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This framework from the Region 19 Comprehensive Center is an educational tool that stimulates thinking about what we teach and how we teach in relation to who we teach. The organizing frame is the five petals, or facets, of the hibiscus flower. Each facet pertains to a different aspect of linguistic and cultural sustainability and is designed to preserve and enhance the region's social, language, and cultural roots. The framework responds to regional inquiries: How might we describe the linguistic and cultural vibrancy of the Pacific region? How might we envision linguistic and cultural sustainability for Pacific islanders? How might we encourage our local and school communities to preserve their rich linguistic and cultural heritage? How might we foster access to our students' and families' multiple languages and cultures in our schools and classrooms? How might we nurture positive linguistic and cultural sustainability across our educational networks? In turn, each facet has an underlying Principle and Practice. The Principle and Practice illustrate how the peoples of the Pacific are contributing to the building, enhancing, and maintaining of their languages and cultures. This framework is to be used in thinking about the impact of language and culture on educational life. In addition, References and Resources (Learn More!) offer readers additional areas to explore. Lastly, there is a glossary for readers to complete (What Does It Mean?) and three tools, one each for student, classroom, and school use (Try It Out!).

This study addresses the burgeoning phenomenon of fully online alternative teacher certification programs (ACPs). In Texas where most teachers are prepared via ACPs, our research zeroes in on the proportion of teachers who are prepared fully online and the relative effectiveness of teacher preparation programs on student achievement and teacher retention. Using statewide longitudinal data from 2014-2023, our findings show that 1 in 4 of Texas students are being taught by teachers prepared fully online Students taught by teachers prepared online exhibit comparable levels of achievement to those taught by uncertified teachers, underperforming compared to students taught by teachers from other preparation pathways. Moreover, these teachers exhibit a markedly higher turnover rate. This study contributes to the ongoing discourse on teacher preparation quality, offering insights for policymakers and stakeholders.

We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment $a_\mu$ in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to $a_\mu$, respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong isospin-breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark connected contribution, we obtain $a^{ll,\,{\mathrm{SD}}}_{\mu}(\mathrm{conn.}) = 48.116(16)(94)[96] \times 10^{-10}$ and $a^{ll,\,{\mathrm{W}}}_{\mu}(\mathrm{conn.}) = 207.06(17)(63)[66] \times 10^{-10}$. We use Bayesian model averaging combined with a global bootstrap to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are $a^{{\mathrm{SD}}}_{\mu} = 69.01(2)(21)[21] \times 10^{-10}$ and $a^{{\mathrm{W}}}_{\mu} = 236.57(20)(94)[96] \times 10^{-10}$. This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few permille level.

We analyse continuum and molecular emission, observed with ALMA, from the dust-enshrouded intermediate-mass AGB star OH 30.1 -0.7. We find a secondary peak in the continuum maps, "feature B", separated by 4.6" from the AGB star, which corresponds to a projected separation of $1.8 \times 10^4$ au, placing a lower limit on the physical separation. This feature is most likely composed of cold dust and is likely to be ejecta associated with the AGB star, though we cannot rule out that it is a background object. The molecular emission we detect includes lines of CO, SiS, CS, SO$_2$, NS, NaCl, and KCl. We find that the NS emission is off centre and arranged along an axis perpendicular to the direction of feature B, indicative of a UV-emitting binary companion (e.g. a G-type main sequence star or hotter), perhaps on an eccentric orbit, contributing to its formation. However, the NaCl and KCl emission constrain the nature of that companion to not be hotter than a late B-type main sequence star. We find relatively warm emission arising from the inner wind and detect several vibrationally excited lines of SiS (3 = 1), NaCl (up to 3 = 4) and KCl (up to 3 = 2), and emission from low energy levels in the mid to outer envelope, as traced by SO$_2$. The CO emission is abruptly truncated around 3.5" or 14,000 au from the continuum peak, suggesting that mass loss at a high rate may have commenced as little as 2800 years ago., Comment: Accepted for publication in MNRAS

Large language models (LLMs) generate diverse, situated, persuasive texts from a plurality of potential perspectives, influenced heavily by their prompts and training data. As part of LLM adoption, we seek to characterize - and ideally, manage - the socio-cultural values that they express, for reasons of safety, accuracy, inclusion, and cultural fidelity. We present a validated approach to automatically (1) extracting heterogeneous latent value propositions from texts, (2) assessing resonance and conflict of values with texts, and (3) combining these operations to characterize the pluralistic value alignment of human-sourced and LLM-sourced textual data.

We review lattice results related to pion, kaon, $D$-meson, $B$-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \to \pi$ transition at zero momentum transfer, as well as the decay-constant ratio $f_K/f_\pi$ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four $B$ parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha_s$. We review the determinations of nucleon charges from the matrix elements of both isovector and flavour-diagonal axial, scalar and tensor local quark bilinears, and momentum fraction, helicity moment and the transversity moment from one-link quark bilinears. We also review determinations of scale-setting quantities. Finally, in this review we have added a new section on the general definition of the low-energy limit of the Standard Model., Comment: 435 pages, 53 Figures, 190 tables. arXiv admin note: substantial text overlap with arXiv:2111.09849, arXiv:1902.08191

Building on a general relativistic magnetohydrodynamic simulation of a short gamma-ray burst (sGRB) jet with initial magnetization $\sigma_0=150$, propagating through the dynamical ejecta from a binary neutron star merger, we identify regions of energy dissipation driven by magnetic reconnection and collisionless sub-shocks within different scenarios. We solve the transport equations for photons, electrons, protons, neutrinos, and intermediate particles up to the photosphere, accounting for all relevant radiative processes, including electron and proton acceleration, and investigate the potential impact of magnetic reconnection occurring in different regions along the jet. We find the photon spectra undergo non-thermal modifications below the photosphere, observable in both on-axis and off-axis emission directions, as well as across different scenarios of energy dissipation and subsequent particle acceleration. Interestingly, the spectral index of the photon energy distribution can at most vary by $\sim20\%$ across all different dissipation scenarios. Depending on the dissipation mechanism at play, neutrino signatures may accompany the photon signal, pointing to efficient proton acceleration and shedding light on jet physics. Although our findings are based on one jet simulation, they point to a potential universal origin of the non-thermal features of the Band spectrum observed in sGRBs., Comment: 21 pages, 10 figures, comments welcome

Most black holes (BHs) formed in collapsing stars have low spin, though some are expected to acquire a magnetic accretion disk during the collapse. While such BH disks can launch magnetically driven winds, their physics and observational signatures have remained unexplored. We present global 3D general relativistic magnetohydrodynamic simulations of collapsing stars that form slowly spinning BHs with accretion disks. As the disk transitions to a magnetically arrested state, it drives mildly relativistic, wobbling, collimated magnetic outflows through two mechanisms: steady outflows along vertical magnetic field lines (''Blandford-Payne jets'') and magnetic flux eruptions. With an isotropic-equivalent energy of $E_{\rm iso}\approx10^{52}\,{\rm erg}$, exceeding that of relativistic jets from BHs with spin $a\lesssim 0.25$, the disk outflows unbind the star, ultimately capping the final BH mass at $ M_{\rm BH} \approx 4\,M_\odot$. Once the outflows emerge from the star, they produce mildly relativistic shock breakout, cooling, and $^{56}{\rm Ni}$-decay emission. Our cooling emission estimates suggest a bright near-ultraviolet and optical signal at absolute magnitude $M_{\rm AB}\approx-16$ lasting for several days. This indicates that disk winds could be responsible for the first peak in the double-peaked light curves observed in Type Ib/c supernovae (SNe) or power another class of transients. The detection rate in the upcoming Rubin Observatory and ULTRASAT/UVEX will enable us to differentiate between competing models for the origin of the first SN peak and provide constraints on the physics and formation rate of accretion disks in core-collapse SNe., Comment: 12 pages, 7 figures

Collapsars - rapidly rotating stellar cores that form black holes (BHs) - can power gamma-ray bursts (GRBs) and are proposed to be key contributors to the production of heavy elements in the Universe via the rapid neutron capture process ($r$-process). Previous neutrino-transport collapsar simulations have been unable to unbind neutron-rich material from the disk. However, these simulations have not included magnetic fields or the BH, both of which are essential for launching mass outflows. We present $\nu$H-AMR, a novel neutrino-transport general relativistic magnetohydrodynamic ($\nu$GRMHD) code, which we use to perform the first 3D $\nu$GRMHD collapsar simulations. We find a self-consistent formation of a disk with initially weak magnetic flux, resulting in a low accretion speed and leaving sufficient time for the disk to neutronize. However, once substantial magnetic flux accumulates near the BH, it becomes dynamically important, leading to a magnetically arrested disk that unbinds some of the neutron-rich material. The strong flux also accelerates the accretion speed, preventing further disk neutronization. The neutron-rich disk ejecta collides with the infalling stellar gas, generating a shocked cocoon with an electron fraction, $Y_\text{e}\gtrsim0.2$. Continuous mixing between the cocoon and neutron-poor stellar gas incrementally raises the outflow $Y_\text{e}$, but the final $r$-process yield is determined earlier at the point of neutron capture freeze-out. Our models require extreme magnetic fluxes and mass accretion rates to eject neutron-rich material ($Y_\text{e}\lesssim0.3$), implying very high $r$-process ejecta masses $M_\text{ej}\lesssim{}M_\odot$. Future work will explore under what conditions more typical collapsar engines become $r$-process factories., Comment: 13 pages, 5 figures, 1 table (plus 7 pages and 7 figures in Appendix) uses aastex62.cls. Submitted to ApJ, comments welcome. Movies available at https://www.youtube.com/playlist?list=PLVsp-mE5pJ_UBsLD1LU1ZZCzPoLgo6wUP

We present results from the first lattice QCD calculation of the two-pion contributions to the light-quark connected vector-current correlation function obtained from staggered-quark operators. We employ the MILC collaboration's gauge-field ensemble with $2+1+1$ flavors of highly improved staggered sea quarks at a lattice spacing of $a\approx 0.15$ fm with a light sea-quark mass at its physical value. The two-pion contributions allow for a refined determination of the noisy long-distance tail of the vector-current correlation function, which we use to compute the light-quark connected contribution to HVP with improved statistical precision. We compare our results with traditional noise-reduction techniques used in lattice QCD calculations of the light-quark connected HVP, namely the so-called fit and bounding methods. We observe a factor of roughly three improvement in the statistical precision in the determination of the HVP contribution to the muon's anomalous magnetic moment over these approaches. We also lay the group theoretical groundwork for extending this calculation to finer lattice spacings with increased numbers of staggered two-pion taste states.

Superluminous supernovae (SLSNe) radiate $\gtrsim 10-100$ times more energy than ordinary stellar explosions, implicating a novel power source behind these enigmatic events. One frequently discussed source, particularly for hydrogen-poor (Type I) SLSNe, is a central engine such as a millisecond magnetar or accreting black hole. Both black hole and magnetar engines are expected to channel a fraction of their luminosity into a collimated relativistic jet. Using 3D relativistic hydrodynamical simulations, we explore the interaction of a relativistic jet, endowed with a luminosity $L_{\rm j}\approx10^{45.5}\,{\rm erg\,s^{-1}}$ and duration $t_{\rm eng} \approx 10\,{\rm days}$ compatible with those needed to power SLSNe, launched into the envelope of the exploding star. The jet successfully breaks through the expanding ejecta, and its shocked cocoon powers ultraviolet/optical emission lasting several days after the explosion and reaching a peak luminosity $\gtrsim 10^{44}\,{\rm erg\,s^{-1}} $, corresponding to a sizable fraction of $L_{\rm j}$. This high radiative efficiency is the result of the modest adiabatic losses the cocoon experiences owing to the low optical depths of the enlarged ejecta at these late times, e.g., compared to the more compact stars in gamma-ray bursts. The luminosity and temperature of the cocoon emission match those of the ``bumps'' in SLSN light curves observed weeks prior to the optical maximum in many SLSNe. Confirmation of jet breakout signatures by future observations (e.g., days-long to weeks-long internal X-ray emission from the jet for on-axis observers, spectroscopy confirming large photosphere velocities $v/c \gtrsim 0.1$, or detection of a radio afterglow) would offer strong evidence for central engines powering SLSNe.

Relativistic jets from a Kerr black hole (BH) following the core collapse of a massive star ("collapsar") is a leading model for gamma-ray bursts (GRBs). However, the two key ingredients for a Blandford-Znajek powered jet $-$ rapid rotation and a strong magnetic field $-$ seem mutually exclusive. Strong fields in the progenitor star's core transport angular momentum outwards more quickly, slowing down the core before collapse. Through innovative multidisciplinary modeling, we first use MESA stellar evolution models followed to core collapse, to explicitly show that the small length-scale of the instabilities $-$ likely responsible for angular momentum transport in the core (e.g., Tayler-Spruit) $ - $ results in a low net magnetic flux fed to the BH horizon, far too small to power GRB jets. Instead, we propose a novel scenario in which collapsar BHs acquire their magnetic "hair" from their progenitor proto-neutron star (PNS), which is likely highly magnetized from an internal dynamo. We evaluate the conditions for the BH accretion disk to pin the PNS magnetosphere to its horizon immediately after the collapse. Our results show that the PNS spin-down energy released before collapse matches the kinetic energy of Type Ic-BL supernovae, while the nascent BH's spin and magnetic flux produce jets consistent with observed GRB characteristics. We map our MESA models to 3D general-relativistic magnetohydrodynamic simulations and confirm that accretion disks confine the strong magnetic flux initiated near a rotating BH, enabling the launch of successful GRB jets, whereas a slower-spinning BH or one without a disk fails to do so., Comment: For movies of the simulations, see https://oregottlieb.com/BH_field.html

Binary interactions have been proposed to explain a variety of circumstellar structures seen around evolved stars, including asymptotic giant branch (AGB) stars and planetary nebulae. Studies resolving the circumstellar envelopes of AGB stars have revealed spirals, discs and bipolar outflows, with shaping attributed to interactions with a companion. For the first time, we have used a combined chemical and dynamical analysis to reveal a highly eccentric and long-period orbit for W Aquilae, a binary system containing an AGB star and a main sequence companion. Our results are based on anisotropic SiN emission, the first detections of NS and SiC towards an S-type star, and density structures observed in the CO emission. These features are all interpreted as having formed during periastron interactions. Our astrochemistry-based method can yield stringent constraints on the orbital parameters of long-period binaries containing AGB stars, and will be applicable to other systems., Comment: This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature's AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1038/s41550-023-02154-y

We present the first numerical study of gravitational waves (GWs) from collapsar disks, using state-of-the-art 3D general relativistic magnetohydrodynamic simulations of collapsing stars. These simulations incorporate a fixed Kerr metric for the central black hole (BH) and employ simplified prescriptions for disk cooling. We find that cooled disks with an expected scale height ratio of $H/R\gtrsim0.1$ at $\sim10$ gravitational radii induce Rossby instability in compact, high-density rings. The trapped Rossby vortices generate vigorous coherent emission regardless of disk magnetization and BH spin. For BH mass of $\sim10\,M_\odot$, the GW spectrum peaks at $\sim100\,{\rm Hz}$ with some breadth due to various nonaxisymmetric modes. The spectrum shifts toward lower frequencies as the disk viscously spreads and the circularization radius of the infalling gas increases. Weaker-cooled disks with $H/R\gtrsim0.3$ form a low-density extended structure of spiral arms, resulting in a broader, lower-amplitude spectrum. Assuming an optimistic detection threshold with a matched-filter signal-to-noise ratio of 20 and a rate similar to Type Ib/c supernovae, LIGO-Virgo-KAGRA (LVK) could detect $\lesssim1$ event annually, suggesting that GW events may already be hidden in observed data. Third-generation GW detectors could detect dozens to hundreds of collapsar disks annually, depending on the cooling strength and the disk formation rate. The GW amplitudes from collapsar disks are $\gtrsim100$ times higher with a substantially greater event rate than those from core-collapse supernovae, making them potentially the most promising burst-type GW class for LVK and Cosmic Explorer. This highlights the importance of further exploration and modeling of disk-powered GWs, promising insights into collapsing star physics., Comment: For movies of the simulations, see https://oregottlieb.com/disk_gw.html

Core collapse initial conditions are a bottleneck in understanding the explosion mechanism(s) of massive stars. Stellar evolution codes struggle after carbon burning, and either stop or adopt numerical simplifications missing crucial physics. The use of small nuclear reaction networks (NRN) that account for energy production but bypass weak reactions is typical, but insufficient to study the dynamics of the collapse. We advise against the use of progenitors computed with small NRN in expensive multi-dimensional simulations of core collapse, bounce, (jet formation), and explosion., Comment: accepted by RNAAS, input/output available at https://doi.org/10.5281/zenodo.11375523, code at https://github.com/mathren/CHE_net_comparison

Mid-infrared emission features probe the properties of ionized gas, and hot or warm molecular gas. The Orion Bar is a frequently studied photodissociation region (PDR) containing large amounts of gas under these conditions, and was observed with the MIRI IFU aboard JWST as part of the "PDRs4All" program. The resulting IR spectroscopic images of high angular resolution (0.2") reveal a rich observational inventory of mid-IR emission lines, and spatially resolve the substructure of the PDR, with a mosaic cutting perpendicularly across the ionization front and three dissociation fronts. We extracted five spectra that represent the ionized, atomic, and molecular gas layers, and measured the most prominent gas emission lines. An initial analysis summarizes the physical conditions of the gas and the potential of these data. We identified around 100 lines, report an additional 18 lines that remain unidentified, and measured the line intensities and central wavelengths. The H I recombination lines originating from the ionized gas layer bordering the PDR, have intensity ratios that are well matched by emissivity coefficients from H recombination theory, but deviate up to 10% due contamination by He I lines. We report the observed emission lines of various ionization stages of Ne, P, S, Cl, Ar, Fe, and Ni, and show how certain line ratios vary between the five regions. We observe the pure-rotational H$_2$ lines in the vibrational ground state from 0-0 S(1) to 0-0 S(8), and in the first vibrationally excited state from 1-1 S(5) to 1-1 S(9). We derive H$_2$ excitation diagrams, and approximate the excitation with one thermal (~700 K) component representative of an average gas temperature, and one non-thermal component (~2700 K) probing the effect of UV pumping. We compare these results to an existing model for the Orion Bar PDR and highlight the differences with the observations., Comment: 26 pages, 12 figures, 3 tables. Submitted to A&A, under review (1st revision)

The dusty winds of cool evolved stars are a major contributor of the newly synthesised material enriching the Galaxy and future generations of stars. However, the details of the physics and chemistry behind dust formation and wind launching have yet to be pinpointed. Recent spatially resolved observations show the importance of gaining a more comprehensive view of the circumstellar chemistry, but a comparative study of the intricate interplay between chemistry and physics is still difficult because observational details such as frequencies and angular resolutions are rarely comparable. Aiming to overcome these deficiencies, ATOMIUM is an ALMA Large Programme to study the physics and chemistry of the circumstellar envelopes of a diverse set of oxygen-rich evolved stars under homogeneous observing conditions at three angular resolutions between ~0.02"-1.4". Here we summarize the molecular inventory of these sources, and the correlations between stellar parameters and molecular content. Seventeen oxygen-rich or S-type asymptotic giant branch (AGB) and red supergiant (RSG) stars have been observed in several tunings with ALMA Band 6, targeting a range of molecules to probe the circumstellar envelope and especially the chemistry of dust formation close to the star. We systematically assigned the molecular carriers of the spectral lines and measured their spectroscopic parameters and the angular extent of the emission of each line from integrated intensity maps. Across the ATOMIUM sample, we detect 291 transitions of 24 different molecules and their isotopologues. This includes several first detections in oxygen-rich AGB/RSG stars: PO v=1, SO2 v1=1 and v2=2, and several high energy H2O transitions. We also find several first detections in S-type AGB stars: vibrationally excited HCN v2=2,3 and SiS v=4,5,6, as well as first detections of the molecules SiC, AlCl, and AlF in W Aql..., Comment: 19 pages plus appendices, forthcoming publication in Astronomy & Astrophysics

Most low-mass stars form in stellar clusters that also contain massive stars, which are sources of far-ultraviolet (FUV) radiation. Theoretical models predict that this FUV radiation produces photo-dissociation regions (PDRs) on the surfaces of protoplanetary disks around low-mass stars, impacting planet formation within the disks. We report JWST and Atacama Large Millimetere Array observations of a FUV-irradiated protoplanetary disk in the Orion Nebula. Emission lines are detected from the PDR; modelling their kinematics and excitation allows us to constrain the physical conditions within the gas. We quantify the mass-loss rate induced by the FUV irradiation, finding it is sufficient to remove gas from the disk in less than a million years. This is rapid enough to affect giant planet formation in the disk.

We compute the vector, scalar, and tensor form factors for the $B\to \pi$, $B\to K$, and $B_s\to K$ amplitudes, which are needed to describe semileptonic $B$-meson decay rates for both the charged and neutral current cases. We use the highly improved staggered quark (HISQ) action for the sea and light valence quarks. The bottom quark is described by the clover action in the Fermilab interpretation. Simulations are carried out on $N_f = 2+1+1$ MILC HISQ ensembles at approximate lattice spacings from $0.15$ fm down to $0.057$ fm. We present blinded preliminary results for the form factors., Comment: 10 pages, 5 figures, proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31 - August 4, 2023, Fermilab, USA

We present an update for results on $B$-meson semileptonic decays using the highly improved staggered quark (HISQ) action for both valence and 2+1+1 sea quarks. The use of the highly improved action, combined with the MILC collaboration's gauge ensembles with lattice spacings down to $\sim$0.03 fm, allows the $b$ quark to be treated with the same discretization as the lighter quarks. The talk will focus on updated results for $B_{(s)} \to D_{(s)}$, $B_{(s)} \to K$ scalar and vector form factors., Comment: Proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermilab, Batavia, Illinois, USA

We report on the ongoing effort of improving the determination of the gradient flow scale on the (2+1+1)-flavor HISQ ensembles generated by the MILC collaboration. We compute the scales $\sqrt{t_0}/a$ and $w_0/a$ with the Wilson and Symanzik flow using three discretizations for the action density: clover, Wilson and tree-level Symanzik improved. For the absolute scale setting, we intend to employ the $\Omega$-baryon mass, but are also using the pion decay constant while the $\Omega$-mass calculations are in progress., Comment: 10 pages, 6 figures, contribution to the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31 - August 4, 2023, Fermilab, USA

This research report presents a proof-of-concept study on the application of machine learning techniques to video and speech data collected during diagnostic cognitive assessments of children with a neurodevelopmental disorder. The study utilised a dataset of 39 video recordings, capturing extensive sessions where clinicians administered, among other things, four cognitive assessment tests. From the first 40 minutes of each clinical session, covering the administration of the Wechsler Intelligence Scale for Children (WISC-V), we extracted head positions and speech turns of both clinician and child. Despite the limited sample size and heterogeneous recording styles, the analysis successfully extracted path signatures as features from the recorded data, focusing on patient-clinician interactions. Importantly, these features quantify the interpersonal dynamics of the assessment process (dialogue and movement patterns). Results suggest that these features exhibit promising potential for predicting all cognitive tests scores of the entire session length and for prototyping a predictive model as a clinical decision support tool. Overall, this proof of concept demonstrates the feasibility of leveraging machine learning techniques for clinical video and speech data analysis in order to potentially enhance the efficiency of cognitive assessments for neurodevelopmental disorders in children., Comment: accepted in IEEE MedAI 2023 conference proceedings

Networks in machine learning offer examples of complex high-dimensional dynamical systems reminiscent of biological systems. Here, we study the learning dynamics of Generalized Hopfield networks, which permit a visualization of internal memories. These networks have been shown to proceed through a 'feature-to-prototype' transition, as the strength of network nonlinearity is increased, wherein the learned, or terminal, states of internal memories transition from mixed to pure states. Focusing on the prototype learning dynamics of the internal memories we observe a strong resemblance to the canalized, or low-dimensional, dynamics of cells as they differentiate within a Waddingtonian landscape. Dynamically, we demonstrate that learning in a Generalized Hopfield Network proceeds through sequential 'splits' in memory space. Furthermore, order of splitting is interpretable and reproducible. The dynamics between the splits are canalized in the Waddington sense -- robust to variations in detailed aspects of the system. In attempting to make the analogy a rigorous equivalence, we study smaller subsystems that exhibit similar properties to the full system. We combine analytical calculations with numerical simulations to study the dynamical emergence of the feature-to-prototype transition, and the behaviour of splits in the landscape, saddles points, visited during learning. We exhibit regimes where saddles appear and disappear through saddle-node bifurcations, qualitatively changing the distribution of learned memories as the strength of the nonlinearity is varied -- allowing us to systematically investigate the mechanisms that underlie the emergence of Waddingtonian dynamics. Memories can thus differentiate in a predictive and controlled way, revealing new bridges between experimental biology, dynamical systems theory, and machine learning.