Transformations in optics: Novel perspectives,approaches, applications and implementations

This paper summarizes a set of novel techniques for obtaining optical transformations, which are useful tools for signal processing. Then the paper focuses on deriving several interesting discrete transformations. The discussed transforms include continuous fractional transformations, hybrid transforms and discrete transform kernels.     

Acetylcholinesterase complexed with bivalent ligands related to huperzine a: experimental evidence for species-dependent protein-ligand complementarity

Acetylcholinesterase (AChE) inhibitors improve the cognitive abilities of Alzheimer patients. (-)-Huperzine A [(-)-HupA], an alkaloid isolated from the club moss, Huperzia serrata, is one such inhibitor, but the search for more potent and selective drugs continues. Recently, alkylene-linked dimers of 5-amino-5,6,7,8-tetrahydroquinolinone (hupyridone, 1a), a fragment of HupA, were shown to serve as more potent inhibitors of AChE than (-)-HupA and monomeric 1a. We soaked two such dimers, (S,S)-(-)-bis(10)-hupyridone [(S,S)-(-)-2a] and (S,S)-(-)-bis(12)-hupyridone [(S,S)-(-)-2b] containing, respectively, 10 and 12 methylenes in the spacer, into trigonal TcAChE crystals, and solved the X-ray structures of the resulting complexes using the difference Fourier technique, both to 2.15 A resolution. The structures revealed one HupA-like 1a unit bound to the "anionic" subsite of the active-site, near the bottom of the active-site gorge, adjacent to Trp84, as seen for the TcAChE/(-)-HupA complex, and the second 1a unit near Trp279 in the "peripheral" anionic site at the top of the gorge, both bivalent molecules thus spanning the active-site gorge. The results confirm that the increased affinity of the dimeric HupA analogues for AChE is conferred by binding to the two "anionic" sites of the enzyme. Inhibition data show that (-)-2a binds to TcAChE approximately 6-7- and > 170-fold more tightly than (-)-2b and (-)-HupA, respectively. In contrast, previous data for rat AChE show that (-)-2b binds approximately 3- and approximately 2-fold more tightly than (-)-2a and (-)-HupA, respectively. Structural comparison of TcAChE with rat AChE, as represented by the closely related mouse AChE structure (1maa.pdb), reveals a narrower gorge for rat AChE, a perpendicular alignment of the Tyr337 ring to the gorge axis, and its conformational rigidity, as a result of hydrogen bonding between its hydroxyl group and that of Tyr341, relative to TcAChE Phe330. These structural differences in the active-site gorge explain the switch in inhibitory potency of (-)-2a and 2b and the larger dimer/(-)-HupA potency ratios observed for TcAChE relative to rat AChE. The results offer new insights into factors affecting protein-ligand complementarity within the gorge and should assist the further development of improved AChE inhibitors.     

Simulations of remote mutants of dihydrofolate reductase reveal the nature of a network of residues coupled to hydride transfer

Recent experimental and theoretical studies have proposed that enzymes involve networks of coupled residues throughout the protein that participate in motions accompanying chemical barrier crossing. Here, we have examined portions of a proposed network in dihydrofolate reductase (DHFR) using quantum mechanics/molecular mechanics simulations. The simulations use a hybrid quantum mechanics‐molecular mechanics approach with a recently developed semiempirical AM1‐SRP Hamiltonian that provides accurate results for this reaction. The simulations reproduce experimentally determined catalytic rates for the wild type and distant mutants of E. coli DHFR, underscoring the accuracy of the simulation protocol. Additionally, the simulations provide detailed insight into how residues remote from the active site affect the catalyzed chemistry, through changes in the thermally averaged properties along the reaction coordinate. The mutations do not greatly affect the structure of the transition state near the bond activation, but we observe differences somewhat removed from the point of C? H cleavage that affect the rate. The mutations have global effects on the thermally averaged structure that propagate throughout the enzyme and the current simulations highlight several interactions that appear to be particularly important. © 2014 Wiley Periodicals, Inc.     

Bicriteria problems to minimize maximum tardiness and due date assignment cost in various scheduling environments

We study bicriteria problems of minimizing maximum tardiness and total due date assignment cost in various scheduling environments. We assume that each job can be assigned a different due date without any restriction, and that each due date assignment cost is a non-decreasing function of the quoted due date. We settle the complexity of most of the problems studied by either proving that they are NP-hard or finding a polynomial time solution for them. We also include approximation and non-approximability results for several parallel-machine problems.     

Spectral- and frequency-encoded fluorescence imaging

A method for obtaining fluorescence images with a high number of resolvable points by using spectral and frequency encoding is presented. Broadband excitation light is encoded with a wavelength-dependent frequency modulation and dispersed onto the sample with a grating to simultaneously illuminate an entire image line. The Fourier transform of the frequency-encoded fluorescence emission provides one line of the image. Mechanical scanning along a direction orthogonal to the wavelength-encoded axis allows creation of the two-dimensional fluorescent image. This method is applicable for developing submillimeter diameter endoscopes. The principles of the technique are validated by imaging indocyanine green fluorescence in microfluidic channels.     

Optimal synthesis of three-dimensional complex amplitude distributions

The synthesis of three-dimensional (3-D) light distributions is important for many applications. For example, in scanning applications it is preferable that the scanning beam preserve its characteristics over a large distance to yield elongated scanning range. It is evident that any 3-D light distribution must satisfy the wave equation or, in second-order approximation, the Fresnel diffraction formula. Thus many desirable 3-D light distributions may not be realizable. We propose a single optical element (OE) that synthesizes a physical beam within a certain 3-D region. The OE provides the optimal physical beam in comparison with a desired one in the sense of minimal mean-square error.     

Analyzing linear mergers

Mergers are functions that transform k (possibly dependent) random sources (distributions) into a single random source, in a way that ensures that if one of the input sources has min‐entropy rate δ then the output has min‐entropy rate close to δ. Mergers have proven to be a very useful tool in explicit constructions of extractors and condensers, and are also interesting objects in their own right. In this work we give a refined analysis of the merger constructed by [Raz, STOC'05] (based on [Lu, Reingold, Vadhan, and Wigderson, STOC'03 pp. 602–611, 2003]). Our analysis uses min‐entropy instead of Shannon's entropy to derive tighter results than the ones obtained in [Raz STOC'05]. We show that for every constant r and k it is possible to construct a merger that takes as input k strings of length n bits each, and outputs a string of length n/r bits, such that if one of the input sources has min‐entropy b, the output will be close to having min‐entropy b/(r + 1). This merger uses a constant number of additional uniform bits. One advantage of our analysis is that b (the min‐entropy of the “good” source) can be as small as a constant (this constant depends on r and k), while in the analysis given in [Raz STOC'05], b is required to be linear in n. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Towards dimension expanders over finite fields

In this paper we study the problem of explicitly constructing a dimension expander raised by [3]: Let \mathbbFⁿ \mathbb{F}^n be the n dimensional linear space over the field \mathbbF\mathbb{F}. Find a small (ideally constant) set of linear transformations from \mathbbFⁿ \mathbb{F}^n to itself {A _i } _i∈I such that for every linear subspace V ⊂ \mathbbFⁿ \mathbb{F}^n of dimension dim(V)<n/2 we have

Optoelectronic implementation of the triple correlation

The auto triple correlation has several fundamental advantages over the ordinary autocorrelation of second order. We present an optoelectronic processor for the computation of the auto triple correlation.     

Proportionate flow-shop scheduling with rejection

In many heavily loaded manufacturing systems, managers routinely make use of outsourcing options in order to maintain reasonable Quality of Service for customers. Thus, there is a strong need to provide tools for managers to economically coordinate sourcing and scheduling decisions. Our main aim is to provide such tools for an important set of flow-shop scheduling problems where rejection (outsourcing) is allowed and processing times are machine-independent. Our scheduling problems are essentially bicriteria problems, which combine a scheduling objective and the total outsourcing cost. We study several problems which differ according to the scheduling criterion considered. Moreover, each problem is divided into four different variations depending on the way the two criteria are dealt with. For example, in one variation the two criteria are aggregated into a single objective function; in two other variations the aim consists of minimizing one criterion subject to ensuring that the value of the other criterion will not exceed a predefined threshold. From a theoretical point of view, a computational complexity classification is provided for all variations of the problems under consideration. Moreover, optimization algorithms have been constructed to solve all problem variations, and approximation schemes have been developed for solving hard variations. Those schemes enable managers to solve large instances of hard variations while controlling the maximal gap between the obtained solution and the (unknown) optimal solution.