Photon Counting Histogram Analysis for Two‐Dimensional Systems

Photon counting statistics in 3D photon counting histogram analysis for one‐photon excitation is a function of the number of molecules of particular brightness in the excitation‐detection volume of a confocal microscope. In mathematical form that volume is approximated by a three‐dimensional Gaussian function which is embedded in the PCH theoretical equations. PCH theory assumes that a molecule can be found anywhere inside the excitation‐detection volume with equal probability. However, one can easily imagine systems in which this assumption is violated because molecules are constrained by the geometry of the sample. For example, molecules on a surface or in a membrane would be constrained to two dimensions. To enable the analysis of such systems by PCH, the theoretical framework requires modification. Herein, we present an extension of the PCH analysis to systems where molecules exist in thin structures that are effectively two‐dimensional. The method, aptly called two‐dimensional photon counting histogram (2D PCH), recovers the number of fluorescent particles per unit area and their molecular brightness. Both theoretical background and experimental results are presented. The theory was tested using computer‐simulated and experimental 2D PCHs obtained from confocal experiments. We demonstrate that this modification of the theoretical framework provides a tool to extract data that reveal states of aggregation, surface photophysics, and reactivity.     

New synthetic route to substituted dihydroazulene photoswitches

A new procedure for functionalization of the dihydroazulene photoswitch on its seven-membered ring was developed, which has allowed isolation of the first dihydroazulene with a phenyl substituent at position 5 from a mixture of regioisomers. Light-induced ring-opening to the corresponding vinylheptafulvene and the thermal back-reaction was studied in detail.     

Synthesis of 1,4-naphthoquinone methides via acid-catalyzed cascade cyclizations of benzannulated enediynyl alcohols

Treatment of benzannulated enediynyl alcohols with trifluoroacetic acid at room temperature promoted a cascade sequence of cyclization reactions, leading to 1,4-naphthoquinone methides. The transformation involved an unusual two-carbon ring expansion from the cyclic alcohols and the construction of the p-quinone methide ring from an acyclic system along the reaction pathway.     

Clocking the melting transition of charge and lattice order in 1T-TaS2 with ultrafast extreme-ultraviolet angle-resolved photoemission spectroscopy

We use time- and angle-resolved photoemission spectroscopy with sub-30-fs extreme-ultraviolet pulses to map the time- and momentum-dependent electronic structure of photoexcited 1T-TaS(2). This compound is a two-dimensional Mott insulator with charge-density wave ordering. Charge order, evidenced by splitting between occupied subbands at the Brillouin zone boundary, melts well before the lattice responds. This challenges the view of a charge-density wave caused by electron-phonon coupling and Fermi-surface nesting alone, and suggests that electronic correlations play a key role in driving charge order.     

Simultaneous chromatography and electrophoresis: two-dimensional planar separations

Single-dimension separations are routinely coupled in series to achieve two-dimensional separations, yet little has been done to simultaneously exploit multiple dimensions during separation. In this work, simultaneous chromatography and electrophoresis is introduced and evaluated for its potential to achieve two-dimensional separations. In simultaneous chromatography and electrophoresis, chromatography occurs via capillary action while an orthogonal electric field concurrently promotes electrophoresis in a second dimension. A novel apparatus with a dual solvent reservoir was designed to apply the concurrent electric field. Various compounds were used to characterize the apparatus and technique, i.e., vitamins, amino acids, and dyes. Improved separation is reported with equivalent analysis times in comparison to planar chromatography alone. The feasibility of simultaneously employing chromatography and electrophoresis in two dimensions is discussed.

Counting Dyck Paths by Area and Rank

The set of Dyck paths of length 2n inherits a lattice structure from a bijection with the set of noncrossing partitions with the usual partial order. In this paper, we study the joint distribution of two statistics for Dyck paths: area (the area under the path) and rank (the rank in the lattice). While area for Dyck paths has been studied, pairing it with this rank function seems new, and we get an interesting (q, t)-refinement of the Catalan numbers. We present two decompositions of the corresponding generating function: One refines an identity of Carlitz and Riordan; the other refines the notion of γ-nonnegativity, and is based on a decomposition of the lattice of noncrossing partitions due to Simion and Ullman. Further, Biane’s correspondence and a result of Stump allow us to conclude that the joint distribution of area and rank for Dyck paths equals the joint distribution of length and reflection length for the permutations lying below the n-cycle (12· · ·n) in the absolute order on the symmetric group.     

Fused Lasso Additive Model

We consider the problem of predicting an outcome variable using p covariates that are measured on n independent observations, in a setting in which additive, flexible, and interpretable fits are desired. We propose the fused lasso additive model (FLAM), in which each additive function is estimated to be piecewise constant with a small number of adaptively chosen knots. FLAM is the solution to a convex optimization problem, for which a simple algorithm with guaranteed convergence to a global optimum is provided. FLAM is shown to be consistent in high dimensions, and an unbiased estimator of its degrees of freedom is proposed. We evaluate the performance of FLAM in a simulation study and on two datasets. Supplemental materials are available online, and the R package flam is available on CRAN.     

Direct formation of beta-glycosides of N-acetyl glycosamines mediated by rare earth metal triflates

A direct, mild and efficient protocol for the preparation of beta-glycosides of N-acetyl glucosamine (GlcNAc) and N-acetyl galactosamine (GalNAc) has been developed using peracetylated beta-GlcNAc and beta-GalNAc as donors. All rare Earth metal triflate promoters screened were found to promote glycosylation with Sc(OTf)(3) being superior in terms of reaction rate. Simple alcohol glycosylation was found to proceed smoothly in refluxing dichloromethane, whereas higher temperatures under microwave conditions were needed to attain acceptable yields with less reactive, carbohydrate based glycosyl acceptors. The protocol developed was applied to provide the first example of direct chemical formation of a disaccharide using both GlcNAc as a glycosyl donor and acceptor. The alpha-acetate donor was found to be significantly less reactive than the corresponding beta-anomer necessitating higher reaction temperatures under which glycoside anomerisation was found to occur. It was established, that the anomerisation only took place in the presence of both Sc(OTf)(3) and acetic acid.