Experimental Evaluation of Approximation and Heuristic Algorithms for Maximum Distance-Bounded Subgraph Problems

In this paper, we consider two distance-based relaxed variants of the maximum clique problem (Max Clique), named Maxd-Clique and Maxd-Club for positive integers d. Max 1-Clique and Max 1-Club cannot be efficiently approximated within a factor of n1−ε for any real ε>0 unless P=NP , since they are identical to Max Clique (Håstad in Acta Math 182(1):105–142, 1999; Zuckerman in Theory Comput 3:103–128, 2007). In addition, it is NP -hard to approximate Maxd-Clique and Maxd-Club to within a factor of n1/2−ε for any fixed integer d≥2 and any real ε>0 (Asahiro et al. in Approximating maximum diameter-bounded subgraphs. In: Proc of LATIN 2010, Springer, pp 615–626, 2010; Asahiro et al. in Optimal approximation algorithms for maximum distance-bounded subgraph problems. In: Proc of COCOA, Springer, pp 586–600, 2015). As for approximability of Maxd-Clique and Maxd-Club, a polynomial-time algorithm, called ReFindStar d, that achieves an optimal approximation ratio of O(n1/2) for Maxd-Clique and Maxd-Club was designed for any integer d≥2 in Asahiro et al. (2015, Algorithmica 80(6):1834–1856, 2018). Moreover, a simpler algorithm, called ByFindStar d, was proposed and it was shown in Asahiro et al. (2010, 2018) that although the approximation ratio of ByFindStar d is much worse for any odd d≥3, its time complexity is better than ReFindStar d. In this paper, we implement those approximation algorithms and evaluate their quality empirically for random graphs. The experimental results show that (1) ReFindStar d can find larger d-clubs (d-cliques) than ByFindStar d for odd d, (2) the size of d-clubs (d-cliques) output by ByFindStar d is the same as ones by ReFindStar d for even d, and (3) ByFindStar d can find the same size of d-clubs (d-cliques) much faster than ReFindStar d. Furthermore, we propose and implement two new heuristics, Hclub d for Maxd-Club and Hclique d for Maxd-Clique. Then, we present the experimental evaluation of the solution size of ReFindStar d, Hclub d, Hclique d and previously known heuristic algorithms for random graphs and Erdős collaboration graphs

Synthesis of Adaptive Robust Controllers for a Class of Nonlinear Systems with Input Saturations

This paper deals with a design problem of an adaptive robust controller for a class of nonlinear systems with specified input saturations. For the nonlinear system under consideration, the nonlinearity means unknown perturbations and satisfies the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed adaptive robust controller giving consideration to input saturations are given in terms of linearmatrix inequalities (LMIs). Finally, simple illustrative examples are shown

Tubulin Polyglutamylation Regulates Axonemal Motility by Modulating Activities of Inner-Arm Dyneins

SummaryTubulin polyglutamylation is a modification that adds multiple glutamates to the γ-carboxyl group of a glutamate residue in the C-terminal tails of α- and β-tubulin [1, 2]. This modification has been implicated in the regulation of axonal transport and ciliary motility. However, its molecular function in cilia remains unknown. Here, using a novel Chlamydomonas reinhardtii mutant (tpg1) that lacks a homolog of human TTLL9, a glutamic acid ligase enzyme [3], we found that the lack of a long polyglutamate side chain in α-tubulin moderately weakens flagellar motility without noticeably impairing the axonemal structure. Furthermore, the double mutant of tpg1 with oda2, a mutation that leads to loss of outer-arm dynein, completely lacks motility. More surprisingly, when treated with protease and ATP, the axoneme of this paralyzed double mutant displayed faster microtubule sliding than the motile oda2 axoneme. These and other results suggest that polyglutamylation directly regulates microtubule-dynein interaction mainly by modulating the function of inner-arm dyneins

Reduced tubulin polyglutamylation suppresses flagellar shortness in Chlamydomonas

Ciliary length control is an incompletely understood process essential for normal ciliary function. The flagella of Chlamydomonas mutants lacking multiple axonemal dyneins are shorter than normal; previously it was shown that this shortness can be suppressed by the mutation suppressor of shortness 1 (ssh1) via an unknown mechanism. To elucidate this mechanism, we carried out genetic analysis of ssh1 and found that it is a new allele of TPG2 (hereafter tpg2-3), which encodes FAP234 functioning in tubulin polyglutamylation in the axoneme. Similar to the polyglutamylation-deficient mutants tpg1 and tpg2-1, tpg2-3 axonemal tubulin has a greatly reduced level of long polyglutamate side chains. We found that tpg1 and tpg2-1 mutations also promote flagellar elongation in short-flagella mutants, consistent with a polyglutamylation-dependent mechanism of suppression. Double mutants of tpg1 or tpg2-1 and fla10-1, a temperature-sensitive mutant of intraflagellar transport, underwent slower flagellar shortening than fla10-1 at restrictive temperatures, indicating that the rate of tubulin disassembly is decreased in the polyglutamylation-deficient flagella. Moreover, alpha-tubulin incorporation into the flagellar tips in temporary dikaryons was retarded in polyglutamylation-deficient flagella. These results show that polyglutamylation deficiency stabilizes axonemal microtubules, decelerating axonemal disassembly at the flagellar tip and shifting the axonemal assembly/disassembly balance toward assembly

Remarks on Hubble Induced Mass from Fermion Kinetic Term

We evaluate the effective mass of a scalar field which interacts with visible sector via Planck-suppressed coupling in supergravity framework. We focus on the radiation-dominated (RD) era after inflation and the contribution from a fermionic field in the thermal bath. We find that, in RD era, the fermion kinetic term gives the effective mass of the order of Hubble scale to the scalar field.Comment: 8 pages, v2: minor corrections made, published in PL

A microtubule-dynein tethering complex regulates the axonemal inner dynein f (I1)

Motility of cilia/flagella is generated by a coordinated activity of thousands of dyneins. Inner dynein arms (IDAs) are particularly important for the formation of ciliary/flagellar waveforms, but the molecular mechanism of IDA regulation is poorly understood. Here, we show using cryo-electron tomography and biochemical analyses of Chlamydomonas flagella that a conserved protein FAP44 forms a complex that tethers IDA f (I1 dynein) head domains to the A-tubule of the axonemal outer doublet microtubule. In wild-type flagella, IDA f showed little nucleotide-dependent movement except for a tilt in the fbeta head perpendicular to the microtubule-sliding direction. In the absence of the tether complex, however, addition of ATP and vanadate caused a large conformational change in the IDA f head domains, suggesting that the movement of IDA f is mechanically restricted by the tether complex. Motility defects in flagella missing the tether demonstrates the importance of the IDA f-tether interaction in the regulation of ciliary/flagellar beating

A conserved flagella-associated protein in Chlamydomonas, FAP234, is essential for axonemal localization of tubulin polyglutamylase TTLL9

Tubulin undergoes various posttranslational modifications, including polyglutamylation, which is catalyzed by enzymes belonging to the tubulin tyrosine ligase-like protein (TTLL) family. A previously isolated Chlamydomonas reinhardtii mutant, tpg1, carries a mutation in a gene encoding a homologue of mammalian TTLL9 and displays lowered motility because of decreased polyglutamylation of axonemal tubulin. Here we identify a novel tpg1-like mutant, tpg2, which carries a mutation in the gene encoding FAP234, a flagella-associated protein of unknown function. Immunoprecipitation and sucrose density gradient centrifugation experiments show that FAP234 and TTLL9 form a complex. The mutant tpg1 retains FAP234 in the cell body and flagellar matrix but lacks it in the axoneme. In contrast, tpg2 lacks both TTLL9 and FAP234 in all fractions. In fla10, a temperature-sensitive mutant deficient in intraflagellar transport (IFT), both TTLL9 and FAP234 are lost from the flagellum at nonpermissive temperatures. These and other results suggest that FAP234 functions in stabilization and IFT-dependent transport of TTLL9. Both TTLL9 and FAP234 are conserved in most ciliated organisms. We propose that they constitute a polyglutamylation complex specialized for regulation of ciliary motility

Toward one‐pot olefin/thiophene block copolymers using an in situ ligand exchange

Block copolymers containing both conducting and insulating segments are of interest due to their enhanced electrical properties arising from their increased crystallization. Yet few methods exist for generating these copolymers, because the reaction conditions for synthesizing each block are often incompatible. Herein, efforts toward identifying a one‐pot, living polymerization method for synthesizing block copolymers of 1‐pentene and 3‐hexylthiophene is described. An in situ ligand exchange enables the optimal catalyst to be utilized for synthesizing each block. Even under these conditions, however, only homopolymers are observed. Computational studies modeling the ligand exchange reveal that the added stabilizing ligands likely inhibit propagation of the second block. These results suggest an ancillary ligand‐based “goldilocks” effect wherein catalysts that are stable yet still reactive are required. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1601–1605Combined experimental and computational studies revealed unexpected challenges in applying sequential catalysis for the streamlined synthesis of insulating/conducting block copolymers.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/150553/1/pola29426_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/150553/2/pola29426.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/150553/3/pola29426-sup-0001-AppendixS1.pd

Effect of Oligomers Derived from Biodegradable Polyesters on Eco- and Neurotoxicity

Biodegradable polymers are eco-friendly materials and have attracted attention for use in a sustainable society because they are not accumulated in the environment. Although the characteristics of biodegradable polymers have been assessed well, the effects of their degradation products have not. Herein, we comprehensively evaluated the chemical toxicities of biodegradable polyester, polycaprolactone (PCL), and synthetic oligocaprolactones (OCLs) with different degrees of polymerization. While the PCL did not show any adverse effects on various organisms, high levels of shorter OCLs and the monomer (1 μg/mL for freshwater microorganisms and 1 mg/mL for marine algae and mammalian cells) damaged the tested organisms, including freshwater microorganisms, marine algae, and mammalian cells, which indicated the toxicities of the degradation products under unnaturally high concentrations. These results highlight the need for a further understanding of the effects of the degradation products resulting from biodegradable polyesters to ensure a genuinely sustainable society

Hubble Induced Mass in Radiation Dominated Universe

We reconsider the effective mass of a scalar field which interact with visible sector via Planck-suppressed coupling in supergravity framework. We focus on the radiation-dominated (RD) era after inflation. In this era, the effective mass is given by thermal average of interaction terms. To make our analysis clear, we rely on Kadanoff-Baym equations to evaluate the thermal average. We find that, in RD era, a scalar field acquires the effective mass of the order of $H$.Comment: 10 pages, v2:minor corrections and a reference added, v3:a footnote added, version accepted by PL