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The easiest exoplanets to detect are those that orbit very close to their hoststars. As a result, even though these planets are quite rare, they represent amajor fraction of the current exoplanet population. A side-effect of theproximity between the planet and the star is that the two have strong mutualinteractions through a number of physical processes. One of the most importantof these processes is tides. Tides are thought to shape the orbits of close-inexoplanets, heat the planet making its radius expand, and even drive someplanets to spiral into their host stars. This chapter briefly introduces thebasics of tidal physics and describes the various fingerprints tides leavewithin the observed exoplanet population., Comment: Preprint of a chapter for the 'Encyclopedia of Astrophysics' (Editor-in-Chief Ilya Mandel, Section Editor Dimitri Veras) to be published by Elsevier as a Reference Module 10 pages, 5 figures

A minimal separator of a graph $G$ is a set $S \subseteq V(G)$ such that there exist vertices $a,b \in V(G) \setminus S$ with the property that $S$ separates $a$ from $b$ in $G$, but no proper subset of $S$ does. For an integer $k\ge 0$, we say that a minimal separator is $k$-simplicial if it can be covered by $k$ cliques and denote by $\mathcal{G}_k$ the class of all graphs in which each minimal separator is $k$-simplicial. We show that for each $k \geq 0$, the class $\mathcal{G}_k$ is closed under induced minors, and we use this to show that the Maximum Weight Stable Set problem can be solved in polynomial time for $\mathcal{G}_k$. We also give a complete list of minimal forbidden induced minors for $\mathcal{G}_2$. Next, we show that, for $k \geq 1$, every nonnull graph in $\mathcal{G}_k$ has a $k$-simplicial vertex, i.e., a vertex whose neighborhood is a union of $k$ cliques; we deduce that the Maximum Weight Clique problem can be solved in polynomial time for graphs in $\mathcal{G}_2$. Further, we show that, for $k \geq 3$, it is NP-hard to recognize graphs in $\mathcal{G}_k$; the time complexity of recognizing graphs in $\mathcal{G}_2$ is unknown. We also show that the Maximum Clique problem is NP-hard for graphs in $\mathcal{G}_3$. Finally, we prove a decomposition theorem for diamond-free graphs in $\mathcal{G}_2$ (where the diamond is the graph obtained from $K_4$ by deleting one edge), and we use this theorem to obtain polynomial-time algorithms for the Vertex Coloring and recognition problems for diamond-free graphs in $\mathcal{G}_2$, and improved running times for the Maximum Weight Clique and Maximum Weight Stable Set problems for this class of graphs., Comment: 24 pages

In this project, we determined the constraints on the modified tidal quality factor, $Q_{pl}'$, of gas-giant planets orbiting close to their host stars. We allowed $Q_{pl}'$ to depend on tidal frequency, accounting for the multiple tidal waves with time-dependent frequencies simultaneously present on the planet. We performed our analysis on 78 single-star and single-planet systems, with giant planets and host stars with radiative cores and convective outer shells. We extracted constraints on the frequency-dependent $Q_{pl}'$ for each system separately and combined them to find general constraints on $Q_{pl}'$ required to explain the observed eccentricity envelope while simultaneously allowing the observed eccentricities of all systems to survive to the present day. Individual systems do not place tight constraints on $Q_{pl}'$. However, since similar planets must have similar tidal dissipation, we require that a consistent, possibly frequency-dependent, model must apply. Under that assumption, we find that the value of $\log_{10}Q_{pl}'$ for HJs is $5.0\pm0.5$ for the range of tidal period from 0.8 to 7 days. We did not see any clear sign of frequency dependence of $Q_{pl}'$., Comment: Accepted for publication in MNRAS 19 pages, 11 figures, 2 tables

Tidal dissipation in binary systems is the primary source for synchronization and circularization of the objects in the system. The efficiency of the dissipation of tidal energy inside stars or planets results in significant changes in observed properties of the binary system and is often studied empirically using a parameter, commonly known as the modified tidal quality factor ($Q_\star'$). Though often assumed constant, in general that parameter will depend on the particular tidal wave experiencing the dissipation and the properties of the tidally distorted object. In this work we study the frequency dependence of $Q_\star'$ for Sun-like stars. We parameterize $Q_\star'$ as a saturating power-law in tidal frequency and obtain constraints using the stellar rotation period of 70 eclipsing binaries observed by Kepler. We use Bayesian analysis to account for the uncertainties in the observational data required for tidal evolution. Our analysis shows that $Q_\star'$ is well constrained for tidal periods > 15 days, with a value of $Q_\star' \sim 10^8$ for periods > 30 days and a slight suggested decrease at shorter periods. For tidal periods < 15 days, $Q_\star'$ is no longer tightly constrained, allowing for a broad range of possible values that overlaps with the constraints obtained using tidal circularization in binaries, which point to much more efficient dissipation: $Q_\star' \sim 10^6$., Comment: Accepted for publication in MNRAS 16 pages, 9 figures

As we reach the limit of Moore's Law, researchers are exploring different paradigms to achieve unprecedented performance. Approximate Computing (AC), which relies on the ability of applications to tolerate some error in the results to trade-off accuracy for performance, has shown significant promise. Despite the success of AC in domains such as Machine Learning, its acceptance in High-Performance Computing (HPC) is limited due to stringent requirements for accuracy. We need tools and techniques to identify regions of code that are amenable to approximations and their impact on the application output quality to guide developers to employ selective approximation. To this end, we propose CHEF-FP, a flexible, scalable, and easy-to-use source-code transformation tool based on Automatic Differentiation (AD) for analyzing approximation errors in HPC applications. CHEF-FP uses Clad, an efficient AD tool built as a plugin to the Clang compiler and based on the LLVM compiler infrastructure, as a backend and utilizes its AD abilities to evaluate approximation errors in C++ code. CHEF-FP works at the source by injecting error estimation code into the generated adjoints. This enables the error-estimation code to undergo compiler optimizations resulting in improved analysis time and reduced memory usage. We also provide theoretical and architectural augmentations to source code transformation-based AD tools to perform FP error analysis. This paper primarily focuses on analyzing errors introduced by mixed-precision AC techniques. We also show the applicability of our tool in estimating other kinds of errors by evaluating our tool on codes that use approximate functions. Moreover, we demonstrate the speedups CHEF-FP achieved during analysis time compared to the existing state-of-the-art tool due to its ability to generate and insert approximation error estimate code directly into the derivative source., Comment: 11 pages, to appear in the 2023 IEEE International Parallel and Distributed Processing Symposium (IPDPS'23)

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as \emph{properness}, which asserts that Bayes' rule is optimal. Recent works have sought to \emph{learn losses} and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps $\mathbb{R}$ to $[0,1]$ to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between $\mathbb{R}^{C-1}$ and the projected probability simplex $\tilde{\Delta}^{C-1}$ by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns \emph{proper canonical losses} and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a $t$-test at 99% significance on all datasets with greater than 10 classes., Comment: Accepted at the 40th International Conference on Machine Learning (ICML 2023)

Tidal friction has long been recognized to circularize the orbits of binary stars over time. In this study, we use the observed distribution of orbital eccentricities in populations of binary stars to probe tidal dissipation. In contrast to previous studies, we incorporate a host of physical effects often neglected in other analyses, provide a much more general description of tides, model individual systems in detail (in lieu of population statistics), and account for all observational uncertainties. The goal is to provide a reliable measurement of the properties of tidal dissipation that is fully supported by the data, properly accounts for different dissipation affecting each tidal wave on each object separately, and evolves with the internal structure of the stars. We extract high precision measurements of tidal dissipation in short period binaries of Sun-like stars in three open clusters. We find that the tidal quality factor on the main sequence falls in the range $5.7 < \log_{10}Q_\star' < 6$ for tidal periods between 3 and 7.5 days. In contrast, the observed circularization in the 150 Myr old M 35 cluster requires that pre-main sequence stars are much more dissipative: $Q_\star' < 4\times10^4$. We test for frequency dependence of the tidal dissipation, finding that for tidal periods between 3 and 7.5 days, if a dependence exists, it is sub-linear for main-sequence stars. Furthermore, by using a more complete physical model for the evolution, and by accounting for the particular properties of each system, we alleviate previously observed tensions in the circularization in the open clusters analyzed., Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Society 28 pages, 18 figures in main text + 7f figures in appendices

The benefits of the wavelet approach for density estimation are well established in the literature, especially when the density to estimate is irregular or heterogeneous in smoothness. However, wavelet density estimates are typically not bona fide densities. In Aya-Moreno et al (2018), a `shape-preserving' wavelet density estimator was introduced, including as main step the estimation of the square-root of the density. A natural concept involving square-root of densities is the Hellinger distance - or equivalently, the Bhattacharyya affinity coefficient. In this paper, we deliver a fully data-driven version of the above 'shape-preserving' wavelet density estimator, where all user-defined parameters, such as resolution level or thresholding specifications, are selected by optimising an original leave-one-out version of the Hellinger-Bhattacharyya criterion. The theoretical optimality of the proposed procedure is established, while simulations show the strong practical performance of the estimator. Within that framework, we also propose a novel but natural 'jackknife thresholding' scheme, which proves superior to other, more classical thresholding options.

Evolution of binary objects under the influence of tides drastically affects the expected observational properties of the system. With the discovery of a large number of close-in hot Jupiter systems and eclipsing binaries from missions such as Kepler and TESS, it has become imperative to understand the extent of tidal influence on their formation and observed properties. In the case of binary systems, an efficient tidal dissipation can lead to either spin up or spin down of the stars and/or spin-orbit synchronization, depending upon the exchange of angular momentum between the star and the orbit. We combine the eclipsing binary systems from the Kepler mission with stellar and orbital parameters available in the literature to create a catalog of 41 eclipsing binaries suitable for analysis of tidal dissipation. Empirically, the efficiency of tidal dissipation is parameterized using a modified Tidal Quality Factor($Q_{\star}^{'}$). We find constraints on $Q_{\star}^{'}$ using the observed rotation period of the primary star in the eclipsing binary systems. We calculate detailed evolutions of binary systems under the combined influence of tides, stellar evolution, and loss of stellar angular momentum to magnetic winds, and perform Markov Chain Monte Carlo simulations to account for the uncertainties in the observed data. Our analysis shows that $\log_{10}{Q^{'}_{\star}}=7.818\pm0.035$ can reproduce the observed primary star spin in almost all systems in our sample., Comment: This article has been accepted for publication in MNRAS Published by Oxford University Press on behalf of the Royal Astronomical Society. https://academic.oup.com/mnras/advance-article-abstract/doi/10.1093/mnras/stac203/6517458

The Astrobiology Graduate Conference (AbGradCon) is an annual conference both organized for and by early career researchers, postdoctoral fellows, and students as a way to train the next generation of astrobiologists and develop a robust network of cohorts moving forward. AbGradCon 2021 was held virtually on September 14-17, 2021, hosted by the Earth-Life Science Institute (ELSI) of Tokyo Institute of Technology after postponement of the in-person event in 2020 due to the COVID-19 pandemic. The meeting consisted of presentations by 120 participants from a variety of fields, two keynote speakers, and other career building events and workshops. Here, we report on the organizational and executional aspects of AbGradCon 2021, including the meeting participant demographics, various digital aspects introduced specifically for a virtual edition of the meeting, and the abstract submission and evaluation process. The abstract evaluation process of AbGradCon 2021 is unique in that all evaluations are done by the peers of the applicants, and as astrobiology is inherently a broad discipline, the abstract evaluation process revealed a number of trends related to multidisciplinarity of the astrobiology field. We believe that meetings like AbGradCon can provide a unique opportunity for students and early career researchers in astrobiology to experience community building, inter- and multidisciplinary collaboration, and career training and would be a welcome sight in other fields as well. We hope that this report provides inspiration and a basic roadmap for organizing future conferences in any field with similar goals.

Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is the asymptotic behavior of data-driven formulations with empirical or smoothing estimators such as kernels or wavelets applied to some or to all functions of the compositions. We analyze the properties of the new estimators and we establish strong law of large numbers, consistency, and bias reduction potential under fairly general assumptions. Our results are germane to risk-averse optimization and to data science in general.

The relative rarity of giant planets around low mass stars compared with solar-type stars is a key prediction from core accretion planet formation theory. In this paper we report on the discovery of four gas giant planets that transit low mass late K and early M dwarfs. The planets HATS-74Ab (TOI 737b), HATS-75b (TOI 552b), HATS-76b (TOI 555b), and HATS-77b (TOI 730b), were all discovered from the HATSouth photometric survey and followed-up using TESS and other photometric facilities. We use the new ESPRESSO facility at the VLT to confirm and systems and measure their masses. We find that that planets have masses of 1.46 +- 0.14 MJ , 0.491 +- 0.039 MJ , 2.629 +- 0.089 MJ and 1.374 +0.100-0.074 MJ , respectively, and radii of 1.032 +- 0.021 RJ , 0.884 +- 0.013 RJ , 1.079 +- 0.031 RJ , and 1.165 +- 0.021 RJ, respectively. The planets all orbit close to their host stars with orbital periods ranging from 1.7319 d to 3.0876 d. With further work we aim to test core accretion theory by using these and further discoveries to quantify the occurrence rate of giant planets around low mass host stars., Comment: Accepted for publication in the Astronomical Journal

We quantify model risk of a financial portfolio whereby a multi-period mean-standard-deviation criterion is used as a selection criterion. In this work, model risk is defined as the loss due to uncertainty of the underlying distribution of the returns of the assets in the portfolio. The uncertainty is measured by the Kullback-Leibler divergence, i.e., the relative entropy. In the worst case scenario, the optimal robust strategy can be obtained in a semi-analytical form as a solution of a system of nonlinear equations. Several numerical results are presented which allow us to compare the performance of this robust strategy with the optimal non-robust strategy. For illustration, we also quantify the model risk associated with an empirical dataset.

Two-dimensional metals offer intriguing possibilities to explore metallicity and other related properties in systems with reduced dimensionality. Here, following recent experimental reports of synthesis of two-dimensional metallic gallium (gallenene) on insulating substrates, we conduct a computational search of gallenene structures using the Particle Swarm Optimization algorithm, and identify stable low energy structures. Our calculations of the critical temperature for conventional superconductivity yield values $\sim 7$ K for gallenene. We also emulate the presence of the substrate by introducing the external confining potential and test its effect on the structures with unstable phonons.

Hot stars with hot Jupiters have a wide range of obliquities, while cool stars with hot Jupiters tend to have low obliquities. An enticing explanation for this pattern is tidal realignment of the cool host stars, although this explanation assumes that obliquity damping occurs faster than orbital decay, an assumption that needs further exploration. Here we revisit this tidal realignment problem, building on previous work identifying a low-frequency component of the time-variable tidal potential that affects the obliquity but not the orbital separation. We adopt a recent empirically-based model for the stellar tidal quality factor and its sharp increase with forcing frequency. This leads to enhanced dissipation at low frequencies, and efficient obliquity damping. We model the tidal evolution of 46 observed hot Jupiters orbiting cool stars. A key parameter is the stellar age, which we determine in a homogeneous manner for the sample, taking advantage of Gaia DR2 data. We explore a variety of tidal histories and futures for each system, finding in most cases that the stellar obliquity is successfully damped before the planet is destroyed. A testable prediction of our model is that hot-Jupiter hosts with orbital periods shorter than 2--3 days should have obliquities much smaller than $1^\circ$. With the possible exception of WASP-19b, the predicted future lifetimes of the planets range from $10^8$\,yr to more than $10^{10}$\,yr. Thus, our model implies that these hot Jupiters are probably not in immediate danger of being devoured by their host stars while they are on the main sequence., Comment: 24 pages, 14 figures, 1 table, accepted for publication in ApJ. Revised version following the referee report

Background: Automated emotion classification could aid those who struggle to recognize emotions, including children with developmental behavioral conditions such as autism. However, most computer vision emotion recognition models are trained on adult emotion and therefore underperform when applied to child faces. Objective: We designed a strategy to gamify the collection and labeling of child emotion-enriched images to boost the performance of automatic child emotion recognition models to a level closer to what will be needed for digital health care approaches. Methods: We leveraged our prototype therapeutic smartphone game, GuessWhat, which was designed in large part for children with developmental and behavioral conditions, to gamify the secure collection of video data of children expressing a variety of emotions prompted by the game. Independently, we created a secure web interface to gamify the human labeling effort, called HollywoodSquares, tailored for use by any qualified labeler. We gathered and labeled 2155 videos, 39,968 emotion frames, and 106,001 labels on all images. With this drastically expanded pediatric emotion-centric database (>30 times larger than existing public pediatric emotion data sets), we trained a convolutional neural network (CNN) computer vision classifier of happy, sad, surprised, fearful, angry, disgust, and neutral expressions evoked by children. Results: The classifier achieved a 66.9% balanced accuracy and 67.4% F1-score on the entirety of the Child Affective Facial Expression (CAFE) as well as a 79.1% balanced accuracy and 78% F1-score on CAFE Subset A, a subset containing at least 60% human agreement on emotions labels. This performance is at least 10% higher than all previously developed classifiers evaluated against CAFE, the best of which reached a 56% balanced accuracy even when combining "anger" and "disgust" into a single class.

We report the discovery by the ground-based HATNet survey of the transiting exoplanet HAT-P-68b, which has a mass of 0.724 $\pm$ 0.043 $M_{Jup}$, and radius of 1.072 $\pm$ 0.012 $R_{Jup}$. The planet is in a circular P = 2.2984-day orbit around a moderately bright V = 13.937 $\pm$ 0.030 magnitude K dwarf star of mass 0.673 $+$ 0.020 $-$0.014 $M_{\odot}$, and radius 0.6726 $\pm$ 0.0069 $R_{\odot}$. The planetary nature of this system is confirmed through follow-up transit photometry obtained with the FLWO~1.2m telescope, high-precision RVs measured using Keck-I/HIRES, FLWO~1.5m/TRES, and OHP~1.9m/Sophie, and high-spatial-resolution speckle imaging from WIYN~3.5m/DSSI. HAT-P-68 is at an ecliptic latitude of $+3^{\circ}$ and outside the field of view of both the NASA TESS primary mission and the K2 mission. The large transit depth of 0.036 mag ($r$-band) makes HAT-P-68b a promising target for atmospheric characterization via transmission spectroscopy., Comment: submitted to AJ on October 1, 2020; accepted on October 27. 15 pages, 8 figures, 6 tables

We report the discovery of two short-period Saturn-mass planets, one transiting the G subgiant TOI-954 (TIC 44792534, $ V = 10.343 $, $ T = 9.78 $) observed in TESS sectors 4 and 5, and one transiting the G dwarf K2-329 (EPIC 246193072, $ V = 12.70 $, $ K = 10.67 $) observed in K2 campaigns 12 and 19. We confirm and characterize these two planets with a variety of ground-based archival and follow-up observations, including photometry, reconnaissance spectroscopy, precise radial velocity, and high-resolution imaging. Combining all available data, we find that TOI-954 b has a radius of $0.852_{-0.062}^{+0.053} \, R_{\mathrm{J}}$ and a mass of $0.174_{-0.017}^{+0.018} \, M_{\mathrm{J}}$ and is in a 3.68 day orbit, while K2-329 b has a radius of $0.774_{-0.024}^{+0.026} \, R_{\mathrm{J}}$ and a mass of $0.260_{-0.022}^{+0.020} \, M_{\mathrm{J}}$ and is in a 12.46 day orbit. As TOI-954 b is 30 times more irradiated than K2-329 b but more or less the same size, these two planets provide an opportunity to test whether irradiation leads to inflation of Saturn-mass planets and contribute to future comparative studies that explore Saturn-mass planets at contrasting points in their lifetimes., Comment: 28 pages, 9 figures, 11 tables, accepted by AJ, ancillary data also available at https://github.com/vulpicastor/toi954-data

We report the discovery of two transiting Neptunes by the HATSouth survey. The planet HATS-37Ab has a mass of 0.099 +- 0.042 M_J (31.5 +- 13.4 M_earth) and a radius of 0.606 +- 0.016 R_J, and is on a P = 4.3315 days orbit around a V = 12.266 mag, 0.843 M_sun star with a radius of 0.877 R_sun. We also present evidence that the star HATS-37A has an unresolved stellar companion HATS-37B, with a photometrically estimated mass of 0.654 M_sun.The planet HATS-38b has a mass of 0.074 +- 0.011 M_J (23.5 +- 3.5 M_earth) and a radius of 0.614 +- 0.017 R_J, and is on a P = 4.3750 days orbit around a V = 12.411 mag, 0.890 M_sun star with a radius of 1.105 R_sun. Both systems appear to be old, with isochrone-based ages of 11.46 +0.79-1.45 Gyr, and 11.89 +- 0.60 Gyr, respectively. Both HATS-37Ab and HATS-38b lie in the Neptune desert and are thus examples of a population with a low occurrence rate. They are also among the lowest mass planets found from ground-based wide-field surveys to date., Comment: Accepted for publication in the Astronomical Journal

We report the discovery and characterization of 7 transiting exoplanets from the HATNet survey. The planets, which are hot Jupiters and Saturns transiting bright sun-like stars, include: HAT-P-58b (with mass Mp = 0.37 MJ, radius Rp = 1.33 RJ, and orbital period P = 4.0138 days), HAT-P-59b (Mp = 1.54 MJ, Rp = 1.12 RJ, P = 4.1420 days), HAT-P-60b (Mp = 0.57 MJ, Rp = 1.63 RJ, P = 4.7948 days), HAT-P-61b (Mp = 1.06 MJ, Rp = 0.90 RJ, P = 1.9023 days), HAT-P-62b (Mp = 0.76 MJ, Rp = 1.07 RJ, P = 2.6453 days), HAT-P-63b (Mp = 0.61 MJ, Rp = 1.12 RJ, P = 3.3777 days), and HAT-P-64b (Mp = 0.58 MJ, Rp = 1.70 RJ, P = 4.0072 days). The typical errors on these quantities are 0.06 MJ, 0.03 RJ, and 0.2seconds, respectively. We also provide accurate stellar parameters for each of the hosts stars. With V = 9.710+/-0.050mag, HAT-P-60 is an especially bright transiting planet host, and an excellent target for additional follow-up observations. With Rp = 1.703+/-0.070 RJ, HAT-P-64b is a highly inflated hot Jupiter around a star nearing the end of its main-sequence lifetime, and is among the largest known planets. Five of the seven systems have long-cadence observations by TESS which are included in the analysis. Of particular note is HAT-P-59 (TOI-1826.01) which is within the Northern continuous viewing zone of the TESS mission, and HAT-P-60, which is the TESS candidate TOI-1580.01., Comment: Submitted to AJ. Many large figures and tables at the end of the paper

C++ Modules come in C++20 to fix the long-standing build scalability problems in the language. They provide an io-efficient, on-disk representation capable to reduce build times and peak memory usage. ROOT employs the C++ modules technology further in the ROOT dictionary system to improve its performance and reduce the memory footprint. ROOT with C++ Modules was released as a technology preview in fall 2018, after intensive development during the last few years. The current state is ready for production, however, there is still room for performance optimizations. In this talk, we show the roadmap for making the technology default in ROOT. We demonstrate a global module indexing optimization which allows reducing the memory footprint dramatically for many workflows. We will report user feedback on the migration to ROOT with C++ Modules., Comment: Submitted as a proceedings to CHEP 2019

We report the discovery of four transiting giant planets around K dwarfs. The planets HATS-47b, HATS-48Ab, HATS-49b, and HATS-72b have masses of $0.369_{-0.021}^{+0.031}$ $M_{J}$, $0.243_{-0.030}^{+0.022}$ $M_{J}$, $0.353_{-0.027}^{+0.038}$ $M_{J}$ and $0.1254\pm0.0039$ $M_{J}$, respectively, and radii of $1.117\pm0.014$ $R_{J}$, $0.800\pm0.015$ $R_{J}$, $0.765\pm0.013$ $R_{J}$, and $0.7224\pm0.0032$ $R_{J}$, respectively. The planets orbit close to their host stars with orbital periods of $3.9228$ d, $3.1317$ d, $4.1480$ d and $7.3279$ d, respectively. The hosts are main sequence K dwarfs with masses of $0.674_{-0.012}^{+0.016}$ $M_{\odot}$, $0.7279\pm0.0066$ $M_{\odot}$, $0.7133\pm0.0075$ $M_{\odot}$, and $0.7311\pm0.0028$ $M_{\odot}$ and with $V$-band magnitudes of $V = 14.829\pm0.010$, $14.35\pm0.11$, $14.998\pm0.040$ and $12.469\pm0.010$. The Super-Neptune HATS-72b (a.k.a.\ WASP-191b and TOI 294.01) was independently identified as a transiting planet candidate by the HATSouth, WASP and TESS surveys, and we present a combined analysis of all of the data gathered by each of these projects (and their follow-up programs). An exceptionally precise mass is measured for HATS-72b thanks to high-precision radial velocity (RV) measurements obtained with VLT/ESPRESSO, FEROS, HARPS and Magellan/PFS. We also incorporate TESS observations of the warm Saturn-hosting systems HATS-47 (a.k.a. TOI 1073.01), HATS-48A and HATS-49. HATS-47 was independently identified as a candidate by the TESS team, while the other two systems were not previously identified from the TESS data. The RV orbital variations are measured for these systems using Magellan/PFS. HATS-48A has a resolved $5.\!\!^{\prime\prime}4$ neighbor in Gaia~DR2, which is a common-proper-motion binary star companion to HATS-48A with a mass of $0.22$ $M_{\odot}$ and a current projected physical separation of $\sim$1,400 au., Comment: Accepted for publication in AJ. 32 pages, 14 figures, 7 tables

We present the discoveries of KELT-25b (TIC 65412605, TOI-626.01) and KELT-26b (TIC 160708862, TOI-1337.01), two transiting companions orbiting relatively bright, early A-stars. The transit signals were initially detected by the KELT survey, and subsequently confirmed by \textit{TESS} photometry. KELT-25b is on a 4.40-day orbit around the V = 9.66 star CD-24 5016 ($T_{\rm eff} = 8280^{+440}_{-180}$ K, $M_{\star}$ = $2.18^{+0.12}_{-0.11}$ $M_{\odot}$), while KELT-26b is on a 3.34-day orbit around the V = 9.95 star HD 134004 ($T_{\rm eff}$ =$8640^{+500}_{-240}$ K, $M_{\star}$ = $1.93^{+0.14}_{-0.16}$ $M_{\odot}$), which is likely an Am star. We have confirmed the sub-stellar nature of both companions through detailed characterization of each system using ground-based and \textit{TESS} photometry, radial velocity measurements, Doppler Tomography, and high-resolution imaging. For KELT-25, we determine a companion radius of $R_{\rm P}$ = $1.64^{+0.039}_{-0.043}$ $R_{\rm J}$, and a 3-sigma upper limit on the companion's mass of $\sim64~M_{\rm J}$. For KELT-26b, we infer a planetary mass and radius of $M_{\rm P}$ = $1.41^{+0.43}_{-0.51}$ $M_{\rm J}$ and $R_{\rm P}$ = $1.940^{+0.060}_{-0.058}$ $R_{\rm J}$. From Doppler Tomographic observations, we find KELT-26b to reside in a highly misaligned orbit. This conclusion is weakly corroborated by a subtle asymmetry in the transit light curve from the \textit{TESS} data. KELT-25b appears to be in a well-aligned, prograde orbit, and the system is likely a member of a cluster or moving group., Comment: 24 pages, 18 figures, 8 tables

The transiting exoplanetary system WASP-174 was reported to be composed by a main-sequence F star (V=11.8 mag) and a giant planet, WASP-174b (orbital period 4.23 days). However only an upper limit was placed on the planet mass (<1.3 Mj), and a highly uncertain planetary radius (0.7-1.7 Rj) was determined. We aim to better characterise both the star and the planet and precisely measure their orbital and physical parameters. In order to constrain the mass of the planet, we obtained new measurements of the radial velocity of the star and joined them with those from the discovery paper. Photometric data from the HATSouth survey and new multi-band, high-quality (precision reached up to 0.37~mmag) photometric follow-up observations of transit events were acquired and analysed for getting accurate photometric parameters. We fit the model to all the observations, including data from the TESS space telescope, in two different modes: incorporating the stellar isochrones into the fit, and using an empirical method to get the stellar parameters. The two modes resulted to be consistent with each other to within 2 sigma. We confirm the grazing nature of the WASP-174b transits with a confidence level greater than 5 sigma, which is also corroborated by simultaneously observing the transit through four optical bands and noting how the transit depth changes due to the limb-darkening effect. We estimate that ~76% of the disk of the planet actually eclipses the parent star at mid-transit of its transit events. We find that WASP-174b is a highly-inflated hot giant planet with a mass of 0.330 Mj and a radius of 1.435 Rj, and is therefore a good target for transmission-spectroscopy observations. With a density of 0.135 g/cm^3, it is amongst the lowest-density planets ever discovered with precisely measured mass and radius., Comment: 12 pages, 14 figures, Accepted for publication in Astronomy & Astrophysics

Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward looking approach is more suitable, whereby the tracking error is expressed as expectation of a function of the difference between the returns of the index and of the portfolio. We also assume that there is an uncertainty in the distribution of the assets, hence a robust version of the optimization problem needs to be adopted. We use Bregman divergence in describing the deviation between the nominal and actual distribution of the components of the index. In this scenario, we derive the optimal robust index tracking strategy in a semi-analytical form as a solution of a system of nonlinear equations. Several numerical results are presented that allow us to compare the performance of this robust strategy with the optimal non-robust strategy. We show that, especially during market downturns, the robust strategy can be very advantageous., Comment: To be published in Quantitative Finance

A ring is a graph $R$ whose vertex set can be partitioned into $k \geq 4$ nonempty sets, $X_1, \dots, X_k$, such that for all $i \in \{1,\dots,k\}$, the set $X_i$ can be ordered as $X_i = \{u_i^1, \dots, u_i^{|X_i|}\}$ so that $X_i \subseteq N_R[u_i^{|X_i|}] \subseteq \dots \subseteq N_R[u_i^1] = X_{i-1} \cup X_i \cup X_{i+1}$. A hyperhole is a ring $R$ such that for all $i \in \{1,\dots,k\}$, $X_i$ is complete to $X_{i-1}\cup X_{i+1}$. In this paper, we prove that the chromatic number of a ring $R$ is equal to the maximum chromatic number of a hyperhole in $R$. Using this result, we give a polynomial-time coloring algorithm for rings. Rings formed one of the basic classes in a decomposition theorem for a class of graphs studied by Boncompagni, Penev, and Vu\v{s}kovi\'c in [Journal of Graph Theory 91 (2019), 192--246]. Using our coloring algorithm for rings, we show that graphs in this larger class can also be colored in polynomial time. Furthermore, we find the optimal $\chi$-bounding function for this larger class of graphs, and we also verify Hadwiger's conjecture for it.

We present the discovery of KELT-24 b, a massive hot Jupiter orbiting a bright (V=8.3 mag, K=7.2 mag) young F-star with a period of 5.6 days. The host star, KELT-24 (HD 93148), has a $T_{\rm eff}$ =$6509^{+50}_{-49}$ K, a mass of $M_{*}$ = $1.460^{+0.055}_{-0.059}$ $M_{\odot}$, radius of $R_{*}$ = $1.506\pm0.022$ $R_{\odot}$, and an age of $0.78^{+0.61}_{-0.42}$ Gyr. Its planetary companion (KELT-24 b) has a radius of $R_{\rm P}$ = $1.272\pm0.021$ $R_{\rm J}$, a mass of $M_{\rm P}$ = $5.18^{+0.21}_{-0.22}$ $M_{\rm J}$, and from Doppler tomographic observations, we find that the planet's orbit is well-aligned to its host star's projected spin axis ($\lambda$ = $2.6^{+5.1}_{-3.6}$). The young age estimated for KELT-24 suggests that it only recently started to evolve from the zero-age main sequence. KELT-24 is the brightest star known to host a transiting giant planet with a period between 5 and 10 days. Although the circularization timescale is much longer than the age of the system, we do not detect a large eccentricity or significant misalignment that is expected from dynamical migration. The brightness of its host star and its moderate surface gravity make KELT-24b an intriguing target for detailed atmospheric characterization through spectroscopic emission measurements since it would bridge the current literature results that have primarily focused on lower mass hot Jupiters and a few brown dwarfs., Comment: 18 pages, 10 Figures, 6 Tables, Accepted to the Astronomical Journal

Wide field surveys for transiting planets are well suited to searching diverse stellar populations, enabling a better understanding of the link between the properties of planets and their parent stars. We report the discovery of HAT-P-69b (TOI 625.01) and HAT-P-70b (TOI 624.01), two new hot Jupiters around A stars from the HATNet survey which have also been observed by the Transiting Exoplanet Survey Satellite (TESS). HAT-P-69b has a mass of 3.58 +0.58/-0.58 MJup and a radius of 1.676 +0.051/-0.033 RJup, residing in a prograde 4.79-day orbit. HAT-P-70b has a radius of 1.87 +0.15/-0.10 RJup and a mass constraint of < 6.78 (3 sigma) MJup, and resides in a retrograde 2.74-day orbit. We use the confirmation of these planets around relatively massive stars as an opportunity to explore the occurrence rate of hot Jupiters as a function of stellar mass. We define a sample of 47,126 main-sequence stars brighter than Tmag=10 that yields 31 giant planet candidates, including 18 confirmed planets, 3 candidates, and 10 false positives. We find a net hot Jupiter occurrence rate of 0.41+/-0.10 % within this sample, consistent with the rate measured by Kepler for FGK stars. When divided into stellar mass bins, we find the occurrence rate to be 0.71+/-0.31% for G stars, 0.43+/-0.15% for F stars, and 0.26+/-0.11% for A stars. Thus, at this point, we cannot discern any statistically significant trend in the occurrence of hot Jupiters with stellar mass., Comment: Accepted for publication by AJ

We announce the discovery of KELT-23Ab, a hot Jupiter transiting the relatively bright ($V=10.3$) star BD+66 911 (TYC 4187-996-1), and characterize the system using follow-up photometry and spectroscopy. A global fit to the system yields host-star properties of $T_{eff}=5900\pm49 K$, $M_*=0.945^{+0.060}_{-0.054} M_{\odot}$, $R_*=0.995\pm0.015 R_{\odot}$, $L_*=1.082^{+0.051}_{-0.048} L_{\odot}$, log$g_{*}=4.418^{+0.026}_{-0.025}$ (cgs), and $\left[{\rm Fe}/{\rm H}\right]=-0.105\pm0.077$. KELT-23Ab is a hot Jupiter with mass $M_P=0.938^{+0.045}_{-0.042} M_{\rm J}$, radius $R_P=1.322\pm0.025 R_{\rm J}$, and density $\rho_P=0.504^{+0.038}_{-0.035}$ g cm$^{-3}$. Intense insolation flux from the star has likely caused KELT-23Ab to become inflated. The time of inferior conjunction is $T_0=2458149.40776\pm0.00091~\rm {BJD_{TDB}}$ and the orbital period is $P=2.255353^{+0.000031}_{-0.000030}$ days. There is strong evidence that KELT-23A is a member of a long-period binary star system with a less luminous companion, and due to tidal interactions, the planet is likely to spiral into its host within roughly a Gyr. This system has one of the highest positive ecliptic latitudes of all transiting planet hosts known to date, placing it near the Transiting Planet Survey Satellite and James Webb Space Telescope continuous viewing zones. Thus we expect it to be an excellent candidate for long-term monitoring and follow-up with these facilities., Comment: 17 pages, 10 figures, Accepted for publication in AJ

We report the discovery of TOI-172 b from the Transiting Exoplanet Survey Satellite (TESS) mission, a massive hot Jupiter transiting a slightly evolved G-star with a 9.48-day orbital period. This is the first planet to be confirmed from analysis of only the TESS full frame images, because the host star was not chosen as a two minute cadence target. From a global analysis of the TESS photometry and follow-up observations carried out by the TESS Follow-up Observing Program Working Group, TOI-172 (TIC 29857954) is a slightly evolved star with an effective temperature of $T_{\rm eff}$ =$5645\pm50$ K, a mass of $M_{\star}$ = $1.128^{+0.065}_{-0.061}$ $M_{\odot}$, radius of $R_{\star}$ = $1.777^{+0.047}_{-0.044}$ $R_{\odot}$, a surface gravity of $\log$ $g_{\star}$ = $3.993^{+0.027}_{-0.028}$, and an age of $7.4^{+1.6}_{-1.5}$ Gyr. Its planetary companion (TOI-172 b) has a radius of $R_{\rm P}$ = $0.965^{+0.032}_{-0.029}$ $R_{\rm J}$, a mass of $M_{\rm P}$ = $5.42^{+0.22}_{-0.20}$ $M_{\rm J}$, and is on an eccentric orbit ($e = 0.3806^{+0.0093}_{-0.0090}$). TOI-172 b is one of the few known massive giant planets on a highly eccentric short-period orbit. Future study of the atmosphere of this planet and its system architecture offer opportunities to understand the formation and evolution of similar systems., Comment: 14 pages, 8 figures, 4 tables, Published in AJ

We report the discovery of HATS-71b, a transiting gas giant planet on a P = 3.7955 day orbit around a G = 15.35 mag M3 dwarf star. HATS-71 is the coolest M dwarf star known to host a hot Jupiter. The loss of light during transits is 4.7%, more than any other confirmed transiting planet system. The planet was identified as a candidate by the ground-based HATSouth transit survey. It was confirmed using ground-based photometry, spectroscopy, and imaging, as well as space-based photometry from the NASA TESS mission (TIC 234523599). Combining all of these data, and utilizing Gaia DR2, we find that the planet has a radius of $1.080 \pm 0.016 R_J$ and mass of $0.45 \pm 0.24 M_J$ (95% confidence upper limit of $0.81 M_J$ ), while the star has a mass of $0.569 \pm^{0.042}_{0.069}\,M_\odot$ and a radius of $0.5161\pm^{0.0053}_{0.0099}\,R_\odot$. The Gaia DR2 data show that HATS-71 lies near the binary main sequence in the Hertzsprung-Russell diagram, suggesting that there may be an unresolved stellar binary companion. All of the available data is well fitted by a model in which there is a secondary star of mass $0.24 M_\odot$, although we caution that at present there is no direct spectroscopic or imaging evidence for such a companion. Even if there does exist such a stellar companion, the radius and mass of the planet would be only marginally different from the values we have calculated under the assumption that the star is single., Comment: Submitted to AJ

We report the discovery by the HATSouth project of 5 new transiting hot Jupiters (HATS-54b through HATS-58Ab). HATS-54b, HATS-55b and HATS-58Ab are prototypical short period ($P = 2.5-4.2$ days, $R_p\sim1.1-1.2$ $R_J$) hot-Jupiters that span effective temperatures from 1350 K to 1750 K, putting them in the proposed region of maximum radius inflation efficiency. The HATS-58 system is composed of two stars, HATS-58A and HATS-58B, which are detected thanks to Gaia DR2 data and which we account for in the joint modelling of the available data --- with this, we are led to conclude that the hot jupiter orbits the brighter HATS-58A star. HATS-57b is a short-period (2.35-day) massive (3.15 $M_J$) 1.14 $R_J$, dense ($2.65\pm0.21$ g cm$^{-3}$) hot-Jupiter, orbiting a very active star ($2\%$ peak-to-peak flux variability). Finally, HATS-56b is a short period (4.32-day) highly inflated hot-Jupiter (1.7 $R_J$, 0.6 $M_J$), which is an excellent target for future atmospheric follow-up, especially considering the relatively bright nature ($V=11.6$) of its F dwarf host star. This latter exoplanet has another very interesting feature: the radial velocities show a significant quadratic trend. If we interpret this quadratic trend as arising from the pull of an additional planet in the system, we obtain a period of $P_c = 815^{+253}_{-143}$ days for the possible planet HATS-56c, and a minimum mass of $M_c\sin i_c = 5.11 \pm 0.94$ $M_J$. The candidate planet HATS-56c would have a zero-albedo equilibrium temperature of $T_\textrm{eq}=332\pm 50$ K, and thus would be orbiting close to the habitable zone of HATS-56. Further radial-velocity follow-up, especially over the next two years, is needed to confirm the nature of HATS-56c., Comment: Submitted to AAS Journals

We report the discovery of HATS-70b, a transiting brown dwarf at the deuterium burning limit. HATS-70b has a mass of Mp=12.9 +1.8/-1.6 Mjup and a radius of Rp=1.384 +0.079/-0.074 Rjup, residing in a close-in orbit with a period of 1.89 days. The host star is a M*=1.78 +/- 0.12 Msun A star rotating at vsini=40.61 +0.32/-0.35 km/s, enabling us to characterize the spectroscopic transit of the brown dwarf via Doppler tomography. We find that HATS-70b, like other massive planets and brown dwarfs previously sampled, orbits in a low projected-obliquity orbit with lambda=8.9 +5.6/-4.5 deg. The low obliquities of these systems is surprising given all brown dwarf and massive planets with obliquities measured orbit stars hotter than the Kraft break. This trend is tentatively inconsistent with dynamically chaotic migration for systems with massive companions, though the stronger tidal influence of these companions makes it difficult to draw conclusions on the primordial obliquity distribution of this population. We also introduce a modeling scheme for planets around rapidly rotating stars, accounting for the influence of gravity darkening on the derived stellar and planetary parameters., Comment: Accepted for publication in AJ

We report the discovery of ten transiting extrasolar planets by the HATSouth survey. The planets range in mass from the Super-Neptune HATS-62b, with $M_{p} < 0.179 M_{J}$, to the Super-Jupiter HATS-66b, with $M_{p} = 5.33 M_{J}$, and in size from the Saturn HATS-69b, with $R_{p} = 0.94 R_{J}$, to the inflated Jupiter HATS-67b, with $R_{p} = 1.69 R_{J}$. The planets have orbital periods between 1.6092 days (HATS-67b) and 7.8180 days (HATS-61b). The hosts are dwarf stars with masses ranging from $0.89 M_{\odot}$ (HATS-69) to $1.56 M_{\odot}$ (HATS-64), and have apparent magnitudes between $V = 12.276 \pm 0.020$ mag (HATS-68) and $V = 14.095 \pm 0.030$ mag (HATS-66). The Super-Neptune HATS-62b is the least massive planet discovered to date with a radius larger than Jupiter. Based largely on the Gaia DR2 distances and broad-band photometry, we identify three systems (HATS-62, -64, and -65) as having possible unresolved binary star companions. We discuss in detail our methods for incorporating the Gaia DR2 observations into our modeling of the system parameters, and into our blend analysis procedures., Comment: Replaced with version accepted for publication in AJ, some changes to parameter values compared to previous version, 41 pages, 12 figures, 19 Tables

The monograph represents analysis of the possibility for time-optimal control of a prototype of an aircraft-mounted scanning-imaging system of a Light Detection and Ranging based wake vortex detection system. The study is a part of the research project "Demonstration of Light Detection and Ranging based wake vortex detection system incorporating an atmospheric hazard map" or GREEN-WAKE (Project ID 213254) of the European Union Seventh Framework Program for Research and Technological Development. The scanning system comprises two light mirror actuators. The study is decomposed into several group of problems. The first and second groups consider the mathematical models of the scanning system and the mirror actuators. The third group of problems deals with the design of closed loop tracking control systems of both the large and small mirror actuators. The control of each one system is synthesized as a near time-optimal control of the precise linear model of the mirror actuator. The control algorithms realize the state of the art method for synthesis of time-optimal control of any order for a class of linear time-optimal control problems developed in the author's dissertation. The last discovers and theoretically proves new properties of a class of linear time-optimal control problems. From the point of view of the control synthesis algorithms the main advantage is that the time-optimal control is produced by a multistage procedure within the class of problems but without the need of describing the hyper-surfaces of switching over. The fourth group of problems considers modeling the real scan picture but with inclusion also of the Coulomb's friction model. The fifth group of problems investigates the ways of improvement of the real scan picture. As a result an excellent repetition and clearness of the scanning alongside with symmetry and matching the scan pattern are seen.

We report the first discovery of a multi-planetary system by the HATSouth network, HATS-59b,c, a planetary system with an inner transiting hot Jupiter and an outer cold massive giant planet, which was detected via radial velocity. The inner transiting planet, HATS-59b, is on an eccentric orbit with $e = 0.129\pm0.049$, orbiting a $V=13.951\pm0.030$ mag solar-like star ($M_* = 1.038\pm0.039 M_{\odot}$, and $R_* = 1.036\pm0.067 R_{\odot}$) with a period of $5.416077\pm0.000017$ days. The outer companion, HATS-59c is on a circular orbit with $ m \sin i = 12.8\pm1.1 M_\mathrm{J}$, and a period of $1422\pm14$ days. The inner planet has a mass of $0.806\pm0.069 M_\mathrm{J}$ and a radius of $1.126\pm0.077 M_\mathrm{J}$, yielding a density of $0.70\pm0.16 {\rm g\,cm^{-3}}$. Unlike most of the planetary systems that include only a single hot Jupiter, HATS-59b,c includes, in addition to the transiting hot Jupiter, a massive outer companion. The architecture of this system is valuable for understanding planet migration., Comment: 12 pages, 9 figures, submitted to AJ. For a short discussion, see https://sites.google.com/view/paulasarkis/research/hats-59

We report the discovery of four transiting hot Jupiters from the HATSouth survey: HATS-39b, HATS-40b, HATS41b and HATS-42b. These discoveries add to the growing number of transiting planets orbiting moderately bright (12.5 < V < 13.7) F dwarf stars on short (2-5 day) periods. The planets have similar radii, ranging from 1.33(+0.29/-0.20) R_J for HATS-41b to 1.58(+0.16/-0.12) R_J for HATS-40b. Their masses and bulk densities, however, span more than an order of magnitude. HATS-39b has a mass of 0.63 +/- 0.13 M_J, and an inflated radius of 1.57 +/- 0.12 R_J, making it a good target for future transmission spectroscopic studies. HATS-41b is a very massive 9.7 +/- 1.6 M_J planet and one of only a few hot Jupiters found to date with a mass over 5 M_J. This planet orbits the highest metallicity star ([Fe/H] = 0.470 +/- 0.010) known to host a transiting planet and is also likely on an eccentric orbit. The high mass, coupled with a relatively young age (1.34 +0.31/-0.51 Gyr) for the host star, are factors that may explain why this planet's orbit has not yet circularised., Comment: 24 pages,accepted in MNRAS

We present the discovery of KELT-22Ab, a hot Jupiter from the KELT-South survey. KELT-22Ab transits the moderately bright ($V\sim 11.1$) Sun-like G2V star TYC 7518-468-1. The planet has an orbital period of $P = 1.3866529 \pm 0.0000027 $ days, a radius of $R_{P} = 1.285_{-0.071}^{+0.12}~R_{J}$, and a relatively large mass of $M_{P} = 3.47_{-0.14}^{+0.15}~ M_{J}$. The star has $R_{\star} = 1.099_{-0.046}^{+0.079}~ R_{\odot}$, $M_{\star} = 1.092_{-0.041}^{+0.045}~ M_{\odot}$, ${T_{\rm eff}\,} = 5767_{-49}^{+50}~$ K, ${\log{g_\star}} = 4.393_{-0.060}^{+0.039}~$ (cgs), and [m/H] = $+0.259_{-0.083}^{+0.085}~$, and thus, other than its slightly super-solar metallicity, appears to be a near solar twin. Surprisingly, KELT-22A exhibits kinematics and a Galactic orbit that are somewhat atypical for thin disk stars. Nevertheless, the star is rotating quite rapidly for its estimated age, shows evidence of chromospheric activity, and is somewhat metal rich. Imaging reveals a slightly fainter companion to KELT-22A that is likely bound, with a projected separation of 6\arcsec ($\sim$1400 AU). In addition to the orbital motion caused by the transiting planet, we detect a possible linear trend in the radial velocity of KELT-22A suggesting the presence of another relatively nearby body that is perhaps non-stellar. KELT-22Ab is highly irradiated (as a consequence of the small semi-major axis of $a/R_{\star} = 4.97$), and is mildly inflated. At such small separations, tidal forces become significant. The configuration of this system is optimal for measuring the rate of tidal dissipation within the host star. Our models predict that, due to tidal forces, the semi-major axis of KELT-22Ab is decreasing rapidly, and is thus predicted to spiral into the star within the next Gyr., Comment: 14 pages, 13 figures, 5 tables

As usual, $P_n$ ($n \geq 1$) denotes the path on $n$ vertices, and $C_n$ ($n \geq 3$) denotes the cycle on $n$ vertices. For a family $\mathcal{H}$ of graphs, we say that a graph $G$ is $\mathcal{H}$-free if no induced subgraph of $G$ is isomorphic to any graph in $\mathcal{H}$. We present a decomposition theorem for the class of $(P_7,C_4,C_5)$-free graphs; in fact, we give a complete structural characterization of $(P_7,C_4,C_5)$-free graphs that do not admit a clique-cutset. We use this decomposition theorem to show that the class of $(P_7,C_4,C_5)$-free graphs is $\chi$-bounded by a linear function (more precisely, every $(P_7,C_4,C_5)$-free graph $G$ satisfies $\chi(G) \leq \frac{3}{2} \omega(G)$). We also use the decomposition theorem to construct an $O(n^3)$ algorithm for the minimum coloring problem, an $O(n^2m)$ algorithm for the maximum weight stable set problem, and an $O(n^3)$ algorithm for the maximum weight clique problem for this class, where $n$ denotes the number of vertices and $m$ the number of edges of the input graph.