On The Parameterized Intractability Of Motif Search Problems*

We show that Closest Substring, one of the most important problems in the field of consensus string analysis, is W[1]-hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This is done by giving a “strongly structure-preserving” reduction from the graph problem Clique to Closest Substring. This problem is therefore unlikely to be solvable in time O(f(k)•n^c) for any function f of k and constant c independent of k, i.e., the combinatorial explosion seemingly inherent to this NP-hard problem cannot be restricted to parameter k. The problem can therefore be expected to be intractable, in any practical sense, for k ≥ 3. Our result supports the intuition that Closest Substring is computationally much harder than the special case of Closest String, althoughb othp roblems are NP-complete. We also prove W[1]-hardness for other parameterizations in the case of unbounded alphabet size. Our W[1]-hardness result for Closest Substring generalizes to Consensus Patterns, a problem arising in computational biology. * An extended abstract of this paper was presented at the 19th International Symposium on Theoretical Aspects of Computer Science (STACS 2002), Springer-Verlag, LNCS 2285, pages 262–273, held in Juan-Les-Pins, France, March 14–16, 2002. † Work was supported by the Deutsche Forschungsgemeinschaft (DFG), research project “OPAL” (optimal solutions for hard problems in computational biology), NI 369/2. ‡ Work was done while the author was with Wilhelm-Schickard-Institut für Informatik, Universit?t Tübingen. Work was partially supported by the Deutsche Forschungsgemeinschaft (DFG), Emmy Noether research group “PIAF” (fixed-parameter algorithms), NI 369/4.     

Characterization of the approach to steady state and the steady-state properties of multimode optical fibers using LED excitation

A simple technique has been developed to characterize the approach to steady state and the steady-state properties of multimode fibers using LED excitation. Results are given for 6 mil Selfoc fibers whose far-field pattern for the steady state is in excellent agreement with a calculation by Marcuse. To first order, the steady-state mode distribution fits a simple model of uniform modal excitation of a fiber with a reduced numerical aperture.     

C70X2(X=H,F, Cl)的稳定性和电子光谱

用INDO方法研究C70H2四种异构体的稳定性, 表明其最稳定异构体为1, 9-C70H2和7, 8-C70H2, 两者能量差为16.3KJ.mol^-^1, 与实验值及ab initio计算值接近; 光谱计算表明, 其特征吸收峰与实验值一致。在此基础上预测C70F2和C70Cl2的稳定性和电子光谱, 表明C70F2四种异构体的稳定性顺序与C70H2一致, 而C70Cl2则以21, 42-异构体最为稳定。二者的电子光谱与C70H2极其相似只是在500nm以上有细微差别。     

氢原子在镍台阶面上吸附、振动和表面扩散行为的理论研究

本文用对势方法研究了氢原子在Ni(510)台阶面上的吸附和振动, 计算结果与实验符合得很好。并考察了氢原子在Ni(997)台阶面上的吸附和扩散, 结果表明,台阶对下台面上扩散的氢原子开成捕获势阱, 对上台面扩散的氢原子形成反射势,这也很好地支持了实验结果。     

Forbidden minors to graphs with small feedback sets

Finite obstruction set characterizations for lower ideals in the minor order are guaranteed to exist by the graph minor theorem. In this paper we characterize several families of graphs with small feedback sets, namely k₁-F V S , k₂-F E S and (k₁,k₂)-F V /E S , for small integer parameters k₁ and k₂. Our constructive methods can compute obstruction sets for any minor-closed family of graphs, provided the pathwidth (or treewidth) of the largest obstruction is known.     

Pulsed‐laser polymerization‐gel permeation chromatographic determination of the propagation‐rate coefficient for the methyl acrylate dimer: A sterically hindered monomer

The methyl acrylate dimer (MAD) is a sterically hindered macromonomer, and the propagating radical can fragment to an unsaturated end group. The propagation‐rate coefficient (k_p) for MAD was obtained by pulsed‐laser polymerization (PLP). The Mark–Houwink–Sakaruda parameters required for the analysis of the molecular weight distributions (MWDs) were obtained by multiple‐detector gel permeation chromatography (GPC) with on‐line viscometry. The small radical created by the fragmentation results in a short‐chain polymer that means the MWD may no longer be given by that expected for “ideal” PLP conditions; simulations suggest that the degree of polymerization required for “ideal” PLP conditions can be obtained from the primary point of inflection provided the GPC traces also show a clear secondary inflection point (radicals terminated by the second, rather than the first, pulse subsequent to initiation). Over the temperature range of 40–75 °C, the data can be best fitted by k_p/dm³ mol^?1 s^?1 = 10^6.1 exp(?29.5 kJ mol^?1), with a moderately large joint confidence interval for the Arrhenius parameters. The data are consistent with an increased activation energy and reduced frequency factor as compared with acrylate or methacrylate; both of these changes can be ascribed to hindrance. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3902–3915, 2001     

Grafting of dodecyl methacrylate onto hydroxylated polybutadiene by miniemulsion polymerization

Homogeneous copolymer latex particles of dodecyl methacrylate (DMA) and low‐molecular‐weight hydroxy‐terminated polybutadiene (HTPB) oligomers were prepared by free‐radical polymerization using miniemulsion methods. Rate data and latex characteristics were consistent with the classical miniemulsion mechanism where nucleation of monomer droplets is the predominant pathway of particle formation. There is essentially no particle formation by secondary nucleation in the water phase. Characterization of the copolymer latex particles using transmission electron microscopy and modulated differential scanning calorimetry suggested that there is a significant amount of grafted poly(DMA)/HTPB polymer contributing to the miscibility of the HTPB and poly(DMA) phases. Particles were more homogeneous at increased HTPB composition, of relatively narrow polydispersity, and could be prepared reproducibly using a number of different initiation systems. The observed trends can all be rationalized in terms of conventional understanding of miniemulsion polymerization systems. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3404–3416, 2004     

Structure–property relationships in modified natural rubber latexes grafted with methyl methacrylate and vinyl neo‐decanoate

A series of modified natural rubber latexes (NRLs) grafted with poly(methyl methacrylate) (PMMA) were prepared by seeded emulsion polymerization with NRL as the seed polymer. Two different redox systems, cumene hydroperoxide (CHP)/tetraethylene pentamine (TEPA) and tert‐butyl hydroperoxide (t‐BHP)/TEPA, were used to initiate polymerization, and phase mixing was promoted by the addition of vinyl neo‐decanoate (VneoD). The CHP/TEPA system was more efficient than t‐BHP/TEPA for the grafting of secondary polymers in modified natural rubber (NR). The enhanced phase mixing in the presence of VneoD was attributed to the solubility parameter of the VneoD‐rich methyl methacrylate–VneoD copolymer formed late in the reaction, lying between that of PMMA and NR, and the extent to which this polymer was grafted to the NR backbone. The viscoelastic properties of the polymers were investigated as a function of composition, temperature, and frequency; changes in viscoelastic behavior consistent with the presence of a high‐T_g PMMA phase (where T_g is the glass‐transition temperature) were observed. This suggested a degree of phase mixing that increased with increasing VneoD content and increasing flux of oxygen‐centered radicals within the NR particles. More phase mixing resulted in poorer film formation, which was consistent with the localization of a high‐T_g secondary polymer phase near the particle surface. The apparent concentration of PMMA near the surface of the particles was also observed with transmission electron microscopy. The localization of PMMA near the particle surfaces was consistent with the presumed locus of radical generation in these systems: the redox couple used to initiate the polymerization consisted of an oil‐soluble hydroperoxide and a water‐soluble amine that reacted predominantly at the water/particle interface. The viscoelastic properties of the modified NRLs that were prepared suggest that these synthetic procedures provide a means of controlling phase mixing and branching, such as for improving the suitability of these modified rubbers in pressure‐sensitive‐adhesive formulations. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 809–822, 2002; DOI 10.1002/pola.10165     

Research problems

A Generalized eigenvector problem for a set of nonnegative matrices