Filippo Giorcelli, Sergej Antonello Sirigu, Giuseppe Giorgi
et al.
Among the challenges generated by the global climate crisis, a significant concern is the constant increase in energy demand. This leads to the need to ensure that any novel energy systems are not only renewable but also reliable in their performance. A viable solution to increase the available renewable energy mix involves tapping into the potential available in ocean waves and harvesting it via so-called wave energy converters (WECs). In this context, a relevant engineering problem relates to finding WEC design solutions that are not only optimal in terms of energy extraction but also exhibit robust behavior in spite of the harsh marine environment. Indeed, the vast majority of design optimization studies available in the state-of-the-art consider only perfect knowledge of nominal (idealized) conditions, neglecting the impact of uncertainties. This study aims to investigate the information that different robustness metrics can provide to designers regarding optimal WEC design solutions under uncertainty. The applied methodology is based on stochastic uncertainty propagation via a Monte Carlo simulation, exploiting a meta-model to reduce the computational burden. The analysis is conducted over a dataset obtained with a genetic algorithm-based optimization process for nominal WEC design. The results reveal a significant deviation in terms of robustness between the nominal Pareto set and those generated by setting different thresholds for robustness metrics, as well as between devices belonging to the same nominal Pareto frontier. This study elucidates the intrinsic need for incorporating robust optimization processes in WEC design.
In this article, we consider a special operator called the two-dimensional rotation operator and analyze its convergence and finite-sample bounds under the $l_2$ norm and $l_\infty$ norm with constant step size. We then consider the same problem with stochastic noise with affine variance. Furthermore, simulations are provided to illustrate our results. Finally, we conclude this article by proposing some possible future extensions.
A combinatorial Gray code for a set of combinatorial objects is a sequence of all combinatorial objects in the set so that each object is derived from the preceding object by changing a small part. In this paper we design a Gray code for ordered trees with n vertices such that each ordered tree is derived from the preceding ordered tree by removing a leaf then appending a leaf elsewhere. Thus the change is just remove-and-append a leaf, which is the minimum.
We present a slight generalization of the result of Kamiyama and Kawase \cite{kamkaw} on packing time-respecting arborescences in acyclic pre-flow temporal networks. Our main contribution is to provide the first results on packing time-respecting arborescences in non-acyclic temporal networks. As negative results, we prove the NP-completeness of the decision problem of the existence of 2 arc-disjoint spanning time-respecting arborescences and of a related problem proposed in this paper.
We present double pooling, a simple, easy-to-implement variation on test pooling, that in certain ranges for the a priori probability of a positive test, is significantly more efficient than the standard single pooling approach (the Dorfman method).
Recently Naserasr, Sopena, and Zaslavsky [R. Naserasr, É. Sopena, T. Zaslavsky,Homomorphisms of signed graphs: An update, arXiv: 1909.05982v1 [math.CO] 12 Sep 2019.] published a report on closed walks in signed graphs. They gave a characterization of the sets of closed walks in a graph $G$ which corespond to the set of negative walks in some signed graph on $G$. In this note we show that their characterization is not valid and give a new characterization.
This article presents proof that the reverse of the Prefer Max De Bruijn sequence can be expanded into an infinite De Bruijn sequence by increasing the size of the alphabet. Furthermore, we show that every De Bruijn sequence possessing this characteristic exhibits behavior similar to that of the reverse of the Prefer Max De Bruijn sequence.
In this survey we overview known results on the strong subgraph $k$-connectivity and strong subgraph $k$-arc-connectivity of digraphs. After an introductory section, the paper is divided into four sections: basic results, algorithms and complexity, sharp bounds for strong subgraph $k$-(arc-)connectivity, minimally strong subgraph $(k, \ell)$-(arc-) connected digraphs. This survey contains several conjectures and open problems for further study.
This paper is devoted to the study of directed graphs with extremal properties relative to certain metric functionals. We characterize up to isomorphism critical digraphs with infinite values of diameter, quasi-diameter, radius and quasi-radius. Moreover, maximal digraphs with finite values of radius and quasi-diameter are studied.
A $k$-subcoloring of a graph is a partition of the vertex set into at most $k$ cluster graphs, that is, graphs with no induced $P_3$. 2-subcoloring is known to be NP-complete for comparability graphs and three subclasses of planar graphs, namely triangle-free planar graphs with maximum degree 4, planar perfect graphs with maximum degree 4, and planar graphs with girth 5. We show that 2-subcoloring is also NP-complete for planar comparability graphs with maximum degree 4.
We show that every trace monoid is isomorphic to a sub-monoid of a monoid of word vectors. It provides a concrete representation of the elements of a trace monoid as processes associated with a resource sharing mechanism. We illustrate this representation by obtaining some results on the ordering structure of the left divisibility relation on trace monoids.
While the game chromatic number of a forest is known to be at most 4, no simple criteria are known for determining the game chromatic number of a forest. We first state necessary and sufficient conditions for forests with game chromatic number 2 and then investigate the differences between forests with game chromatic number 3 and 4. In doing so, we present a minimal example of a forest with game chromatic number 4, criteria for determining in polynomial time the game chromatic number of a forest without vertices of degree 3, and an example of a forest with maximum degree 3 and game chromatic number 4. This gives partial progress on the open question of the computational complexity of the game chromatic number of a forest.
We prove the conjecture by M. Yip stating that counting genus one partitions by the number of their elements and parts yields, up to a shift of indices, the same array of numbers as counting genus one rooted hypermonopoles. Our proof involves representing each genus one permutation by a four-colored noncrossing partition. This representation may be selected in a unique way for permutations containing no trivial cycles. The conclusion follows from a general generating function formula that holds for any class of permutations that is closed under the removal and reinsertion of trivial cycles. Our method also provides another way to count rooted hypermonopoles of genus one, and puts the spotlight on a class of genus one permutations that is invariant under an obvious extension of the Kreweras duality map to genus one permutations.
A recent result has demonstrated that the Bethe partition function always lower bounds the true partition function of binary, log-supermodular graphical models. We demonstrate that these results can be extended to other interesting classes of graphical models that are not necessarily binary or log-supermodular: the ferromagnetic Potts model with a uniform external field and its generalizations and special classes of weighted graph homomorphism problems.
In this paper, we construct a strongly universal cellular automaton on the line with 11 states and the standard neighbourhood. We embed this construction into several tilings of the hyperbolic plane and of the hyperbolic 3D space giving rise to strongly universal cellular automata with 10 states.
We study the binomial and monomial ideals arising from linear equivalence of divisors on graphs from the point of view of Gröbner theory. We give an explicit description of a minimal Gröbner basis for each higher syzygy module. In each case the given minimal Gröbner basis is also a minimal generating set. The Betti numbers of $I_G$ and its initial ideal (with respect to a natural term order) coincide and they correspond to the number of ``connected flags'' in $G$. Moreover, the Betti numbers are independent of the characteristic of the base field.
We introduce the notion of a matroid $M$ over a commutative ring $R$, assigning to every subset of the ground set an $R$-module according to some axioms. When $R$ is a field, we recover matroids. When $R=\mathbb{Z}$, and when $R$ is a DVR, we get (structures which contain all the data of) quasi-arithmetic matroids, and valuated matroids, respectively. More generally, whenever $R$ is a Dedekind domain, we extend the usual properties and operations holding for matroids (e.g., duality), and we compute the Tutte-Grothendieck group of matroids over $R$.