Generic observability for port-Hamiltonian descriptor systems. - In: Mathematics of control, signals, and systems, ISSN 1435-568X, Bd. 0 (2024), 0, insges. 43 S.
The present work is a successor of Ilchmann and Kirchhoff (Math Control Signals Syst 33:359-377, 2021. https://doi.org/10.1007/s00498-021-00287-x), Ilchmann and Kirchhoff (Math Control Signals Syst 35:45-76, 2023. https://doi.org/10.1007/s00498-021-00287-x) on (relative) generic controllability of unstructured linear differential-algebraic systems and of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156) on (relative) generic controllability of port-Hamiltonian descriptor systems. We extend their results to (relative) genericity of observability. For unstructured differential-algebraic systems, criteria for (relative) generic observability are derived from Ilchmann and Kirchhoff (Math Control Signals Syst 35:45-76, 2023. https://doi.org/10.1007/s00498-021-00287-x) using duality. This is not possible for port-Hamiltonian systems. Hence, we tweak the results of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156) and derive similar criteria as for the unstructured case. Additionally, we consider certain rank constraints on the system matrices.
https://doi.org/10.1007/s00498-024-00388-3
PT-symmetric dynamical confinement: Fermi acceleration, quantum force, and Berry phase. - In: Physical review, ISSN 2469-9934, Bd. 109 (2024), 5, 053519
We consider a quantum particle under the dynamical confinement caused by PT-symmetric box with a moving wall. The latter is described in terms of the time-dependent Schrödinger equation obeying the time-dependent PT-symmetric boundary conditions. The class of the functions, describing time dependence of the wall's position and keeping the system as PT-symmetric is found. Physically observable characteristics, such as average kinetic energy and the average quantum force are calculated as a function of time. It is found that the behavior of the average kinetic energy as a function of time is completely different than that for of Hermitian counterpart of the model, while the average quantum force behaves similarly to that for Hermitian system. Also, geometric phase is calculated for the harmonically oscillating wall regime. The experimental realization of the proposed model is discussed.
https://doi.org/10.1103/PhysRevA.109.053519
Sharp threshold for embedding balanced spanning trees in random geometric graphs. - In: Journal of graph theory, ISSN 1097-0118, Bd. 107 (2024), 1, S. 107-125
A rooted tree is balanced if the degree of a vertex depends only on its distance to the root. In this paper we determine the sharp threshold for the appearance of a large family of balanced spanning trees in the random geometric graph G(n,r,d). In particular, we find the sharp threshold for balanced binary trees. More generally, we show that all sequences of balanced trees with uniformly bounded degrees and height tending to infinity appear above a sharp threshold, and none of these appears below the same value. Our results hold more generally for geometric graphs satisfying a mild condition on the distribution of their vertex set, and we provide a polynomial time algorithm to find such trees.
https://doi.org/10.1002/jgt.23106
Adjustable robust energy operation planning under uncertain renewable energy production. - In: Energies, ISSN 1996-1073, Bd. 17 (2024), 8, 1917, S. 1-14
In this paper, the application of the method of affinely adjustable robust optimization to a planning model of an energy system under uncertain parameters is presented, and the total scheduling costs in comparison with the deterministic model are evaluated. First, the basics of optimization under uncertain data are recapped, and it is described how these methods can be used in different applications for energy systems. This is followed by the methodology of adjustable robust optimization by defining the affinely adjustable robust counterpart. Finally, a numerical case study is conducted to compare the adjustable robust method with a rolling deterministic scheduling method. Both are implemented on a model of an energy system and compared with each other by simulation using real-world data. By calculating the total operating costs for both methods, it can be concluded that the adjustable robust optimization provides a significantly more cost-effective solution to the scheduling problem.
https://doi.org/10.3390/en17081917
GraphLearner: an approach to sequence recognition and generation. - In: IEEE Xplore digital library, ISSN 2473-2001, (2024), S. 445-451
This paper presents GraphLearner a neuromorphic sequence generator with similarities to Markov Chain Models. GraphLearner is proposed as an alternative to ‘black box’ deep neural network models which lack explainability and adaptability. Bloom Filters are used to simplify otherwise computationally expensive Markov chain probability calculations. It is demonstrated with Natural Language Processing tasks, generating sentences of remarkable quality.
https://doi.org/10.1109/BigComp60711.2024.00098
The mystery of Carleson frames. - In: Applied and computational harmonic analysis, ISSN 1096-603X, Bd. 72 (2024), 101659, S. 1-5
In 2016 Aldroubi et al. constructed the first class of frames having the form {Tkφ}k=0∞ for a bounded linear operator on the underlying Hilbert space. In this paper we show that a subclass of these frames has a number of additional remarkable features that have not been identified for any other frames in the literature. Most importantly, the subfamily obtained by selecting each Nth element from the frame is itself a frame, regardless of the choice of N∈N. Furthermore, the frame property is kept upon removal of an arbitrarily finite number of elements.
https://doi.org/10.1016/j.acha.2024.101659
Notes on the value function approach to multiobjective bilevel optimization. - In: Optimization, ISSN 1029-4945, Bd. 0 (2024), 0, S. 1-37
This paper is concerned with the value function approach to multiobjective bilevel optimization which exploits a lower-level frontier-type mapping in order to replace the hierarchical model of two interdependent multiobjective optimization problems by a single-level multiobjective optimization problem. As a starting point, different value-function-type reformulations are suggested and their relations are discussed. Here, we focus on the situations where the lower-level problem is solved up to efficiency or weak efficiency, and an intermediate solution concept is suggested as well. We study the graph-closedness of the associated efficiency-type and frontier-type mappings. These findings are then used for two purposes. First, we investigate existence results in multiobjective bilevel optimization. Second, for the derivation of necessary optimality conditions via the value function approach, it is inherent to differentiate frontier-type mappings in a generalized way. Here, we are concerned with the computation of upper coderivative estimates for the frontier-type mapping associated with the setting where the lower-level problem is solved up to weak efficiency. We proceed in two ways, relying, on the one hand, on a weak domination property and, on the other hand, on a scalarization approach. Illustrative examples visualize our findings and some flaws in the related literature.
https://doi.org/10.1080/02331934.2024.2323107
Error bounds for kernel-based approximations of the Koopman operator. - In: Applied and computational harmonic analysis, ISSN 1096-603X, Bd. 71 (2024), 101657, S. 1-25
We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the data are collected from long-term ergodic simulations. We derive both an exact expression for the variance of the kernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and probabilistic bounds for the finite-data estimation error. Moreover, we derive a bound on the prediction error of observables in the RKHS using a finite Mercer series expansion. Further, assuming Koopman-invariance of the RKHS, we provide bounds on the full approximation error. Numerical experiments using the Ornstein-Uhlenbeck process illustrate our results.
https://doi.org/10.1016/j.acha.2024.101657
Minimum degree conditions for containing an r-regular r-connected spanning subgraph. - In: European journal of combinatorics, Bd. 118 (2024), 103940, S. 1-23
We study optimal minimum degree conditions when an n-vertex graph G contains an r-regular r-connected spanning subgraph. We prove for r fixed and n large the condition to be δ (G) ≥ n+r-2 / 2 when nr ≡ 0 (mod 2). This answers a question of M. Kriesell.
https://doi.org/10.1016/j.ejc.2024.103940
Criteria for the construction of MDS convolutional codes with good column distances. - In: Advances in mathematics of communications, ISSN 1930-5338, Bd. 18 (2024), 2, S. 595-613
Maximum-distance separable (MDS) convolutional codes are characterized by the property that their free distance reaches the generalized Singleton bound. In this paper, new criteria to construct MDS convolutional codes are presented. These codes also possess optimal first (reverse) column distances. The new criteria allow to relate the construction of MDS convolutional codes to those of reverse superregular Toeplitz matrices. Moreover, using the new criteria as well as the help of computer search, examples for MDS convolutional codes over small finite fields are given.
https://doi.org/10.3934/amc.2023060