Couples therapy requires managing complex, evolving emotional dynamics between partners, but traditional training methods for therapists, like role-play, lack realism, consistency, and control. We present a multi-modal simulation that models therapy as a controlled, multi-agent dynamical system with structured interaction stages. Therapists practice with a pair of client-agents who go through six evolving stages that respond to therapist actions. This simulation enables practice with demand-withdraw conflict patterns in a closed-loop environment. The simulation uses a sense-plan-act architecture: it detects the therapist's input, updates agents' interaction states based on psychotherapy theory and transcript analysis, and generates realistic verbal and emotional responses. In an experiment with 21 licensed U.S. therapists, participants more accurately identified state transitions and rated the system as more realistic and responsive than a prompt-based baseline, demonstrating the value of stateful, interpretable simulation for therapist training.

The tropical row span and column span of a real matrix are, from the polyhedral point of view, different objects living in different ambient spaces. These polytopes are known to be combinatorially isomorphic as polyhedral complexes; we prove that they are isometric under a Hilbert projective metric. We show that this isometry, along with a considerable amount of additional metric and polyhedral structure, is a direct consequence of a single categorical construction: the Isbell nucleus of the matrix, viewed as a profunctor enriched over the extended reals. The projective nucleus carries two canonical structures inherited from enrichment. The first is a Hilbert projective metric, with respect to which the Isbell conjugate maps are mutually inverse isometries -- this is the Isometry Theorem. The second is a polyhedral cell decomposition cut out by the Isbell inequalities, recovering the type decomposition of tropical convexity. These two structures are linked pointwise by the \emph{gap matrix}. The Events Theorem identifies each positive entry of the gap matrix with the exact projective distance to the locus where the corresponding inequality becomes tight: algebraic slack in the Isbell inequalities equals geometric distance to the cell walls. Thresholding the gap matrix at successive radii produces a constructible sheaf of formal concept lattice towers, extracting discrete algebraic structure from the continuous geometry at each point. In the square case there is generically a unique full-dimensional cell. The Centering Theorem identifies its Chebyshev center -- the point maximally insulated from all cell walls -- and shows that the optimal radius equals the minimum directed cycle mean of an associated digraph, connecting the projective geometry of the nucleus to the classical theory of optimal assignments.

Advances in instrumentation and computation have enabled increasingly sophisticated tomographic reconstruction methods. However, existing evaluation practices -- often based on simple phantoms and global image metrics -- are limited in their ability to differentiate among modern high-fidelity reconstructions. A standardized, quantitative framework capable of revealing subtle yet meaningful differences is therefore required. We introduce such a framework, built upon two core components. The first is a set of four standardized reference images -- Source, Detector, Ideal, and Realistic -- each derived from physical modeling and representing a distinct stage in the imaging and reconstruction chain. The second is a suite of diagnostic and quantitative tools that remain sensitive in regimes where conventional metrics (e.g., SSIM, PSNR, NMSE, CC) tend to saturate. These include pixel-wise $χ^2$ and difference maps, their quantitative characterization, spectral decomposition of intensity distributions, and Region-of-Interest (RoI)-based metrics. Application of this framework to MLEM and RISE-1 reconstructions using software phantoms demonstrates its ability to expose discrepancies that might elude detection by conventional global metrics. While developed in the context of SPECT, the methodology generalizes to other tomographic modalities, providing a reproducible, interpretable, and physically grounded basis for evaluating reconstruction fidelity in the high-performance regime.

Losses from two-level systems (TLS) associated with amorphous oxides remain one of the primary limitations to the performance of superconducting qubits and microwave cavities. Niobium resonators are widely used in quantum science experiments, yet niobium's natural oxide layer contains various types of oxides whose relative contributions to TLS loss have not been clearly distinguished. Here, we use a superconducting 3D microwave cavity to measure commercial 99.9\% trace metal pure, microcrystalline oxide powders \ch{Nb2O5} and \ch{NbO2} in bulk amounts. Using this approach, we directly compare the loss characteristics of \ch{Nb2O5} and \ch{NbO2}. Our measurements show that the nominal \ch{Nb2O5} bulk oxide powder samples exhibit losses which have the power and temperature behavior expected for TLS. Moreover, the measurements agree with existing theoretical models. Analogous measurements performed on \ch{NbO2} bulk powder samples do not show any detectable TLS loss signatures. Based on our results we propose that the TLS losses might be reduced if a high quality microcrystalline \ch{NbO2} oxide dominates the \ch{Nb2O5} oxide in practical Nb cavities. These results establish a materials based strategy for isolating oxide specific TLS losses and provide a reference measurement for niobium oxide phases relevant to superconducting quantum devices.

The purpose of this thesis is to introduce two new kinds of hyperplane arrangements, inspired by the graphic arrangements and $q$-deformations of graphic arrangements. In this thesis, the author extends the definition of $q$-deformation to simplicial complexes, with the conjecture by Nian, Tsujie, Uchiumi and Yoshinaga. The author also investigates a special case called graphic monomial arrangement, including the characteristic polynomials and freeness with a further extension to fields with primitive roots.

In this work, we aim to achieve a minimal extension of the quantum-number projected generator coordinate method (PGCM) to describe Gamow-Teller (GT) transition strengths in even-even nuclei and to compute the NME of $2νββ$ decay. Within the PGCM framework, the wave functions of odd-odd nuclei are constructed as superpositions of neutron and proton quasiparticle configurations built on quasiparticle vacua constrained to have, on average, odd neutron and odd proton particle numbers. The angular momentum and particle numbers associated with the underlying mean-field states are restored through projection techniques. Using a shell-model Hamiltonian defined in the $fp$ shell, we assess the validity of this approach by benchmarking GT transitions in calcium and titanium isotopes, as well as the $2νββ$ decay of $^{48}$Ca to $^{48}$Ti, against exact solutions. For comparison, we also confront our results with those obtained from configuration-interaction calculations employing different particle-hole truncation schemes, both with and without in-medium similarity renormalization group (IMSRG) evolution.

We consider random linear unbounded operators on a Banach space $\mathcal{X}$. For example, such random operators may be random quantum channels. The Law of Large Numbers is known when $\mathcal{X}$ is a Hilbert space, in the form of the usual Law of Large Numbers for random operators, and in some other particular cases. Instead of the sum of i.i.d. variables, there may be considered the composition of random semigroups $e^{A_i t/n}$. We obtain the Strong Law of Large Numbers in Strong Operator Topology for random semigroups of unbounded linear operators on a uniformly smooth Banach space.

In this paper we study restricted overpartitions and concave compositions. In several cases the resulting generating functions involve simultaneously modular forms, mock theta functions, mock Maass theta functions, and false theta functions, illustrating the appearance of mixed modular structures in restricted partition problems. Moreover, we obtain their asymptotic main terms. We also study related rank statistics.

Semileptonic $τ$ decays mainly proceed via interactions between charged lepton and quark currents. The hadronization of the quark current is intrinsically nonperturbative and generally cannot be addressed analytically. In these proceedings, we propose using symmetry arguments alone to construct clean angular observables, which, within the Standard Model and in the absence of long-distance electromagnetic corrections, remain form-factor independent. These predictions can be experimentally tested, and any observed deviation could signal either effects of physics beyond the Standard Model or provide a clean benchmark for long-distance electromagnetic corrections. We also perform a first estimate of the expected impact of new physics in an EFT framework.

Full-disk observations from missions such as the SDO and SOHO have enabled comprehensive studies of solar oscillations and dynamics. Interpreting helioseismic and photospheric data is complicated by systematic center-to-limb variations. To explore the physical origin of these variations, we perform local 3D radiative hydrodynamic simulations that include effects of solar rotation to generate 24-hour synthetic time series of continuum intensity and Doppler velocity for nine viewing angles spanning from $-75^{\circ}$ to $75^{\circ}$. The simulations reveal a systematic decrease in 1D oscillation power toward the limbs and a pronounced East-West asymmetry that increases with frequency, primarily due to rotation-induced flows. Analysis of $\ell-ν$ diagrams shows a decrease in the amplitude and width of the surface gravity ($f$) and resonant pressure ($p$) modes with increasing angular distance from the disk center. The amplitudes of the corresponding pseudo-modes with frequencies above the acoustic cut-off frequency increase in the intensity power spectra and are suppressed in the velocity spectra. The ring-diagram analysis of the simulation data further demonstrates anisotropic broadening of the modes, and the impact of the foreshortening effect on the energy distribution, and distinct differences in background noise and pseudo-mode structure between the intensity and velocity data. These results indicate that the center-to-limb effects arise from both geometric projection and physical factors such as line-formation height and potential effects of the radial differential rotation. The findings provide a framework for correcting helioseismic observations and demonstrate that realistic simulations are a powerful tool for disentangling geometric and physical biases in solar data.

The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry breaking (SSB). We demonstrate that the tensor renormalization group (TRG) offers an efficient framework to compute the symmetry-twisted partition functions, which enables us to detect the symmetry-breaking transition and also to study associated critical phenomena. As concrete examples of SSB, we investigate the two-dimensional (2D) classical Ising model and the three-dimensional (3D) classical $O(2)$ nonlinear sigma model, and we identify their critical points solely from the twisted partition function. By employing the finite-size scaling argument, we find the critical temperature $T_c=2.2017(2)$ with the critical exponent $ν= 0.663(33)$ for the 3D $O(2)$ model. In addition, we also study the Berezinskii-Kosterlitz-Thouless (BKT) criticality of the 2D classical $O(2)$ model by extracting the helicity modulus from the twisted partition functions, and we obtain the BKT transition temperature, $T_{\mathrm{BKT}}=0.8928(2)$.

Detecting a scalar singlet interacting through the Higgs portal demands a pivot from conventional particle detection strategies to a comprehensive examination of the effective potential's landscape. The presence, intensity, and first-order nature of the electroweak phase transition are dictated by the critical manifold, with its universal traits encapsulated in the Milnor number $μ$ -- the dimensionality of the local Jacobian algebra. Throughout the parameter space consistent with experimental observations, the portal potential exhibits a non-simple singularity with $μ= 9$, maintaining topological stability amid substantial fluctuations in mixing angle, singlet mass, and cubic interactions. High-precision assessments of the Higgs trilinear self-coupling ($κ_λ$), the uniform rescaling of Higgs couplings ($c_H$), and the stochastic gravitational-wave spectrum ($Ω_{\mathrm{GW}}$) collectively delineate the catastrophe, extending beyond mere mass matrix analysis. Projections for 2027--2040 collider and LISA capabilities indicate that no viable region supporting a strong first-order transition will evade scrutiny; thus, the singlet will either be identified or conclusively dismissed via direct interrogation of the electroweak vacuum's critical structure.

We investigate the phenomenon of mass inflation in the interior of regular black holes arising in quasitopological gravity (QTG). These geometries are characterized by a bounded curvature core and the presence of an inner (Cauchy) horizon located near the fundamental scale $\ell$. To examine whether mass inflation persists in this setting, we model the interaction of ingoing and outgoing perturbations by considering the collision of two spherical null shells inside the black hole. Using the Dray-'t\,Hooft-Barrabes-Israel junction condition, we derive conditions under which the metric function and curvature invariants may experience significant amplification near the inner horizon. Our analysis shows that, unlike in classical Reissner--Nordström or Kerr geometries, significant mass inflation requires shell intersection at radii very close to the horizon, with radial separations from it of the order $r-r_* \lesssim \ell \big(\ell/r_g\big)^{2n(D-3)}$, where $r_g$ is the gravitational radius of the black hole, $D$ is the number of spacetime dimensions and $n\ge 1$ is a parameter depending on a concrete QTG model. For macroscopic black holes with $r_g\gg \ell$ this distance is much smaller than the fundamental scale $\ell$. We discuss possible consequences of this effect.

Vascular diseases such as atherosclerosis, thrombosis, and aneurysms can lead to life-threatening medical events. Conventional catheter- or guidewire-based interventional devices often struggle to navigate through highly tortuous vasculature. The recently developed multifunctional magnetic milli-spinner offers a promising wireless solution by integrating a central through-hole and side slits into a cylindrical body with helical fins, enabling rapid and stable navigation for clot debulking, targeted drug delivery, and aneurysm treatment. Here, we combine computational fluid dynamics simulations with experimental validation to optimize the milli-spinner's structural design for high-velocity propulsion and high-efficiency clot debulking in tubular flow environments. By systematically investigating the effects of through-hole radius, fin number, fin helical angle, and slit dimension on propulsion performance, the optimized milli-spinner achieves swimming velocities of 55 cm/s (175 body lengths per second) in saline water and 44 cm/s (140 body lengths per second) in a fluid with viscosity (3.5 mPa.s) comparable to that of arterial blood at high shear rates, far exceeding existing untethered magnetic robots in tubular environments (less than 80 body lengths per second). This exceptional velocity enables stable upstream operation against strong physiological flows representative of major arteries and veins, establishing the milli-spinner as a robust untethered navigation platform for operation in high-flow, tortuous vasculature.

The SMC orbits within the LMC's dark matter (DM) halo in a $\sim$1:10 mass-ratio encounter. The LMC:Milky Way (MW) interaction is also $\sim$1:10, and is expected to perturb the MW's DM distribution. However, no framework exists to quantify the severity of these perturbations over multiple pericenters and longer periods of time, such as the LMC-SMC interaction history. We construct basis function expansions of a high-resolution \textit{N}-body simulation of the Clouds interacting in isolation and analyze their DM distributions at an epoch approximating the time of their infall to the MW. Our goal is to quantify how the Clouds distort each other's DM distributions \textit{without} the MW. The LMC halo's response to the SMC includes a $\sim 20$ kpc long dynamical friction wake and the displacement of the LMC's density center during each SMC pericenter, which produces two overdensities in the LMC halo (at $\sim$60 and $\sim$100 kpc) at MW infall. The SMC's tidal radius at infall is just $\sim4$ kpc, at which point the SMC has lost two-thirds of its initial DM mass to the LMC. The distortions to the Clouds' halos produce a highly asymmetric acceleration field. Accurate orbit integration in the LMC-SMC system must account for the time-dependent shapes of both halos. The SMC-induced perturbations in the LMC DM halo resemble the MW-LMC system, and persist over multiple SMC pericenters. We conclude that 1:10 satellite-host encounters induce characteristic deformations in both DM halos across host-mass scales, with implications for merger rates and tests of DM models.

Following the death of Jeffrey Epstein, the subreddit r/conspiracy experienced a significant visibility shock that brought mainstream users into direct contact with established conspiracy narratives. In this work, we explore how large-scale surges in public attention reshape participation and discourse within online conspiracy communities. We ask whether a sudden increase in exposure changes who join r/conspiracy, how long they stay, and how they adapt linguistically, compared with users who arrive through organic discovery. Using a computational framework that combines toxicity scores, survival analysis, and lexical and semantic measures over a period of 12 months, we observe that mainstream visibility is is associated with patterns consistent with a selection mechanism rather than a simple amplifier. Users who join the conspiracy community during the arrest-period tend to show higher linguistic similarity to core users, especially regarding linguistic and thematic norms and showing more stable engagement over time. By contrast, users who arrive during the height of public visibility remain semantically distant from core discourse and participate more briefly. Overall, we find that mainstream visibility is connected with changes in audience size, community composition, and linguistic cohesion. However, incidental exposure during attention shocks does not typically produce durable, integrated community members. These results provide a more nuanced understanding of how external events and platform visibility influence the growth and evolution of conspiracy spaces, offering insights for the design of responsible and transparent recommendation systems.

We propose a simple and accurate approach to estimate the random close packing (RCP) fraction of binary hard-disk mixtures. By introducing a parameter based on the mixture's reduced third virial coefficient -- which effectively captures three-body correlations and excluded-area constraints -- we show that the RCP fraction depends nearly linearly on this parameter, leading to a near-universal collapse of simulation data over a wide range of size ratios and compositions. Comparisons with previous models by Brouwers and Zaccone indicate that the present approach provides more accurate and consistent predictions. The method can be naturally extended to polydisperse mixtures with continuous size distributions and is structurally consistent with the surplus equation-of-state formulation, offering a compact framework for understanding the near universality of RCP in hard-disk systems.

Federated learning (FL) has been considered a promising privacy preserving distributed edge learning framework. Over-the-air computation (AirComp) leveraging analog transmission enables the aggregation of local updates directly over-the-air by exploiting the superposition properties of wireless multiple-access channels, thereby alleviating the communication bottleneck issues of FL compared with digital transmission schemes. This work points out that existing AirComp-FL overlooks a key practical constraint, the instantaneous peak-power constraints due to the non-linearity of radio-frequency power amplifiers. Operating directly in non-linear region causes in-band and out-of-band distortions. We present and analyze the effect of the default method that limits the signal's peak power and out-of-band distortions, iterative amplitude clipping combined with filtering. We investigate the effect of imposing instantaneous peak-power constraints in AirComp-FL for both single-carrier and multi-carrier orthogonal frequency-division multiplexing (OFDM) systems. Simulation results demonstrate that, in practical settings, the instantaneous transmit power in AirComp-FL regularly exceeds the power-amplifier linearity limit. As the first work of this line of research, it is essential to evaluate if this is an actual problem that has an impact on FL performance. We therefore apply the classic method of iterative clipping and filtering, and show that the FL performance degrades more or less depending on the scenarios. The degradation becomes pronounced especially in multi-carrier OFDM systems due to the in-band distortions caused by clipping and filtering.

In in a nutshell, the classical geometric $q$-Langlands duality can be viewed as a correspondence between the space of $(G,q)$-opers and the space of solutions of $^L\mathfrak{g}$ XXZ Bethe Ansatz equations. The latter describe spectra of closed spin chains with twisted periodic boundary conditions and, upon the duality, the twist elements are identified with the $q$-oper connections on a projective line in a certain gauge. In this work, we initiate the geometric study of Bethe Ansatz equations for spin chains with open boundary conditions. We introduce the space of $q$-opers whose defining sections are invariant under reflection through the unit circle in a selected gauge. The space of such reflection-invariant $q$-opers in the presence of certain nondegeneracy conditions is thereby described by the corresponding Bethe Ansatz problem. We compare our findings with the existing results in integrable systems and representation theory. This paper discusses the type-A construction leaving the general case for the upcoming work.

We present H$α$ luminosity function (LF) measurements at redshifts $z\sim1.3$ and $z\sim2.0$ using JWST NIRISS grism data from the GLASS-JWST survey. Based on emission lines spectroscopically identified in the F115W, F150W and F200W filters, we select 99 H$α$ emitters. Through detailed effective volume and completeness analysis for each source, we construct the H$α$ LF in two redshift bins. Thanks to the sensitivity of NIRISS WFSS and gravitational lensing magnification, our sample reaches intrinsic H$α$ luminosities $\sim$10 times deeper than previous grism surveys, down to $L_{\rm Hα}\sim10^{40.5}~\rm erg~s^{-1}$ at $z\sim1.3$ and $L_{\rm Hα}\sim10^{40.9}~\rm erg~s^{-1}$ at $z\sim2.0$ with completeness larger than 0.8, corresponding to star formation rates of 0.4 and 1.0 $M_{\odot}~\rm yr^{-1}$, respectively. We robustly constrain the faint-end slope of the H$α$ luminosity function to be $-1.50^{+0.14}_{-0.08}$ at $z\sim1.3$ and $-1.60^{+0.17}_{-0.09}$ at $z\sim2.0$ after considering the cosmic variance of $\sim 20\%$, consistent with previous estimations. The emission-line samples presented here will enable further detailed studies of galaxy properties including metallicities. We find a negligible contribution from bright active galactic nuclei in our sample. We estimate integrated cosmic star formation rate densities of $0.097^{+0.015}_{-0.016}~M_{\odot}~\rm yr^{-1}~Mpc^{-3}$ at $z\sim1.3$ and $0.129^{+0.025}_{-0.030}~M_{\odot}~\rm yr^{-1}~Mpc^{-3}$ at $z\sim2.0$. The methodology presented here can be readily applicable to other JWST slitless spectroscopic datasets and future wide-field slitless surveys, including those from Euclid, Roman, and the Chinese Space Station Telescope.

The heavy-fermion superconductor CeRh2As2 exhibits a non-superconducting phase transition that precedes the emergence of superconductivity. The nature of the corresponding order parameter remains under debate, with competing proposals involving magnetic dipoles or electric quadrupoles. We derive the momentum-dependent multipolar susceptibilities and effective interactions among the localized 4f electrons, based on the framework of density functional theory combined with dynamical mean-field theory. Magnetic fluctuations within the crystalline-electric-field (CEF) ground-state doublet are dominated by q=(1/2,1/2,0), corresponding to a two-dimensional checkerboard configuration of the magnetic moment M_z along the c axis. Hybridization between the CEF ground-state and the first-excited doublet gives rise to leading magnetic octupole fluctuations of z(x^2-y^2) symmetry, followed by electric quadrupole fluctuations of x^2-y^2 and {yz, zx} symmetries. By taking into account the anisotropic magnetic-field dependence of the transition temperature T_0, we conclude that an antiferromagnetic order of M_z at q=(1/2,1/2,0) is consistent with the experiments, owing to the enhancement of T_0 caused by fluctuations of the field-induced quadrupole of {yz, zx} type under an in-plane magnetic field.

In case there are tensor interactions beyond the SM in the low-energy effective Lagrangian, their interference with the SM V-A currents yields a contribution for tau decays into three or more mesons that cannot be included in the famous structure functions introduced by Kühn and Mirkes in their seminal 1992 paper. We present this generalization here, highlighting again the importance of measuring the (generalized) spectral functions, as being model-independent and exploiting maximally the data. This can be particularly relevant for CP and T violation studies with at least three mesons in the final state of the tau decay.

Let $G$ and $H$ be unital associative algebras over a field $K$, such that $G$ satisfies the identity $[x_1, \dots, x_p] = 0$ for some integer $p \geq 3$ and $H$ satisfies the identities $[x_1, x_2, x_3] = 0$ and $[x_1, x_2] \cdots [x_{2k-1}, x_{2k}]=0$ for some $k \geq 2$. In this paper, extending results of Deryabina and Krasilnikov, we show that the tensor product $G \otimes H$ is again a Lie nilpotent associative algebra, i.e., it satisfies $[x_1, \dots, x_{q}] = 0$ for some $q \geq p$. We also determine an explicit value of $q$ in the case $k = 2$, i.e., when $H$ satisfies the identity $[x_1, x_2][x_3, x_4] = 0$. As a corollary, we reprove a result of Drensky saying that any product of Grassmann algebras of the form $E\otimes E_{i_1}\otimes \cdots \otimes E_{i_s}$ or $E_{j_1} \otimes E_{j_2} \otimes \cdots \otimes E_{j_t}$, where $E$ denotes the Grassmann algebra over a countable dimensional vector space and $E_r$ denotes the Grasmann algebra over an $r$-dimensional vector space, satisfies an identity of the form $[x_1, \dots, x_q] = 0$ for some integer $q \geq 3$. In addition, we show that for products of the form $E\otimes E_{i_1}\otimes \cdots \otimes E_{i_s}$ the minimal value of $q$ is always and odd integer. We also provide several particular cases in which a value of $q$ can be explicitly computed. As an application, we consider a field of characteristic zero, the variety $\mathfrak{N}_p$ of Lie nilpotent associative algebras of index at most $p$ and the corresponding relatively free algebras of finite rank, $F_n(\mathfrak{N}_p)$. We exhibit many explicit irreducible $S_n$-modules in the $S_n$-module decomposition of the space of proper multilinear polynomials in $F_n(\mathfrak{N}_p)$ for any $p$. This gives a lower bound for the dimensions of the spaces of multilinear and proper multilinear polynomials in $F_n(\mathfrak{N}_p)$.

The Kerr-Schild gauge is generalized to the case that the vector generating the deformation is not null. Contrary to naive expectations, this vector generates a finite expansion for the curvature tensor. We prove a theorem on the conditions for the deformed metric being Ricci flat, namely that the deformation vector must be irrotational (then geodesic) in the background spacetime.

Synthetic data generation is gaining traction as a privacy enhancing technology (PET). When properly generated, synthetic data preserve the analytic utility of real data while avoiding the retention of information that would allow the identification of specific individuals. However, the concept of data privacy remains elusive, making it challenging for practitioners to evaluate and benchmark the degree of privacy protection offered by synthetic data. In this paper, we propose a framework to empirically assess the efficacy of tabular synthetic data privacy quantification methods through controlled, deliberate risk insertion. To demonstrate this framework, we survey existing approaches to synthetic data privacy quantification and the related legal theory. We then apply the framework to the main privacy quantification methods with no-box threat models on publicly available datasets.

The energy levels and optical transitions of tetrahedral core/shell InP/ZnSe quantum dots (QDs) are investigated by means of multi-band k$\cdot$p theory. Despite the $\overline{T}_d$ symmetry relaxing spherical selection rules, the near-band-edge excitonic spectrum is reminiscent of that obtained for spherical nanocrystals. Exceptions appear in large (red-emitting) QDs, where transitions violating the (quasi-)angular momentum selection rule ($ΔL=0,\pm 2$) are observed, and the ground state does not become dark ($P_{3/2}$-like). Valence band coupling is important in determining the symmetry, degeneracy and energy of hole states, with split-off holes playing a greater role than in CdSe QDs. The ($1S_e$-like) electron ground state exhibits moderate delocalization into the ZnSe shell. The confinement regime is then strong even for thick shells, which results in Coulomb interactions being mostly perturbative. Electrons remain largely localized in the InP core even in negative trions, despite electron-electron repulsions. At the same time, the asymmetry between Coulomb attractions and repulsions leads to negative (positive) trions being bound (antibound) by tens of meV. The biexciton binding energy switches from positive to negative, depending on the QD size.

We introduce and study \emph{brachistochrone-ruled timelike surfaces} in Newtonian and relativistic spacetimes. Starting from the classical cycloidal brachistochrone in a constant gravitational field, we construct a Newtonian ``brachistochrone-ruled worldsheet'' whose rulings are time-minimizing trajectories between pairs of endpoints. We then generalize this construction to stationary Lorentzian spacetimes by exploiting the reduction of arrival-time functionals to Finsler- or Jacobi-type length functionals on a spatial manifold. In this framework, relativistic brachistochrones arise as geodesics of an associated Finsler structure, and brachistochrone-ruled timelike surfaces are timelike surfaces ruled by these time-minimizing worldlines. We work out explicit examples in Minkowski spacetime and in the Schwarzschild exterior: in the flat case, for a bounded-speed time functional, the brachistochrones are straight timelike lines and a simple family of brachistochrone-ruled surfaces turns out to be totally geodesic; in the Schwarzschild case, we show how coordinate-time minimization at fixed energy reduces to geodesics of a Jacobi metric on the spatial slice, and outline a numerical scheme for constructing brachistochrone-ruled timelike surfaces. Finally, we discuss basic geometric properties of such surfaces and identify natural Jacobi fields along the rulings.

We investigate complex self-testing, a generalization of standard self-testing that accounts for quantum strategies whose statistics is indistinguishable from their complex conjugate's. We show that many structural results from standard self-testing extend to the complex setting, including lifting of common assumptions. Our main result is an operator-algebraic characterization: complex self-testing is equivalent to uniqueness of the real parts of higher moments, leading to a basis-independent formulation in terms of real C* algebras. This leads to a classification of non-local strategies, and a tight boundary where standard self-testing does not apply and complex self-testing is necessary. We further construct a strategy involving quaternions, establishing the first standard self-test for genuinely complex strategy. Our work clarifies the structure of complex self-testing and highlights the subtle role of complex numbers in bipartite Bell non-locality.

Metal-organic framework (MOF) databases have grown rapidly through experimental deposition and large-scale literature extraction, but recent analyses show that nearly half of their entries contain substantial structural errors. These inaccuracies propagate through high-throughput screening and machine-learning workflows, limiting the reliability of data-driven MOF discovery. Correcting such errors is exceptionally difficult because true repairs require integrating crystallographic files, synthesis descriptions, and contextual evidence scattered across the literature. Here we introduce LitMOF, a large language model-driven multi-agent framework that validates crystallographic information directly from the original literature and cross-validates it with database entries to repair structural errors. Applying LitMOF to the experimental MOF database (the CSD MOF Subset), we constructed LitMOF-DB, a curated set of 186,773 computation-ready structures, including the successful repair of 8,771 invalid entries, which accounts for 65.3% of the not-computation-ready MOFs in the latest CoRE MOF database. Additionally, the system uncovered 12,646 experimentally reported MOFs absent from existing resources, substantially expanding the known experimental design space. Using direct air capture screening as a case study, we demonstrate that structural errors severely distort predicted adsorption energies and CO2/H2O selectivity, leading to systematic misranking of materials, false positives, and the omission of high-performance candidates. This work establishes a scalable pathway toward self-correcting scientific databases and a generalizable paradigm for LLM-driven curation in materials science.

Photon structure function has been a solid platform in testing strong interaction along with nucleon structure function. Strong Interaction has the property that it is perturbatively calculable at high energy but becomes non-perturbative at low energy. This nature makes QCD hard to handle theoretically in factorizing these two regions. The fundamental dimensional parameter, so called the QCD scale parameter, $Λ_{\overline{\textrm{MS}}}$, is one of key players to factorize two energy regions. In this work, we extract the QCD scale parameter from the photon structure function by separating the perturbative QCD and non-perturbative QCD. In the process we use the vector dominance model for the non-perturbative energy region of the photon structure function.