On the distribution of comparisons in sorting algorithms

We considered the following natural conjecture: For every sorting algorithm every key will be involved in(logn) comparisons for some input. We show that this is true for most of the keys and prove matching upper and lower bounds. Every sorting algorithm for some input will involven–n /2+1 keys in at leastlog₂ n comparisons,>0. Further, there exists a sorting algorithm that will for every input involve at mostn–n ^/c keys in greater thanlog₂ n comparisons, wherec is a constant and>0. The conjecture is shown to hold for natural algorithms from the literature.     

The Power of Kinetic Inertness in Improving Platinum Anticancer Therapy by Circumventing Resistance and Ameliorating Nephrotoxicity

Even in the modern era of precision medicine and immunotherapy, chemotherapy with platinum (Pt) drugs remains among the most commonly prescribed medications against a variety of cancers. Unfortunately, the broad applicability of these blockbuster Pt drugs is severely limited by intrinsic and/or acquired resistance, and high systemic toxicity. Considering the strong interconnection between kinetic lability and undesired shortcomings of clinical Pt drugs, we rationally designed kinetically inert organometallic Pt based anticancer agents with a novel mechanism of action. Using a combination of in vitro and in vivo assays, we demonstrated that the development of a remarkably efficacious but kinetically inert Pt anticancer agent is feasible. Along with exerting promising antitumor efficacy in Pt-sensitive as well as Pt-resistant tumors in vivo, our best candidate has the ability to mitigate the nephrotoxicity issue associated with cisplatin. In addition to demonstrating, for the first time, the power of kinetic inertness in improving the therapeutic benefits of Pt based anticancer therapy, we describe the detailed mechanism of action of our best kinetically inert antitumor agent. This study will certainly pave the way for designing the next generation of anticancer drugs for effective treatment of various cancers.     

A scaling technique for finding the weighted analytic center of a polytope

Let a bounded full dimensional polytope be defined by the systemAx b whereA is anm × n matrix. Leta _i denote theith row of the matrixA, and define theweighted analytic center of the polytope to be the point that minimizes the strictly convex barrier function – _i=1 ^m w _i ln(a _i ^T x –b _i ). The proper selection of weightsw _i can make any desired point in the interior of the polytope become the weighted analytic center. As a result, the weighted analytic center has applications in both linear and general convex programming. For simplicity we assume that the weights are positive integers.If some of thew _i 's are much larger than others, then Newton's method for minimizing the resulting barrier function is very unstable and can be very slow. Previous methods for finding the weighted analytic center relied upon a rather direct application of Newton's method potentially resulting in very slow global convergence. We present a method for finding the weighted analytic center that is based on the scaling technique of Edmonds and Karp and is an enhancement of Newton's method. The scaling algorithm runs in iterations, wherem is the number of constraints defining the polytope andW is the largest weight given on any constraint. Each iteration involves taking a step in the Newton direction and its complexity is dominated by the time needed to solve a system of linear equations.Supported by the Campus Research Board, University of Illinois at Urbana-Champaign.Supported by the National Science Foundation under Grants CCR-9057481 and CCR-9007195.     

AnO(n logn) algorithm for the all-nearest-neighbors Problem

Given a setV ofn points ink-dimensional space, and anL _q -metric (Minkowski metric), the all-nearest-neighbors problem is defined as follows: for each pointp inV, find all those points inV–{p} that are closest top under the distance metricL _q . We give anO(n logn) algorithm for the all-nearest-neighbors problem, for fixed dimensionk and fixed metricL _q . Since there is an (n logn) lower bound, in the algebraic decision-tree model of computation, on the time complexity of any algorithm that solves the all-nearest-neighbors problem (fork=1), the running time of our algorithm is optimal up to a constant factor.This research was supported by a fellowship from the Shell Foundation. The author is currently at AT&T Bell Laboratories, Murray Hill, New Jersey, USA.     

Design,synthesis of novel quinazolin-4-one derivatives and biological evaluation against human MCF-7 breast cancer cell line

A new series of 6,8-dibromo-2-(4-chlorophenyl)quinazolin-4(3H)-one derivatives VI–XIII were synthesized. Their chemical structures were confirmed by spectral and elemental analysis. The cytotoxic effect of the newly synthesized compounds was tested in vitro against human breast cancer cell line (MCF-7). Most of the tested compounds have shown promising cytotoxic activity. Compounds X and XIIIb exerted a powerful cytotoxic effect against MCF-7 with a very low IC50 (0.0015 and 0.0047 µmol/ml), while compounds VI, VII, VIII, XIIb, XI, XIIIc and IX exerted a moderate cytotoxic effect (IC50 0.01523, 0.0213, 0.031, 0.0478, 0.049, 0.068 and 0.079 µmol/ml respectively), compared to doxorubicin (0.0025 µmol/ml). Exploring their apoptotic effect; interestingly,all compounds activated apoptotic cascade in MCF-7. Compounds VI, XIIIb, XIIb, XI, XIIa, VII, V and VIII showed potent effect even much more than doxorubicin by 12.87–5.91 folds, while compounds XIIIc, IX, XIIIa, XIIc and X showed moderate increase in CASP3 activity by 4.96–3.22 folds relative to untreated cells more or less similar to doxorubicin (5.57 folds).     

Simple, facile and one-pot conversion of the Baylis-Hillman acetates into 3,5,6-trisubstituted-2-pyridones

A facile route for the synthesis of novel 3,5,6-trisubstituted-2-pyridones from the acetylated Baylis-Hillman esters with β-enamino esters or β-enamino nitriles in one pot with good yields is described.     

Status of sol–gel process for nuclear fuels

Sol–gel process provides an alternate route for fabrication of ceramic nuclear fuel. The sol–gel process provides several advantages over the conventional powder pellet fabrication process by eliminating handling of radioactive powders. The sol–gel process uses only fluids or fluid like materials, thus become amenable to remote handling. The sol–gel process has been developed for the production of coated particle fuels for High Temperature Gas Cooled Reactors (HTGRs), as sphere-pac fuel for Fast Breeder Reactors (FBRs) and as SGMP fuel for Thermal Reactors. Internal Gelation Process is one of the most important routes of the sol–gel process and has been accepted as the most promising process route globally. Several countries having plutonium or ²³³U based fuel program have developed sol–gel process for nuclear fuels. In India there is special interest for the development of the sol–gel process for the thorium–uranium fuels keeping in view the large resources of thorium in India. Sol–gel process for fuel fabrication is also very attractive route for closing the nuclear fuel cycle efficiently. Author is BRNS Raja Ramanna Fellow.     

Ultra-low-frequency dust-electromagnetic modes in self-gravitating magnetized dusty plasmas

Obliquely propagating altra-low-frequency dust-electromagnetic waves in a self-gravitating, warm, magnetized, two fluid dusty plasma system have been investigated. Two special cases, namely, dust-Alfvén mode propagating parallel to the external magnetic field and dustmagnetosonic mode propagating perpendicular to the external magnetic field have also been considered. It has been shown that effects of self-gravitational field, dust fluid temperature, and obliqueness significantly modify the dispersion properties of these ultra-low-frequency dust-electromagnetic modes. It is also found that in parallel propagating dust-Alfvén mode these effects play no role, but in obliquely propagating dust-Alfvén mode or perpendicular propagating dust-magnetosonic mode the effect of self-gravitational field plays destabilizing role whereas the effect of dust/ion fluid temperature plays stabilizing role.     

Process and equipment development for the preparation of small size UO<Subscript>2</Subscript> microspheres by Jet Entrainment Technique

This paper describes Jet Entrainment Technique (JET) developed at Bhabha Atomic Research Centre (BARC) for the preparation of small microspheres of UO₂ in the size range of 100±20 μm diameter. The UO₂ microspheres were prepared by Internal Gelation Process (IGP) using selected feed solution compositions. Equipment development and the optimized process operations for obtaining more than 90% of high density UO₂ microspheres in the desired size range are described.