The 3-rainbow index of a graph

Let $G$ be a nontrivial connected graph with an edge-coloring $c: E(G)\rightarrow \{1,2,...,q\},$ $q \in \mathbb{N}$, where adjacent edges may be colored the same. A tree $T$ in $G$ is a $rainbow tree$ if no two edges of $T$ receive the same color. For a vertex subset $S\subseteq V(G)$, a tree that connects $S$ in $G$ is called an $S$-tree. The minimum number of colors that are needed in an edge-coloring of $G$ such that there is a rainbow $S$-tree for each $k$-subset $S$ of $V(G)$ is called $k$-rainbow index, denoted by $rx_k(G)$. In this paper, we first determine the graphs whose 3-rainbow index equals 2, $m,$ $m-1$, $m-2$, respectively. We also obtain the exact values of $rx_3(G)$ for regular complete bipartite and multipartite graphs and wheel graphs. Finally, we give a sharp upper bound for $rx_3(G)$ of 2-connected graphs and 2-edge connected graphs, and graphs whose $rx_3(G)$ attains the upper bound are characterized.Comment: 13 page

The Path to Extreme Precision Radial Velocity With EXPRES

The field of exoplanets is currently poised to benefit hugely from improved radial velocity (RV) precision. Extreme precision radial-velocity (EPRV) measurements, capable of detecting planetary signals on the order of 10-30 cm/s, will deliver integral planetary parameters, be sensitive to a missing category of lower-mass planets, grant a deeper understanding of multi-planet architectures, and support both current and future space missions such as TESS and JWST. The ability of EPRV to deliver mass estimates is essential for comprehensively characterizing planets, understanding formation histories, and interpreting atmospheric spectra. Until recently, RV precision had stalled at around 1 m/s, i.e. signals with a semi-amplitude of less than 1 m/s could not be faithfully detected. We demonstrate with HARPS, UVES, and CHIRON observations of alpha Cen the need for better data, not just more data. Even with over a decade of observations at around 1 /mas precision, large areas of mass/period parameter space remained unprobed. Higher-fidelity data is needed to significantly push down detection limits. EXPRES, the EXtreme PREcision Spectrograph, was one of the first next-generation spectrographs to go on sky. Installed at the 4.3-m Lowell Discovery Telescope in 2017 and commissioned through 2019, EXPRES is a fiber-fed, ultra-stabilized, echelle spectrograph with a high median resolving power of R~137,000 and an instrument calibration stability of 4-7 cm/s, a factor of 10 better than previous instruments. The stringent requirements of EPRV measurements along with the stability of EXPRES and similar instruments changes how we must extract, calibrate, and model the resultant spectral data. This dissertation discusses the work that must be done in this new regime in terms of data pipelines and modeling stellar signals and showcases some initial progress. We present EXPRES\u27 data pipeline, a new data-driven method for wavelength calibration, and the current state of the field for disentangling stellar signals. The EXPRES extraction pipeline implements a flat-relative, optimal extraction model and excalibur for wavelength calibration. Excalibur is a hierarchical, non-parametric method for wavelength calibration developed as part of this thesis work. Calibration line-positions are de-noised by using all calibration images to construct a model of the accessible calibration space of the instrument. This denoising returns wavelengths a factor of five more precise than previous polynomial-based methods. With EXPRES data, excalibur reduced the overall RMS of RV data sets for all targets tested by 0.2-0.5 m/s. This consistent reduction in overall RMS implies that excalibur is addressing an instrumental, red-noise component that would otherwise permeate all exposures. With instrumental noise lowered and extraction error reduced, intrinsic stellar variability and the resulting apparent RVs now dominate the error budget for EPRV measurements. The EXPRES Stellar Signals Project (ESSP) released high-fidelity, spectroscopic data from EXPRES and photometric observations from the automatic photoelectric telescopes (APT) for four different stars. This allowed for a self-consistent comparison of the 19 different methods submitted, which represent the current state of the field in disentangling stellar signals. The analysis of results is ongoing work. Currently, the best performing method give a final RV RMS of 1.2 m/s. Submitted methods nearly always do better than classic methods of decorrelating RVs from stellar signals. We found that methods returning the lowest RV RMS often used the full spectra and/or flexible statistical models such as Gaussian processes or principal component analysis. However, there was a concerning lack of agreement between methods. If we hope to improve on current advancements and develop methods achieving sub-meter-per-second RMS, we must introduce more interpretability to methods to understand what is and is not working. A densely sampled, high-resolution data sensitive to all categories of stellar variation is needed to understand all types of stellar signals. This dissertation work centers on the question of achieving EPRV capabilities for detecting planets incurring reflex velocity signals on the order of 10-30 cm/s. We consider what needs to be done, describe current development towards this goal, and discuss the future work that remains before sub-meter-per-second precision can become a regular reality. We emphasize the power of data-driven pipelines to account for variations in data for EPRV applications and beyond. Empirically backed conclusions for mitigating photospheric velocities are summarized from the results of the ESSP along with next steps and additional data requirements. Progress is being made, but there remains much work to be done

Effects of Noise, Reverberation and Foreign Accent on Native and Non-Native Listeners’ Performance of English Speech Comprehension

A large number of non-native English speakers may be found in American classrooms, both as listeners and talkers. Little is known about how this population comprehends speech in realistic adverse acoustical conditions. A study was conducted to investigate the effects of background noise level (BNL), reverberation time (RT), and talker foreign accent on native and non-native listeners\u27 speech comprehension, while controlling for English language abilities. A total of 115 adult listeners completed comprehension tasks under 15 acoustic conditions: three BNLs (RC-30, RC-40, and RC-50) and five RTs (from 0.4 to 1.2 s). Fifty-six listeners were tested with speech from native English-speaking talkers and 59 with native Mandarin-Chinese-speaking talkers. Results show that, while higher BNLs were generally more detrimental to listeners with lower English proficiency, all listeners experienced significant comprehension deficits above RC-40 with native English talkers. This limit was lower (i.e., above RC-30), however, with Chinese talkers. For reverberation, non-native listeners as a group performed best with RT up to 0.6 s, while native listeners performed equally well up to 1.2 s. A matched foreign accent benefit has also been identified, where the negative impact of higher reverberation does not exist for non-native listeners who share the talker\u27s native language

Effects of acoustic environments on speech comprehension by native-English-speaking listeners

This study investigates the effects of acoustic conditions on speech comprehension, rather than speech intelligibility as often reported in existing literature. Sets of 15-minute-long listening comprehension tests were developed based on the format of the Test of English for International Communication (TOEIC). Each test set includes four types of tasks: matching aural phrases to photographs, selecting appropriate responses to aural questions, and answering questions after listening to conversations (between two talkers) and talks (single talker). Within the Nebraska acoustics test chamber, native-English-speaking participants are asked to perform these tests under 15 acoustic conditions, from combinations of three background noise levels (RC-30, 40 and 50) and five mid-frequency reverberation times (0.4 to 1.2 seconds). The background noise levels are varied via an Armstrong i-Ceiling system, while the reverberation times are simulated from convolving the anechoic test signals with binaural room impulse responses (BRIR), simulated in ODEON for a typical classroom. A two-channel playback system is used to present the convolved audio signals, with loudspeaker-listener configuration embedded in the BRIR auralization output. Pilot testing of three subjects showed no variation of performance scores on overall tasks among all acoustical conditions. However, participants generally scored lowest in tasks to comprehend conversations in the longest RT scenarios

Satisfaction in Similarity: The association between perceived communication styles and relational satisfaction

In our research, we hypothesized that partners in romantic relationships who reported higher levels of similarity in communication would also express higher levels of relational satisfaction. We used Martin Buber’s theory of dialogic communication to establish the idea that people are attracted to others who are similar to them and are therefore attracted to those who share similar communication styles. To test this theory, we surveyed perceived similarity in communication using the following aspects: humor, introversion, conflict management, and criticalness, followed by a measurement of relational satisfaction, in a sample of people in dating relationships at Pepperdine University to examine the correlation between perceived similarity and relational satisfaction. The results showed weak, but positive correlations between the two main variables. Though the correlations found were not enough to substantiate a strong relationship, post hoc analysis yielded possible explanations for the weak correlation and promising topics for further study

Association Signals Unveiled by a Comprehensive Gene Set Enrichment Analysis of Dental Caries Genome-Wide Association Studies

Gene set-based analysis of genome-wide association study (GWAS) data has recently emerged as a useful approach to examine the joint effects of multiple risk loci in complex human diseases or phenotypes. Dental caries is a common, chronic, and complex disease leading to a decrease in quality of life worldwide. In this study, we applied the approaches of gene set enrichment analysis to a major dental caries GWAS dataset, which consists of 537 cases and 605 controls. Using four complementary gene set analysis methods, we analyzed 1331 Gene Ontology (GO) terms collected from the Molecular Signatures Database (MSigDB). Setting false discovery rate (FDR) threshold as 0.05, we identified 13 significantly associated GO terms. Additionally, 17 terms were further included as marginally associated because they were top ranked by each method, although their FDR is higher than 0.05. In total, we identified 30 promising GO terms, including 'Sphingoid metabolic process,' 'Ubiquitin protein ligase activity,' 'Regulation of cytokine secretion,' and 'Ceramide metabolic process.' These GO terms encompass broad functions that potentially interact and contribute to the oral immune response related to caries development, which have not been reported in the standard single marker based analysis. Collectively, our gene set enrichment analysis provided complementary insights into the molecular mechanisms and polygenic interactions in dental caries, revealing promising association signals that could not be detected through single marker analysis of GWAS data. © 2013 Wang et al

DP-4-colorability of two classes of planar graphs

DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvo\v{r}\'ak and Postle (2017). In this paper, we prove that every planar graph $G$ without $4$-cycles adjacent to $k$-cycles is DP-$4$-colorable for $k=5$ and $6$. As a consequence, we obtain two new classes of $4$-choosable planar graphs. We use identification of verticec in the proof, and actually prove stronger statements that every pre-coloring of some short cycles can be extended to the whole graph.Comment: 12 page