This paper provides a complete characterization of the Dirichlet boundary outputs that can be exactly tracked in the one-dimensional heat equation with Neumann boundary control. The problem consists in describing the set of boundary traces generated by square-integrable controls over a finite or infinite time horizon. We show that these outputs form a precise functional space related to Gevrey regularity of order 2. In the infinite-time case, the trackable outputs are precisely those functions whose successive derivatives satisfy a weighted summability condition, which corresponds to specific Gevrey classes. For finite-time horizons, an additional compatibility condition involving the reachable space of the system provides a full characterization. The analysis relies on Fourier-Laplace transform, properties of Hardy spaces, the flatness method, and a new Plancherel-type theorem for Hilbert spaces of Gevrey functions. Beyond control theory, our results yield an optimal solution to the classical interpolation problem in Gevrey-2 classes, which improves results of Mitjagin on the optimal loss factor. The techniques developed here also extend to variants of the heat system with different boundary conditions or observation points.
The Unit Commitment (UC) problem seeks optimal generation schedules under technical and economic constraints. Increasing renewable energy penetration amplifies uncertainty in net load forecasting. Classical approaches, such as stochastic and robust UC models, partially address this challenge but face well-known drawbacks: stochastic formulations may overfit sampled scenarios, while robust methods tend to yield overly conservative solutions. To overcome these limitations, Distributionally Robust Optimization (DRO) has emerged as a promising alternative by explicitly accounting for ambiguity in probability distributions. While prior DRO studies in UC rely on moment constraints, ϕ-divergences or the Wasserstein distance with the L1 norm, the potential of other Wasserstein distances, especially with the L2-norm, remains unexplored. This paper presents a unified Benders decomposition framework for two-stage UC models with right-hand side uncertainty that efficiently solves various approaches, including DRO using Wasserstein distance. Numerical experiments on IEEE test systems evaluate out-of-sample performance and computational times across different uncertainty levels.
In vitro reconstitutions of microtubule assemblies have provided essential mechanistic insights into the molecular bases of microtubule dynamics and their interactions with associated proteins. The tubulin code has emerged as a regulatory mechanism for microtubule functions, which suggests that tubulin isotypes and post-translational modifications (PTMs) play important roles in controlling microtubule functions. To investigate the tubulin code mechanism, it is essential to analyze different tubulin variants in vitro. Until now, this has been difficult, as most reconstitution experiments have used heavily post-translationally modified tubulin purified from brain tissue. Therefore, we developed a protocol that allows purification of tubulin with controlled PTMs from limited sources through cycles of polymerization and depolymerization. Although alternative protocols using affinity purification of tubulin also yield very pure tubulin, our protocol has the unique advantage of selecting for fully functional tubulin, as non-polymerizable tubulin is excluded in the successive polymerization cycles. It thus provides a novel procedure for obtaining tubulin with controlled PTMs for in vitro reconstitution experiments. We describe specific procedures for tubulin purification from adherent cells, cells grown in suspension cultures and single mouse brains. The protocol can be combined with drug treatment, transfection of cells before tubulin purification or enzymatic treatment during the purification process. The amplification of cells and their growth in spinner bottles takes ~13 d; the tubulin purification takes 6-7 h. The tubulin can be used in total internal reflection fluorescence (TIRF)-microscopy-based experiments or pelleting assays for the investigation of intrinsic properties of microtubules and their interactions with associated proteins.
We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical languages for both affinely constrained classical mechanical systems, as well as odd-prime-dimensional stabiliser quantum circuits. To this end, we present affine Lagrangian relations by a particular class of undirected coloured graphs. In order to reason about composite systems, we introduce a powerful scalable notation where the vertices of these graphs are themselves coloured by graphs. In the setting of stabiliser quantum mechanics, this scalable notation gives an extremely concise description of graph states, which can be composed via “phased spider fusion.” Likewise, in the classical mechanical setting of electrical circuits, we show that impedance matrices for reciprocal networks are presented in essentially the same way.
This paper presents a thorough manufacturability study of 2507 super duplex stainless steel (SDSS) produced by the Laser Powder-Directed Energy Deposition (LP-DED) process. First, experimental observations on single-track surface morphology and geometrical characteristics are described. Then, dimensional and porosity analyses of thin walls and bulk samples are presented and discussed in order to identify the optimal process parameter combinations, from a process point of view, for further characterizations to determine the general properties of LP-DED-printed samples. Finally, the results obtained on wrought steel of the same grade are compared to those of the printed material in terms of microstructure, texture, and ferrite/austenite ratio. A set of meticulously chosen process parameters with regard to the process and the machine (nozzle size, maximum power deliverable) gives the optimal results for the as-built LP-DED material in terms of porosity and microstructure quality but with smaller grains (irrespective of the phase studied) and a higher proportion of ferrite (about 75
