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Qualitative timeline-based planning models domains as sets of independent, but interacting, components whose behaviors over time, the timelines, are governed by sets of qualitative temporal constraints (ordering relations), called synchronization rules. Its plan-existence problem has been shown to be PSPACE-complete; in particular, PSPACE-membership has been proved via reduction to the nonemptiness problem for nondeterministic finite automata. However, nondeterministic automata cannot be directly used to synthesize planning strategies as a costly determinization step is needed. In this paper, we identify a large fragment of qualitative timeline-based planning whose plan-existence problem can be directly mapped into the nonemptiness problem of deterministic finite automata, which can then be exploited to synthesize strategies. In addition, we identify a maximal subset of Allen's relations that fits into such a deterministic fragment., Comment: In Proceedings GandALF 2024, arXiv:2410.21884

For every given $\beta<0$, we study the problem of maximizing the first Robin eigenvalue of the Laplacian $\lambda_\beta(\Omega)$ among convex (not necessarily smooth) sets $\Omega\subset\mathbb{S}^{n}$ with fixed perimeter. In particular, denoting by $\sigma_n$ the perimeter of the $n$-dimensional hemisphere, we show that for fixed perimeters $P<\sigma_n$, geodesic balls maximize the eigenvalue. Moreover, we prove a quantitative stability result for this isoperimetric inequality in terms of volume difference between $\Omega$ and the ball $D$ of the same perimeter.

We investigate the behavior of the solution to an elliptic diffraction problem in the union of a smooth set $\Omega$ and a thin layer $\Sigma$ locally described by $\varepsilon h$, where $h$ is a positive function defined on the boundary $\partial\Omega$, and $\varepsilon$ is the ellipticity constant of the differential operator in the thin layer $\Sigma$. We study the problem in the limit for $\varepsilon$ going to zero and prove a first-order asymptotic development by $\Gamma$-convergence of the associated energy functional.

Quantum utility has been severely limited in superconducting quantum hardware until now by the modest number of qubits and the relatively high level of control and readout errors, due to the intentional coupling with the external environment required for manipulation and readout of the qubit states. Practical applications in the Noisy Intermediate Scale Quantum (NISQ) era rely on Quantum Error Mitigation (QEM) techniques, which are able to improve the accuracy of the expectation values of quantum observables by implementing classical post-processing analysis from an ensemble of repeated noisy quantum circuit runs. In this work, we focus on a recent QEM technique that uses Fuzzy C-Means (FCM) clustering to specifically identify measurement error patterns. For the first time, we report a proof-of-principle validation of the technique on a 2-qubit register, obtained as a subset of a real NISQ 5-qubit superconducting quantum processor based on transmon qubits. We demonstrate that the FCM-based QEM technique allows for reasonable improvement of the expectation values of single- and two-qubit gates based quantum circuits, without necessarily invoking state-of-the-art coherence, gate, and readout fidelities.

We investigate the relationship between the Neumann and Steklov principal eigenvalues emerging from the study of collapsing convex domains in $\mathbb{R}^2$. Such a relationship allows us to give a partial proof of a conjecture concerning estimates of the ratio of the former to the latter: we show that thinning triangles maximize the ratio among convex thinning sets, while thinning rectangles minimize the ratio among convex thinning with some symmetry property.

In the timeline-based approach to planning, the evolution over time of a set of state variables (the timelines) is governed by a set of temporal constraints. Traditional timeline-based planning systems excel at the integration of planning with execution by handling temporal uncertainty. In order to handle general nondeterminism as well, the concept of timeline-based games has been recently introduced. It has been proved that finding whether a winning strategy exists for such games is 2EXPTIME-complete. However, a concrete approach to synthesize controllers implementing such strategies is missing. This paper fills this gap, by providing an effective and computationally optimal approach to controller synthesis for timeline-based games., Comment: arXiv admin note: text overlap with arXiv:2209.10319

We are interested in the thermal insulation of a bounded open set $\Omega$ surrounded by a set whose thickness is locally described by $\varepsilon h$, where $h$ is a non-negative function defined on the boundary $\partial\Omega$. We study the problem in the limit for $\varepsilon$ going to zero using a first-order asymptotic development by $\Gamma$-convergence.

One of the main challenges concerning next generation tokamaks (such as DEMO) will be the development of a heat and power exhaust system able to withstand the large loads expected in the divertor region. A dedicated Divertor Tokamak Test (DTT) facility has been proposed in the EUROfusion Roadmap, with the aim of testing unconventional solutions, such as advanced magnetic configurations and liquid metal divertors. Magnetic control of alternative plasma configurations, such as the X-Divertor, will play a key role in the solution of the heat exhaust and yet can be a challenging point, due to increased sensitivity introduced by secondary x-points. To overcome the complications introduced by secondary x-points in advanced plasma shapes, magnetic control in DTT is achieved by resolving to the eXtreme Shape Controller, in order to control both the plasma shape and the secondary x-point position.

The Divertor Tokamak Test (DTT) facility will be equipped with in-vessel divertor coils able to locally modify the flux surfaces in the divertor region. When the first DTT divertor had not been selected, four in-vessel divertor coils were considered, with 10 turns each, fed by independent 4-quadrant SCR (thyristor) 0.5 kV - 5 kA - power supplies. This configuration was able to meet the design criteria in terms of requested performance and operational constraints, but one of the coils is not compatible with the geometry of the first DTT divertor, and another coil, scarcely efficient, can be removed. This paper discusses the design criteria, illustrates the possible revised layout, and illustrates the performance that can be achieved.

In the timeline-based approach to planning, originally born in the space sector, the evolution over time of a set of state variables (the timelines) is governed by a set of temporal constraints. Traditional timeline-based planning systems excel at the integration of planning with execution by handling temporal uncertainty. In order to handle general nondeterminism as well, the concept of timeline-based games has been recently introduced. It has been proved that finding whether a winning strategy exists for such games is 2EXPTIME-complete. However, a concrete approach to synthesize controllers implementing such strategies is missing. This paper fills this gap, outlining an approach to controller synthesis for timeline-based games., Comment: In Proceedings GandALF 2022, arXiv:2209.09333

In this paper, we generalize the notion of relative $p$-capacity of $K$ with respect to $\Omega$, by replacing the Dirichlet boundary condition with a Robin one. We show that, under volume constraints, our notion of $p$-capacity is minimal when $K$ and $\Omega$ are concentric balls. We use the $H$-function and a derearrangement technique.

We study a nonlinear generalization of a free boundary problem that arises in the context of thermal insulation. We consider two open sets $\Omega\subseteq A$, and we search for an optimal $A$ in order to minimize a non-linear energy functional, whose minimizers $u$ satisfy the following conditions: $\Delta_p u=0$ inside $A\setminus\Omega$, $u=1$ in $\Omega$, and a nonlinear Robin-like boundary $(p,q)$-condition on the free boundary $\partial A$. We study the variational formulation of the problem in SBV, and we prove that, under suitable conditions on the exponents $p$ and $q$, a minimizer exists and its jump set satisfies uniform density estimates.

We study the thermal insulation of a bounded body $\Omega\subset\mathbb{R}^n$, under a prescribed heat source $f>0$, via a bulk layer of insulating material. We consider a model of heat transfer between the insulated body and the environment determined by convection; this corresponds to Robin boundary conditions on the free boundary of the layer. We show that a minimal configuration exists and that it satisfies uniform density estimates.