On partitions of {1,…,2m + 1}\{k} into differences d,…,d + m − 1: Extended Langford sequences of large defect

It is shown that for m = 2d ? 1, 2d, 2d + 1, and d ≥ 1, the set {1, 2,…, 2m + 2}, ? {2,k} can be partitioned into differences d,d + 1,…,d + m ? 1 whenever (m,k) ≡ (0,0), (1,d + 1), (2, 1), (3,d) (mod (4,2)) and (d,m,k) ≠ (1,1,3), (2,3,7) (where (x,y) ≡ (u,ν) mod (m,n) iff x ≡ u (mod m) and y ≡ ν (mod n)). It is also shown that if m ≥ 2d ? 1 and m ? [2d + 2, 8d ? 5], then the set {1, 2, …, 2m + 1} ? {k} can be partitioned into differences d,d + 1,…,d + m ? 1 whenever (m,k) ≡ (0, 1), (1,d), (2,0), (3,d + 1) mod (4,2). Finally, for d = 4 we obtain a complete result for when {1,…,2m + 1} ? {k} can be partitioned into differences 4,5,…,m + 3. © 2004 Wiley Periodicals, Inc.     

Reducing The Seed Length In The Nisan-Wigderson Generator*

The Nisan–Wigderson pseudo-random generator [19] was constructed to derandomize probabilistic algorithms under the assumption that there exist explicit functions which are hard for small circuits. We give the first explicit construction of a pseudo-random generator with asymptotically optimal seed length even when given a function which is hard for relatively small circuits. Generators with optimal seed length were previously known only assuming hardness for exponential size circuits [13,26]. We also give the first explicit construction of an extractor which uses asymptotically optimal seed length for random sources of arbitrary min-entropy. Our construction is the first to use the optimal seed length for sub-polynomial entropy levels. It builds on the fundamental connection between extractors and pseudo-random generators discovered by Trevisan [29], combined with the construction above. The key is a new analysis of the NW-generator [19]. We show that it fails to be pseudorandom only if a much harder function can be efficiently constructed from the given hard function. By repeatedly using this idea we get a new recursive generator, which may be viewed as a reduction from the general case of arbitrary hardness to the solved case of exponential hardness. * This paper is based on two conference papers [11,12] by the same authors. † Research Supported by NSF Award CCR-9734911, NSF Award CCR-0098197, Sloan Research Fellowship BR-3311, grant #93025 of the joint US-Czechoslovak Science and Technology Program, and USA-Israel BSF Grant 97-00188. ‡ Part of this work was done while at the Hebrew University and the Institute for advanced study. § This research was supported by grant number 69/96 of the Israel Science Foundation, founded by the Israel Academy for Sciences and Humanities and USA-Israel BSF Grant 97-00188.     

Plasticization of a polymer layer harnessed to a silicon microcantilever as a highly sensitive and selective means to detect nitroaromatic derivatives

A new approach to the chemo‐mechanical detection of trace amounts of nitroaromatics, even in the presence of high concentrations of background materials, is presented. The detection scheme is based on the plasticization of an aminopropyl silane layer that is harnessed to a silicon beam following its reaction with nitroaromatic systems. The reaction‐induced plasticization attenuates the temperature induced bending of the polymer‐beam sandwich, offering a simple and very sensitive tool for the detection of nitroaromatic systems. Using this approach, it was possible to detect a sample of 100 pg TNT even in the presence of a ～10⁹ fold excess of a background material such as acetonitrile. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 2124–2130     

Symmetrical gas-phase dissociation of noncovalent protein complexes via surface collisions

Previous gas-phase dissociation experiments of protein-protein complexes have resulted in product ion distributions that are asymmetric by charge and mass, providing limited insight into the chemical nature of subunit organization and interaction. In these experiments, a symmetric charge distribution results from an "energy sudden" collision of protein-protein complexes with a surface, indicating that it may be possible to probe the suboligomeric structure of noncovalent complexes in the gas phase. It is proposed that energy sudden surface activation of cytochrome C homodimers results in dissociation without significant unfolding of one of the monomeric subunits. Previously proposed mechanisms for the dissociation of protein-protein complexes are discussed in the context of these results. These experiments demonstrate the potential to preserve the structural details of subunit interaction within a protein-protein complex and help elucidate the asymmetric nature of macromolecular dissociation in the gas phase.     

Manifestations of the roton mode in dipolar Bose-Einstein condensates

We investigate the structure of trapped Bose-Einstein condensates (BECs) with long-range anisotropic dipolar interactions. We find that a small perturbation in the trapping potential can lead to dramatic changes in the condensate's density profile for sufficiently large dipolar interaction strengths and trap aspect ratios. By employing perturbation theory, we relate these oscillations to a previously identified "rotonlike" mode in dipolar BECs. The same physics is responsible for radial density oscillations in vortex states of dipolar BECs that have been predicted previously.     

Phase locking of lasers with intracavity polarization elements

New configurations for phase locking several laser beams with intracavity polarization elements are presented. With this configuration we demonstrated efficient phase lock of up to 24 ND:YAG laser beams with only two polarization beam displacers.     

Learning the geometry of common latent variables using alternating-diffusion

One of the challenges in data analysis is to distinguish between different sources of variability manifested in data. In this paper, we consider the case of multiple sensors measuring the same physical phenomenon, such that the properties of the physical phenomenon are manifested as a hidden common source of variability (which we would like to extract), while each sensor has its own sensor-specific effects (hidden variables which we would like to suppress); the relations between the measurements and the hidden variables are unknown. We present a data-driven method based on alternating products of diffusion operators and show that it extracts the common source of variability. Moreover, we show that it extracts the common source of variability in a multi-sensor experiment as if it were a standard manifold learning algorithm used to analyze a simple single-sensor experiment, in which the common source of variability is the only source of variability.     

Enumerating traceless matrices over compact discrete valuation rings

We show that the non-separable Banach space SL∞ is primary. This is achieved by directly solving the infinite-dimensional factorization problem in SL∞. In particular, we bypass Bourgain’s localization method.     

Anatomical correlates of the functional organization in the human occipitotemporal cortex

The connectivity between functionally distinct areas in the human brain is unknown because of the limitations posed by current postmortem anatomical labeling techniques. Diffusion tensor imaging (DTI) has previously been used to define large white matter tracts based on well-known anatomical landmarks in the living human brain. In the present study, we used DTI coupled with functional magnetic resonance imaging (fMRI) to assess neuronal connections between human striate and functionally defined extrastriate ventral cortical areas. Functional areas were identified with conventional fMRI mapping procedures and then used as seeding points in a DTI analysis to ascertain connectivity patterns between cortical areas, thus yielding the pattern of connections between human occipitoventral visual areas in vivo.