On the deque conjecture for the splay algorithm

Splay is a simple, efficient algorithm for searching binary search trees, devised by Sleator and Tarjan, that reorganizes the tree after each search by means of rotations. An open conjecture of Sleator and Tarjan states that Splay is, in essence, the fastest algorithm for processing any sequence of search operations on a binary search tree, using only rotations to reorganize the tree. Tarjan proved a basic special case of this conjecture, called theScanning Theorem, and conjectured a more general special case, called theDeque Conjecture. The Deque Conjecture states that Splay requires linear time to process sequences of deque operations on a binary tree. We prove the following results:

1. Almost tight lower and upper bounds on the maximum numbers of occurrences of various types of right rotations in a sequence of right rotations performed on a binary tree. In particular, the lower bound for right 2-turns refutes Sleator's Right Turn Conjecture.
2. A linear times inverse Ackerman upper bound for the Deque Conjecture. This bound is derived using the above upper bounds.
3. Two new proofs of the Scanning Theorem, one, a simple potential-based proof that solves Tarjan's problem of finding a potential-based proof for the theorem, the other, an inductive proof that generalizes the theorem.

     

Law of the iterated logarithm for solutions of stochastic differential equations

We prove the law of the iterated logarithm for solutions of Stochastic Differential Equations (SDEs) driven by continuous semiraartingales, under suitable conditions. This extends a result of Kulinich for classical diffusions to solutions of SDEs which are not necessarily Markov     

Green synthesis and bioactivity of 2-amino-4H-chromen-4-yl-phosphonates

A simple and efficient one pot synthesis of 2-amino-4H-chromen-4-yl phosphonate derivatives has been accomplished by the condensation of salicylaldehyde, malononitrile/ethylcyanoacetate and triethyl phosphite/trimethyl phosphite in the presence of molecular iodine as catalyst in water at room temperature. All the reactions were very clean and the products were obtained in very good to excellent yields. The title compounds are characterized by IR, 1H-, 13C-, 31P-NMR and mass spectra, also studied their antimicrobial and antioxidant activity.     

Facile synthesis, antioxidant and antimicrobial activity of amino methylene bisphosphonates

A green and efficient preparation method for the amino bisphosphonates is accomplished by simple mixing and stirring of diethylphosphite, triethylorthoformate and various amines in the presence of amberlyst-15 as catalyst at room temperature under solvent free conditions. The title compounds are characterized by IR, (1)H-, (13)C-, (31)P-NMR and mass spectra, also studied their antimicrobial and antioxidant activity.     

New insights in the activation of human cholesterol esterase to design potent anti-cholesterol drugs

Primary hypercholesterolemia is the root cause for major health issues like coronary heart disease and atherosclerosis. Regulating plasma cholesterol level, which is the product of biosynthesis as well as dietary intake, has become one of the major therapeutic strategies to effectively control these diseases. Human cholesterol esterase (hCEase) is an interesting target involved in the regulation of plasma cholesterol level and thus inhibition of this enzyme is highly effective in the treatment of hypercholesterolemia. This study was designed to understand the activation mechanism that enables the enzyme to accommodate long chain fatty acids and to identify the structural elements for the successful catalysis. Primarily the activation efficiencies of three different bile salts were studied and compared using molecular dynamics simulations. Based on the conformations of major surface loops, hydrogen bond interactions, and distance analyses, taurocholate was concluded as the preferred activator of the enzyme. Furthermore, the importance of two bile salt binding sites (proximal and remote) and the crucial role of $7\upalpha $ -OH group of the bile salts in the activation of hCEase was examined and evidenced. The results of our study explain the structural insights of the activation mechanism and show the key features of the bile salts responsible for the enzyme activation which are very useful in hypolipidemic drug designing strategies.     

Infrared spectroscopic study of the local structural changes across the metal insulator transition in nickel-doped GdBaCo2O5.5

Phonons in GdBaCo₂O_5.5 have been identified using infrared spectroscopy and their mode assignments have been carried out using ab initio lattice dynamical calculations. Metal insulator transitions in undoped and nickel-doped GdBaCo₂O_5.5 have been probed using infrared absorption spectroscopy. The phonon modes corresponding to the bending mode of the CoO₆ octahedra/pyramids are seen to soften, broaden and develop an asymmetry across the insulator-metal transition pointing to extensive electron phonon interaction effects in these systems. Correlated changes of the phonon line shape parameters associated with the transition indicate a suppression of T_MIT with increased nickel doping of the cobalt sublattice. Temperature dependence of the octahedral stretching mode frequencies in undoped GdBaCo₂O_5.5 points to distinct structural distortions accompanying the high temperature metallic transition.     

Probing the local structural changes across the amorphous to crystalline transition in iron phosphate glass: Positron annihilation and micro Raman studies

Iron phosphate glasses have been investigated using positron lifetime and micro Raman spectroscopy to study the crystallization kinetics and defect evolution across the glass and crystallization transitions. Positron lifetime parameters show distinct changes at temperatures corresponding to both the transitions. These changes have been understood as the signature of the evolution of open volume defects and their clustering across the amorphous to crystalline interfaces. Micro Raman measurements on annealed samples have identified the crystalline phases as Fe₃(P₂O₇)₂ and FePO₄. Ab-initio positron lifetime computations reveal that the positron probes the Fe/P sites in defect free crystals. The nature of open volume defects produced upon annealing is identified by computing positron lifetimes for various possible defect clusters. A combination of both experimental and theoretical techniques has provided insights in understanding the evolution of defects across the phase transition in these glasses.     

Flow injection amperometric sensing of uric acid and ascorbic acid using the self-assembly of heterocyclic thiol on Au electrode

Au electrode modified with the self-assembled monolayer of a heterocyclic thiol, mercaptotriazole (MTz), is used for the electroanalysis of uric acid (UA) and ascorbic acid (AA). MTz forms a less compact self-assembly on Au electrode. The self-assembly of MTz on Au electrode favors the oxidation of UA and AA at less positive potential. Significant decrease (∼400 mV) in the overpotential and enhancement in the peak current for the oxidation of interfering AA with respect to the unmodified electrode is observed. The negative shift in the oxidation peak potential of AA favors electrochemical sensing of UA without any interference. Two well-separated voltammetric peaks for AA and UA are observed in their coexistence. The large separation between the two voltammetric peaks allows the simultaneous or selective sensing of the analytes without compromising the sensitivity. Linear response is obtained for a wide concentration range. This electrode could sense as low as 1 μM of UA in the presence of 10-fold excess of interfering AA. No change in the sensitivity (0.012 μA/μM) of the electrode toward UA in the presence and absence of AA is observed. Reproducible and stable amperometric flow injection response was obtained upon repetitive injection.     

A bacterial one-hybrid selection system for interrogating zinc finger-DNA interactions

We have developed two bacterial one-hybrid systems for interrogating and selecting zinc finger-DNA interactions. Our systems utilize two plasmids: a zinc finger-plasmid containing the gene for the zinc finger fused to a fragment of the alpha subunit of RNA polymerase and a reporter plasmid where the zinc finger-binding site is located upstream of a reporter gene-either the gene encoding the green fluorescent protein (GFP) or chloramphenicol acetyltransferase (CAT). Binding of the zinc finger domain to the target binding site results in a 10-fold increase in chloramphenicol resistance with the CAT reporter and an 8- to 22-fold increase in total cell fluorescence with the GFP reporter. The CAT reporter allows for sequence specific zinc fingers to be isolated in a single selection step whereas the GFP reporter enables quantitative evaluation of libraries using flow cytometry and theoretically allows for both negative and positive selection. Both systems have been used to select for zinc fingers that have affinity for the motif 5'-GGGGCAGAA-3' from a library of approximately 2 x 10(5) variants. The systems have been engineered to report on zinc finger-DNA binding with dissociation constants less than about 1 microM in order to be most applicable for evaluating binding specificity in an in vivo setting.