Pell graphs

In this paper, we introduce the Pell graphs, a new family of graphs similar to the Fibonacci cubes. They are defined on certain ternary strings (Pell strings) and turn out to be subgraphs of Fibonacci cubes of odd index. Moreover, as well as ordinary hypercubes and Fibonacci cubes, Pell graphs have several interesting structural and enumerative properties. Here, we determine some of them. Specifically, we obtain a canonical decomposition giving a recursive structure, some basic properties (bipartiteness and existence of maximal matchings), some metric properties (radius, diameter, center, periphery, medianicity), some properties on subhypercubes (cube coefficients and polynomials, cube indices, decomposition in subhypercubes), and, finally, the distribution of the degrees.     

Rapid and selective determination of UV filters in seawater by liquid chromatography-tandem mass spectrometry combined with stir bar sorptive extraction

Fast liquid chromatography coupled to triple-quadrupole tandem mass spectrometry was employed for the determination of six UV filters in seawater. The separation of the analytes was achieved in less than 5 min; polarity switching was used as four of the analytes were ionized in positive mode and the remaining two in negative mode. Two ionization sources were employed and compared: atmospheric pressure chemical ionization (APCI) gave better results than electrospray ionization (ESI) for all analytes, with higher reproducibility and lower detection limits. Therefore APCI was chosen for the determination of the analytes in seawater samples using stir bar sorptive extraction-liquid desorption (SBSE-LD).Quantitative analysis was performed in multiple reaction monitoring (MRM) mode; fragmentation pathways of the analytes with regard to the formation of the MRM ions were also proposed.For the analysis of seawater samples, calibration curves were drawn using SBSE in spiked seawater. All figures of merit of the method were satisfactory; limits of detection were particularly low for the four analytes ionized in positive mode, being in the range 8-31 ng/L. The method was applied to the determination of the six UV filters in seawater samples from Liguria, Italy. Only benzophenone-3 (BP-3) and ethylhexyl methoxycinnamate (EHMC) were measured in the analyzed samples; some of the remaining analytes were also detected but always below the limit of quantitation.     

Functional MRI changes in the central motor system in myotonic dystrophy type 1

Myotonic dystrophy type 1 (DM1) is a multisystemic disease involving multiple organ systems including central nervous system (CNS) and muscles. Few studies have focused on the central motor system in DM1, pointing to a subclinical abnormality in the CNS. The aim of our study was to investigate patterns of cerebral activation in DM1 during a motor task using functional MRI (fMRI). Fifteen DM1 patients, aged 20 to 59 years, and 15 controls of comparable age were scanned during a self-paced sequential finger-to-thumb opposition task of their dominant right hand. Functional MRI images were analyzed using SPM99. Patients underwent clinical and genetic assessment; all subjects underwent a conventional MR study. Myotonic dystrophy type 1 patients showed greater activation than controls in bilateral sensorimotor areas and inferior parietal lobules, basal ganglia and thalami, in the ipsilateral premotor area, insula and supplementary motor area (corrected P<.05). Analysis of the interaction between disease and age showed that correlation with age was significantly greater in patients than in controls in bilateral sensorimotor areas and in contralateral parietal areas. Other clinical and MR characteristics did not correlate with fMRI. Functional changes in DM1 may represent compensatory mechanisms such as reorganization and redistribution of functional networks to compensate for ultrastructural and neurochemical changes occurring as part of the accelerated aging process.     

Mapping nonlinear gravity into General Relativity with nonlinear electrodynamics

We show that families of nonlinear gravity theories formulated in a metric-affine approach and coupled to a nonlinear theory of electrodynamics can be mapped into general relativity (GR) coupled to another nonlinear theory of electrodynamics. This allows to generate solutions of the former from those of the latter using purely algebraic transformations. This correspondence is explicitly illustrated with the Eddington-inspired Born–Infeld theory of gravity, for which we consider a family of nonlinear electrodynamics and show that, under the map, preserve their algebraic structure. For the particular case of Maxwell electrodynamics coupled to Born–Infeld gravity we find, via this correspondence, a Born–Infeld-type nonlinear electrodynamics on the GR side. Solving the spherically symmetric electrovacuum case for the latter, we show how the map provides directly the right solutions for the former. This procedure opens a new door to explore astrophysical and cosmological scenarios in nonlinear gravity theories by exploiting the full power of the analytical and numerical methods developed within the framework of GR.     

Extreme gravity tests with gravitational waves from compact binary coalescences: (II) ringdown

The LIGO/Virgo detections of binary black hole mergers marked a watershed moment in astronomy, ushering in the era of precision tests of Kerr dynamics. We review theoretical and experimental challenges that must be overcome to carry out black hole spectroscopy with present and future gravitational wave detectors. Among other topics, we discuss quasinormal mode excitation in binary mergers, astrophysical event rates, tests of black hole dynamics in modified theories of gravity, parameterized “post-Kerr” ringdown tests, exotic compact objects, and proposed data analysis methods to improve spectroscopic tests of Kerr dynamics by stacking multiple events.     

Expanding the Chemical Space of Non-Proteinogenic N4-Substituted Asparagine: Racemic,Enantioenriched, and Deuterated Derivatives

A site-selective carbamoylation strategy to access non-proteinogenic N⁴-modified asparagines has been described. The protocol is characterized by mild reaction conditions, high functional group compatibility, and a wide diversity of functionalized carbamoyl radicals making possible the access to peptides, pharmaceuticals, and natural N⁴-asparagine conjugates, as well as enantioenriched unnatural N⁴-asparagines. Besides that, deuterated analogues were achieved with the insertion of D₂O and enantioenriched derivatives could be obtained in 15 min in continuous-flow conditions.     

The configurational free energy of a polymer chain

The configurational, or elastic, free energy A_el of a polymer chain is discussed in terms of the Fourier configurational approach. The importance of accounting for all degrees of freedom of the chain is shown in comparison with affine mean-field theories and with scaling theories of chain expansion and contraction. In case of strong contraction the chain does show neither affinity nor self-similarity, and we get A_el ∼ N^1/3, N being the number of chain bonds. Conversely, in case of good-solvent expansion we find A_el ∼ N. The same result holds in the vicinity of the Θ-temperature, where A_el is also proportional to [(T − Θ)/T]².