Rainbow Coloring Hardness via Low Sensitivity Polymorphisms

A k-uniform hypergraph is said to be r-rainbow colorable if there is an r-coloring of its vertices such that every hyperedge intersects all r color classes. Given as input such a hypergraph, finding a r-rainbow coloring of it is NP-hard for all k >= 3 and r >= 2. Therefore, one settles for finding a rainbow coloring with fewer colors (which is an easier task). When r=k (the maximum possible value), i.e., the hypergraph is k-partite, one can efficiently 2-rainbow color the hypergraph, i.e., 2-color its vertices so that there are no monochromatic edges. In this work we consider the next smaller value of r=k-1, and prove that in this case it is NP-hard to rainbow color the hypergraph with q := ceil[(k-2)/2] colors. In particular, for k <=6, it is NP-hard to 2-color (k-1)-rainbow colorable k-uniform hypergraphs. Our proof follows the algebraic approach to promise constraint satisfaction problems. It proceeds by characterizing the polymorphisms associated with the approximate rainbow coloring problem, which are rainbow colorings of some product hypergraphs on vertex set [r]^n. We prove that any such polymorphism f: [r]^n -> [q] must be C-fixing, i.e., there is a small subset S of C coordinates and a setting a in [q]^S such that fixing x_{|S} = a determines the value of f(x). The key step in our proof is bounding the sensitivity of certain rainbow colorings, thereby arguing that they must be juntas. Armed with the C-fixing characterization, our NP-hardness is obtained via a reduction from smooth Label Cover

Sex-related differences in chromatic sensitivity

Generally women are believed to be more discriminating than men in the use of colour names and this is often taken to imply superior colour vision. However, if both X-chromosome linked colour deficient males (~8%) and females (<1%) as well as heterozygote female carriers (~15%) are excluded from comparisons, then differences between men and women in red-green colour discrimination have been reported as not being significant (e.g., Pickford, 1944; Hood et al., 2006). We re-examined this question by assessing the performance of 150 males and 150 females on the Colour Assessment and Diagnosis (CAD) test (Rodriguez-Carmona, 2005). This is a sensitive test that yields small colour detection thresholds. The test employs direction-specific, moving, chromatic stimuli embedded in a background of random, dynamic, luminance contrast noise. A four-alternative, forced-choice procedure is employed to measure the subject’s thresholds for detection of colour signals in 16 directions in colour space, while ensuring that the subject cannot make use of any residual luminance contrast signals. In addition, we measured the Rayleigh anomaloscope matches in a subgroup of 111 males and 114 females. All the age-matched males (30.8 ± 9.7) and females (26.7 ± 8.8) had normal colour vision as diagnosed by a battery of conventional colour vision tests. Females with known colour deficient relatives were excluded from the study. Comparisons between the male and female groups revealed no significant differences in anomaloscope midpoints (p=0.709), but a significant difference in matching ranges (p=0.040); females on average tended to have a larger mean range (4.11) than males (3.75). Females also had significantly higher CAD thresholds than males along the red-green (p=0.0004), but not along the yellow-blue discrimination axis. The differences between males and females in red-green discrimination may be related to the heterozygosity in X-linked cone photopigment expression common among females

Frequency-dependent and correlational selection pressures have conflicting consequences for assortative mating in a color-polymorphic lizard, Uta stansburiana

Acknowledgments We would like to thank the numerous undergraduate researchers involved with this project for their invaluable assistance in lizard rearing and data collection. We also thank D. Haisten, A. Runemark, Y. Takahashi, and M. Verzijden for insightful comments on the manuscript. This project was funded by National Science Foundation DEBOS-15973 to A.G.M. and B.R.S.Peer reviewedPublisher PD

Examination of the Monoamine Oxidase a Gene Promoter on Motivation to Exercise and Levels of Voluntary Physical Activity

Purpose: Monoamine oxidase A (MAO-A) is an enzyme that causes inactivation of monoamine neurotransmitters, such as dopamine. Polymorphisms in the promoter region of the MAO-A gene can change transcriptional activity and the amount of MAO-A produced, leading to alterations in available dopamine levels. MAO-A polymorphisms have been associated with physical activity level. This study examined whether motivation to exercise, and levels of voluntary physical activity are associated with MAO-A gene polymorphisms. Methods: Seventy-one participants (18-24 years, 13 males & 58 females) completed the Behavioral Regulation in Exercise Questionaire-2 (BREQ-2) to assess their motivation to exercise and the International Physical Activity Questionnaire (IPAQ) to assess their level of physical activity. DNA was isolated from a cheek cell sample. MAO-A 3/3 and 4/4 genotype individuals were used for analysis. Results: External motivation to exercise was significantly higher (p \u3c 0.01) in the high transcription 4/4 genotype (ave 1.17 ± 0.7) compared to the low transcription 3/3 genotype (ave 0.42 ± 0.5). Internal motivation to exercise, body mass index, and weekly MET minutes were comparable between genotypes. Conclusion: The results suggest a polymorphism in this monoamine pathway may play a role in increasing sensitivity to external factors that motivate individuals to exercise

Separating Use and Reuse to Improve Both

Context: Trait composition has inspired new research in the area of code reuse for object oriented (OO) languages. One of the main advantages of this kind of composition is that it makes possible to separate subtyping from subclassing; which is good for code-reuse, design and reasoning. However, handling of state within traits is difficult, verbose or inelegant. Inquiry: We identify the this-leaking problem as the fundamental limitation that prevents the separation of subtyping from subclassing in conventional OO languages. We explain that the concept of trait composition addresses this problem, by distinguishing code designed for use (as a type) from code designed for reuse (i.e. inherited). We are aware of at least 3 concrete independently designed research languages following this methodology: TraitRecordJ, Package Templates and DeepFJig. Approach: In this paper, we design $42_\mu$ a new language, where we improve use and reuse and support the This type and family polymorphism by distinguishing code designed for use from code designed for reuse. In this way $42_\mu$ synthesise the 3 approaches above, and improves them with abstract state operations: a new elegant way to handle state composition in trait based languages. Knowledge and Grounding: Using case studies, we show that $42_\mu$'s model of traits with abstract state operations is more usable and compact than prior work. We formalise our work and prove that type errors cannot arise from composing well typed code. Importance: This work is the logical core of the programming language 42. This shows that the ideas presented in this paper can be applicable to a full general purpose language. This form of composition is very flexible and could be used in many new languages

A two-step method for identifying photopigment opsin and rhodopsin gene sequences underlying human color vision phenotypes.

PurposeTo present a detailed, reliable long range-PCR and sequencing (LR-PCR-Seq) procedure to identify human opsin gene sequences for variations in the long wavelength-sensitive (OPN1LW), medium wavelength-sensitive (OPN1MW), short wavelength-sensitive (OPN1SW), and rhodopsin (RHO) genes.MethodsColor vision was assessed for nine subjects using the Farnsworth-Munsell 100 hue test, Ishihara pseudoisochromatic plates, and the Rabin cone-contrast threshold procedure (ColorDX, Konan Medical). The color vision phenotypes were normal trichromacy (n = 3), potential tetrachromacy (n = 3), dichromacy (n = 2), and unexplained low color vision (n = 1). DNA was isolated from blood or saliva and LR-PCR amplified into individual products: OPN1LW (4,045 bp), OPN1MW (4,045 bp), OPN1SW (3,326 bp), and RHO (6,715 bp). Each product was sequenced using specific internal primer sets. Analysis was performed with Mutation Surveyor software.ResultsThe LR-PCR-Seq technique identified known single nucleotide polymorphisms (SNPs) in OPN1LW and OPN1MW gene codons (180, 230, 233, 277, and 285), as well as those for lesser studied codons (174, 178, 236, 274, 279, 298 and 309) in the OPN1LW and OPN1MW genes. Additionally, six SNP variants in the OPN1MW and OPN1LW genes not previously reported in the NCBI dbSNP database were identified. An unreported poly-T region within intron 5(c.36+126) of the rhodopsin gene was also found, and analysis showed it to be highly conserved in mammalian species.ConclusionsThis LR-PCR-Seq procedure (single PCR reaction per gene followed by sequencing) can identify exonic and intronic SNP variants in OPN1LW, OPN1MW, OPN1SW, and rhodopsin genes. There is no need for restriction enzyme digestion or multiple PCR steps that can introduce errors. Future studies will combine the LR-PCR-Seq with perceptual behavior measures, allowing for accurate correlations between opsin genotypes, retinal photopigment phenotypes, and color perception behaviors

Anomalous phase behavior of a soft-repulsive potential with a strictly monotonic force

We study the phase behavior of a classical system of particles interacting through a strictly convex soft-repulsive potential which, at variance with the pairwise softened repulsions considered so far in the literature, lacks a region of downward or zero curvature. Nonetheless, such interaction is characterized by two length scales, owing to the presence of a range of interparticle distances where the repulsive force increases, for decreasing distance, much more slowly than in the adjacent regions. We investigate, using extensive Monte Carlo simulations combined with accurate free-energy calculations, the phase diagram of the system under consideration. We find that the model exhibits a fluid-solid coexistence line with multiple re-entrant regions, an extremely rich solid polymorphism with solid-solid transitions, and water-like anomalies. In spite of the isotropic nature of the interparticle potential, we find that, among the crystal structures in which the system can exist, there are also a number of non-Bravais lattices, such as cI16 and diamond.Comment: 21 pages, 7 figures, in press on Phys. Rev.

ProtocadherinX/Y, a Candidate Gene-Pair for Schizophrenia and Schizoaffective Disorder: A DHPLC Investigation of Gonomic Sequence

Protocadherin X and Protocadherin Y (PCDHX and PCDHY) are cell-surface adhesion molecules expressed predominantly in the brain. The PCDHX/Y gene-pair was generated by an X-Y translocation approximately 3 million years ago (MYA) that gave rise to the Homo sapiens-specific region of Xq21.3 and Yp11.2 homology. Genes within this region are expected to code for sexually dimorphic human characteristics, including, for example, cerebral asymmetry a dimension of variation that has been suggested is relevant to psychosis. We examined differences in patients with schizophrenic or schizoaffective psychosis in the genomic sequence of PCDHX and PCDHY in coding and adjacent intronic sequences using denaturing high performance liquid chromatography (DHPLC). Three coding variants were detected in PCDHX and two in PCDHY. However, neither the coding variants nor the intronic polymorphisms could be related to psychosis within families. Low sequence variation suggests selective pressure against sequence change in modern humans in contrast to the structural chromosomal and sequence changes including fixed X-Y differences that occurred in this region earlier in hominid evolution. Our findings exclude sequence variation in PCDHX/Y as relevant to the aetiology of psychosis. However, we note the unusual status of this region with respect to X-inactivation. Further investigation of the epigenetic control of PCDHX/Y in relation to psychosis is warran