Classical and Almost Sure Local Limit Theorems

We present and discuss the many results obtained concerning a famous limit theorem, the local limit theorem, which has many interfaces, with Number Theory notably, and for which, in spite of considerable efforts, the question concerning conditions of validity of the local limit theorem, has up to now no satisfactory solution. These results mostly concern sufficient conditions for the validity of the local limit theorem and its interesting variant forms: strong local limit theorem, strong local limit theorem with convergence in variation. Quite importantly are necessary conditions, and the results obtained are sparse, essentially: Rozanov's necessary condition, Gamkrelidze's necessary condition, and Mukhin's necessary and sufficient condition. Extremely useful and instructive are the counter-examples due to Azlarov and Gamkrelidze, as well as necessary and sufficient conditions obtained for a class of random variables, such as Mitalauskas' characterization of the local limit theorem in the strong form for random variables having stable limit distributions. The method of characteristic functions and the Bernoulli part extraction method, are presented and compared. A second part of the survey is devoted to the more recent study of the almost sure local limit theorem, instilled by Denker and Koch. The almost sure local limit theorems established already cover the i.i.d. case, the stable case, Markov chains, the model of the Dickman function. Our aim in writing this monograph was notably to bring to knowledge many interesting results obtained by the Lithuanian and Russian Schools of Probability during the sixties and after, and which are essentially written in Russian, and moreover often published in Journals of difficult access

Hemipiperazines as peptide-derived molecular photoswitches with low-nanomolar cytotoxicity

The development of photochromic systems is an important and growing area of research, in particular for bioactive molecular photoswitches. Here, the authors report on photopharmacological antimitotic agents, operational under visible light, based on a peptide-derived hemipiperazine photochrome. Molecular photoswitches transform light energy into reversible structural changes. Their combination with known pharmacophores often allows for photomodulation of the biological activity. The effort to apply such compounds in photopharmacology as light-activated pro-drugs is, however, hampered by serious activity reduction upon pharmacophore modifications, or limited biostability. Here we report that a potent antimitotic agent plinabulin and its derivatives demonstrate up to 56-fold reversible activity photomodulation. Alternatively, irreversible photoactivation with cyan light can enhance the cytotoxicity up to three orders of magnitude-all without compromising the original activity level, as the original pharmacophore structure is unchanged. This occurs due to the presence of a peptide-derived photoswitchable motif hemipiperazine inside the plinabulin scaffold. Furthermore, we systematically describe photochromism of these thermally stable and biocompatible hemipiperazines, as well as a photoswitchable fluorophore derived from plinabulin. The latter may further expand the applicability of hemipiperazine photochromism towards super-resolution microscopy.Peer reviewe

Hemipiperazines as peptide-derived molecular photoswitches with low-nanomolar cytotoxicity

The development of photochromic systems is an important and growing area of research, in particular for bioactive molecular photoswitches. Here, the authors report on photopharmacological antimitotic agents, operational under visible light, based on a peptide-derived hemipiperazine photochrome. Molecular photoswitches transform light energy into reversible structural changes. Their combination with known pharmacophores often allows for photomodulation of the biological activity. The effort to apply such compounds in photopharmacology as light-activated pro-drugs is, however, hampered by serious activity reduction upon pharmacophore modifications, or limited biostability. Here we report that a potent antimitotic agent plinabulin and its derivatives demonstrate up to 56-fold reversible activity photomodulation. Alternatively, irreversible photoactivation with cyan light can enhance the cytotoxicity up to three orders of magnitude-all without compromising the original activity level, as the original pharmacophore structure is unchanged. This occurs due to the presence of a peptide-derived photoswitchable motif hemipiperazine inside the plinabulin scaffold. Furthermore, we systematically describe photochromism of these thermally stable and biocompatible hemipiperazines, as well as a photoswitchable fluorophore derived from plinabulin. The latter may further expand the applicability of hemipiperazine photochromism towards super-resolution microscopy.Peer reviewe

Common variant p.D19H of the hepatobiliary sterol transporter ABCG8 increases the risk of gallstones in children

Introduction Gallstones are increasingly common in children. Genetic analyses of adult cohorts demonstrated that the sterol transporter ABCG8 p.D19H and Gilbert UGT1A1*28 variants enhance the odds of developing gallstones. The genetic background of common lithiasis in children remains unknown. Methods Overall, 214 children with gallstone disease (1 month–17 years, 107 boys) were inclueded. The control cohorts comprised 214 children (age 6–17 years, 115 boys) and 172 adults (age 40–92 years, 70 men) without gallstones. The ABCG8 p.D19H and UGT1A1*28 polymorphisms as well as ABCB4 (c.504C>T rs1202283, c.711A>T rs2109505) and NPC1L1 variants (p.V1296V rs217434, c.−18C>A rs41279633) were genotyped using TaqMan assays. Serum concentrations of plant sterols and cholesterol precursors were measured by gas chromatography/mass spectrometry. Results The ABCG8 risk allele was associated with an increased risk of stones (OR = 1.82, p = .03). Children carrying the p.19H allele presented with lower serum concentrations of surrogate markers of intestinal cholesterol absorption and decreased ratios of phytosterols to the cholesterol precursor desmosterol. Carriers of the common NPC1L1 rs217434 allele had an increased gallstone risk compared with stone-free adults (OR 1.90, p < .01). This variant also affected the ratio of phytosterols to cholesterol precursors (p = .03). Other tested variants were not associated with gallstone risk. Conclusions The p.D19H ABCG8 and, to a lesser extent, NPC1L1 rs217434 variants increase the risk of early-onset gallstone formation. These results point to the presence of a common lithogenic pathway in children and adults

Free Radicals, Salicylic Acid and Mycotoxins in Asparagus After Inoculation with Fusarium proliferatum and F. oxysporum

Electron paramagnetic resonance was used to monitor free radicals and paramagnetic species like Fe, Mn, Cu generation, stability and status in Asparagus officinalis infected by common pathogens Fusarium proliferatum and F. oxysporum. Occurrence of F. proliferatum and F. oxysporum, level of free radicals and other paramagnetic species, as well as salicylic acid and mycotoxins content in roots and stems of seedlings were estimated on the second and fourth week after inoculation. In the first term free and total salicylic acid contents were related to free radicals level in stem (P = 0.010 and P = 0.033, respectively). Concentration of Fe3+ ions in porphyrin complexes (g = 2.3, g = 2.9) was related to the species of pathogen. There was no significant difference between Mn2+ concentrations in stem samples; however, the level of free radicals in samples inoculated with F. proliferatum was significantly higher when compared to F. oxysporum

Measurement of the cosmic ray spectrum above 4×10184{\times}10^{18} eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-\gamma}$ with index $\gamma=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.Comment: Replaced with published version. Added journal reference and DO

Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.Comment: Replaced with published version. Added journal reference and DO

Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.Comment: Replaced with published version. Added journal reference and DOI. Supplemental material in the ancillary file