Kernel-independent adaptive construction of $$\mathcal {H}^2$$-matrix approximations

A method for the kernel-independent construction of $$\mathcal {H}^2$$ H 2 -matrix approximations to non-local operators is proposed. Special attention is paid to the adaptive construction of nested bases. As a side result, new error estimates for adaptive cross approximation (ACA) are presented which have implications on the pivoting strategy of ACA.

Graphs with equal domination and covering numbers

A dominating set of a graph G is a set $$D\subseteq V_G$$D⊆VG such that every vertex in $$V_G-D$$VG-D is adjacent to at least one vertex in D, and the domination number $$\gamma (G)$$γ(G) of G is the minimum cardinality of a dominating set of G. A set $$C\subseteq V_G$$C⊆VG is a covering set of G if every edge of G has at least one vertex in C. The covering number $$\beta (G)$$β(G) of G is the minimum cardinality of a covering set of G. The set of connected graphs G for which $$\gamma (G)=\beta (G)$$γ(G)=β(G) is denoted by $${\mathcal {C}}_{\gamma =\beta }$$Cγ=β, whereas $${\mathcal {B}}$$B denotes the set of all connected bipartite graphs in which the domination number is equal to the cardinality of the smaller partite set. In this paper, we provide alternative characterizations of graphs belonging to $${\mathcal {C}}_{\gamma =\beta }$$Cγ=β and $${\mathcal {B}}$$B. Next, we present a quadratic time algorithm for recognizing bipartite graphs belonging to $${\mathcal {B}}$$B, and, as a side result, we conclude that the algorithm of Arumugam et al. (Discrete Appl Math 161:1859–1867, 2013) allows to recognize all the graphs belonging to the set $${\mathcal {C}}_{\gamma =\beta }$$Cγ=β in quadratic time either. Finally, we consider the related problem of patrolling grids with mobile guards, and show that it can be solved in $$O(n \log n + m)$$O(nlogn+m) time, where n is the number of line segments of the input grid and m is the number of its intersection points.

Deterrence Theory in Paraguay: Exploring Fraud and Violation of Trust Cases

This research paper contributes to the literature of deterrence theory in general, and in particular, with respect to white-collar crime, offering valuable insight by using a unique dataset of fraud and violation of trust incidents within the jurisdiction of Paraguay. Descriptive evidence shows a clear and continuous misallocation of funds and human capital, therefore providing less efficient services for the public. Regression analysis suggests that clearance rate exerts a highly significant effect in deterring fraud, but the results are not clear for violation of trust incidents. Despite the limitations of available data, results confirm the deterrence theory in Paraguay. However, for more than two-thirds of victims, not even an attempt was made to seek justice. As a side-result, it seems that a soft-on-crime strategy, induced from the former German penal code, has led to an increasing share of pre-trial diversion, therefore enhancing white-collar crimes like fraud and violation of trust, due to impunity.

Tau decays into two mesons: an overview

We review the state-of-the-art theoretical analyses of tau decays into a pair of mesons and a neutrino. The participant vector and scalar form factors, f+ (s) and f0(s), are described in the frame of Chiral Perturbation Theory with resonances supplemented by dispersion relations, and the physical parameters of the intermediate resonances produced in the decay are extracted through the pole position of f+,0(s) in the complex plane. As a side result, we also determine the low-energy observables associated to the form factors. We hope our study to be of interest for present and future experimental analyses of these decays.

Deterrence Theory in Paraguay: An Exploratory Study

This research paper contributes to the literature of deterrence theory in general, and in particular with respect to white-collar crime, offering valuable inside by using a unique data set of fraud and violation of trust incidents for Paraguay. Descriptive evidence show a clear and continuous misallocation of funds and human capital, and therefore providing less efficient services for the public. Regression analysis suggests that clearance rate exerts a highly significant effect in deterring fraud but results are not clear for violation of trust incidents. Despite the limitations of available data, results confirm deterrence theory in Paraguay. However, to more than two-thirds of victims, not even the attempt was made to seek justice. As a side-result, it seems that a soft on crime strategy, induced from the former German penal code, has led to an increasing share of pre-trial diversion and therefore enhancing white-collar crimes like fraud and violation of trust due to impunity.

Is it Reasonable to Obtain Information on the Polarizability and Hyperpolarizability Only from the Electron Density?

Formulae for the static electronic polarizability and hyperpolarizability are derived in terms of moments of the ground-state electron density matrix by applying the Unsöld approximation and a generalization of the Fermi-Amaldi approximation. The latter formula for the hyperpolarizability appears to be new. The formulae manifestly transform correctly under rotations, and they are observed to be essentially cumulant expressions. Consequently, they are additive over different regions. The properties of the formula are discussed in relation to others that have been proposed in order to clarify inconsistencies. The formulae are then tested against coupled-perturbed Hartree-Fock results for a set of 40 donor-π-acceptor systems. For the polarizability, the correlation is reasonable; therefore, electron density matrix moments from theory or experiment may be used to predict polarizabilities. By constrast, the results for the hyperpolarizabilities are poor, not even within one or two orders of magnitude. The formula for the two- and three-particle density matrices obtained as a side result in this work may be interesting for density functional theories.

On the density of coprime m-tuples over holomorphy rings

Let [Formula: see text] be a finite field, [Formula: see text] be a function field of genus [Formula: see text] having full constant field [Formula: see text], [Formula: see text] a set of places of [Formula: see text] and [Formula: see text] the holomorphy ring of [Formula: see text]. In this paper, we compute the density of coprime [Formula: see text]-tuples of elements of [Formula: see text]. As a side result, we obtain that whenever the complement of [Formula: see text] is finite, the computation of the density can be reduced to the computation of the [Formula: see text]-polynomial of the function field. In the genus zero case, classical results for the density of coprime [Formula: see text]-tuples of polynomials are obtained as corollaries.

Pentapods With Mobility 2

In this paper, we give a full classification of all pentapods with mobility 2, where neither all platform anchor points nor all base anchor points are located on a line. Therefore, this paper solves the famous Borel–Bricard problem for two-dimensional motions beside the excluded case of five collinear points with spherical trajectories. But even for this special case, we present three new types as a side-result. Based on our study of pentapods, we also give a complete list of all nonarchitecturally singular hexapods with two-dimensional self-motions.

Optimising the information flow of one-way quantum computations

In the one-way quantum computing model, the information processing is driven by measurements performed on an entangled state, called the resource state. In order to achieve parallelism, one aims to increase the number of simultaneous measurements, such that the effects of decoherence on the resource state are minimised due to the reduction of the time required to run the computation. At the heart of this question is the notion of quantum information flow, which specifies the dependency relations between the measurements in the computations. There exist two well-known techniques for reducing the time required to perform a one-way quantum computation without changing its semantics. The first one, called signal-shifting, transforms the flow of a graph (representing the resource state) within the measurement calculus formalism, whereas the second one, namely finding the maximally-delayed generalised flow, explores the geometry of the graph to increase the number of operations that can be performed simultaneously. In this paper, we show for the first time how these two techniques relate to each other. We prove that the application of the signal-shifting rules to a measurement pattern with flow results in a generalised flow for the pattern. Then, we prove that in the particular case when the input size equals the output size, the gflow obtained using signal-shifting has the lowest possible depth. As a side result, we construct an $O(n^3)$-algorithm for finding maximally delayed gflows on graphs with flow. For those graphs, our algorithm is more efficient than the best previously known algorithm for the same task, which takes $O(n^4)$ operations to complete.

Graphs with many valencies and few eigenvalues

Dom de Caen posed the question whether connected graphs with three distinct eigenvalues have at most three distinct valencies. We do not answer this question, but instead construct connected graphs with four and five distinct eigenvalues and arbitrarily many distinct valencies. The graphs with four distinct eigenvalues come from regular two-graphs. As a side result, we characterize the disconnected graphs and the graphs with three distinct eigenvalues in the switching class of a regular two-graph.