Clustering of financial time series

This paper addresses the topic of classifying financial time series in a fuzzy framework proposing two fuzzy clustering models both based on GARCH models. In general clustering of financial time series, due to their peculiar features, needs the definition of suitable distance measures. At this aim, the first fuzzy clustering model exploits the autoregressive representation of GARCH models and employs, in the framework of a partitioning around medoids algorithm, the classical autoregressive metric. The second fuzzy clustering model, also based on partitioning around medoids algorithm, uses the Caiado distance, a Mahalanobis-like distance, based on estimated GARCH parameters and covariances that takes into account the information about the volatility structure of time series. In order to illustrate the merits of the proposed fuzzy approaches an application to the problem of classifying 29 time series of Euro exchange rates against international currencies is presented and discussed, also comparing the fuzzy models with their crisp version.     

Determination of Phonon Dispersion Curves at Gigapascal Pressures by Inelastic X-ray Scattering

The study of phonon dispersion curves of materials under hydrostatic pressure provides important information such as the evolution of sound velocities, elastic constants, interatomic potentials, phase transition mechanisms, etc. Until very recently, coherent inelastic neutron scattering was the only spectroscopic technique, which allowed performing these types of studies up to typically 10 GPa. Today, inelastic X-ray scattering with meV energy resolution provides a complementary spectroscopic technique, where, using diamond anvil cell techniques, pressures beyond 100 GPa can be reached.     

Personalized Metabolic Profile by Synergic Use of NMR and HRMS

A new strategy that takes advantage of the synergism between NMR and UHPLC–HRMS yields accurate concentrations of a high number of compounds in biofluids to delineate a personalized metabolic profile (SYNHMET). Metabolite identification and quantification by this method result in a higher accuracy compared to the use of the two techniques separately, even in urine, one of the most challenging biofluids to characterize due to its complexity and variability. We quantified a total of 165 metabolites in the urine of healthy subjects, patients with chronic cystitis, and patients with bladder cancer, with a minimum number of missing values. This result was achieved without the use of analytical standards and calibration curves. A patient’s personalized profile can be mapped out from the final dataset’s concentrations by comparing them with known normal ranges. This detailed picture has potential applications in clinical practice to monitor a patient’s health status and disease progression.     

Controlling unpredictability in the randomly driven Hénon–Heiles system

Noisy scattering dynamics in the randomly driven Hénon–Heiles system is investigated in the range of initial energies where the motion is unbounded. In this paper we study, with the help of the exit basins and the escape time distributions, how an external perturbation, be it dissipation or periodic forcing with a random phase, can enhance or mitigate the unpredictability of a system that exhibit chaotic scattering. In fact, if basin boundaries have the Wada property, predictability becomes very complicated, since the basin boundaries start to intermingle, what means that there are points of different basins close to each other. The main responsible of this unpredictability is the external forcing with random phase, while the dissipation can recompose the basin boundaries and turn the system more predictable. Therefore, we do the necessary simulations to find out the values of dissipation and external forcing for which the exit basins present the Wada property. Through these numerical simulations, we show that the presence of the Wada basins have a specific relation with the damping, the forcing amplitude and the energy value. Our approach consists on investigating the dynamics of the system in order to gain knowledge able to control the unpredictability due to the Wada basins.     

An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficient.     

Ab initio pseudopotential study of vacancies and self-interstitials in hcp titanium

By means of an ab initio plane-wave pseudopotential method, monovacancy, divacancy and self-interstitials in hcp titanium are investigated. The calculated monovacancy formation energy is 1.97 eV, which is in excellent agreement with other theoretical calculations, and agrees qualitatively with published experimental results. The relaxation of the atoms around a single vacancy is observed to be small. Two divacancy configurations, the in-plane and the off-plane, have also been shown to be equally stable. With regards to the interstitials, of the eight configurations studied, two (octahedral and basal octahedral) have relatively lower formation energies and are, thus, the most likely stable configurations. We find small energy differences between them, suggesting their possible co-existence. It is also observed that the tetrahedral configuration decays to a split dumbbell configuration, whereas both the basal tetrahedral and the basal pseudocrowdion interstitials decay to the basal octahedral configuration. Using the nudged elastic band method (NEB), we determine a possible minimum energy path (MEP) for the diffusion of self-interstitial titanium atoms from an octahedral site to the nearest octahedral site. The energy barrier for this migration mechanism is shown to be about 0.20 eV.     

A variational method for the calculation of spin-rovibronic energy levels of triatomic molecules with three interacting electronic states

A general method is presented for the evaluation of the spin rovibronic energy levels of triatomic molecules with up to three interacting potential energy surfaces. The full theory is outlined in detail, both for singlet and for doublet electronic states and the method is then applied to the benchmark example of C₂H. High quality multireference configuration interaction calculations have been carried out to generate the 3-dimensional near-equilibrium adiabatic potential energy surfaces of the three lowest 1²A'(X²Σ⁺), 2²A'(A²Π), 1²A''(A²Π) electronic states of C₂H, and the pair of interacting states of A 0 symmetry have then been diabatized. Results are presented for J up to 7/2 and compared with gas-phase high resolution experimental results for energies up to 5600 cm¹.     

Relational Representation of Groupoid Quantales

In Palmigiano and Re (J Pure Appl Algebra 215(8):1945–1957, 2011), spatial SGF-quantales are axiomatically introduced and proved to be representable as sub unital involutive quantales of quantales arising from set groupoids. In the present paper, spatial SGF-quantales of this class are shown to be optimally representable as unital involutive quantales of relations. The results of the present paper have several aspects in common with Jónsson and Tarski’s representation theory for relation algebras (Jónsson and Tarski, Am J Math 74(2):127–162, 1952).     

Cyclometalated AuIII Complexes for Cysteine Arylation in Zinc Finger Protein Domains: towards Controlled Reductive Elimination

With the aim of exploiting the use of organometallic species for the efficient modification of proteins through C-atom transfer, the gold-mediated cysteine arylation through a reductive elimination process occurring from the reaction of cyclometalated Au^III C^N complexes with a zinc finger peptide (Cys₂His₂ type) is here reported. Among the four selected Au^III cyclometalated compounds, the [Au(C^CON)Cl₂] complex featuring the 2-benzoylpyridine (C^CON) scaffold was identified as the most prone to reductive elimination and Cys arylation in buffered aqueous solution (pH 7.4) at 37 °C by high-resolution LC electrospray ionization mass spectrometry. DFT and quantum mechanics/molecular mechanics (QM/MM) studies permitted to propose a mechanism for the title reaction that is in line with the experimental results. Overall, the results provide new insights into the reactivity of cytotoxic organogold compounds with biologically important zinc finger domains and identify initial structure–activity relationships to enable Au^III-catalyzed reductive elimination in aqueous media.