Finite‐size corrections at the hard edge for the Laguerre β ensemble

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general .     

Correction to: Accelerating Reactive Transport Modeling: On-Demand Machine Learning Algorithm for Chemical Equilibrium Calculations

Transport in Porous Media - In the original publication of the article, Table 2 was published incorrectly.     

Computational Analysis of Mesomerism in para-Substituted mer-NCN Pincer Platinum(II) Complexes,Including its Relationships with Hammett σp Substituent Parameters

Density Functional Theory studies of square-planar Pt^II pincer structures, (4-Z-NCN)PtCl ([4-Z-NCN]⁻=[4-Z-2,6-(Me₂NCH₂)₂C₆H₂-N,C,N]⁻, Z=H, NO₂, CF₃, CO₂H, CHO, Cl, Br, I, F, SMe, SiMe₃, tBu, OH, NH₂, NMe₂), enable characterisation of mesomerism for the pincer-Pt interaction. Relationships between Hammett σ_p substituent parameters of Z and DFT data obtained from NBO6 and AOMix computation are used to probe the interaction of the 5d_yz orbital of platinum with π-orbitals of the arene ring. Analogous computation for 2,6-(Me₂CH₂)₂C₆H₃Z (Z=H, CF₃, CHO, Cl, Br, I, F, SMe, SiMe₃, tBu, OH, NH₂) and (4-H-NCN)PtZ allows an estimation of the relative substituent effects of “(CH₂NMe₂)₂PtZ” on π-delocalisation in the pincer system.     

Synthesis of PAN/ferrocyanide composite incorporated with cetrimonium bromide and its employment as a bifunctional adsorbent for coremoval of Cs+ and HCrO4− from aqueous solutions

Polyacrylonitrile/ferrocyanide composite incorporated with cetrimonium bromide (PFICB) was synthesized and evaluated as a novel bifunctional adsorbent for coremoval of Cs⁺ and HCrO₄^?. Results of the reaction time effect showed that adsorption of Cs⁺ and HCrO₄^? onto PFICB were rapid processes. The effect of the solution pH in the range 2.5–10 revealed that PFICB had the ability to simultaneously remove Cs⁺ and HCrO₄^?. The maximum adsorption capacity of PFICB was found to be 41.79 mg/g for Cs⁺ and 19.39 mg/g for HCrO₄^?. These values were compared with those reported in literature using other adsorbents.

     

Synthesis and formulation of self-immolative PEG-aryl azide block copolymers and click-to-release reactivity with trans-cyclooctene

Self-immolative aryl azides can react with trans-cyclooctenes (TCO), triphenylphosphines or hydrogen sulfide (H₂S) to activate prodrugs, imaging probes and drug delivery systems. To date, the synthesis of polymers containing these aryl azide self-immolative linkers and their reactivity with a strained alkene (i.e., in a bioorthogonal reaction) has not been explored. Also, due to the instability of aryl azides towards light and high temperatures, the polymerization methods compatible with aryl azides are limited. Through systematic investigation of the reversible addition-fragmentation chain transfer (RAFT) and atom transfer radical polymerization (ATRP) methods, a self-immolative PEG-aryl azide block copolymer (PEG₄₅-b-ABOC₂₈ 2 ) and a non-responsive 4-fluoroaryl block copolymer (PEG₄₅-b-FBOC₂₄ 3 ) was prepared. ATRP provided the desired polymers in a highly controlled manner, whereas the RAFT conditions led to higher levels of aryl azide polymer degradation. The ATRP derived polymers 2 and 3 were formulated into nanoparticles of approximately 200 nm diameter, and particle triggering was demonstrated by the [3+2]-cycloaddition reaction of TCO with PEG₄₅-b-ABOC₂₈ 2 in solution (pure polymer) and as a formulated nanoparticle. Preliminary in vitro cell viability studies suggested that the stimuli-responsive aryl azide polymers/nanoparticles are not cytotoxic up to 200 μg/ml concentrations.     

Forced Folding of a Disordered Protein Accesses an Alternative Folding Landscape

Intrinsically disordered proteins (IDPs) are involved in diverse cellular functions. Many IDPs can interact with multiple binding partners, resulting in their folding into alternative ligand‐specific functional structures. For such multi‐structural IDPs, a key question is whether these multiple structures are fully encoded in the protein sequence, as is the case in many globular proteins. To answer this question, here we employed a combination of single‐molecule and ensemble techniques to compare ligand‐induced and osmolyte‐forced folding of α‐synuclein. Our results reveal context‐dependent modulation of the protein′s folding landscape, suggesting that the codes for the protein′s native folds are partially encoded in its primary sequence, and are completed only upon interaction with binding partners. Our findings suggest a critical role for cellular interactions in expanding the repertoire of folds and functions available to disordered proteins.     

Limit theorems for counting variables based on records and extremes

Hsu and Robbins (Proc. Nat. Acad. Sci. USA 33, 25–31, 1947) introduced the concept of complete convergence as a complement to the Kolmogorov strong law, in that they proved that \( {\sum }_{n=1}^{\infty } P(|S_{n}|>n\varepsilon )<\infty \) provided the mean of the summands is zero and that the variance is finite. Later, Erd?s proved the necessity. Heyde (J. Appl. Probab. 12, 173–175, 1975) proved that, under the same conditions, \(\lim _{\varepsilon \searrow 0} \varepsilon ^{2}{\sum }_{n=1}^{\infty } P(| S_{n}| \geq n\varepsilon )=EX^{2}\), thereby opening an area of research which has been called precise asymptotics. Both results above have been extended and generalized in various directions. Some time ago, Kao proved a pointwise version of Heyde’s result, viz., for the counting process \(N(\varepsilon ) ={\sum }_{n=1}^{\infty }1\hspace *{-1.0mm}\text {{I}} \{|S_{n}|>n\varepsilon \}\), he showed that \(\lim _{\varepsilon \searrow 0} \varepsilon ^{2} N(\varepsilon )\overset {d}{\to } E\,X^{2}{\int }_{0}^{\infty } 1\hspace *{-1.0mm}\text {I}\{|W(u)|>u\}\,du\), where W(?) is the standard Wiener process. In this paper we prove analogs for extremes and records for i.i.d. random variables with a continuous distribution function.