Pseudo Approximation Algorithms with Applications to Optimal Motion Planning

We introduce a technique for computing approximate solutions to optimization problems. If $X$ is the set of feasible solutions, the standard goal of approximation algorithms is to compute $x\in X$ that is an $\varepsilon$-approximate solution in the following sense: $$d(x) \leq (1+\varepsilon)\, d(x^*),$$ where $x^* \in X$ is an optimal solution, $d\colon\ X\rightarrow {\Bbb R}_{\geq 0}$ is the optimization function to be minimized, and $\varepsilon>0$ is an input parameter. Our approach is first to devise algorithms that compute pseudo $\varepsilon$-approximate solutions satisfying the bound $$d(x) \leq d(x_R^*) + \varepsilon R,$$ where $R>0$ is a new input parameter. Here $x^*_R$ denotes an optimal solution in the space $X_R$ of $R$-constrained feasible solutions. The parameter $R$ provides a stratification of $X$ in the sense that (1) $X_R \subseteq X_{R}$ for $R < R$ and (2) $X_R = X$ for $R$ sufficiently large. We first describe a highly efficient scheme for converting a pseudo $\varepsilon$-approximation algorithm into a true $\varepsilon$-approximation algorithm. This scheme is useful because pseudo approximation algorithms seem to be easier to construct than $\varepsilon$-approximation algorithms. Another benefit is that our algorithm is automatically precision-sensitive. We apply our technique to two problems in robotics: (A) Euclidean Shortest Path (3ESP), namely the shortest path for a point robot amidst polyhedral obstacles in three dimensions, and (B) $d_1$-optimal motion for a rod moving amidst planar obstacles (1ORM). Previously, no polynomial time $\varepsilon$-approximation algorithm for (B) was known. For (A), our new solution is simpler than previous solutions and has an exponentially smaller complexity in terms of the input precision.     

Catalytic construction and reconstruction of guanidines: Ti-mediated guanylation of amines and transamination of guanidines

Bis(guanidinate) titanium imido complexes [{(Me2N)C(NiPr)2}2TiNAr'] (Ar' = 2,6-Me2C6H3 (1a); C6F5 (1b)) are competent catalysts for the guanylation of a variety of arylamines with carbodiimide. The reversible [2 + 2] addition of iPrN=C=NiPr to 1b is demonstrated and is proposed to be part of the catalytic cycle. Compounds 1a and 1b are also effective precatalysts for the transamination of trialkylguanidines with arylamines to yield aryldialkylguanidines.     

Comparative evaluation of software for retention time alignment of gas chromatography/time-of-flight mass spectrometry-based metabonomic data

In chromatography-based metabonomic research, retention time (RT) alignment of chromatographic peaks poses a challenge for the accurate profiling of biomarkers. Although a number of RT alignment software has been reported, the performance of these software packages have not been comprehensively evaluated. This study aimed to evaluate the RT alignment accuracy of publicly available and commercial RT alignment software. Two gas chromatography/mass spectrometry (GC/MS) datasets acquired from a mixture of standard metabolites and human bladder cancer urine samples, were used to assess three publicly available software packages, MetAlign, MZmine and TagFinder, and two commercial applications comprising the Calibration feature and Statistical Compare of ChromaTOF software. The overall RT alignment accuracies in aligning standard compounds mixture were 93, 92, 74, 73 and 42% for Calibration feature, MZmine, MetAlign, Statistical Compare and TagFinder, respectively. Additionally, unique trends were observed for the individual software with regards to the different experimental conditions related to extent and direction of RT shifts. Conflicting performance was observed for human urine samples suggesting that RT misalignments still occurred despite the use of RT alignment software. While RT alignment remains an inevitable step in data preprocessing, metabonomic researchers are recommended to perform manual check on the RT alignment of important biomarkers as part of their validation process.     

Costly punishment and cooperation in the evolutionary snowdrift game

The role of punishments in promoting cooperation is an important issue. We incorporate costly punishments into the snowdrift game (SG) by introducing a third punishing (P) character, and study the effects. The punishers, who carry basically a cooperative (C) character, are willing to pay a cost α so as to punish a non-cooperative (D) opponent by β. Depending on the initial fractions of the characters, α, β, and the cost-to-benefit ratio r in the SG, the three-character system evolves into a steady state consisting either only of C and P characters or only of C and D characters, in a well-mixed population. The former situation represents an enhancement in cooperation relative to the SG, while the latter is similar to the SG. The dynamics in approaching these different steady states are found to be different. Analytically, the key features in the dynamics and the steady states observed in simulations are captured by a set of differential equations. The sensitivity to the initial distribution of characters is studied by depicting the flow in a phase portrait and analyzing the nature of fixed points. The analysis also shows the role of P-character agents in preventing a system from invasion by D-character agents. Starting from a population consisting only of C and P agents, a D-character agent intended to invade the system cannot survive when the initial fraction of P agents is greater than r/β. Our model, defined intentionally as a simulation algorithm, can be readily generalized to incorporate many interesting effects, such as those in a networked population.     

Synthesis and molecular and extended structures for a diaminonaphthalene-derived bis(amido)stannylene

The cyclic bis(amido)tin(II) compound Sn[1,8-((iPrN)2C10H6] (2) was isolated from the reaction of Li2[1,8-((iPrN)2C10H6] (1) and SnCl2. Solid-state structural analysis of 2 showed it to be a mononuclear species with a pyramidal Sn center as part of a nonplanar metallaheterocycle. The packing diagram of 2 revealed an extended one-dimensional head-to-tail chain structure with short intermolecular Sn/arene-C interactions. Computational examination of 2 (DFT/PW91 and MP2 with 6-31G* and 6-311G** basis functions) indicated that the optimum gas-phase structure of 2,which displays a Sn center in the plane of the naphthyl backbone with a slightly twisted metallaheterocycle, is approximately 24 kcal/mol lower in energy than the X-ray structure. The solid-state geometry of 2 is attributed to the intermolecular donation of the naphthalene pi-electrons to a Lewis acidic Sn center, which leads to the observed supramolecular structure. The crystal structure of 1 is also reported.     

Synthesis of novel acetylenic cyclophanes with helical chirality: potential new structures for liquid crystals

The synthesis of a series of novel acetylenic cyclophanes is described. X-ray crystallographic analysis of the core structure revealed a twisted conformation with helical chirality. Preliminary results suggest that these cyclophanes, with appropriate functionality, have the potential to act as unique liquid crystalline materials.     

Fourier multipliers of Lipschitz spaces

Let G denote an infinite, compact, metrizable, 0-dimensional, Abelian group. The following are characterized: (i) the multipliers from one Lipschitz space Lip(α, p; G) to another Lipschitz space Lip(β, q; G) for 0 < α < β < ∞ and 1 ? p, q ? ∞; and (ii) the multipliers from Lip(α, p; G) to Lip(β, q; G) for 0 < β ? α < ∞ and 1 < q ? 2 ? p < ∞. Two special cases of (i), namely the case q = ∞ and the case p = 1, were obtained by the authors in an earlier publication (1981). A. Zygmund (J. Math. Mech.8 (1959), 889–895) and T. Mizuhara (Tôhoku Math. J.24 (1972), 263–268) have characterized the multipliers of certain Lipschitz spaces defined on the circle group.     

Consensus model for identification of novel PI3K inhibitors in large chemical library

Phosphoinositide 3-kinases (PI3Ks) inhibitors have treatment potential for cancer, diabetes, cardiovascular disease, chronic inflammation and asthma. A consensus model consisting of three base classifiers (AODE, kNN, and SVM) trained with 1,283 positive compounds (PI3K inhibitors), 16 negative compounds (PI3K non-inhibitors) and 64,078 generated putative negatives was developed for predicting compounds with PI3K inhibitory activity of IC₅₀ ≤ 10 μM. The consensus model has an estimated false positive rate of 0.75%. Nine novel potential inhibitors were identified using the consensus model and several of these contain structural features that are consistent with those found to be important for PI3K inhibitory activities. An advantage of the current model is that it does not require knowledge of 3D structural information of the various PI3K isoforms, which is not readily available for all isoforms.     

A carbon-centered radical unreactive toward oxygen: unusual radical stabilization by a lactone ring

A lactone ring confers unusual stability to a diphenylmethyl-like radical that is virtually unreactive toward oxygen. Thus, the radical derived from HP-136 is about 10,000 times less reactive than typical carbon-centered radicals. A reversible reaction with oxygen is proposed by analogy with triphenylmethyl; however, the association constant is about 1000 times smaller for HP-136 than for triphenylmethyl. While the lactone ring greatly influences the reactivity, the spectroscopy of the HP-136-derived radical is in line with that expected for a substituted diphenylmethyl radical.     

Issues in Managing Information Technology

This paper describes three case studies which investigated issues relating to the implementation and management of advanced information technology. The benefits derived from information technology were found to vary from one organization to another. These studies provide further evidence to support earlier research findings that senior management has an important role to play in the effective exploitation of information technology, and that the investment approach taken by an organization has a significant effect on the development of computer-based information systems. The effectiveness of a system depends not only on applying the appropriate technology, but also on how successfully technical and behavioural issues are resolved.