We present a semi-analytical theoretical kp-study of the energy structure and optical transitions in spherical core-shell InP/ZnSe nanocrystals. We use the eight-band Kane model and the six-band Luttinger Hamiltonian in the spherical approximation to calculate the electron and hole energy spectra, respectively. The influence of the Coulomb interaction is considered perturbatively. The one- and two-photon absorption spectra are calculated as functions of the band offsets between the InP core and ZnSe shell. Exciton states responsible for the main features in the two-photon absorption spectra of InP/ZnSe nanocrystals are identified and the spectral dependence of the linear-circular dichroism signal is predicted. We show that in the presence of inhomogeneous broadening, the transition to the ground two-photon-active exciton state can be hidden behind intense transitions to higher-lying states. A comparison of the calculated one- and two-photon absorption spectra with the available experimental data shows that, depending on the lattice strain in the InP core, the range of possible valence band offsets is 0.85-1 eV. The determined range exceeds the natural valence band offset of 0.57 eV and indicates the presence of electric dipoles formed by the preferential Zn-P bonds at the InP/ZnSe heterointerface.

Understanding which subclasses of quantum circuits are efficiently classically simulable is fundamental to delineating the boundary between classical and quantum computation. In this context, it is well known that certain tasks based on permutation-equivariant unitaries-i.e., $n$-qubit circuits whose action commutes with the qubit-permuting representation of the symmetric group $S_n$-can be simulated in polynomial time. However, existing approaches scale as $O(n^7)$, and can rapidly become prohibitively expensive. In this work, we introduce a practical algorithm for simulating $S_n$-equivariant circuits under the assumption that the gate generators are at most $k$-local, with $k\in O(1)$. The resulting method runs in $O(n^{ω+1})$ time for constant depth, where $ω$ is the matrix multiplication exponent, significantly lowering the polynomial degree compared to existing techniques. Finally, we numerically validate this scaling by simulating the dynamical evolution of the Lipkin-Meshkov-Glick model, and show that for $n=512$ spins, a standard laptop can compute the concurrence of the evolved state in under two minutes.

We investigate the algebraic structure of the two-time physics introduced some time ago by I. Bars and his co-authors, clarifying its relations with quadratic and cubic Jordan algebras, as well as with reduced Freudenthal triple systems (FTS) based on them. In particular, the `extended' phase space introduced by Bars can be endowed with the structure of a reduced FTS constructed over a semi-simple cubic Jordan algebra (named Lorentzian spin factor), characterized by a primitive, invariant symmetric tensor of rank $4$. The $Sp(2,\mathbb{R})$-gauge fixing procedure typical of two-time physics yields algebraic-differential constraints on the quartic polynomial associated to such a tensor, implying that only two (isomorphic) nilpotent orbits of the non-transitive action of the automorphism group of the Lorentzian spin factor are spanned by the conjugated variables which coordinatize the `extended' phase space. We illustrate our results in relativistic, manifestly Lorentz-covariant physical systems, as well as in non-relativistic systems (such as the non-relativistic massive particle, the hydrogen atom, and the Carroll particle with non-vanishing energy).

The material conditional has long been charged with paradox. Defined truth-functionally, it renders true any conditional whose antecedent is false or consequent true -- hence, seemingly absurd statements such as `If unicorns exist, then $2+2=4$'. This has been taken as proof that the connective cannot capture the meaning of ordinary if-then sentences, which appear to imply a causal or evidential link. I argue, by contrast, that the paradoxes arise from a confusion of what it expresses caused by cognitive biases. The material conditional properly belongs to the class of indicative, not subjunctive, conditionals -- those that register patterns of co-variation rather than counterfactual dependence. When understood as a formal device marking entailment under a background theory, it faithfully represents a mode of reasoning essential to science itself: correlation without causation. The faults ascribed to it, therefore, are not flaws in meaning or standard use, but as misapplication and misreading.

The third medium contact method has recently come into popularity as an alternative to traditional contact methods in contexts where search for contact boundaries is problematic, i.e. topology optimization. To enforce the contact constraints, it relies on a fictitious compliant material occupying the void space. In finite strain setting, this necessitates regularization techniques to improve the behavior of the third medium material. A number of existing models rely on penalization of locally computed second gradients of displacements, either through direct calculation on second-order elements or through additional degrees of freedom. Here we propose an alternative approach using element-wise deformation gradient averaging to effectively penalize spatial variations of the deformation gradient, together with a linear elastic term enforcing constant third medium stiffness. Our approach enables the use of first-order finite element formulations without any additional degrees of freedom and is therefore easy to implement. We demonstrate the robustness of the proposed method on several well-established benchmarks.

We provide an adelic relative trace formula proof to the Petersson/Bruggeman-Kuznetsov (PBK) formulas, specifically in the holomorphic case for $κ=2$ and the non-holomorphic case for $m_1m_2<0$. Given two sets of hypothesis on the non archimedean test function $f$, called the geometric and spectral assumptions, this approach allows us to obtain refined PBK formulas.

This survey reviews a collection of parallel phenomena between free boundary submanifolds in the Euclidean unit ball and closed submanifolds in the sphere, with particular emphasis on rigidity mechanisms, pinching thresholds, and canonical models. We do not regard the two theories as a unified system in one-to-one correspondence. Rather, we emphasize that in several typical settings -- including low topology, strong pinching, spectral extremality, and symmetry reduction -- the free boundary condition often forces stronger rigidity in the unit ball than in the closed setting. The exposition is organized around six interconnected themes. We first contrast the failure of the spherical Bernstein problem in high dimensions with the dimension-independent rigidity of free boundary minimal disks in the unit ball. We then discuss the parallel roles played by the Clifford torus and the critical catenoid in uniqueness, Morse index, and eigenvalue characterizations. Next, we review the transition from the Lawson--Simons stable currents method to the Bochner--Hardy techniques developed for free boundary problems, summarize pinching and gap theorems driven by the second fundamental form and its traceless part, and outline the linear comparison framework between Morse index and topology in the minimal, constant mean curvature, and weighted settings. Finally, we survey existence results obtained from group actions, isoparametric foliations, and recent equivariant eigenvalue optimization, thereby illustrating both the striking analogies and the essential boundary-driven differences between the closed spherical theory and the free boundary theory in the ball.

We present a new quantum error mitigation technique (QEM), called GUiding Extrapolations from Symmetry decayS (GUESS), which exploits Hamiltonian symmetries to improve accuracy of noisy quantum computations. This method is explicitly designed for quantum algorithms that estimate expectation values of observables and consists in learning the extrapolation coefficients from a symmetry observable of the system to then estimate the value of a target observable. Furthermore, we propose a Hamiltonian impurity technique to enforce symmetries allowing the mitigation of local observables of interest. We employ the IBM Heron r2 quantum processing unit '\texttt{ibm\_basquecountry}' to simulate the time evolution of average magnetization and nearest-neighbor correlator observables for transverse field Ising and $XZ$ Heisenberg models in 1D with open boundary conditions. We benchmark the accuracy of our method against baseline Zero Noise Extrapolation (ZNE) and tensor network simulations for systems of $100$ qubits. Remarkably, GUESS achieves a relative error around $10\%$ for circuits containing up to $8000$ CZ gates, while showcasing lower variance than ZNE on average across $20$ observables and requiring only twice the number of shots per observable compared to baseline ZNE. Furthermore, we demonstrate that GUESS enables statistical post-selection based on the outcomes of the symmetry observable, which provides critical information about the quality of the target qubits by means of its mean and variance. These results indicate that GUESS is a powerful QEM technique capable of mitigating utility-scale circuit outcomes, delivering high accuracy and reduced variance for large-scale circuits with minimal quantum overhead.

We present an algorithm that, given an index $t$, produces the $t$-th (lexicographically ordered) answer of an MSO query over a string. The algorithm requires linear-time preprocessing, and builds a data structure that answers each of these calls in logarithmic time. We then show how to extend this algorithm for a string that is compressed by a straight-line program (SLP), also with linear-time preprocessing in the (compressed encoding of the) string, and maintaining direct access in logtime of the original string. Lastly, we extend the algorithm by allowing complex edits on the SLP after the direct-access data structure has been processsed, which are translated into the data structure in logtime. We do this by adapting a document editing framework introduced by Schmid and Schweikardt (PODS 2022). This work improves on a recent result of dynamic direct access of MSO queries over strings (Bourhis et. al., ICDT 2025) by a log-factor on the access procedure, and by extending the results to SLPs.

We study topological bound states in quantum dots defined by an electric field in bilayer graphene. An external field is perpendicular to the bilayer and changes sign in a finite region that defines the quantum dot. The electric field opens a gap in the bilayer graphene, and the reversed field creates a domain wall with one-dimensional chiral gapless bands localized therein. The finite size of dots leads to the quantization of these bands and the appearance of discrete bound states localized at the dot boundary. We consider rectangular dots oriented along the armchair and zigzag directions. We go beyond a simple continuum one-valley model and use an atomistic tight-binding approach. This allows us to identify new effects related to the atomic structure of graphene, strengths of the electric field, valley mixing, and valley asymmetry.

The Migdal effect in semiconductors, prompt ionization from a primary nuclear scattering event, can be described across all kinematic regimes using an effective field theory that encodes the complex vibrational and electronic degrees of freedom of the crystal in measurable structure factors. Simultaneously, general dark matter-nucleus interactions can be systematically described using non-relativistic effective field theory operators. We combine these two effective field theory frameworks to calculate the Migdal effect in semiconductors for all ten dimension-six non-relativistic operators. From the effective Hamiltonian, we find that DM-nucleus scattering factorizes from the ionization and vibrational excitation signal as it does in the free-atom case. Using data from EDELWEISS that was taken with a germanium detector, we derive new experimental bounds on each operator and compare these limits to other direct-detection constraints in the literature. We find the accessible parameter space to be disfavored by bounds on heavy mediators contained in simple UV completions that generate the effective operators.

Thyristor rectifiers are a well-established and cost-effective solution for controlled high-power rectification, commonly used for hydrogen electrolysis and HVDC transmission. However, small-signal modeling and analysis of thyristor rectifiers remain challenging due to their line-commutated operation and nonlinear switching dynamics. This paper first revisits conventional RMS-based modeling of thyristor rectifiers and subsequently proposes a novel nonlinear state-space EMT model in the dq domain that can be linearized for small-signal analysis. The proposed model accurately captures all the relevant dynamic phenomena, including PLL dynamics, the commutation process, and switching delays. It is derived in polar coordinates, offering novel insights into the impact of the PLL and commutation angle on the thyristor rectifier dynamics. We verify the RMS and EMT models against a detailed switching model and demonstrate their applicability through small-signal stability analysis of a modified IEEE 39-bus test system that incorporates thyristor rectifier-interfaced hydrogen electrolyzers, synchronous generators, and grid-forming converters.

The presence of multiple stable states and associated nonlinear phenomena, such as hysteresis, in multistable mechanical metamaterials enables frequency-independent energy harvesting and shock absorption. This study focuses on shock absorption achieved by locking transition waves to trap energy at designed locations within a multistable metamaterial. We further demonstrate that the same system can simultaneously harvest energy from impact loading, thereby exhibiting multifunctionality. The model of the multistable metamaterial is a one-dimensional chain of bistable units whose transition wave dynamics are related to topological solitary waves governed by the $ϕ^4$ equation. This connection enables analytical estimation of critical design parameters required for energy trapping and also the amount of energy trapped. Numerical simulations and experiments show that trapping energy in transition waves leads to enhanced damping performance compared to corresponding linear metamaterials. We further propose design variations to increase the amount of energy trapped in the transition wave. Additionally, we identify energy splitting as a damping mechanism that arises when there are repeated impulses or a single high-amplitude impulse that generates multiple transition waves. The transition waves interact to produce localized, fast-dissipating breathers, leading to a damped response. Furthermore, experiments demonstrate that multistable metamaterials can simultaneously achieve improved energy harvesting and better damping performance compared to their linear counterparts. Together, these results highlight the use of transition waves for creating multifunctional multistable metamaterials.

Mental health remains a major public health concern, while access to timely psychological support is often limited. AI-based dialogue systems have emerged as promising tools to address these barriers, and recent advances in large language models (LLMs) have significantly transformed this research area. However, a systematic understanding of this technological transition is still limited. This study reviews the technological evolution of AI-driven dialogue systems for mental health, focusing on the shift from task-specific deep learning models to LLM-based approaches. We conducted a bibliometric analysis and qualitative trend review of studies published between 2020 and May 2024 using Web of Science, Scopus, and the ACM Digital Library. The qualitative analysis compared research conducted before and after the widespread adoption of LLMs. Pre-LLM research was represented by highly cited studies and work based on the ESConv dataset, while post-LLM research included highly cited dialogue systems built on LLMs. A total of 146 studies met the inclusion criteria, showing a steady growth in publications over time. Before the widespread use of LLMs, empathetic response generation mainly relied on task-specific deep learning models. Highly cited and ESConv-based studies commonly focused on multi-task learning and the integration of external knowledge. In contrast, recent LLM-based dialogue systems demonstrate improved linguistic flexibility and generalization for emotional support. However, these systems also raise concerns related to reliability and safety in mental health applications. This review highlights the technological transition of AI-based dialogue systems for mental health in the LLM era. By identifying current research trends and limitations, the findings provide guidance for developing more effective and reliable AI-driven counseling systems.

The quantum metric encodes the geometric structure of Bloch wave functions and governs a wide range of physical responses. Its Brillouin-zone integral, the quantum weight, appears in the structure factor and provides lower bounds on observables such as the optical gap and dielectric constant. In symmetry-protected topological (SPT) phases, the nontrivial band topology imposes a lower bound on the quantum weight and constraints on the observables. Here, we generalize the topological bound on quantum geometry to encompass systems beyond the SPT phases. We show that topological invariants defined via the projected spectrum lower-bound the quantum weight with a symmetry-breaking correction to the quantum metric. Our proposed bound holds even when the underlying symmetries are broken, and it would be amenable to experimental verification via the optical conductivity sum rule under external fields. We illustrate our theory by adding a nonzero spin-orbit coupling term to a spin Chern insulator model, where we show that our proposed bound applies even though the conventional topological bound does not hold.

As electronic devices approach the atomic limit, the charge dynamics of individual dopant atoms increasingly constrain performance, stability, and coherence. In scanning tunnelling microscopy (STM), donor ionization is typically interpreted as a static threshold process arising from tip-induced band bending. Here we show that the ionization of individual sulfur donors in InAs is intrinsically dynamic and governed by the local electric field. Using MHz-frequency STM noise spectroscopy with atomic-scale spatial mapping, we resolve pronounced random telegraph noise that is invisible in time-averaged tunnelling spectra. A bias-dependent model quantitatively links the noise spectra to microscopic ionization and neutralization processes of the donor states, enabling direct extraction of nanosecond charge-state lifetimes. The switching rate is strongly bias dependent, demonstrating that the electric field continuously drives charge-state transitions. Unexpectedly, we show that the degenerately doped bulk leads to a sharp bias-dependent onset of donor ionization as the donor level crosses the Fermi level, giving rise to a characteristic shoulder in the noise power spectrum that is captured by our model. These results establish donor ionization as a non-equilibrium dynamical process with nontrivial contribution by the bulk electrons, and identify impurity switching as a universal nanoscale charge-noise mechanism relevant to quantum devices.

Hole spin qubits hosted in Germanium quantum dots are promising candidates for scalable quantum computing. The strong spin-orbit interaction can enable fast and all-electrical quantum control. Furthermore, the platform can implement universal quantum control using only baseband signals, which may mitigate the impact of crosstalk and microwave-induced heating. At the same time, spin-orbit interaction gives rise to an anisotropic exchange interaction, whose potential for implementing two-qubit gates has remained largely unexplored. However, the current performance of operating a hole-based quantum computer is mostly limited by dephasing due to low-frequency charge noise. In this work, we propose a novel two-qubit gate protocol for Germanium hole spin qubits operated in the gapless regime. This gate protocol exploits the anisotropic exchange interaction between neighboring spins and utilizes a composite pulse scheme implemented solely through electrical baseband signals. Using this approach, we predict high-fidelity two-qubit controlled-Z operations that can suppress exchange-energy fluctuations, offering a pathway toward fault-tolerant semiconductor quantum processors.

We study an embedded Trefftz discontinuous Galerkin method for the Helmholtz equation. The method starts from a polynomial DG space and enforces the Trefftz property through local constraints, avoiding an explicit construction of Trefftz basis functions. For the global coupling we use a simple symmetric interior penalty DG bilinear form. Since the resulting formulation is not coercive, stability is proved by a $T$-coercivity argument combined with a Schatz-type duality technique. This yields wavenumber-explicit stability, quasi-optimality, and convergence estimates in standard DG norms under an explicit mesh resolution condition.

Extracting cosmological information from Stage IV weak lensing surveys requires non-linear modelling of the matter power spectrum that is accurate across a broad range of scales and redshifts and robust to baryonic feedback. We forecast the application of the two-loop effective field theory of large-scale structure (EFTofLSS) to Roman Space Telescope, carefully considering parameterization, scale cuts, and priors. We develop neural network emulators for the two-loop integrals, allowing rapid evaluation of the likelihood. Weak lensing demands a continuous-in-redshift description of the EFT, potentially introducing tens of nuisance parameters. We address this by calibrating the counterterm redshift evolution against the Euclid Emulator 2 and accounting for the residual freedom in redshift with spline functions. A principal component analysis of the free parameters reduces the dimensionality to a few degrees of freedom that the data can constrain. Next, we calibrate the priors on those degrees of freedom by using a suite of hydrodynamical simulations. We forecast the $S_8$ constraints as a function of scale cuts, showing that the two-loop EFT with Roman cosmic shear provides unbiased $S_8=σ_8\sqrt{Ω_{\rm m}/0.3}$ constraints with relative errors of about $0.9\%$ and $1.4\%$ when allowing for $5\%$ and $1\%$ contamination from ultraviolet modes, respectively. The two-loop EFT improves the scale reach beyond the one-loop EFT and non-linear dark matter-only models when baryonic effects are included. This framework provides a robust path for extracting small-scale information from future cosmic shear data.

Dissipative phase transitions (DPTs) are traditionally characterized through the spectral properties of a time-independent Liouvillian superoperator. However, this definition cannot be applied to time-periodic (Floquet) systems that cannot be exactly recast into equivalent time-independent problems. In this article, we develop a general framework to characterize DPTs in time-periodic open quantum systems by analyzing the spectrum of the Floquet propagator. We first study driven-dissipative Kerr resonators, known to display a DPT, showing that counter-rotating terms in the drive induce a shift in the critical point and a significant change in the time scales associated with the transition. We then investigate DPTs in the driven quantum Rabi model and in its time-independent approximated counterpart, the driven Jaynes-Cummings model. We find that the Rabi model exhibits distinct critical features as the ultrastrong coupling regime is approached. Moreover, our Floquet analysis unveils the disappearance of the DPT in the deep strong coupling regime of the quantum Rabi model due to light-matter decoupling. Our rigorous approach sets the stage for the study of dissipative criticality in a broad class of time-dependent open quantum systems.

We construct a deformed algebraic quantum field theory on bifurcate Killing horizons in stationary axisymmetric spacetimes. The deformation is generated by the commuting actions of affine dilations along the null generators of the horizon and rotations about the axis of symmetry, analogously to the Moyal-Rieffel deformation. Physically, this effectively implements a noncommutative geometric structure of the horizon. Moreover, we compute the relative entropy between coherent states in the deformed horizon theory, which remains strictly positive and exhibits a novel second-order correction in the deformation parameter, which becomes particularly significant for black holes whose horizon area is sufficiently small for Planck-scale effects to become non-negligible.

We prove that the maximal and minimal displacement of branching random walks with mean offspring number $ρ>1$ on free products of finite groups grows linearly almost surely. More precisely, we establish that the linear speed for the maximal (respectively minimal) displacement is given by the largest (respectively smallest) intersection point of the large deviation rate function of the underlying random walk with the horizontal line at height $\logρ$. The proof is based on constructing an associated multitype branching process which consists of particles that travel fast enough, and distinguishing the types via the suffix of the particles locations.

For an exact category we provide two constructions of an ambient category in which the initial category is resolving: In the derived category and in the Gabriel--Quillen embedding. For the first construction we describe a pre-aisle and its right orthogonal using different acyclicty conditions. We provide necessary and sufficient conditions when this pair is a t-structure.

Electrohydrodynamic flows of weak electrolytes at the nanoscale are significantly influenced by the molecular structure of water-like polar solvents within the electric double layer (EDL). Moreover, unlike in microfluidics, at these length scales the time scale of evolution of EDL often becomes comparable to the consequent fluidic phenomena of interest. While continuum descriptions to model such phenomena typically assume a constant dielectric and viscous solvent background, this study incorporates dipolar solvent physics, specifically both dielectric saturation and the viscoelectric effect together, into a Poisson-Nernst-Planck-Stokes (PNP-S) framework, using the Langevin-Bikerman solvent permittivity distribution and empirical viscoelectric coefficients, respectively. Numerical simulations in a one-dimensional geometry reveal substantial modifications to the electrohydrodynamic body force density and transient electroosmotic mobility during EDL evolution. The magnitude and temporal evolution of these corrections are characterized across parametric regimes, revealing systematic departures from standard constant-permittivity and constant-viscosity models, with electroosmotic mobility reductions of up to 50% governed by a characteristic dimensionless parameter. The results provide a solvent-consistent continuum framework for transient nanoscale electroosmotic flows and quantify the impact of molecular solvent structure on electrohydrodynamic transport relevant to modern nanofluidic applications.

Quantum optimal control is often judged by nominal fidelity alone, even though realistic pulse-design studies must also account for bandwidth, amplitude, and smoothness constraints. I study this structured-control regime with an inexact Proximal-ADMM framework that combines gate-infidelity minimization with $L_1$ sparsity, total-variation regularization, explicit band-limit projection, and box constraints in a single loop. The method is benchmarked against GRAPE, standard Krotov, and L-BFGS-B on a single-qubit $X$ gate, a leakage-prone qutrit task, and a two-qubit entangling gate. Across ten random seeds, Pareto scans, ablations, filtered-baseline fairness checks, significance analysis with false-discovery-rate correction, and robustness tests, the method is not a universal winner in either nominal fidelity or wall-clock cost. Its value is instead to expose and stabilize a low-complexity frontier of the fidelity-complexity landscape. After retuning the PADMM budgets and warm-start lengths, the qutrit and two-qubit structured fidelities rise to 0.6672 +- 0.0001 and 0.6342 +- 0.0003, respectively, while preserving markedly lower complexity than unconstrained quasi-Newton solutions. These values remain well below deployment-grade gate thresholds, so the contribution should still be read as a numerical framework for constrained pulse synthesis rather than as a finished route to immediately deployable high-fidelity gates. Training-time robust optimization yields only task-dependent gains, with the clearest effect appearing in qutrit drift robustness and amounting to a small absolute improvement. The results therefore position PADMM as a constraint-native framework for low-complexity frontier exploration, not as a replacement for unconstrained high-fidelity solvers.

Sandqvist's base-extension semantics for intuitionistic propositional logic defines a support relation parametrised by atomic bases, with validity identified as support in every base. Sandqvist's completeness theorem answers the global question: which formulae are valid? This paper addresses the local question: given a fixed base, what does support in that base correspond to? We show that support in a fixed base coincides with proof-search in a second-order hereditary Harrop logic program, via an encoding of formulae as logic-programming goals. This encoding proceeds by reading the semantic clauses in continuation-passing style, revealing that the universal quantifiers over base extensions and atoms appearing in those clauses are not domain-ranging quantifiers over a completed totality, but eigenvariables governed by a standard freshness discipline. Base-extension semantics thereby admits a fully constructive and computationally transparent interpretation: support is proof-search. The result complements Sandqvist's global theorem with a local correspondence, vindicates the anti-realist foundations of the framework on its own terms, and opens the way for implementing the semantics in modelling tasks.

Protoplanetary disks are the birthplaces of planetary systems, and deviations from Keplerian rotation imprinted in disk gas kinematics serve as key tracers of physical processes and the presence of protoplanets within disks. Using the the CO (J=3-2) data from the exoALMA Large Program encompassing 15 disks, we constructed two-dimensional (2D) maps of centroid velocity, line width, and peak intensity, and extracted non-Keplerian deviations by subtracting smooth Keplerian models. This paper provides the first systematic and uniform overview of 2D gas substructures across the entire exoALMA sample. We find that all targets exhibit large-scale deviations from smooth Keplerian disks, displaying a variety of morphologies including spiral-like structures, arc- or ring-like features, and patterns indicative of variations in the emitting surface height. Non-axisymmetric spiral-arm features are detected or suggested in five disks (CQ Tau, MWC 758, HD 135344B, HD 34282, and SY Cha), and are preferentially found in Herbig Ae/Fe systems. In contrast, some other sources (J1852, PDS 66, and V4046 Sgr), despite exhibiting noticeable deviations, appear to be dynamically quieter. This 2D atlas suggests that kinematic substructures are ubiquitous in large ($\gtrsim$ 100 au) protoplanetary disks with ages of a few million years, based on the observations obtained with sufficient sensitivity at moderate-to-high spatial resolution of $\sim$20 au and high velocity resolution of $\sim$0.1 km s$^{-1}$.

We study the relation between the Jones index and the Rényi entropies of two disjoint intervals on the line and of the ground state for a generic value of the Rényi index in the two conformal field theory models given by the Ising model and a free Majorana fermion, where Haag duality is satisfied. The analytic expressions of the crossing asymmetry for all the submodels displaying a violation of the Haag duality that are closed under the fusion rules are obtained. In the limiting regime where the two intervals become adjacent, the leading term of the expansion of the crossing asymmetry provides the Jones global index, for any finite value of the Rényi index.

A model for studying the ultrametricity of the energy landscape in a disordered heteropolymer is presented. It is treated as a simplified model of a protein molecule in which amino acid residues are modeled as point masses. Pairwise interactions include universal repulsion, the Lennard-Jones potential, the Coulomb potential with screening, and the elastic potential for bonds between adjacent residues. An analogy with spin glass models is used, allowing the application of replica theory methods. Unlike the standard approach to disordered systems, averaging over disorder is not performed. The overlap between replicas is defined as the Pearson correlation coefficient between the vectors of average pairwise energies, which corresponds to a comparison of thermodynamic averages in the spirit of spin glass theory. The results of a computational experiment conducted using the developed algorithm on a graphics processing unit (GPU) are presented. The simulations were performed using a 128-residue-long sequence, with 50 independent disorder realizations and 50 replicas for each sequence at a temperature of T = 1.0. It was found that for 90.0% of the sequences, the distance matrix between replicas contains more than half of the ultrametric triangles, and nontrivial ultrametricity predominates in 97.8% of them, indicating a hierarchical organization of the energy landscape. A repeated computational experiment for selected sequences confirms the reliability of the observations: 95.5% of them again demonstrated ultrametricity, of which 97.7% showed a predominance of the nontrivial type of ultrametricity. The obtained results confirm Frauenfelder's hypothesis of protein ultrametricity and pave the way for a systematic study of ultrametric properties in more realistic protein models.

The time since a galaxy first became a satellite is central to understanding how environment drives galaxy evolution, yet it cannot be measured directly. Using the TNG300 and TNG-Cluster simulations, we track satellites from $z=1$ to $z=0$ and derive a simple, redshift-dependent prescription for ${T}_{\rm{inf}}$ based on position in projected phase space and stellar mass, via symbolic regression. The resulting calibration provides continuous, observation-ready estimates of infall time across projected phase space. In projected phase space, ${T}_{\rm{inf}}$ is often well described by two components, and we provide analytic expressions for the corresponding characteristic timescales. This framework can be applied directly to spectroscopic samples to infer environmental histories in galaxy groups and clusters.