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.).     

Thick points for intersections of planar sample paths

Let denote the number of visits to of the simple planar random walk , up to step . Let be another simple planar random walk independent of . We show that for any , there are points for which . This is the discrete counterpart of our main result, that for any , the Hausdorff dimension of the set of thick intersection points for which , is almost surely . Here is the projected intersection local time measure of the disc of radius centered at for two independent planar Brownian motions run until time . The proofs rely on a ``multi-scale refinement' of the second moment method. In addition, we also consider analogous problems where we replace one of the Brownian motions by a transient stable process, or replace the disc of radius centered at by for general sets .

     

High-frequency backscatter from a finned cylinder at grazing incidence--Comparison of two theoretical methods

A closed-form, high-frequency approximation is obtained for the diffracted-reflected-diffracted field contribution to the backscattered field resulting from the grazing illumination of a perfectly conducting, infinitely long, finned cylinder by a normally incident cylindrical transverse magnetic (TM) wave. The result, which is valid for any relative magnitudes of the cylinder radius and the fin width provided both of them are electrically large, is derived by two different methods. One of them is the radiation integral method related to the physical theory of diffraction. The other is the complex ray tracing method related to the spectral theory of diffraction (STD). Relative merits and disadvantages of the two methods are pointed out.     

Geometrization in the Yang-Mills extended supergravity and Klein-Kaluza versions

We relate personal encounters of three kinds with geometrical approaches, in the development of a relativistic quantum field theory of the fundamental interactions—including interactions with Nathan Rosen. We characterize the geometrical structures involved and discuss the more recent attempts to develop a unified theory based on a Klein-Kaluza contraction of the eightfold extended supergravity.Invited paper, dedicated to Nathan Rosen on the occasion of his seventy-fifth birthday.On leave from Tel Aviv University, Israel, and the University of Texas at Austin, Texas.     

Electrodeposited quantum dots IV. Epitaxial short-range order in amorphous semiconductor nanostructures

The structure of diffraction-amorphous CdSe (a-CdSe) quantum dots (QDs) electrodeposited on evaporated Pd substrate was studied by high resolution transmission electron microscopy (HRTEM), and compared with epitaxial (crystalline) QDs obtained by the same procedure on Au, as well as with a simulated image of random a-CdSe. Digital analysis of HRTEM images established the existence of repeating ordered motifs in a-CdSe QDs on Pd substrates, in the form of epitaxial sub-nanometre to nanometre size clusters. The QDs are shown to be intermediate between crystalline and random amorphous material. Digital Fourier analysis indicated epitaxial relationship with the 111inPd substrate, rotated 30° relative to the orientational relationship on 111_Au.