Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments

We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks.     

A chemoselective reduction of alkynes to (E)-alkenes

The trans reduction of all types of alkynes to give (E)-olefins is achieved through a two-stage trans hydrosilylation and protodesilylation. Reaction of an alkyne and a silane with the ruthenium catalyst [Cp*Ru(MeCN)3]PF6 results in clean hydrosilylation to give only the (Z)-trans addition product at ambient temperature with catalyst loadings of 1-5 mol %. The crude vinylsilane products are then protodesilylated by the action of cuprous iodide and TBAF at rt-35 degrees C. The reaction is compatible with many sensitive functional groups and provides a general trans-alkyne reduction not possible by other means.     

H2/CO2 separations in multicomponent metal-adeninate MOFs with multiple chemically distinct pore environments

Metal–organic frameworks constructed from multiple (≥3) components often exhibit dramatically increased structural complexity compared to their 2 component (1 metal, 1 linker) counterparts, such as multiple chemically unique pore environments and a plurality of diverse molecular diffusion pathways. This inherent complexity can be advantageous for gas separation applications. Here, we report two isoreticular multicomponent MOFs, bMOF-200 (4 components; Cu, Zn, adeninate, pyrazolate) and bMOF-201 (3 components; Zn, adeninate, pyrazolate). We describe their structures, which contain 3 unique interconnected pore environments, and we use Kohn–Sham density functional theory (DFT) along with the climbing image nudged elastic band (CI-NEB) method to predict potential H₂/CO₂ separation ability of bMOF-200. We examine the H₂/CO₂ separation performance using both column breakthrough and membrane permeation studies. bMOF-200 membranes exhibit a H₂/CO₂ separation factor of 7.9. The pore space of bMOF-201 is significantly different than bMOF-200, and one molecular diffusion pathway is occluded by coordinating charge-balancing formate and acetate anions. A consequence of this structural difference is reduced permeability to both H₂ and CO₂ and a significantly improved H₂/CO₂ separation factor of 22.2 compared to bMOF-200, which makes bMOF-201 membranes competitive with some of the best performing MOF membranes in terms of H₂/CO₂ separations.

Tailorable multicomponent MOFs and MOF membranes for efficient H₂/CO₂ separation.     

α-CGRP disrupts amylin fibrillization and regulates insulin secretion: implications on diabetes and migraine

Despite being relatively benign and not an indicative signature of toxicity, fibril formation and fibrillar structures continue to be key factors in assessing the structure–function relationship in protein aggregation diseases. The inability to capture molecular cross-talk among key players at the tissue level before fibril formation greatly accounts for the missing link toward the development of an efficacious therapeutic intervention for Type II diabetes mellitus (T2DM). We show that human α-calcitonin gene-related peptide (α-CGRP) remodeled amylin fibrillization. Furthermore, while CGRP and/or amylin monomers reduce the secretion of both mouse Ins1 and Ins2 proteins, CGRP oligomers have a reverse effect on Ins1. Genetically reduced Ins2, the orthologous version of human insulin, has been shown to enhance insulin sensitivity and extend the life-span in old female mice. Beyond the mechanistic insights, our data suggest that CGRP regulates insulin secretion and lowers the risk of T2DM. Our result rationalizes how migraine might be protective against T2DM. We envision the new paradigm of CGRP : amylin interactions as a pivotal aspect for T2DM diagnostics and therapeutics. Maintaining a low level of amylin while increasing the level of CGRP could become a viable approach toward T2DM prevention and treatment.

CGRP concentration is elevated in migraine conditions. The protective effect of migraine against type 2 diabetes is attributed to the ability of CGRP to remodel human amylin aggregation and to suppress the secretion of mouse insulin 2 (the orthologue of human insulin).     

Reduced matrix effects for anionic compounds with paired ion electrospray ionization mass spectrometry

It is well-known that matrix effects in high performance liquid chromatography coupled to electrospray ionization mass spectrometry (HPLC-ESI-MS) can seriously compromise quantitative analysis and affect method reproducibility. Paired ion electrospray ionization (PIESI) mass spectrometry is an approach for analyzing ultra-low levels of anions in the positive ion mode. This approach uses a structurally optimized ion pairing reagent to post-column associate with the anionic analyte, subsequently forming positively charged complexes. These newly formed complex ions are often more surface-active as compared to either the native anion or the ion pairing reagent. No studies have examined whether or not the PIESI approach mitigates matrix effects. Consequently, a controlled study was done using five analytes in highly controlled and reproducible synthetic groundwater and urine matrices. In addition, two different mass spectrometers (linear ion trap and triple quadrupole) were used. Compared to the negative ion mode, the PIESI-MS approach was less susceptible to matrix effects when performed on two different MS platforms. Using PIESI-MS, less dilution of the sample is needed to eliminate ionization suppression which, in turn, permits lower limits of detection and quantitation.     

Photomechanical Actuation of Ligand Geometry in Enantioselective Catalysis

A catalyst that couples a photoswitch to the biaryl backbone of a chiral bis(phosphine) ligand, thus allowing photochemical manipulation of ligand geometry without perturbing the electronic structure is reported. The changes in catalyst activity and selectivity upon switching can be attributed to intramolecular mechanical forces, thus laying the foundation for a new class of catalysts whose selectivity can be varied smoothly and in situ over a useful range by controlling molecular stress experienced by the catalyst during turnover. Forces on the order of 100 pN are generated, thus leading to measurable changes in the enantioselectivities of asymmetric Heck arylations and Trost allylic alkylations. The differential coupling between applied force and competing stereochemical pathways is quantified and found to be more efficient for the Heck arylations.     

On actions of Drinfel'd doubles on finite dimensional algebras

Let q be an nth root of unity for $n>2$ and let $T_n(q)$ be the Taft (Hopf) algebra of dimension $n^2$. In 2001, Susan Montgomery and Hans-Jürgen Schneider classified all non-trivial $T_n(q)$-module algebra structures on an n-dimensional associative algebra A. They further showed that each such module structure extends uniquely to make A a module algebra over the Drinfel'd double of $T_n(q)$. We explore what it is about the Taft algebras that leads to this uniqueness, by examining actions of (the Drinfel'd double of) Hopf algebras H “close” to the Taft algebras on finite-dimensional algebras analogous to A above. Such Hopf algebras H include the Sweedler (Hopf) algebra of dimension 4, bosonizations of quantum linear spaces, and the Frobenius–Lusztig kernel $u_q({\mathfrak{sl}}_2)$.     

Concise complexity analyses for trust region methods

Concise complexity analyses are presented for simple trust region algorithms for solving unconstrained optimization problems. In contrast to a traditional trust region algorithm, the algorithms considered in this paper require certain control over the choice of trust region radius after any successful iteration. The analyses highlight the essential algorithm components required to obtain certain complexity bounds. In addition, a new update strategy for the trust region radius is proposed that offers a second-order complexity bound.     

Three‐Dimensional Architectures Incorporating Stereoregular Donor–Acceptor Stacks

We report the synthesis of two [2]catenane‐containing struts that are composed of a tetracationic cyclophane (TC⁴⁺) encircling a 1,5‐dioxynaphthalene (DNP)‐based crown ether, which bears two terphenylene arms. The TC⁴⁺ rings comprise either 1) two bipyridinium (BIPY²⁺) units or 2) a BIPY²⁺ and a diazapyrenium (DAP²⁺) unit. These degenerate and nondegenerate catenanes were reacted in the presence of Cu(NO₃)₂?2.5 H₂O to yield Cu‐paddlewheel‐based MOF‐1050 and MOF‐1051. The solid‐state structures of these MOFs reveal that the metal clusters serve to join the heptaphenylene struts into grid‐like 2D networks. These 2D sheets are then held together by infinite donor–acceptor stacks involving the [2]catenanes to produce interpenetrated 3D architectures. As a consequence of the planar chirality associated with both the DNP and hydroquinone (HQ) units present in the crown ether, each catenane can exist as four stereoisomers. In the case of the nondegenerate (bistable) catenane, the situation is further complicated by the presence of translational isomers. Upon crystallization, however, only two of the four possible stereoisomers—namely, the enantiomeric RR and SS forms—are observed in the crystals. An additional element of co‐conformational selectivity is present in MOF‐1051 as a consequence of the substitution of one of the BIPY²⁺ units by a DAP²⁺ unit: only the translational isomer in which the DAP²⁺ unit is encircled by the crown ether is observed. The overall topologies of MOF‐1050 and MOF‐1051, and the selective formation of stereoisomers and translational isomers during the kinetically driven crystallization, provide evidence that weak noncovalent bonding interactions play a significant role in the assembly of these extended (super)structures.