Novel technologies for the formation of 2-D and 3-D droplet interface bilayer networks

Droplet interface bilayer (DIB) networks have vast potential in the field of membrane biophysics, synthetic biology, and functional bio-electronics. However a technological bottleneck exists in network fabrication: existing methods are limited in terms of their automation, throughput, versatility, and ability to form well-defined 3-D networks. We have developed a series of novel and low-cost methodologies which address these limitations. The first involves building DIB networks around the contours of a microfluidic chip. The second uses flow rate and droplet size control to influence droplet packing geometries within a microfluidic chamber. The latter method enables the controlled formation of various 3-D network arrays consisting of thousands of interconnected symmetric and asymmetric lipid bilayers for the first time. Both approaches allow individual droplet position and composition to be controlled, paving the way for complex on-chip functional network synthesis.     

The impact of solvent polarity on intramolecular proton and electron transfer in 2-alkylamino-4-nitro-5-methyl pyridine N-oxides

The crystal structure of 2-butylamino-4-nitro-5-methyl pyridine N-oxide (2B5M) and solution studies of both 2B5M and 2-methylamino-4-nitro-5-methyl pyridine (2M5M) N-oxide are presented. Steady-state absorption and emission measurements were employed for both molecules while a picosecond fluorescence up-conversion technique was used to follow the dynamic behavior of the 2M5M system. The experimental methods were complemented by DFT and TD DFT B3LYP/6-31G(d,p) calculations involving ground and excited-state optimization which in the case of the smaller 2M5M molecule were extended to the CAM-B3LYP/6-31G(d,p) method. The solvent effect is incorporated by applying the polarizable continuum (PCM) model. The data reveal that the 2B5M molecule crystallizes in the monoclinic space group P2(1)/c and its crystal lattice is composed of monomers with intramolecular N-H···O [2.572(3) ?] hydrogen bonds, connected into a polymer network by weak intermolecular C-H…O [3.2-3.4 ?]-type interactions. Quantum-chemical calculations show that the aminoalkyl substitutent in aminoalkyl-pyridine N-oxides is a specific determinant of the CT nature of the lowest-lying excited electronic ππ* state, distinguishing them from other nitroaromatic compounds. The results of both picosecond fluorescence up-conversion experiments in different solvents and quantum-chemical calculations suggest that in nonpolar media the ESIPT process in 2M5M is favored, while in polar acetonitrile, the N* → PT* transition demands barrier-crossing and thus unfavorable thermodynamic conditions do not allow the ESIPT to occur. The signals of picosecond fluorescence up-conversion of 2M5M are solvent- and emission-wavelength dependent. The three time components found in a weakly polar isooctane-dioxane mixture have been attributed to solvation dynamics (～500 fs), and to relaxation of N* and PT* forms while in acetonitrile, a very rapid fluorescence decay with a time constant (2.3-4.0 ps) indicative of the presence of the normal (N*) form was observed. Much shorter fluorescence lifetimes in alcohols (a few picoseconds) and in D(2)O (less than 200 fs) than in aprotic solvents suggest that in protic media, the solvent molecules participate in the ESIPT, bridging between the methylamine group and the N-oxide group of 2M5M.     

Arc permutations

Arc permutations and unimodal permutations were introduced in the study of triangulations and characters. This paper studies combinatorial properties and structures on these permutations. First, both sets are characterized by pattern avoidance. It is also shown that arc permutations carry a natural affine Weyl group action, and that the number of geodesics between a distinguished pair of antipodes in the associated Schreier graph, and the number of maximal chains in the weak order on unimodal permutations, are both equal to twice the number of standard Young tableaux of shifted staircase shape. Finally, a bijection from non-unimodal arc permutations to Young tableaux of certain shapes, which preserves the descent set, is described and applied to deduce a conjectured character formula of Regev.     

Harmonic analysis on the Iwahori–Hecke algebra

These are purely expository notes of Opdam’s analysis [O1] of the trace form τ(f) = f(e) on the Hecke algebra H = C _c (I\G/I) of compactly supported functions f on a connected reductive split p-adic group G which are biinvariant under an Iwahori subgroup I, extending Macdonald’s work. We attempt to give details of the proofs, and choose notations which seem to us more standard. Many objects of harmonic analysis are met: principal series, Macdonald’s spherical forms, trace forms, Bernstein forms. The latter were introduced by Opdam under the name Eisenstein series for H. The idea of the proof is that the last two linear forms are proportional, and the proportionality constant is computed by projection to Macdonald’s spherical forms. Crucial use is made of Bernstein’s presentation of the Iwahori–Hecke algebra by means of generators and relations, as an extension of a finite dimensional algebra by a large commutative subalgebra. We give a complete proof of this using the universal unramified principal series right H-module M = C _c (A(O)N\G/I) to develop a theory of intertwining operators algebraically.     

The Social Amplifier—Reaction of Human Communities to Emergencies

This paper develops a methodology to aggregate signals in a network regarding some hidden state of the world. We argue that focusing on edges around hubs will under certain circumstances amplify the faint signals disseminating in a network, allowing for more efficient detection of that hidden state. We apply this method to detecting emergencies in mobile phone data, demonstrating that under a broad range of cases and a constraint in how many edges can be observed at a time, focusing on the egocentric networks around key hubs will be more effective than sampling random edges. We support this conclusion analytically, through simulations, and with analysis of a dataset containing the call log data from a major mobile carrier in a European nation.     

Maximal Crossed Product Orders Over Discrete Valuation Rings

The problem of determining when a (classical) crossed product T = S ^f ?G of a finite group G over a discrete valuation ring S is a maximal order, was answered in the 1960s for the case where S is tamely ramified over the subring of invariants S ^G . The answer was given in terms of the conductor subgroup (with respect to f) of the inertia. In this article we solve this problem in general when S/S ^G is residually separable. We show that the maximal order property entails a restrictive structure on the subcrossed product graded by the inertia subgroup. In particular, the inertia is abelian. Using this structure, one is able to extend the notion of the conductor. As in the tame case, the order of the conductor is equal to the number of maximal two-sided ideals of T and hence to the number of maximal orders containing T in its quotient ring. Consequently, T is a maximal order if and only if the conductor subgroup is trivial.     

Catalytic Microcapsules Assembled from Enzyme–Nanoparticle Conjugates at Oil–Water Interfaces

Involuntary association : Anionic β‐galactosidase enzymes associate with positively charged Au nanoparticles to produce reduced‐charge conjugates, which assemble at oil–water interfaces to result in stable microcapsules (see picture). The microcapsules were formed quickly and showed high enzymatic activity, which makes them promising materials for biotechnology applications.

     

A simple trace formula

The Selberg trace formula is of unquestionable value for the study of automorphic forms and related objects. In principal it is a simple and natural formula, generalizing the Poisson summation formula, relating traces of convolution operators with orbital integrals. This paper is motivated by the belief that such a fundamental and natural relation should admit asimple and short proof. This is accomplished here for test functions with a single supercusp-component, and another component which is spherical and “sufficiently-admissible” with respect to the other components. The resulting trace formula is then use to sharpen and extend the metaplectic correspondence, and the simple algebras correspondence, of automorphic representations, to the context of automorphic forms with asingle supercuspidal component, over any global field. It will be interesting to extend these theorems to the context of all automorphic forms by means of a simple proof. Previously a simple form of the trace formula was known for test functions with two supercusp components; this was used to establish these correspondences for automorphic forms with two supercuspidal components. The notion of “sufficiently-admissible” spherical functions has its origins in Drinfeld's study of the reciprocity law for GL(2) over a function field, and our form of the trace formula is analogous to Deligne's conjecture on the fixed point formula in étale cohomology, for a correspondence which is multiplied by by a sufficiently high power of the Frobenius, on a separated scheme of finite type over a finite field. Our trace formula can be used (see [FK′]) to prove the Ramanujan conjecture for automorphic forms with a supercuspidal component on GL(n) over a function field, and to reduce the reciprocity law for such forms to Deligne's conjecture. Similar techniques are used in ['t'F] to establish base change for GL (n) in the context of automorphic forms with a single supercuspidal component. They can be used to give short and simple proofs of rank one lifting theorems forarbitrary automorphic forms; see [″F] for base change for GL(2), [F′] for base change forU(3), and [′F′] for the symmetric square lifting from SL(2) to PGL(3). Partially supported by NSF grants.     

Bernoulli convolutions and an intermediate value theorem for entropies of<Emphasis Type="Italic">K</Emphasis>-partitions

We establish a strong regularity property for the distributions of the random sums Σ±λ ⁿ , known as “infinite Bernoulli convolutions”: For a.e. λ ∃ (1/2, 1) and any fixed ℓ, the conditional distribution of (w _n+1...,w _n+ℓ) given the sum Σ _n=0 ^∞ w _n λ ⁿ , tends to the uniform distribution on {±1}^ℓ asn → ∞. More precise results, where ℓ grows linearly inn, and extensions to other random sums are also obtained. As a corollary, we show that a Bernoulli measure-preserving system of entropyh hasK-partitions of any prescribed conditional entropy in [0,h]. This answers a question of Rokhlin and Sinai from the 1960’s, for the case of Bernoulli systems. The authors were partially supported by NSF grants DMS-9729992 (E. L.), DMS-9803597 (Y. P.) and DMS-0070538 (W. S.).