Further Exploiting c-Closure for FPT Algorithms and Kernels for Domination Problems

For a positive integer c, a graph G is said to be c-closed if every pair of nonadjacent vertices in G have at most c - 1 neighbors in common. The closure of a graph G, denoted by cl(G), is the least positive integer c for which G is c-closed. The class of c-closed graphs was introduced by J. Fox, T. Roughgarden, C. Seshadhri, F. Wei, and N. Wein [Proceedings of the International Colloquium on Automata, Languages, and Programming (2018), 55; SIAM J. Comput., 49 (2020), pp. 448-464]. T. Koana, C. Komusiewicz, and F. Sommer [Proceedings of the European Symposium on Algorithms (2020), 65; SIAM J. Discrete Math., 36 (2022), pp. 2798-2821] started the study of using cl(G) as an additional structural parameter to design kernels for problems that are W-hard under standard parameterizations. In particular, they studied problems such as Independent Set, Induced Matching, Irredundant Set, and (Threshold) Dominating Set and showed that each of these problems admits a polynomial kernel when parameterized either by k + c or by k for each fixed value of c. Here, k is the solution size and c = cl(G). The work of Koana et al. left several questions open, one of which was whether the Perfect Code problem admits a fixed-parameter tractable (FPT) algorithm and a polynomial kernel on c-closed graphs. In this paper, among other results, we answer this question in the affirmative. Inspired by the FPT algorithm for Perfect Code, we further explore two more domination problems on the graphs of bounded closure. The other problems that we study are Connected Dominating Set and Partial Dominating Set. We show that Perfect Code and Connected Dominating Set are fixed-parameter tractable when parameterized by k + cl(G), whereas Partial Dominating Set, parameterized by k, is W[1]-hard even when cl(G) = 2. We also show that for each fixed c, Perfect Code admits a polynomial kernel on the class of c-closed graphs. And we observe that Connected Dominating Set has no polynomial kernel even on 2-closed graphs unless NP ⊆ co-NP/poly

Delocalization and Universality of the Fractional Quantum Hall Plateau-to-Plateau Transitions

Disorder and electron-electron interaction play essential roles in the physics of electron systems in condensed matter. In two-dimensional, quantum Hall systems, extensive studies of disorder-induced localization have led to the emergence of a scaling picture with a single extended state, characterized by a power-law divergence of the localization length in the zero-temperature limit. Experimentally, scaling has been investigated via measuring the temperature dependence of plateau-to-plateau transitions between the integer quantum Hall states (IQHSs), yielding a critical exponent $\kappa\simeq 0.42$. Here we report scaling measurements in the fractional quantum Hall state (FQHS) regime where interaction plays a dominant role. Our study is partly motivated by recent calculations, based on the composite fermion theory, that suggest identical critical exponents in both IQHS and FQHS cases to the extent that the interaction between composite fermions is negligible. The samples used in our experiments are two-dimensional electron systems confined to GaAs quantum wells of exceptionally high quality. We find that $\kappa$ varies for transitions between different FQHSs observed on the flanks of Landau level filling factor $\nu=1/2$, and has a value close to that reported for the IQHS transitions only for a limited number of transitions between high-order FQHSs with intermediate strength. We discuss possible origins of the non-universal $\kappa$ observed in our experiments

Implicit Theories of Attraction

Implicit Theories of Attraction, Bohns, V. K., Scholer, A. A., & Rehman, U. © 2015. Copyright Guilford Press. Reprinted with permission of The Guilford PressSexual satisfaction is an important component of relationship well-being within romantic relationships. Yet, relatively little is known about the psychological factors that predict responses to the inevitable sexual challenges couples face. Four studies provide evidence that implicit theories of sexual attraction as either fixed or malleable predict responses to sexual challenges. In Studies 1 and 2, individual differences in these beliefs predicted (above and beyond other implicit theories, relationship beliefs, and measures of sexual desire) perceptions of success for a relationship lacking sexual chemistry. In Study 3, these beliefs predicted actual relationship outcomes in committed couples. Finally, in Study 4, these beliefs predicted willingness to engage in destructive behaviors in response to a sexual challenge—but not in response to a non-sexual challenge—in a hypothetical long-term relationship. This latter finding was mediated by expectations that the problem faced by the couple was solvable

The Molecular Switching Mechanism at the Conserved D(E)RY Motif in Class-A GPCRs

The disruption of ionic and H-bond interactions between the cytosolic ends of transmembrane helices TM3 and TM6 of class-A (rhodopsin-like) G protein-coupled receptors (GPCRs) is a hallmark for their activation by chemical or physical stimuli. In the bovine photoreceptor rhodopsin, this is accompanied by proton uptake at Glu134 in the class-conserved D(E)RY motif. Studies on TM3 model peptides proposed a crucial role of the lipid bilayer in linking protonation to stabilization of an active state-like conformation. However, the molecular details of this linkage could not be resolved and have been addressed in this study by molecular dynamics (MD) simulations on TM3 model peptides in a bilayer of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). We show that protonation of the conserved glutamic acid alters the peptide insertion depth in the membrane, its side-chain rotamer preferences, and stabilizes the C-terminal helical structure. These factors contribute to the rise of the side-chain pKa (> 6) and to reduced polarity around the TM3 C terminus as confirmed by fluorescence spectroscopy. Helix stabilization requires the protonated carboxyl group; unexpectedly, this stabilization could not be evoked with an amide in MD simulations. Additionally, time-resolved Fourier transform infrared (FTIR) spectroscopy of TM3 model peptides revealed a different kinetics for lipid ester carbonyl hydration, suggesting that the carboxyl is linked to more extended H-bond clusters than an amide. Remarkably, this was seen as well in DOPC-reconstituted Glu134- and Gln134-containing bovine opsin mutants and demonstrates that the D(E)RY motif is a hydrated microdomain. The function of the D(E)RY motif as a proton switch is suggested to be based on the reorganization of the H-bond network at the membrane interface

Interplay of brain structure and function in neonatal congenital heart disease

Objective: To evaluate whether structural and microstructural brain abnormalities in neonates with congenital heart disease (CHD) correlate with neuronal network dysfunction measured by analysis of EEG connectivity. Methods: We studied a prospective cohort of 20 neonates with CHD who underwent continuous EEG monitoring before surgery to assess functional brain maturation and network connectivity, structural magnetic resonance imaging (MRI) to determine the presence of brain injury and structural brain development, and diffusion tensor MRI to assess brain microstructural development. Results: Neonates with MRI brain injury and delayed structural and microstructural brain development demonstrated significantly stronger high-frequency (beta and gamma frequency band) connectivity. Furthermore, neonates with delayed microstructural brain development demonstrated significantly weaker low-frequency (delta, theta, alpha frequency band) connectivity. Neonates with brain injury also displayed delayed functional maturation of EEG background activity, characterized by greater background discontinuity. Interpretation: These data provide new evidence that early structural and microstructural developmental brain abnormalities can have immediate functional consequences that manifest as characteristic alterations of neuronal network connectivity. Such early perturbations of developing neuronal networks, if sustained, may be responsible for the persistent neurocognitive impairment prevalent in adolescent survivors of CHD. These foundational insights into the complex interplay between evolving brain structure and function may have relevance for a wide spectrum of neurological disorders manifesting early developmental brain injury

TAPCHA: An Invisible CAPTCHA Scheme

TAPCHA is a universal CAPTCHA scheme designed for touch-enabled smart devices such as smartphones, tablets and smartwatches. The main difference between TAPCHA and other CAPTCHA schemes is that TAPCHA retains its security by making the CAPTCHA test ‘invisible’ for the bot. It then utilises context effects to maintain the readability of the instruction for human users which eventually guarantees the usability of the scheme. Two reference designs, namely TAPCHA SHAPE & SHADE and TAPCHA MULTI are developed to demonstrate the use of this scheme

The Roles of Transmembrane Domain Helix-III during Rhodopsin Photoactivation

Background: Rhodopsin, the prototypic member of G protein-coupled receptors (GPCRs), undergoes isomerization of 11- cis-retinal to all-trans-retinal upon photoactivation. Although the basic mechanism by which rhodopsin is activated is well understood, the roles of whole transmembrane (TM) helix-III during rhodopsin photoactivation in detail are not completely clear. Principal Findings: We herein use single-cysteine mutagenesis technique to investigate conformational changes in TM helices of rhodopsin upon photoactivation. Specifically, we study changes in accessibility and reactivity of cysteine residues introduced into the TM helix-III of rhodopsin. Twenty-eight single-cysteine mutants of rhodopsin (P107C-R135C) were prepared after substitution of all natural cysteine residues (C140/C167/C185/C222/C264/C316) by alanine. The cysteine mutants were expressed in COS-1 cells and rhodopsin was purified after regeneration with 11-cis-retinal. Cysteine accessibility in these mutants was monitored by reaction with 4, 49-dithiodipyridine (4-PDS) in the dark and after illumination. Most of the mutants except for T108C, G109C, E113C, I133C, and R135C showed no reaction in the dark. Wide variation in reactivity was observed among cysteines at different positions in the sequence 108–135 after photoactivation. In particular, cysteines at position 115, 119, 121, 129, 131, 132, and 135, facing 11-cis-retinal, reacted with 4-PDS faster than neighboring amino acids. The different reaction rates of mutants with 4-PDS after photoactivation suggest that the amino acids in different positions in helix-III are exposed to aqueous environment to varying degrees. Significance: Accessibility data indicate that an aqueous/hydrophobic boundary in helix-III is near G109 and I133. The lack of reactivity in the dark and the accessibility of cysteine after photoactivation indicate an increase of water/4-PDS accessibility for certain cysteine-mutants at Helix-III during formation of Meta II. We conclude that photoactivation resulted in water-accessible at the chromophore-facing residues of Helix-III.National Institutes of Health (U.S.) (grant GM28289)National Eye Institute (Grant Grant EY11716)National Science Foundation (U.S.) (grant EIA-0225609