints the classical version is known to be NP-Complete. Formally, given an undirected graph G = (V, E) with a forcing graph H = (E, F) such that the vertex set of H is same as the edge set of G. The goal is to find a set S of at most k edges from G such that S forms a vertex cover in H and there is a path from s to t in the subgraph of G induced by the edge set S. In this paper, we consider two natural parameterizations for this problem. One natural parameter is the solution size, i.e. k for which we provide a kernel with O(k^5) vertices when both G and H are general graphs. Additionally, when either G or H (but not both) belongs to some special graph classes, we provied kernelization results with O(k^3) vertices . The other natural parameter we consider is structural properties of H, i.e. the size of a vertex deletion set of H to some special graph classes. We provide some fixed-parameter tractability results for those structural parameterizations.

Ground Delay Programs (GDPs) mitigate demand-capacity imbalances by holding flights on the ground when an airport's arrival capacity is reduced, thereby reducing costly airborne holding. A central challenge is that day-to-day demand-capacity balancing relies on accurate predictions of airport capacities. However, these predictions are deeply uncertain: forecast errors, operational disruptions, and climate change-driven shifts in weather severity can induce distribution shifts in capacity outcomes. Thus, policies optimized for a single predicted distribution may be brittle out of sample. We address this challenge by developing a \emph{distributionally robust} framework for the single airport ground holding problem (dr-SAGHP). We also propose a method integrates Kelly's cutting plane method with the integer L-shaped method, and that is applicable more broadly to two-stage distributionally robust integer programs with relatively complete recourse and continuous second-stage decision variables. Our method includes a novel dual bisection and primal recovery algorithm that makes use of the structure of the distributionally robust integer program in order to quickly generate subgradients required by Kelly's cutting plane method. In computational experiments, our proposed algorithm delivers up to two orders-of-magnitude speedups compared to solving the convex reformulation directly, while maintaining negligible optimality gaps. We generate capacity scenarios via Gaussian process regression and evaluate out-of-sample performance by perturbing the posterior mean and variance. The numerical experiment results show that dr-SAGHP delivers significant out-of-sample gains under moderate-to-severe shifts, improving the resilience and effectiveness of GDP decision-making under capacity uncertainty.

Privacy in multi-agent control is receiving increased attention, though often a networked system and privacy protections are designed separately, which can harm performance. Therefore, this paper presents a co-design framework for networks and private controllers, and we apply it to private formation control. Agents' state trajectories are protected using differential privacy, and we quantify its impact by bounding the steady-state error for private formations. Then, we analyze tradeoffs between privacy level, system performance, and connectedness of the network's communication topology. These tradeoffs are used to formulate a co-design optimization framework to jointly design agents' communication topology and their privacy levels. Simulation results illustrate the success of this framework.

We define a new family of discrete representations of relatively hyperbolic groups which unifies many existing definitions and examples of geometrically finite behavior in higher rank. The definition includes the relative Anosov representations defined by Kapovich-Leeb and Zhu, and Zhu-Zimmer, as well as holonomy representations of various different types of "geometrically finite" convex projective manifolds. We prove that these representations are all stable under deformations whose restriction to the peripheral subgroups satisfies a dynamical condition, in particular allowing for deformations which do not preserve the conjugacy class of the peripheral subgroups.

We introduce the notion of formal multiparameter quantum universal enveloping algebras - in short FoMpQUEA - as a straightforward generalization of Drinfeld's quantum group. Then we show that the class of FoMpQUEA's is closed under deformations by ("toral") twists and deformations by ("toral") 2-cocycles: as a consequence, all "multiparameter formal QUEA's" considered so far are recovered, as falling within this class. In particular, we prove that any FoMpQUEA is isomorphic to a suitable deformation, by twist or by 2-cocycle, of Drinfeld's standard QUEA. We introduce also multiparameter Lie bialgebras (in short, MpLbA's), and we consider their deformations, by twist and by 2-cocycles. The semiclassical limit of every FoMpQUEA is a suitable MpLbA, and conversely each MpLbA can be quantized to a suitable FoMpQUEA. In the end, we prove that, roughly speaking, the two processes of "specialization" (of FoMpQUEA to a MpLbA) and of "deformation (by toral twist or toral 2-cocycle)" - at the level of FoMpQUEA's or of MpLbA's - do commute with each other.

A fundamental problem with nonlinear models is that maximum likelihood estimates are not guaranteed to exist. Though nonexistence is a well known problem in the binary response model literature, it presents significant challenges for other models and is not as well understood in more general settings. These challenges are only magnified for models that feature many fixed effects and other high-dimensional parameters. We address the current ambiguity surrounding this topic by studying the conditions that govern the existence of estimates for (pseudo-)maximum likelihood estimators used to estimate a wide class of generalized linear models (GLMs). We show that some, but not all, of these GLM estimators can still deliver consistent estimates of at least some of the linear parameters when these conditions fail to hold. We also demonstrate how to verify these conditions in models with high-dimensional parameters, such as panel data models with multiple levels of fixed effects.

We calculate the renormalization constants of the N=1, N=2, N=4 supersymmetric Yang-Mills theories in an arbitrary covariant gauge in the dimensional reduction scheme up to three loops. We have found, that the beta-functions for N=1 and N=4 SYM theories are the same from the different triple vertices. This means that the dimensional reduction scheme works correctly in these models up to third order of perturbative theory.

Coherent elastic neutrino-nucleus scattering (CE$ν$NS) is predominantly governed by vector neutral-current interactions, with subleading contributions arising from the axial current in nuclei with non-zero ground-state spin. Experimentally, the extraction of axial-current contributions has been so far of little interest, mainly because of the challenges its measurement entail. In this work, we investigate the relative size of the vector and axial components for target materials currently employed by the neutrino and dark matter experimental communities. We identify fluorine-based compounds as the most promising targets for probing the axial-current event rate. Among them, octafluoropropane ($\text{C}_3\text{F}_8$) emerges as a particularly suitable candidate, given its widespread use in spin-dependent dark matter searches and its relevance for upcoming dedicated CE$ν$NS experiments. Considering both pion decay-at-rest and reactor neutrino fluxes, we show that such measurements can allow an indirect determination of the axial coupling at the $\sim 10\%$ level, depending on flux uncertainties and detector thresholds. We further emphasize that measurements of the axial current will allow to probe spin-dependent new physics scenarios through CE$ν$NS.

Large language models (LLMs) can be used to support software development tasks, e.g., through code completion or code generation. However, their effectiveness drops significantly when considering less popular programming languages such as domain-specific languages (DSLs). In this paper, we propose a generic framework for evaluating the capabilities of LLMs generating DSL code from textual specifications. The generated code is assessed from the perspectives of well-formedness and correctness. This framework is applied to a particular type of DSL, constraint languages, focusing our experiments on OCL and Alloy and comparing their results to those achieved for Python, a popular general-purpose programming language. Experimental results show that, in general, LLMs have better performance for Python than for OCL and Alloy. LLMs with smaller context windows such as open-source LLMs may be unable to generate constraint-related code, as this requires managing both the constraint and the domain model where it is defined. Moreover, some improvements to the code generation process such as code repair (asking an LLM to fix incorrect code) or multiple attempts (generating several candidates for each coding task) can improve the quality of the generated code. Meanwhile, other decisions like the choice of a prompt template have less impact. All these dimensions can be systematically analyzed using our evaluation framework, making it possible to decide the most effective way to set up code generation for a particular type of task.

Most statistical process monitoring methods for multichannel profiles focus solely on the mean and are almost ineffective when changes involve the covariance structure. Although it is known to be crucial, covariance monitoring requires estimating a much larger number of parameters, which may shift in a subtle and sparse fashion. That is, an out-of-control (OC) state may manifest with small deviations and affect only a very limited subset of these parameters. To address these difficulties, we propose a multichannel profile covariance (MPC) control chart based on functional graphical models that provide an interpretable representation of conditional dependencies between profiles. A nonparametric combination of the likelihood-ratio tests corresponding to different sparsity levels is then used to draw an overall inference and signal whether an OC state may have occurred. Between-profile relationships that are likely to have shifted are naturally identified at no additional computational cost. An extensive Monte Carlo simulation study compares the MPC control chart with state-of-the-art competitors, and a case study on monitoring multichannel temperature profiles in a roasting machine illustrates its practical applicability.

We present a new approach for solving string equations as extensions of Nielsen transformations. Key to our work are the combination of three techniques: a power operator for strings; generalisations of Parikh images; and equality decomposition. Using these methods allows us to solve complex string equations, including less commonly encountered SMT inputs over strings.