Standing on the shoulders of giants, we resolve the quantum pyramids conjecture, confirming the globally information-optimal measurement for an ensemble of equiangular equiprobable pure states, as conjectured by Englert and Řeháček (arXiv:0905.0510). We do so by proving the remaining entropy inequalities of Holevo and Utkin (arXiv:2506.06700), which certify optimality for obtuse and flat pyramids. For obtuse pyramids, our key contribution is a rigorous proof that local minimizers of the corresponding entropy inequality cannot have three distinct coordinate values. We show that eliminating this family can be reduced to a neat algebraic reciprocal inequality relating branches of the Lambert $W$ function, which may be of independent interest. For flat pyramids, we prove a tight $\ell^p$ inequality for zero-sum vectors that was recently conjectured, proved analytically in dimension $d=3$, and computationally verified for $d\leq 200$ by Holevo and Utkin (arXiv:2603.24017). We prove this bound for all $d\geq 2$ via a technique in symmetric inequalities known as the equal variables method.

We revisit the problem of scalar dissipation anomaly and scaling of scalar gradients in passive scalar turbulence using theory and data from well-resolved direct numerical simulations (DNS) on grid sizes of up to $8192^3$, spanning Taylor-scale Reynolds numbers $Re_λ=140-1000$ and Schmidt numbers $Sc = 1-512$. The theory is based on a joint multifractal description of longitudinal velocity increments and scalar increments, constrained by Yaglom's law and extended to gradients via a fluctuating Batchelor cutoff scale. The DNS data show that the normalized mean scalar dissipation approaches a single asymptotic value as both $Re_λ$ and $Sc$ increase, although larger $Sc$ requires larger $\re$ to reach this state. In the multifractal framework, this corresponds to an effective scalar Hölder exponent tending to zero, associated with sharp cliff-like scalar fronts, and saturation of inertial-range scaling scalar structure-function exponents. The joint velocity-scalar fractal dimension of the dissipative structures is inferred to approach $7/3$, indicating a non-space-filling support. The framework further predicts that for fixed $Re_λ$, higher-order central moments of scalar gradients are independent of $Sc$. This prediction is confirmed by DNS data and by the collapse of standardized probability distributions of scalar-gradient across Schmidt numbers. These results suggest that the $Sc$-scaling of scalar gradients is dictated solely by scalar dissipation anomaly. In contrast, their $Re_λ$-dependence reflects strong intermittency, which can be directly related to mixed velocity-scalar structure function exponents.

The maturation of quantitative tools for studying the high-level structure of animal behavior, and especially tools which represent spontaneous behavior as a sequence of stereotyped and neurally well-defined 'syllables', demands that the field revisit a fundamental theoretical question: if the coarse structure of behavior can be accurately described by Markov models, what do these models really tell us about behavior? In this work, we explore the theoretical implications of these models and discuss how they allow us to quantitatively formulate questions about the sequence-like nature and effective dimensionality of behavior. One important insight is that the eigenvalues and eigenvectors of various model-associated matrices furnish interpretable time scales and modifications of behavior that occur on those time scales. We illustrate our points using both toy examples and Markov models fit to real data. By analyzing the consequences of Markov representations, we clarify the theoretical meaning of progress in quantifying behavior.

Lehner (1999) derived elegant formulas for the operator norm $\|\mathfrak{X}\|$ of operators of the form $\mathfrak{X} = \mathbf{A}_0 \otimes \mathfrak{1} + \sum_{i = 1}^n \mathbf{A}_i \otimes \mathfrak{m}_i$, also easily generalized to the spectral edge $λ_{\max}(\mathfrak{X})$, in terms of nonlinear optimization problems over positive definite matrices. Here the $\mathbf{A}_i$ are finite-dimensional Hermitian matrices, the $\mathfrak{m}_i$ are either free semicircular or free Rademacher families of operators, and $\mathfrak{1}$ is the identity operator. We first show that both of Lehner's nonlinear optimizations can be rewritten as linear semidefinite programs (SDPs), even in the Rademacher case where Lehner's optimization is not itself convex. We give the primal and dual forms of these SDPs, derive the complementary slackness relations and consequences thereof, and propose that the SDPs are more stable and accurate than the iterative numerical scheme proposed in Lehner's original work. We then apply the SDPs from the semicircular case to spiked matrix models, studied recently via Lehner's formula by Bandeira, Cipolloni, Schröder, and van Handel (2024). We give a new proof of the Baik--Ben Arous--Péché (BBP) transition they establish in models with isotropic (but possibly correlated) Gaussian noise by constructing feasible variables for the associated primal and dual SDPs. Combining our construction with a sensitivity interpretation of optimal dual variables, we study the fluctuations of leading eigenvectors of such models. We conjecture and give numerical evidence that these fluctuations are Gaussian but anisotropic and non-universal, and that their covariance may be computed in terms of the optimizer of the dual of Lehner's formula, which in turn is approximately the leading eigenmatrix of a completely positive operator associated to the covariance of the noise model.

Gate-tunable superconductivity in magic-angle twisted bilayer graphene (MATBG) has enabled the realization of superconducting devices, such as Josephson junctions, within a single crystal. This interface-free platform provides a reconfigurable and scalable architecture that overcomes limitations of conventional superconducting-semiconducting systems. Incorporating single-electron control enables access to regimes in which flat-band superconductivity competes with strong Coulomb repulsion, providing a platform for studying correlated physics phenomena. Here, we report a new class of quantum devices that combines electrostatic confinement with tunable superconductivity in a monolithic MATBG architecture. Within a single device, we demonstrate two complementary hybrid systems: superconducting islands and proximitized quantum dots. The superconducting island exhibits $2e$-periodic transport, indicating a well-defined gap protected against quasiparticle poisoning. The proximitized quantum dot hosts subgap Andreev states together with a strongly parity-modulated supercurrent.

Hole spin qubits provide one of the leading platforms for spin-based quantum computing due to their large intrinsic spin-orbit interaction (SOI), which enables fast electrical manipulation. The SOI of planar quantum dots has mostly been investigated in theoretical studies by examining the SOI already present in the two-dimensional hole gas (2DHG). Here, we study the SOI created by the in-plane confinement by deriving non-perturbative effective Hamiltonians numerically for hole spin qubits. We find that the quantum geometry of the 2DHG naturally emerges, leading to a meaningful non-perturbative definition of pseudospin valid far away from the $Γ$-point. The SOI of the 2DHG and of the in-plane confinement have different forms; therefore, they cannot be turned off simultaneously, ruining the perfect spin-orbit switch functionality of spin qubits. We construct effective Hamiltonians using the symmetry approach for various low-dimensional hole systems: (i) a heavy-hole confined in a SiGe/Ge/SiGe heterostructure, (ii) a light-hole confined in SnGe/Ge, (iii) a gate-defined nanowire in SiGe/Ge/SiGe, and (iv) a hole confined in a Ge/Si core/shell nanowire. The non-perturbative effective Hamiltonians provide results with excellent agreement with the full Hamiltonians.

The 21-cm signal probes the intergalactic medium during the Epoch of Reionization (EoR) but is overwhelmed by astrophysical foregrounds orders of magnitude stronger than the cosmological signal. We evaluate two mitigation strategies: (i) Foreground Avoidance, restricting analysis to the EoR window in Fourier space, and (ii) Foreground Removal via Gaussian Process Regression, which exploits spectral smoothness to statistically separate contaminants and reclaim modes within the contaminated wedge. Both introduce systematic biases of up to $\approx$1$σ$ in astrophysical parameters such as the minimum star-forming halo mass and ionising escape fraction, with avoidance posteriors consistently broader than removal owing to its restricted visibility coverage. The global reionization history is recovered within the 95% credible interval, though the neutral fraction at late reionization epochs shows a persistent bias reflecting the difficulty of its inference from the power spectrum alone. Multi-redshift inference is susceptible to contamination from poorly mitigated bins. Excluding such bins significantly reduces parameter biases, but identifying them requires independent quality metrics. When restricted to identical length scales, both strategies recover similar power spectra, yielding posteriors in similar regions.

The origin of the extreme broadening observed in chromospheric metal lines during solar and stellar flares, particularly Mg II h&k and Ca II H&K, remains poorly understood. These lines often display Lorentzian like wings whose widths exceed standard Stark broadening predictions by factors of approx. 30, with no known collisional mechanism capable of producing such enhancements. We posit that magnetic fields are responsible for this additional broadening due to the increase of magnetic activity during flares. A magnetic-field distribution of the form where P(B) goes as B^-3 reproduces the observed Mg II profile wings while leaving H I Balmer lines and optically thin transitions largely unaffected. To explain the broadening using magnetic fields, the high B tail can extend up to 10^6 G with extremely low probabilities where the filling factors are less than about 10^-6. We propose that observations of flares using spectropolarimetry can verify whether the anomalous broadening is from magnetic structures in flare ribbons.

In this paper, we obtain several Ramanujan-type congruences modulo 5 and 7 for sum of certain non-overlined parts in overpartitions classified by parity and sum of certain parts in partitions without repeated odd parts classified by parity. Our proofs for the congruences are elementary, depending only on classical theta function identities.

Complex chemistry in nano- and microscale compartments is often governed by how quickly reagents transit a fluid-fluid interface. Mass transport across interfaces is commonly modeled by assuming local equilibrium, enforcing continuity of chemical potential across the interface. While adequate at large scales, this approximation may break down at the microscale, where interfacial processes can become rate-limiting. Here, we extend linear irreversible thermodynamics to describe nonequilibrium interfacial mass transport. We identify an interface-limited regime, in which transport is governed by interfacial resistance and exhibits exponential relaxation. Combining microfluidic and spectroscopic techniques, we introduce an experimental technique that explores this regime and provides a direct measurement of the interfacial mass transfer coefficient. For a model system consisting of acetonitrile transport across a surfactant-stabilized water-oil interface, we obtain an interfacial transport coefficient ${M \sim 7\,{\rm nm/s}}$. These results establish interfacial mass transfer resistance as a governing mechanism in microscale transport and provide a framework to predict, control and measure mass transport in multiphase systems at microscale.

A Detector Error Model (DEM) is a structured representation of error mechanisms in quantum circuits, which has gained popularity in quantum compilation pipelines for its ability to capture fault-tolerance at a circuit level. It lists error mechanisms as instructions targeting detectors and observables, specifying for each physical fault channel the probability that the fault fires, the detectors it triggers, and the observables it flips. In this paper, we develop an equational theory for DEMs, with its associated categorical semantics. We present a sound, terminating, confluent rewriting system for DEM terms, formulating it as a symmetric monoidal theory (a PROP) over the Giry monad. We prove that every DEM term has a unique normal form, which can be computed efficiently in quasilinear time $O(k|E|\log|E|)$, where $|E|$ is the number of instructions and $k$ bounds the size of a target set. This provides a complete set of invariants (via Tanner graphs) for structural DEM equivalence. We provide the first static decision procedure for DEM equivalence, with rigorous correctness guarantees. It is complete (decides full decoder-equivalence exactly) for non-adaptive quantum error correction (QEC) pipelines, and scales to a sound and applicable decision procedure for partially-adaptive circuits (lattice surgery, distributed QEC, ...) without suffering exponential overhead. We discuss its application to the verification and optimisation of quantum compilers.

We introduce a basis for tree-level meromorphic scattering amplitudes suitable for describing pion scattering in the large-N limit. The basis is constructed as linear combinations of Lovelace-Shapiro-like amplitudes with varying Regge slopes and intercepts. The resulting amplitudes satisfy by construction the fundamental requirements of analyticity, crossing symmetry, and Regge behavior. We analyze their behavior in specific kinematical regimes, including the high-energy fixed-angle limit. We also show that finite linear combinations of our basis elements need not violate unitarity. Nonetheless, because unitarity is not imposed by construction, we enforce it a posteriori by requiring positivity of the partial-wave decomposition. This condition can be formulated as an optimization problem and solved numerically. The solutions to this primal bootstrap problem yield meromorphic amplitudes that satisfy all the aforementioned constraints. We compare several observables with the bounds obtained from the dual positivity conditions and show that our family of amplitudes spans the full allowed parameter space. With appropriate modifications, this method can be extended to construct amplitude families for broader applications.

This paper introduces a model-theoretic generalization of the notion of forcing with random reals, in which forcing gives rise to random generic structures. Specifically, we consider forcing with $κ$-Borel probability measures on the space of $L$-structures with a (possibly uncountable) infinite set $X$, focusing on those that are invariant under the action of the symmetric group $Sym(X)$. We demonstrate how any $Sym(X)$-invariant measure where $X$ is countable can be uniquely extended to a $Sym(Y)$-invariant measure where $Y$ is uncountable, and prove that forcing with such measures satisfies the countable chain condition. We also show that we can uniformly distinguish between these random generic structures and the Cohen generic structures that arise from forcing with a strong Fraïssé class: There is a $κ$-Borel set of low complexity that contains every Cohen generic structure that is not highly homogeneous but contains no random generic structure, implying that a structure that is not highly homogeneous cannot be both Cohen generic and random generic. Finally, we answer an open question of Kostana in the case of $ω_1$, by establishing a connection between forcing with a strong Fraïssé class and Cohen forcing.

Understanding the sources and evolution of cosmic reionization remains a central challenge in astrophysics, with the escape of ionizing Lyman-continuum (LyC) photons from early galaxies representing a major uncertainty. In this work, we use more than 35,000 galaxy realisations from the THESAN-ZOOM cosmological radiation-hydrodynamic simulations to identify indirect diagnostics of the LyC photon escape fraction ($f_\mathrm{esc}$) and the LyC photon escape rate ($\dot{N}_\mathrm{ion,esc}$) across the redshift range $z=3-16$. We train random forest regression models using these diagnostics to predict both quantities. We present four models: two trained with the full set of simulation-derived indicators to predict $f_\mathrm{esc}$ and $\dot{N}_\mathrm{ion,esc}$, and two restricted to observables accessible to JWST photometric surveys. We find the 10-to-100$\,$Myr star-formation rate ratio ($\mathrm{SFR}_{10} / \mathrm{SFR}_{100}$) and the gas-to-stellar mass ratio ($M_\mathrm{gas} / M_*$) to be the strongest diagnostics of $f_\mathrm{esc}$, suggesting a strong relationship between ionizing photon escape and gas clearing through bursty star formation. In contrast, rest-frame UV ($1500 \, Å$) absolute magnitude ($M_\mathrm{UV}$) dominates $\dot{N}_\mathrm{ion,esc}$ prediction. Motivated by the strong predictive power of $M_\mathrm{UV}$, we combine observed UV luminosity functions with derived $\dot{N}_\mathrm{ion,esc} - M_\mathrm{UV}$ relations to construct histories of reionization. These are consistent with observational constraints, avoiding the recently reported crisis in the ionizing photon budget. Our analysis suggests that the bulk of reionization occurred rapidly after $z \approx 8$, driven by UV-bright galaxies, with the $M_\mathrm{UV} < -17$ populations providing the dominant contribution.

Low-frequency gravitational waves ($\lessapprox$ 50 Hz) from core-collapse supernovae are becoming more important for current and future gravitational wave studies. This frequency region is dominated by the global morphology of the explosion and the anisotropic emission of neutrinos from the event. This paper serves as a brief review of both theory and detection (prospects) for gravitational waves in the low-frequency region. We discuss the generation of the linear gravitational wave memory sourced from neutrino emission and show results from an example 15 $M_{\odot}$ Solar metallicity progenitor. We also discuss the detection of the linear gravitational wave memory in current detectors, utilizing a combination of a linear predictive filter and matched templating. Finally we will discuss detection prospects in future detectors such as Cosmic Explorer, Einstein Telescope, the Laser Interferometer Space Antenna, and the Lunar Gravitational-wave Antenna.

We report a measurement of the muon neutrino charged-current (CC) interaction cross section on tungsten using the electronic detectors of the SND@LHC experiment at the CERN Large Hadron Collider. The analysis uses proton--proton collision data at a centre-of-mass energy of $\sqrt{s} = 13.6$ TeV, corresponding to an integrated luminosity of $68.6 ~\text{fb}^{-1}$ collected during LHC Run 3 in 2022 and 2023. A total of 31 $ν_μ$ CC candidates are selected against an expected background of $5.0 \pm 1.1$ events, consistent with a signal expectation of $24^{+10}_{-9}$ events. The signal strength is measured to be $\hatμ = 1.09^{+0.72}_{-0.37}$, and the combined muon neutrino and anti-neutrino CC cross section on tungsten is determined to be $σ(ν_μ+ \barν_μ) = (37^{+24}_{-12})\times 10^{-35}~\text{cm}^2$ at a median energy of $228$ GeV. In addition, a calorimetric measurement of the hadronic energies of the neutrino candidate events is performed, making use of calibration data from dedicated test-beam campaigns.

This chapter presents a framework for designing therapeutic sonic interaction technologies, with a focus on movement sonification: the real-time conversion of bodily motion into sound that serves as feedback during motor rehabilitation. Despite growing evidence for their effectiveness, technologies implementing movement sonification are yet to be systematically adopted as part of clinical practice, potentially due to a lack of standardized development methodologies as well as inadequate integration of clinical stakeholder perspectives into interaction design. The framework addresses these barriers through three interconnected contributions. The first is a conceptual reframing of the design task as the calibration of sonic variability to the perceptual affordances of the listener and the demands of the clinical context. The second is a practical design platform inspired by professional audio mixing workflows, which imposes a structured and learnable signal-flow architecture on the interaction design process and enables rapid iterative exploration. The third is a user-centered development methodology adapted from healthcare intervention science, which grounds design decisions in engagement with the clinicians and patients who will use the resulting systems. The HearWalk biofeedback system for hemiparetic gait rehabilitation illustrates the framework, and the chapter concludes by examining where large language models and AI tools can meaningfully assist each stage of this design process, as well as where human clinical and perceptual expertise remains irreplaceable.

Jackson and Tanigawa conjectured that the rigidity matroid $\mathcal{R}^d_n$ and the hyperconnectivity matroid $\mathcal{H}^d_n$ are the unique maximal matroids in the posets of $\{K_{d+2}, K_{d+2,d+2}\}$-matroids and $\{K_{d+2},K_{d+1,d+1}\}$-matroids, respectively. We disprove these conjectures by showing the existence of maximal matroids that are distinct from the proposed candidates.

We numerically investigate percolation of independent frictionless glued-sphere rod-like particles under gravity through a disordered static bed of larger spheres. We identify two distinct regimes: a \emph{trapping} regime, where rods stop after percolating a limited distance in the bed and a \emph{passing} regime, where rods percolate continuously with constant mean velocity. The transition between these regimes is governed by the length of the rod and the geometrical trapping threshold for spherical particles based on the rod diameter and the minimum pore throat diameter defined by three touching large spheres. The percolation velocity for all rod geometries, including the single sphere limit, collapses onto a single curve when scaled with the gravitational acceleration and the bed sphere diameter. The results also demonstrate that short rods percolate nearly twice as fast as long rods due to the geometric constraints associated with the disordered pore structure of the static bed. Consequently, long rods are more susceptible to trapping via specific contact configurations with the bed spheres, which differ from those for short rods. These results reveal how shape anisotropy introduces dynamical constraints and thresholds in granular percolation, with implications for predicting segregation in mixtures of non-spherical particles.

We prove an analogue of Hilbert's basis theorem for Poisson Ore extensions and Poisson Laurent Ore extensions. We also obtain corresponding results for iterated Poisson Ore extensions and iterated Poisson Laurent Ore extensions associated to commuting Poisson-pairs. Finally, we give examples of Poisson Ore extensions that are Poisson-Noetherian without being Noetherian as ordinary algebras.

We introduce parRSB - a parallel, highly scalable graph partitioner for spectral element meshes that produce high quality partitions. parRSB is based on Recursive Spectral Bisection (RSB) algorithm implemented on the dual graph of the input mesh. RSB uses the Fiedler vector, which is the eigenvector associated with the smallest non-zero eigenvalue of the Laplacian matrix of the dual graph for making partitioning decisions and tries to minimize the communication volume between the partitions. We implemented two numerical methods: Lanczos, and Inverse iteration using Conjugate Gradient method to compute the Fiedler vector. We present partitioning results using parRSB on Summit and Frontier supercomputers at Oak Ridge National Laboratory to illustrate the quality of the partitions produced by parRSB and the scalability of our implementation. We also present results for some of the optimizations we did to speed up the partitioning process.

Pairwise compatibility graphs (PCGs) represent graph adjacency by an interval of leaf-to-leaf distances in a weighted tree. We study grid graphs under the PCG model and two natural extensions: multi-interval PCGs and OR-PCGs. First, we prove that every $d$-dimensional grid graph is a $(d-1)$-interval-PCG. The construction decomposes the grid into hyperplanes of constant coordinate sum and uses a large-base encoding so that distances between consecutive hyperplanes identify the coordinate direction of an edge. A pair of nearby code values is then merged into one interval, reducing the number of intervals from $d$ to $d-1$. Second, we prove that every $d$-dimensional grid is a $\lceil d/2\rceil$-OR-PCG by grouping coordinate directions into pairs; each paired-direction graph is a disjoint union of two-dimensional grid graphs and is therefore a PCG. Finally, an exact tree-metric satisfiability computation shows that $P_3\square P_3\square P_3$ is not a PCG. Consequently, the minimum number of intervals sufficient for all three-dimensional grid graphs is exactly two, resolving a previously posed open problem. The same obstruction shows that the OR-PCG bound is tight in dimension three and implies that every grid with at least three factors of order at least three is not a PCG.

The Jordan-Moore-Gibson-Thompson (JMGT) equation models nonlinear acoustic wave propagation in thermally relaxing media and in the vanishing relaxation limit approaches the damped Westervelt equation. We investigate discontinuous Galerkin spatial discretizations of the JMGT equation on simplicial meshes and analyze their behavior uniformly with respect to the relaxation parameter. Under practically relevant mixed Neumann and absorbing boundary conditions, we derive a priori error estimates independent of the relaxation parameter. These estimates enable a rigorous singular limit analysis, yielding convergence of the semi-discrete JMGT approximations to the corresponding Westervelt pressure profile at a linear rate. This also sheds light on the expected behavior of exact solutions in the vanishing relaxation limit. For the fully discrete problem, we propose a Newmark-type method based on a reformulation as a coupled second-/first-order system. Numerical experiments support the theoretical findings and demonstrate the robustness of the approach in the small-parameter regime.

We discuss three families of twisted graded Calabi--Yau algebras of dimension three that arise through the process of normal extensions. In addition to the twisted Calabi--Yau condition, we prove that these algebras are noetherian piecewise domains under a non-degeneracy condition. We show that these algebras can also be constructed as certain iterated skew polynomial rings. Finally, we discuss how these algebras shed light on possible types of twisted graded Calabi--Yau algebras of dimension four.

The logical principles of focalisation and polarisation can be used to design well-behaved term syntaxes for sequent calculus, which play a role as meta-languages for describing effectful computation. On the semantics side, this corresponds to an axiomatic and polarised notion of model of computation stated in terms of adjunctions over non-associative categories. In this paper, we study the special and delicate cases of resource and effect modalities in a general intuitionistic and linear setting: an exponential comonad $!$ (refining $\square$) and a strong monad $\lozenge$. The starting point of our contribution is noticing that the completeness for a polarised syntax for $!$ and $\lozenge$ with respect to (co)monads in linear call-by-push-value models can be achieved if we move to relative (co)monads: more precisely, comonads relative to $\downarrow$ (the positive shift functor) for $!$ and monads relative to $\uparrow$ (the negative shift functor) for $\lozenge$. These specialisations of the concept of relative (co)monad to call-by-push-value adjunctions recently appeared. Yet the syntax we present arose from proof-theoretic consideration, without the link with relative (co)monads being noticed at the time. Our first remark is thus that (co)monads relative to a call-by-push-value adjunction have been motivated previously from a proof-theoretic perspective in the context of focalisation, which also provides a meta-language for these concepts in an effectful setting. We carry out the study of these modalities from the axiomatic, non-associative point of view. We recall the notion of adjunction over non-associative categories, and establish correspondence results between this notion of adjunction and that of relative adjunction. This correspondence is then extended to linear-non-linear and strong versions of adjunctions as needed to model $!$ and $\lozenge$.

We study correlation functions in generic non-equilibrium mixtures, including multi-temperature systems and non-reciprocal field theories. The corresponding linear theory is short-ranged, and nonlinearities are irrelevant in the renormalization-group sense. Nonetheless, we find that these nonlinearities generate long-ranged three-point correlations in the isotropic disordered phase. Our analytical predictions, which are based on a phenomenological theory, are confirmed by numerical simulations of Brownian colloids in contact with thermal baths at different temperatures. Dangerously irrelevant nonlinearities in non-equilibrium mixtures thus offer a new route to long-range correlations, supporting the hypothesis that such correlations are not the exception but the rule out of equilibrium.

Continuous Attractor Neural Networks (CANNs) traditionally rely on pre-wired recurrent connectivity to model spatial representations, path integration, and anticipatory dynamics. However, the biological mechanisms through which this structured connectivity emerges via learning remain relatively unexplored. This work presents a theoretical framework revealing how continuous attractor connectivity and its computational properties self-organize through Hebbian plasticity, firing-rate adaptation, and global inhibition. We show that translationally invariant inputs naturally drive the emergence of stable, Gaussian-profiled feedforward weights. Crucially, anticipatory dynamics arise spontaneously within these feedforward architectures, shifting the activity bump forward without requiring recurrent excitatory collaterals. This predictive shift can be linearly amplified across multilayer networks, consistent with anticipatory activity observed in the superficial layers of the entorhinal cortex. Furthermore, introducing recurrent interactions allows the network to learn connections capable of self-sustaining a moving bump of activity. Finally, by modulating the network with an external, time-varying baseline current that encodes speed, the system adjusts its intrinsic velocity to function as a precise unidirectional path integrator. Ultimately, this study suggests that prospective coding and path integration are not manually engineered features, but rather naturally co-emergent properties of a single self-organizing competitive network.

Sub-Neptunes' molten interiors are expected to accommodate large quantities of volatiles, potentially altering their radius evolution. Previous studies have examined this effect in isolation with simplified evolution modeling, often assuming idealized interior and atmospheric conditions. To address this limitation, we introduce SEAMIST, a unified evolution model for sub-Neptunes and super-Earths that self-consistently combines, for the first time, interior structure, cooling, rock/iron solidification, boil-off, photoevaporation, H/He dissolution, and atmospheric composition. SEAMIST considers both a partially soluble case, in which hydrogen partitions into the magma ocean with a fraction set by mantle-envelope boundary conditions, and a fully miscible case, in which hydrogen may fully dissolve into the magma ocean at high temperatures. We identify a novel catastrophic boil-off mechanism, triggered by a positive feedback between hydrogen outgassing and mass loss that can operate billions of years after disk dispersal. In partially soluble models, the impact of H/He dissolution on radius evolution is modest. This contrasts with previous expectations, as we find that increasing hydrogen abundance from outgassing enhances mass-loss efficiency, counterbalancing volatile replenishment from the rock/iron interior. Fully miscible hydrogen, in contrast, significantly enhances envelope survival especially around low-mass stars. Overall, at intermediate to low masses, mass-radius curves from partially soluble models match observed distributions. The fully miscible case predicts a pronounced radius peak and excess planets around low stellar masses that appear inconsistent with current observations, although it reproduces the observed radius ``cliff" near 4$R_\oplus$ at higher masses. Our results suggest that high metallicity may explain the cliff, although alternatives cannot be entirely ruled out.

An ensemble study using the CESM climate model is used to investigate the response of the atmosphere to changes in sea surface temperatures along the path of the North Equatorial Counter Current. The results support those of a previous study which concentrated on a single run, confirming the sensitivity of deep convection in the central Pacific to the temperature of the counter current, and its impact on the Hadley Circulation, the Southern Oscillation and the equatorial winds in the Pacific. A comparison with the ECMWF ERA5 data, finds that the atmospheric reanalysis fields show similar correlation with the temperature of the counter current.

We perform a theoretical study of the $B^+ \to D^+ D^- K^+$, $B^0 \to D^+ D^- K^0$ and $Λ_b \to D^+ D^- Λ$ reactions by looking at the production mechanisms, with special emphasis in the final state interaction of the charmed mesons, which gives rise to the $X_{c0}(3930)$, coupling strongly to $D_s\bar{D}_s$, and another state that we call $X(3700)$, coupling strongly to $D \bar D$ that qualifies as a $D \bar D$ bound state. The combined study of all these reactions shows that the final state interaction responsible for the production of these resonances is more important in the $B^+ \to D^+ D^- K^+$ reaction than in the $Λ_b \to D^+ D^- Λ$ one. We have taken this into account and shown that normalizing the $D^+ D^-$ mass distributions to the same value at the peak of the $ψ(3770)$ production, the two mass distributions are quite different in a range of 10 MeV above the $D^+ D^-$ threshold, with a value about 13 times bigger for the $B^+ \to D^+ D^- K^+$ reaction than for the $Λ_b \to D^+ D^- Λ$ one. We make a call to measure these magnitudes in the coming LHCb upgrades, which would bring great support to the existence of the bound $D^+ D^-$ state.