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Item EasyCSPeasy: a server-side and language-agnostic XSS mitigation by devising and ensuring compliance with CSP(2024-10-31) Kaleli, Beliz; Egele, Manuel; Stringhini, GianlucaItem Unleashing performance insights with online probabilistic tracing(IEEE, 2024-09-24) Toslali, M.; Qasim, S.; Parthasarathy, S.; Oliveira, F.A.; Huang, H.; Stringhini, G.; Liu, Z.; Coskun, A.K.Item PraxiPaaS: a decomposable machine learning system for efficient container package discovery(IEEE, 2024-09-24) Zhang, Zongshun; Kumar, Rohan; Li, Jason; Korver, Lisa; Byrne, Anthony; Stringhini, Gianluca; Matta, Ibrahim; Coskun, AyseItem Does economics make you sexist?(MIT Press, 2023) Paredes, Valentina; Paserman, M. Daniele; Pino, Francisco J.We provide direct evidence on explicit and implicit biases against women among students in economics relative to other fields. We conducted a large scale survey among undergraduates in Chile, among both entering first-year students and students in years 2 and above, combining a wide battery of measures to create an index of gender bias. Economics students are more biased than students in other fields. There is some evidence that economics students are more biased already upon entry, before exposure to economics classes. The gap becomes more pronounced among students in years 2 and above, especially for male students.Item Data science education in undergraduate physics: lessons learned from a community of practice(American Association of Physics Teachers (AAPT), 2024-09-01) Soltanieh Ha, Mohammad; Shah, Karan; Butler, Julie; Knaub, Alexis; Zenginoğlu, Anıl; Ratcliff, WilliamIt is becoming increasingly important that physics educators equip their students with the skills to work with data effectively. However, many educators may lack the necessary training and expertise in data science to teach these skills. To address this gap, we created the Data Science Education Community of Practice (DSECOP), bringing together graduate students and physics educators from different institutions and backgrounds to share best practices and lessons learned from integrating data science into undergraduate physics education. In this article, we present insight and experiences from this community of practice, highlighting key strategies and challenges in incorporating data science into the introductory physics curriculum. Our goal is to provide guidance and inspiration to educators who seek to integrate data science into their teaching, helping to prepare the next generation of physicists for a data-driven world.Item The emergence of the socioeconomic gradient in women's marriage outcomes(MIT Press, 2024-08-22) Olivetti, Claudia; Paserman, M. Daniele; Salisbury, Laura; Weber, E. AnnaWe present new findings about the relationship between marriage and socioeconomic background in the United States in the late 19th and early 20th centuries. Imputing socioeconomic status of family of origin from first names, we document a socioeconomic gradient for women in the probability of marriage and the socioeconomic status of husbands, which widens over this period. Regional divergence in occupational structure explains half of the divergence in the probability of marriage, and most of the increase in marital sorting. Urbanization and the associated improvement in women's labor market opportunities drive most of these differences.Item Uniting the observed dynamical dark energy preference with the discrepancies in Ω m Ω m and H 0 H 0 across cosmological probes(2024-12-05) Brout, Dillon; Tang, XianzheItem Amalgame: cosmological constraints from the first combined photometric supernova sample(Oxford University Press (OUP), 2024-03-18) Popovic, Brodie; Scolnic, Daniel; Vincenzi, Maria; Sullivan, Mark; Brout, Dillon; Chen, Rebecca; Patel, Utsav; Peterson, Erik R.; Kessler, Richard; Kelsey, Lisa; Sanchez, Bruno O.; Bailey, Ava Claire; Wiseman, Phil; Toy, MarcusFuture constraints of cosmological parameters from Type Ia supernovae (SNe Ia) will depend on the use of photometric samples, those samples without spectroscopic measurements of the SNe Ia. There is a growing number of analyses that show that photometric samples can be utilized for precision cosmological studies with minimal systematic uncertainties. To investigate this claim, we perform the first analysis that combines two separate photometric samples, SDSS and Pan-STARRS, without including a low-redshift anchor. We evaluate the consistency of the cosmological parameters from these two samples and find they are consistent with each other to under 1σ. From the combined sample, named Amalgame, we measure ΩM = 0.328 ± 0.024 with SN alone in a flat ΛCDM model, and ΩM = 0.330 ± 0.018 and w = $-1.016^{+0.055}_{-0.058}$ when combining with a Planck data prior and a flat wCDM model. These results are consistent with constraints from the Pantheon+ analysis of only spectroscopically confirmed SNe Ia, and show that there are no significant impediments to analyses of purely photometric samples of SNe Ia. The data and results are made available at https://github.com/bap37/AmalgameDR.Item Modelling the impact of host galaxy dust on type Ia supernova distance measurements(Oxford University Press (OUP), 2024-10-04) Popovic, B.; Wiseman, P.; Sullivan, M.; Smith, M.; González-Gaitán, S.; Scolnic, D.; Duarte, J.; Armstrong, P.; Asorey, J.; Brout, D.; Carollo, D.; Galbany, L.; Glazebrook, K.; Kelsey, L.; Kessler, R.; Lidman, C.; Lee, J.; Lewis, G.F.; Möller, A.; Nichol, R.C.; Sánchez, B.O.; Toy, M.; Tucker, B.E.; Vincenzi, M.; Abbott, T.M.C.; Aguena, M.; Andrade-Oliveira, F.; Bacon, D.; Brooks, D.; Burke, D.L.; Carnero Rosell, A.; Carretero, J.; Castander, F.J.; da Costa, L.N.; Pereira, M.E.S.; Davis, T.M.; Desai, S.; Everett, S.; Ferrero, I.; Flaugher, B.; García-Bellido, J.; Gaztanaga, E.; Gruendl, R.A.; Gutierrez, G.; Hinton, S.R.; Hollowood, D.L.; Honscheid, K.; James, D.J.; Kuehn, K.; Lahav, O.; Lee, S.; Marshall, J.L.; Mena-Fernández, J.; Miquel, R.; Myles, J.; Ogando, R.L.C.; Palmese, A.; Pieres, A.; Plazas Malagón, A.A.; Sanchez, E.; Sanchez Cid, D.; Schubnell, M.; Sevilla-Noarbe, I.; Suchyta, E.; Swanson, M.E.C.; Tarle, G.; Vikram, V.; Weaverdyck, N.Type Ia Supernovae (SNe Ia) are a critical tool in measuring the accelerating expansion of the universe. Recent efforts to improve these standard candles have focused on incorporating the effects of dust on distance measurements with SNe Ia. In this paper, we use the state-of-the-art Dark Energy Survey 5 year sample to evaluate two different families of dust models: empirical extinction models derived from SNe Ia data and physical attenuation models from the spectra of galaxies. In this work, we use realistic simulations of SNe Ia to forward-model different models of dust and compare summary statistics in order to test different assumptions and impacts on SNe Ia data. Among the SNe Ia-derived models, we find that a logistic function of the total-to-selective extinction $R_V$ best recreates the correlations between supernova distance measurements and host galaxy properties, though an additional 0.02 mag of grey scatter is needed to fully explain the scatter in SNIa brightness in all cases. These empirically derived extinction distributions are highly incompatible with the physical attenuation models from galactic spectral measurements. From these results, we conclude that SNe Ia must either preferentially select extreme ends of galactic dust distributions, or that the characterization of dust along the SNe Ia line-of-sight is incompatible with that of galactic dust distributions.Item The dark energy survey: cosmology results with ∼1500 new high-redshift type Ia supernovae using the full 5 yr data set(American Astronomical Society, 2024-09-01) Abbott, DES Collaboration T.M.C.; Acevedo, M.; Aguena, M.; Alarcon, A.; Allam, S.; Alves, O.; Amon, A.; Andrade-Oliveira, F.; Annis, J.; Armstrong, P.; Asorey, J.; Avila, S.; Bacon, D.; Bassett, B.A.; Bechtol, K.; Bernardinelli, P.H.; Bernstein, G.M.; Bertin, E.; Blazek, J.; Bocquet, S.; Brooks, D.; Brout, D.; Buckley-Geer, E.; Burke, D.L.; Camacho, H.; Camilleri, R.; Campos, A.; Carnero Rosell, A.; Carollo, D.; Carr, A.; Carretero, J.; Castander, F.J.; Cawthon, R.; Chang, C.; Chen, R.; Choi, A.; Conselice, C.; Costanzi, M.; da Costa, L.N.; Crocce, M.; Davis, T.M.; DePoy, D.L.; Desai, S.; Diehl, H.T.; Dixon, M.; Dodelson, S.; Doel, P.; Doux, C.; Drlica-Wagner, A.; Elvin-Poole, J.; Everett, S.; Ferrero, I.; Ferté, A.; Flaugher, B.; Foley, R.J.; Fosalba, P.; Friedel, D.; Frieman, J.; Frohmaier, C.; Galbany, L.; García-Bellido, J.; Gatti, M.; Gaztanaga, E.; Giannini, G.; Glazebrook, K.; Graur, O.; Gruen, D.; Gruendl, R.A.; Gutierrez, G.; Hartley, W.G.; Herner, K.; Hinton, S.R.; Hollowood, D.L.; Honscheid, K.; Huterer, D.; Jain, B.; James, D.J.; Jeffrey, N.; Kasai, E.; Kelsey, L.; Kent, S.; Kessler, R.; Kim, A.G.; Kirshner, R.P.; Kovacs, E.; Kuehn, K.; Lahav, O.; Lee, J.; Lee, S.; Lewis, G.F.; Li, T.S.; Lidman, C.; Lin, H.; Malik, U.; Marshall, J.L.; Martini, P.; Mena-Fernández, J.; Menanteau, F.; Miquel, R.; Mohr, J.J.; Mould, J.; Muir, J.; Möller, A.; Neilsen, E.; Nichol, R.C.; Nugent, P.; Ogando, R.L.C.; Palmese, A.; Pan, Y.-C.; Paterno, M.; Percival, W.J.; Pereira, M.E.S.; Pieres, A.; Plazas Malagón, A.A.; Popovic, B.; Porredon, A.; Prat, J.; Qu, H.; Raveri, M.; Rodríguez-Monroy, M.; Romer, A.K.; Roodman, A.; Rose, B.; Sako, M.; Sanchez, E.; Sanchez Cid, D.; Schubnell, M.; Scolnic, D.; Sevilla-Noarbe, I.; Shah, P.; Smith, J. Allyn; Smith, M.; Soares-Santos, M.; Suchyta, E.; Sullivan, M.; Suntzeff, N.; Swanson, M.E.C.; Sánchez, B.O.; Tarle, G.; Taylor, G.; Thomas, D.; To, C.; Toy, M.; Troxel, M.A.; Tucker, B.E.; Tucker, D.L.; Uddin, S.A.; Vincenzi, M.; Walker, A.R.; Weaverdyck, N.; Wechsler, R.H.; Weller, J.; Wester, W.; Wiseman, P.; Yamamoto, M.; Yuan, F.; Zhang, B.; Zhang, Y.We present cosmological constraints from the sample of Type Ia supernovae (SNe Ia) discovered and measured during the full 5 yr of the Dark Energy Survey (DES) SN program. In contrast to most previous cosmological samples, in which SNe are classified based on their spectra, we classify the DES SNe using a machine learning algorithm applied to their light curves in four photometric bands. Spectroscopic redshifts are acquired from a dedicated follow-up survey of the host galaxies. After accounting for the likelihood of each SN being an SN Ia, we find 1635 DES SNe in the redshift range 0.10 < z < 1.13 that pass quality selection criteria sufficient to constrain cosmological parameters. This quintuples the number of high-quality z > 0.5 SNe compared to the previous leading compilation of Pantheon+ and results in the tightest cosmological constraints achieved by any SN data set to date. To derive cosmological constraints, we combine the DES SN data with a high-quality external low-redshift sample consisting of 194 SNe Ia spanning 0.025 < z < 0.10. Using SN data alone and including systematic uncertainties, we find ΩM = 0.352 ± 0.017 in flat ΛCDM. SN data alone now require acceleration (q 0 < 0 in ΛCDM) with over 5σ confidence. We find ( Ω M , w ) = ( 0.264 − 0.096 + 0.074 , − 0.80 − 0.16 + 0.14 ) in flat wCDM. For flat w 0 w a CDM, we find ( Ω M , w 0 , w a ) = ( 0.495 − 0.043 + 0.033 , − 0.36 − 0.30 + 0.36 , − 8.8 − 4.5 + 3.7 ) , consistent with a constant equation of state to within ∼2σ. Including Planck cosmic microwave background, Sloan Digital Sky Survey baryon acoustic oscillation, and DES 3 × 2pt data gives (ΩM, w) = (0.321 ± 0.007, −0.941 ± 0.026). In all cases, dark energy is consistent with a cosmological constant to within ∼2σ. Systematic errors on cosmological parameters are subdominant compared to statistical errors; these results thus pave the way for future photometrically classified SN analyses.Item The MOST hosts survey: spectroscopic observation of the host galaxies of ∼40,000 transients using DESI(American Astronomical Society, 2024-12-01) Soumagnac, Maayane T.; Nugent, Peter; Knop, Robert A.; Ho, Anna Y.Q.; Hohensee, William; Awbrey, Autumn; Andersen, Alexis; Aldering, Greg; Ventura, Matan; Aguilar, Jessica N.; Ahlen, Steven; Benzvi, Segev Y.; Brooks, David; Brout, Dillon; Claybaugh, Todd; Davis, Tamara M.; Dawson, Kyle; de la Macorra, Axel; Dey, Arjun; Dey, Biprateep; Doel, Peter; Douglass, Kelly A.; Forero-Romero, Jaime E.; Gaztañaga, Enrique; Gontcho A Gontcho, Satya; Graur, Or; Guy, Julien; Hahn, ChangHoon; Honscheid, Klaus; Howlett, Cullan; Kim, Alex G.; Kisner, Theodore; Kremin, Anthony; Lambert, Andrew; Landriau, Martin; Lang, Dustin; Le Guillou, Laurent; Manera, Marc; Meisner, Aaron; Miquel, Ramon; Moustakas, John; Myers, Adam D.; Nie, Jundan; Palmese, Antonella; Parkinson, David; Poppett, Claire; Prada, Francisco; Qin, Fei; Rezaie, Mehdi; Rossi, Graziano; Sanchez, Eusebio; Schlegel, David J.; Schubnell, Michael; Silber, Joseph H.; Tarlé, Gregory; Weaver, Benjamin A.; Zhou, ZhiminWe present the Multi-Object Spectroscopy of Transient (MOST) Hosts survey. The survey is planned to run throughout the 5 yr of operation of the Dark Energy Spectroscopic Instrument (DESI) and will generate a spectroscopic catalog of the hosts of most transients observed to date, in particular all the supernovae observed by most public, untargeted, wide-field, optical surveys (Palomar Transient Factory, PTF/intermediate PTF, Sloan Digital Sky Survey II, Zwicky Transient Facility, DECAT, DESIRT). Science cases for the MOST Hosts survey include Type Ia supernova cosmology, fundamental plane and peculiar velocity measurements, and the understanding of the correlations between transients and their host-galaxy properties. Here we present the first release of the MOST Hosts survey: 21,931 hosts of 20,235 transients. These numbers represent 36% of the final MOST Hosts sample, consisting of 60,212 potential host galaxies of 38,603 transients (a transient can be assigned multiple potential hosts). Of all the transients in the MOST Hosts list, only 26.7% have existing classifications, and so the survey will provide redshifts (and luminosities) for nearly 30,000 transients. A preliminary Hubble diagram and a transient luminosity–duration diagram are shown as examples of future potential uses of the MOST Hosts survey. The survey will also provide a training sample of spectroscopically observed transients for classifiers relying only on photometry, as we enter an era when most newly observed transients will lack spectroscopic classification. The MOST Hosts DESI survey data will be released on a rolling cadence and updated to match the DESI releases. Dates of future releases and updates are available through the https://mosthosts.desi.lbl.gov website.Item Landscapes architecture and infrastructure of the twentieth century: selections from Docomomo chapters(Docomomo International, 2024-09-23) Cengiz, Gulnur; Haenraets, Jan; Saniga, Andrew; Cengiz, GulnurThis book presents a wide range of landscapes that have been integral to the Modern Movement era. It aims to raise awareness of their design significance and to broaden understanding of their diversity. It demonstrates the breadth of roles that landscape architects and affiliated designers have played in response to the demands wrought by social, political and environmental change, particularly in the post-World War II years. In this sense it draws attention to people and places that previously may have been marginally understood—‘invisible’ or ‘dislocated’—thus enabling them to be appreciated in new ways and to be considered more carefully in comparative analyses into the future. Included in this book are eighty-six landscapes spanning the twentieth century and representing the following thirty-eight countries: Argentina, Australia, Austria, Belgium, Brazil, Bulgaria, Canada, Croatia, Cuba, Cyprus, Czech Republic, Finland, France, Ghana, Greece, Guatemala, India, Iran, Israel, Italy, Japan, Lebanon, Lithuania, Mexico, Portugal, Puerto Rico, Romania, Scotland, Serbia, Slovakia, Slovenia, Spain, Syria, Thailand, the Netherlands, Turkey, United States of America, and Venezuela. The book is published by Docomomo International as an initiative by the Docomomo International Specialist Committee on Urbanism and Landscape, and received publishing grants from Boston University’s College of Arts and Sciences Humanities Research Fund and the Australian Centre for Architectural History, Urban and Cultural Heritage at the University of Melbourne.Item Diverse responses of oligodendrocytes to different FGF-family members: uncoupling structure-function relationship within FGF subfamilies(Informa UK Limited, 2024-01) Guardiola-Diaz, Hebe M.; DiBenedictis, Brett T.; Prendaj, Erealda; Bansal, RashmiItem Robust single-shot 3D fluorescence imaging in scattering media with a simulator-trained neural network(Optica Publishing Group, 2023-12-08) Alido, Jeffrey; Greene, Joseph; Xue, Yujia; Hu, Guorong; Li, Yunzhe; Gilmore, Mitchell; Monk, Kevin J.; Dibenedictis, Brett T.; Davison, Ian G.; Tian, LeiImaging through scattering is a pervasive and difficult problem in many biological applications. The high background and the exponentially attenuated target signals due to scattering fundamentally limits the imaging depth of fluorescence microscopy. Light-field systems are favorable for high-speed volumetric imaging, but the 2D-to-3D reconstruction is fundamentally ill-posed, and scattering exacerbates the condition of the inverse problem. Here, we develop a scattering simulator that models low-contrast target signals buried in heterogeneous strong background. We then train a deep neural network solely on synthetic data to descatter and reconstruct a 3D volume from a single-shot light-field measurement with low signal-to-background ratio (SBR). We apply this network to our previously developed Computational Miniature Mesoscope and demonstrate the robustness of our deep learning algorithm on scattering phantoms with different scattering conditions. The network can robustly reconstruct emitters in 3D with a 2D measurement of SBR as low as 1.05 and as deep as a scattering length. We analyze fundamental tradeoffs based on network design factors and out-of-distribution data that affect the deep learning model's generalizability to real experimental data. Broadly, we believe that our simulator-based deep learning approach can be applied to a wide range of imaging through scattering techniques where experimental paired training data is lacking.Item Convergence analysis of real-time recurrent learning (RTRL) for a class of recurrent neural networks(2025-01-14) Lam, Samuel; Sirignano, Justin; Spiliopoulos, KonstantinosItem On the large-time behaviour of affine Volterra processesJacquier, Antoine; Spiliopoulos, Konstantinos; Pannier, AlexanderWe show the existence of a stationary measure for a class of multidimensional stochastic Volterra systems of affine type. These processes are in general not Markovian, a shortcoming which hinders their large-time analysis. We circumvent this issue by lifting the system to a measure-valued stochastic PDE introduced by Cuchiero and Teichmann, whence we retrieve the Markov property. Leveraging on the associated generalised Feller property, we extend the Krylov-Bogoliubov theorem to this infinite-dimensional setting and thus establish an approach to the existence of invariant measures. We present concrete examples, including the rough Heston model from Mathematical Finance.Item Uniform in time bounds for a stochastic hybrid system with fast periodic sampling and small white-noise(2024-04-28) Dhama, Shivam; Spiliopoulos, KonstantinosWe study the asymptotic behavior, uniform-in-time, of a non-linear dynamical system under the combined effects of fast periodic sampling with period δ and small white noise of size ε,0<ε,δ≪1. The dynamics depend on both the current and recent measurements of the state, and as such it is not Markovian. Our main results can be interpreted as Law of Large Numbers (LLN) and Central Limit Theorem (CLT) type results. LLN type result shows that the resulting stochastic process is close to an ordinary differential equation (ODE) uniformly in time as ε,δ↘0. Further, in regards to CLT, we provide quantitative and uniform-in-time control of the fluctuations process. The interaction of the small parameters provides an additional drift term in the limiting fluctuations, which captures both the sampling and noise effects. As a consequence, we obtain a first-order perturbation expansion of the stochastic process along with time-independent estimates on the remainder. The zeroth- and first-order terms in the expansion are given by an ODE and SDE, respectively. Simulation studies that illustrate and supplement the theoretical results are also provided.Item An examination of the effects of dorsal fin-mounted SPOT on carcharodon carcharias, the great white shark(MDPI AG, 2024) Hicks, Grace L.; Lobel, Phillip S.This opinion piece presents empirical evidence to examine possible negative consequences of the use of penetrative tagging as used on the great white shark (GWS). Tagging programs currently using this method attach SPOT (Spatial Positioning Only Tags) using corrodible bolts inserted through the dorsal fin while the shark is taken out of water. Such methods can cause harm to the tagged individual. Possible adverse effects include impacts on growth, tag biofouling, wounds, heightened stress, and hemorrhaging. This method may adversely impact dorsal fin structure and the shark’s hydrodynamics. As a result, data collected may not be reflective of natural behavior. Bolted SPOT are semi-permanently affixed to the shark but can have a battery life of approximately 3.5 years. Most of these tags (69%) ceased transmitting in less than 2 years. Alternative tagging technologies exist as more humane options.Item Metabolic flux modeling in marine ecosystems(Annual Reviews, 2025-01) Scott, Helen; Segrè, DanielOcean metabolism constitutes a complex, multiscale ensemble of biochemical reaction networks harbored within and between the boundaries of a myriad of organisms. Gaining a quantitative understanding of how these networks operate requires mathematical tools capable of solving in silico the resource allocation problem each cell faces in real life. Toward this goal, stoichiometric modeling of metabolism, such as flux balance analysis, has emerged as a powerful computational tool for unraveling the intricacies of metabolic processes in microbes, microbial communities, and multicellular organisms. Here, we provide an overview of this approach and its applications, future prospects, and practical considerations in the context of marine sciences. We explore how flux balance analysis has been employed to study marine organisms, help elucidate nutrient cycling, and predict metabolic capabilities within diverse marine environments, and highlight future prospects for this field in advancing our knowledge of marine ecosystems and their sustainability.Item The metastable state of Fermi-Pasta-Ulam-Tsingou models(MDPI AG, 2023-02-06) Reiss, Kevin A.; Campbell, David K.Classical statistical mechanics has long relied on assumptions such as the equipartition theorem to understand the behavior of the complicated systems of many particles. The successes of this approach are well known, but there are also many well-known issues with classical theories. For some of these, the introduction of quantum mechanics is necessary, e.g., the ultraviolet catastrophe. However, more recently, the validity of assumptions such as the equipartition of energy in classical systems was called into question. For instance, a detailed analysis of a simplified model for blackbody radiation was apparently able to deduce the Stefan-Boltzmann law using purely classical statistical mechanics. This novel approach involved a careful analysis of a "metastable" state which greatly delays the approach to equilibrium. In this paper, we perform a broad analysis of such a metastable state in the classical Fermi-Pasta-Ulam-Tsingou (FPUT) models. We treat both the α-FPUT and β-FPUT models, exploring both quantitative and qualitative behavior. After introducing the models, we validate our methodology by reproducing the well-known FPUT recurrences in both models and confirming earlier results on how the strength of the recurrences depends on a single system parameter. We establish that the metastable state in the FPUT models can be defined by using a single degree-of-freedom measure-the spectral entropy (η)-and show that this measure has the power to quantify the distance from equipartition. For the α-FPUT model, a comparison to the integrable Toda lattice allows us to define rather clearly the lifetime of the metastable state for the standard initial conditions. We next devise a method to measure the lifetime of the metastable state tm in the α-FPUT model that reduces the sensitivity to the exact initial conditions. Our procedure involves averaging over random initial phases in the plane of initial conditions, the P1-Q1 plane. Applying this procedure gives us a power-law scaling for tm, with the important result that the power laws for different system sizes collapse down to the same exponent as Eα2→0. We examine the energy spectrum E(k) over time in the α-FPUT model and again compare the results to those of the Toda model. This analysis tentatively supports a method for an irreversible energy dissipation process suggested by Onorato et al.: four-wave and six-wave resonances as described by the "wave turbulence" theory. We next apply a similar approach to the β-FPUT model. Here, we explore in particular the different behavior for the two different signs of β. Finally, we describe a procedure for calculating tm in the β-FPUT model, a very different task than for the α-FPUT model, because the β-FPUT model is not a truncation of an integrable nonlinear model.