High-precision cosmological observations have revealed persistent tensions within the standard $Λ$CDM paradigm, most notably the discrepancy in the Hubble constant and the lower than predicted amplitude of late-time matter clustering quantified by $S_8$. We propose a unified thermodynamic framework in which entropic backreaction generated during cosmic structure formation modifies both the background expansion history and the growth of matter perturbations. As gravitational instability drives the growth of cosmic structures, the configuration entropy associated with the matter distribution decreases through the nonlinear redistribution of gravitational binding energy. The resulting entropic energy density contributes a late-time backreaction that enhances the cosmic expansion rate without altering early-Universe physics or the CMB sound horizon. Simultaneously, the same irreversible entropy dissipation process induces a dissipative correction within the cosmic velocity flow, suppressing the efficiency of coherent gravitational clustering at late times. The framework operates entirely within standard General Relativity: the Einstein field equations, Poisson equation, and gravitational coupling remain unmodified, and no new propagating degrees of freedom or fifth forces are introduced. Entropic backreaction therefore provides a thermodynamically motivated, theoretically conservative, and observationally testable mechanism that may simultaneously alleviate the major late-time cosmological tensions.

For an algebraic group $Q$ with $\mathsf{Lie\,} Q=\mathfrak q$, we develop a method for estimating the index of a subalgebra $\mathfrak h$ in $\mathfrak q$ via the use of coadjoint $Q$-orbits in $\mathfrak q^*$. Let $\mathfrak q^ξ$ denote the stabiliser of $ξ\in\mathfrak q^*$. In the special case when $\mathfrak q^ξ\oplus\mathfrak h=\mathfrak q$, our estimate implies that $\mathsf{ind\,}\mathfrak h=0$. Using our theory, we also answer a question of Duflo. An orbit $Q{\cdot}η\subset\mathfrak q^*$ is said to be strange, if $\mathfrak q^η\oplus\mathfrak h=\mathfrak q$ for some $\mathfrak h$. In the second part of the paper, we study strange orbits for a semisimple algebra $\mathfrak g$. It is shown that an orbit ${\mathcal O}\subset\mathfrak g\simeq\mathfrak g^*$ is strange whenever the complexity of ${\mathcal O}$ is at most 1. Furthermore, if ${\mathcal S}\subset\mathfrak g$ is a sheet containing a strange nilpotent orbit, then all orbits in ${\mathcal S}$ are strange. We also show that strange orbits in $\mathfrak{sl}_n$ are not as sparse, as one might expect, and discuss some conjectures on strange orbits.

Sharing entanglement among multiple users remains a central challenge for scalable quantum networks. Recent work proposed an on-demand entanglement packet architecture in which a controller uses a Time Division Multiple Access (TDMA) approach to allocate network resources. Quantum nodes are assigned a periodic schedule that probabilistically fulfills application requests for end-to-end entanglements. The schedule is recomputed periodically using well-known algorithms, such as Earliest Deadline First (EDF). However, a static schedule offers limited flexibility when outcomes are stochastic and arrivals are asynchronous. To overcome this limitation, we propose an online scheduler that dynamically schedules, defers, retries, or drops entanglement distribution reservations. In our simulations, the dynamic scheduler achieves lower completion time, higher completion ratio, and higher throughput than the static baseline. Furthermore, when the network is overloaded, the dynamic scheduler continues to construct deadline-feasible schedules and degrades gracefully.

We propose a definition of a non-invertible symmetry enriched topological order (NI-SETO), and we implement our definition for string net models. We do so in two ways, using full inclusions of unitary fusion categories (UFCs), as well as anyon condensation. In both cases, the NI-SETO is a relative center of UFCs. All NI-SETOs can be realized in either model, where we can use enriched UFCs to get chiral examples on the boundary of a 3D Walker-Wang model representing the anomaly. We describe several examples of NI-SETOs and compute the qualitative symmetry action on anyons and symmetry defects using tube algebra techniques.

We demonstrate electron magnetic linear dichroism as a quantitative probe of vectorial magnetic order parameters with nanometer resolution in transmission electron microscopy. Explicit inclusion of vectorial core-level exchange splitting into mixed dynamic form factor simulations accounting for dynamical diffraction enables direct reconstruction of the magnetic spin axis from momentum-resolved electron energy-loss spectra. The resulting dichroic signal is intrinsically separable from nonmagnetic anisotropy, exhibits a well-defined dependence on the Néel vector or magnetization orientation, and remains robust down to the atomic scale. Applied to the collinear antiferromagnetic and ferromagnetic phase of cubic FeRh, this approach allows quantitative real-space mapping of the magnetic vector. These results open a pathway to nanoscale spectroscopy and imaging of antiferromagnets and altermagnets where the generalized approach to electron dichroism provides direct access to different magnetic order parameters.

We construct an explicit family of smooth finite-time blow-up solutions for the focusing Calogero--Sutherland derivative NLS given by $$ i \partial_t u = -\partial_x^2 u - 2 D Π(|u|^2) u \quad \mbox{with} \quad (t,x) \in \mathbb{R} \times \mathbb{T} , $$ where $D=-i \partial_x$ and $Π$ denotes the Cauchy--Szegő projector. This is a mass-critical NLS-type equation with a Lax pair structure. The Cauchy problem is global well-posed in the class of Hardy-Sobolev spaces $H^s_+(\mathbb{T})=L^2_+(\mathbb{T}) \cap H^s(\mathbb{T})$ for small $L^2$-mass $\| u_0 \|_{L^2}^2 < 1$ as recently proven in [R.~Badreddine, Pure Appl. Anal. 6 (2024)]. By a non-perturbative method, we construct smooth blow-up initial data with $L^2$-mass in the entire range $1 < \|u_0 \|_{L^2}^2 <2$. The strategy is based on a stability analysis for the explicit formula for (CS) combined with a suitable choice of finite-gap potentials as initial data that bifurcate from the discrete set of trivial plane waves $e^{i m x}$ with $m \in \mathbb{Z}_{\ge 0}$. More precisely, we find a parametrized family of smooth initial data $u_0$ in $L^2_+(\mathbb{T})$ such that the corresponding solution $u(t)$ of (CS) blows up with $$ \| u(t) \|_{H^s} \sim \frac{1}{(T-t)^{2s}} \quad \mbox{as} \quad \mbox{$t \nearrow T$} \quad \mbox{for all $s > 0$} $$ for some finite time $0 < T < \infty$. Moreover, we give a full description of the blow-up dynamics and we identify the unique weak limit of $u(t)$ in $L^2_+(\mathbb{T})$ as $t \nearrow T$. Finally, we show instability of these blow-up solutions and complement our results by showing global existence for a class of finite-gap potentials as initial data with arbitrarily large $L^2$-mass.

Randomized controlled trials (RCTs) are the gold standard for evaluating causal effects but are often costly and difficult to scale; consequently, they are frequently augmented with auxiliary external controls in many applications. Prior approaches for borrowing such data typically rely on exchangeability, under which the external controls are readily usable for inference in the trial population. In practice, however, differences in eligibility criteria, standard of care, and data collection procedures may induce distribution shifts between the RCT and the external controls, rendering exchangeability implausible. In this paper, we propose a novel framework for integrating external controls by explicitly modeling these distribution shifts. We construct augmented estimators by adapting trial-only efficient influence functions through calibration equations that balance the trial and external populations, thereby fully exploiting the external control data even when exchangeability fails. We further develop an adaptive shrinkage estimator that preserves consistency while guaranteeing efficiency dominance over the trial-only benchmark. Synthetic experiments and a real data application demonstrate the practical advantages of the proposed approaches.

We study a class of quantum error-correcting codes through the geometry of complex abelian varieties. These codes, introduced by Gottesman--Kitaev--Preskill, are built from symplectically integral lattices and therefore naturally define polarized complex abelian varieties. We give a precise mathematical formulation of this relationship and extend it to a dictionary between the main structures of GKP code theory and classical objects in the theory of abelian varieties. For instance, under this dictionary, the finite-dimensional code space becomes the space of theta functions $H^0(X, L)$, logical Pauli gates arise from the theta group, passive logical Clifford gates correspond to automorphisms of the polarized abelian variety, and concatenation with stabilizer codes corresponds to isogeny. We also prove several key results that give precise mathematical formulations of statements about these codes that often appear in heuristic form in the physics literature. In particular, we prove that the encoding is asymptotically isometric, that every logical Clifford gate is realized by a Gaussian unitary, and that, for noise of small variance, the failure probability is governed to first order by the shortest nontrivial displacement in the kernel of the polarization isogeny, a systolic invariant of the underlying polarization. This leads naturally to optimization problems on the moduli space of polarized abelian varieties.

We disprove the sum-product conjecture for real numbers by constructing arbitrarily large $A\subset \mathbb{R}$ (whose elements are algebraic integers in a number field of degree $\asymp \log\lvert A\rvert$) such that \[\max(\lvert A+A\rvert ,\lvert AA\rvert)\leq \lvert A\rvert^{2-c}\] where $c>0$ is an absolute constant. We also disprove the many sums and products conjecture by constructing, for any $k\geq 3$, arbitrarily large $A\subset \mathbb{R}$ such that \[\max(\lvert kA\rvert,\lvert A^{(k)}\rvert)\leq \lvert A\rvert^{C\frac{\log k}{\log\log k}}\] for some constant $C>0$. We obtain similar constructions for $p$-adics, finite fields, and function fields in positive characteristic, and also obtain new lower bounds for the number of solutions to linear equations in a multiplicative group and the number of solutions to the unit equation in sufficiently many variables.

Supermassive Population III.1 stars, i.e., formed from pristine, metal-free gas leading to conditions where dark matter annihilation heating is significant, have been proposed as the progenitors of supermassive black holes (SMBHs) in the early universe ($z \sim 20-40$). Since such Pop III.1 stars only form from non-irradiated gas in dark matter minihalos, they are predicted to appear isolated from each other and other sources of feedback. The previous papers in this series used the isolation distance of Pop III.1 stars as a free parameter to seed SMBH in cosmological simulations of dark matter halos. Here we develop a feedback-regulated model of Pop III.1 isolation, based on the growth of HII regions around each Pop III.1 star and lower-mass, irradiated Pop III.2 stars. Our model considers the time delay between the formation of a minihalo and its Pop III.1 star, R-type expansion of HII regions that expand into the intergalactic medium (IGM), and the redshift dependence of Strömgren spheres for longer-lived ionizing sources. For a fiducial Pop III.1 star H-ionizing photon luminosity of $10^{53}\:{\rm s}^{-1}$ and lifetime of $10\:$Myr we find an R-type HII region radius of $R_{\rm R}\simeq1.3\:$cMpc, approximately independent of redshift. The median formation redshift is $\sim20$, with the process essentially complete by $z\sim16$. The overall number density of SMBHs produced in this model is then $n_{\rm SMBH}\simeq 3 ϕ_V/(4πR_{\rm R}^3)\simeq 0.2\:{\rm cMpc}^{-3}$. We also discuss predictions for the abundance of binary SMBHs, which may appear as dual active galactic nuclei (AGN; $\lesssim 0.3\%$ for $z>6$), and SMBH binary merger rates, measurable by the forthcoming LISA mission.

We derive distributional approximations for the number of triangles in the linear preferential attachment model $\mathrm{PAM}(m,δ)$, where $m\ge 2$ and $δ>-m$, with explicit rates of convergence. The limiting distribution undergoes a phase transition from Gaussian to another nontrivial distribution, which we characterize explicitly. The asymptotic behavior is governed by the interplay between the hidden random environment and the mean-field interaction effect. In particular, our analysis also yields a continuous phase transition in the expected number of triangles as $δ$ varies.

A fundamental step in knowledge discovery is statistically assessing data mining results. In network analysis, such evaluation compares the outcome of a given procedure with the outcomes obtained from randomized versions of the observed network. Despite its importance, available graph null models only preserve simple characteristics of the observed graph, such as its degree sequence. In this paper we introduce the Colored Configuration Model (CCM), a new null model for vertex-colored multigraphs. Our main motivation is the study of online social networks, where the color of a user represents their side in a debate. The key novelty of CCM is preserving the Colored Degree Matrix (CDM), which encodes, for each vertex, the number of neighbors of any given color. Preserving the CDM allows fixing the color assortativity of all nodes, e.g., the propensity of each user to interact with other like-minded users. This allows testing whether a given phenomenon is explained by the observed CDM, or whether other characteristics of the network might play a key role. Available graph null models do not preserve the CDM, so they cannot assess its impact on real-world tasks, such as testing the significance of network polarization measures. To sample from the CCM, we develop Sirius-B, a simple baseline adapting the Metropolis-Hastings approach, and Sirius, a refined algorithm tailored to preserve the CDM, thus achieving provably faster mixing. In our experimental evaluation, we test Sirius on real-world networks, comparing it with related network null models. We observed that the evaluation of the statistical significance of polarization measures with Sirius may lead to different insights compared to available null models. Thus, Sirius is an effective tool for the statistically-sound analysis of social networks.

We present a comprehensive study of the spectrophotometric evolution of the classical nova QY Mus from eruption to quiescence. The light curve shows a notable dust dip, classifying it as a D (137)-type nova, with dust formation beginning at $\sim$123 days post-outburst and reaching a maximum optical depth of $τ\sim 3.2$. We classify QY Mus as a slow nova with $t_2 = 87 \pm 6$ days, and derive an absolute magnitude of $M_V = -6.55 \pm 0.54$ using the MMRD relation. The spectroscopic evolution, traced from 94 to 1348 days, shows prominent P-Cygni profiles in Balmer and Fe II lines during the early decline, consistent with an Fe II-type nova. The transition to the nebular phase occurs around $\sim$233 days, marked by the emergence of [O III] emission. Photoionization modeling using \textsc{Cloudy} of 41 emission lines on day 590 yields a central source temperature of $(7.08 \pm 0.20)\times10^{5}$ K, with enhanced nitrogen and oxygen abundances and moderate neon enrichment, suggesting that QY Mus is not a neon nova. Mid-infrared WISE observations at $\sim$502 days indicate the presence of cool dust at $\sim$400 K. Using a Gaia-based color magnitude diagram constructed in this work for 34 quiescent novae, we find that QY Mus occupies a region consistent with systems hosting main-sequence or subgiant secondaries; its orbital period further supports a subgiant companion. These results establish QY Mus as a slow, dust-forming nova with well-characterized evolution and a subgiant secondary.

We prove asymptotic equivalents for finite-level representations of symmetric groups, that is, for Young diagrams having all but finitely many boxes on their first row. We deduce that random walks on symmetric groups generated by conjugacy classes with a macroscopic number of fixed points have a Poissonian cutoff profile. We also prove that the random involution walk exhibits cutoff and find its cutoff profile. Finally, we obtain numerics for the random transposition walk on a deck of 52 cards, giving concrete estimates on the question that originally motivated Diaconis and Shahshahani.

The chemical and mass evolution of exoplanet atmospheres is shaped by their specific X-ray through ultraviolet (5 - 3200 Angstroms) irradiance history. X-ray and EUV (5 - 911 Angstroms) radiation largely contributes to atmospheric heating via photoionization, while far- and near-UV emission (912 - 3200 Angstroms) drives photochemistry. The (uncharacterized) variance between young star spectra in this wavelength range for the same spectral type causes significant uncertainty in interpreting present-day transmission spectra of young exoplanets, directly impacting the science return of the James Webb Space Telescope and other programs. Additionally, the lack of direct X-ray through UV characterization for stars of all ages leads to large uncertainties in the high-energy irradiance history of all planetary systems, propagating into uncertainties in their chemical and mass evolution. This influences current and future observing programs, as well as the goal of the future flagship Habitable Worlds Observatory to find and characterize habitable exoplanets. There are less than a handful of young planet hosts with well-characterized X-ray through UV environments. The Hubble Space Telescope is the only observatory capable of measuring the UV spectrum and enabling the characterization of exoplanet high-energy environments. We advocate for an observing program to measure the UV, estimate the EUV, and measure the X-ray where possible and needed of all amenable young planet hosts, addressing the Space Telescope Science Institute's call for Building a Roadmap for Hubble Science into the 2030s.

Inspired by strict-monotonicity criteria for the time constant in first passage percolation, we investigate convex ordering of point processes in relation to the time constant in first contact percolation. In a nutshell, first contact percolation models the spread of an infection as a contact process without recovery based on a generalized graphical representation, where the usual homogeneous Poisson point processes on the edges are replaced by general simple point processes. Based on a notion of convex ordering for point processes, we prove monotonicity in the number and existence of infection paths. We argue that this convex ordering is however not enough to ensure strict monotonicities in the asymptotic speed of the infection. Instead, we propose a criterion based on an ordering of void probabilities and prove a speed-up for one-dimensional systems based on $\mathbb{Z}$-stationary point processes.

Integrating probability and nonprobability survey samples is an important problem in modern survey sampling. Nonprobability samples often contain rich outcome information but may lack population representativeness, whereas probability samples provide design-based auxiliary information but may not contain the study variable. We propose a deep neural network (DNN)-assisted doubly robust framework for estimating the finite population mean from these two data sources. The proposed method models the logit sampling score for the nonprobability sample as an unknown nonparametric function and estimates it by maximizing a pseudo-likelihood that combines information from the nonprobability sample and a reference probability sample. The DNN parameters are optimized using the ADAM algorithm. The resulting DNN-estimated sampling scores are incorporated into a DNN-assisted inverse-probability weighted estimator and a deep doubly robust estimator. We establish consistency and convergence rates under regularity conditions and evaluate the finite-sample performance of the proposed estimators through simulation studies and an empirical application using Pew Research Center and Behavioral Risk Factor Surveillance System data. The results suggest that the proposed estimators can improve robustness to parametric propensity-score misspecification, especially when the true selection mechanism is nonlinear.

When the Fermi surface and the Brillouin zone boundary touch at a Van Hove point, mean-field analysis predicts a ferromagnetic (Stoner) instability at finite $T_{MF}$ for any coupling strength due to the divergent density of states. However, the predicted effect has not been observed experimentally. Several qualitative theoretical proposals have been put forward to explain why the mean-field prediction fails. Based on numerically exact results for the two-dimensional Hubbard model with an ordinary Van Hove singularity, we uncover the mechanisms behind the suppression of the ferromagnetic instability. We employ two diagrammatic Monte Carlo approaches: (i) the four-channel self-consistent approximation and (ii) numerically exact method of combinatorial summation of diagrams with controlled resummation of the truncated expansion. We find that the system avoids the Stoner instability down to temperatures an order of magnitude below $T_{MF}$ due to the combination of the downward renormalization of the effective coupling and the suppression of the density of states by the loss of the quasiparticle residue.

We investigate how the environment of a dynamically unrelaxed galaxy cluster influences the structure and dynamics of stellar bars. In particular, we examine cluster-centric variations in normalised bar size and bar pattern speed in Abell 2199. Our analysis is based on 578 spectroscopically confirmed members of Abell 2199, including a master sample of 325 galaxies with homogeneous stellar mass and star formation rate measurements. We identify 39 barred galaxies and measure their structural properties using isophotal ellipse fitting and three-component (bulge+disc+bar) photometric decompositions. For 22 barred galaxies with MaNGA integral-field spectroscopy, we estimate bar pattern speeds using the Tremaine-Weinberg method, obtaining robust measurements for 12 galaxies. Stellar population age and projected specific angular momentum are analysed using $D4000_{R_{\mathrm{e}}}$ and $λ_{R_{\mathrm{e}}}$ from the MaNGA Pipe3D catalogue. Abell2199 exhibits star formation-density and morphology-density relations despite its non-relaxed dynamical state. Early-type spiral (ETS) barred galaxies show systematic cluster-centric variations in normalised bar size, with relatively larger bars towards the cluster centre and smaller bars at intermediate radii. A corresponding variation in bar pattern speed with cluster-centric distance is also observed. These trends motivate a division at $\sim$0.5$R_{\mathrm{vir}}$, within which morphology-dependent environmental signatures become clearer, as barred galaxies in the inner region tend to host older stellar populations and lower projected angular momentum than those in the outskirts, with ETS+Bar galaxies retaining higher angular momentum compared to S0+Bar galaxies at comparable radii.

We propose a learning-based approach for approximating solution mappings of multiparametric generalized Nash equilibrium problems (GNEPs) with coupling in both objectives and constraints. Rather than solving a standard regression problem on a training dataset of GNEP solutions, which are expensive and possibly difficult to collect, we use the Nikaido-Isoda (NI) gap function as a training loss, which requires only best-response data. To avoid bilevel optimization, a value-function surrogate approximates each agent's optimal best-response cost and is substituted into the NI loss, yielding a single-level learning problem. Learning approximate solutions to standard multiparametric programming problems is a special case of the approach. We also establish new sufficient conditions for the existence of a continuous parametric variational GNE selection under a strong variational stability assumption that generalizes strong monotonicity. The trained neural network delivers approximate GNE solutions with speedups of several orders of magnitude over online solvers. Numerical experiments on different problem classes confirm the effectiveness of the approach. A Python library is available at https://github.com/bemporad/mpfit.

In the standard Breit-Wigner approach to scattering the phase shift is to have a form $\tanδ_{\rm BW} =Γ_1/(E_1-E)$ at a real energy resonance. This leads to complex energy poles in the scattering amplitude at $E_{\rm BW}=E_1-iΓ_1$, poles that are identified with unstable physical particles. By solving the square well scattering problem we identify some challenges to this approach. We find that setting $\tanδ_{\rm BW} =Γ_1/(E_1-E)$ is not always a good description of the real energy scattering amplitude, that $Γ_1$ can be negative, that $E_{\rm BW}$ is not in fact an energy eigenvalue (and thus not a physical particle), and that states that decay in energy possess spatial wave functions that unacceptably grow exponentially. All of this is resolved by noting that because of its antilinear $PT$ symmetry solutions to the square well Schrödinger equation appear in complex conjugate energy pairs $E_{\mp}=E_2\mp i Γ_2$ with $E_- \neq E_{\rm BW}$, doing so in a way that gives a time independent probability amplitude that neither grows nor decays in time or space, and leads to just one now observable physical resonance not two.

Close-in substellar companions experience strong tidal and magnetic interactions with their host stars and are therefore subject to fast orbital evolution. The solar-type pulsator KIC 9139163 exhibits in its light curve a stable 0.6-day modulation for which the best explanation is the presence of a close-in non-transiting companion that we therefore attempt to characterise. We combine Kepler and TESS photometric data with spectroscopic observations obtained with HARPS-N. The analysis of the radial velocities obtained with HARPS-N provides a companion mass $M_p \sin i = 7.3 \pm 1.4 \, \mathrm{M}_{\oplus}$. We infer a planetary radius of $2.43 \pm 0.14 \, \mathrm{R}_\oplus$, which, combined with the measured mass and retrieved inclination, implies a bulk density consistent with a hot water-rich world. This places the non-transiting companion candidate of KIC 9139163 within the Neptunian desert, a regime where planets are expected either to have lost their primordial hydrogen/helium envelopes or to harbour metal-enriched atmospheres. We further detect significant variations in amplitude between the Kepler and TESS phase curves, obtained six years apart, as well as a secular increase in amplitude over the Kepler baseline. Our fit favours a model with two distinct longitudinal cloud offsets over a single-offset scenario. Both datasets indicate a moderate-to-high geometric albedo and low-to-moderate heat redistribution. The opposite phase offsets observed in the Kepler and TESS datasets suggest a time-variable longitudinal brightness distribution. While making KIC 9139163 an interesting candidate for future ground follow-ups, it also suggests that searching for other non-transiting planets around fast stellar rotators in space-borne photometric surveys might provide new insights into the physics of the Neptunian planets located in the desert. [shortened]

Stokes' theorem turns Abelian Berry phases into curvature fluxes, whereas path ordering precludes such a simple formula for non-Abelian holonomies. We show that a quantitative form of this intuition survives: arbitrary Wilczek--Zee holonomies obey a universal quantum geometric limit~(QGL), in which the holonomy magnitude is bounded by a surface integral of the non-Abelian curvature norm. Recasting holonomic evolution as an effective Stokes--Schrödinger dynamics driven by transported curvature, we identify the QGL as the geometric counterpart of conventional quantum speed limits, with a time-integrated generator norm replaced by a surface-integrated curvature cost. The induced contour--surface variational problem is governed by a non-Abelian Lorentz force, which we address with a brachistochrone ansatz of curvature-weighted geodesics. Applied to an SU(2) tripod dark subspace, near-optimal protocols spontaneously align the transported curvature along a single Lie-algebra direction, effectively taming non-Abelianity.

We demonstrate how the two-dimensional gravity emerges within ``GR from RG'' program initiated in \cite{Adami:2025pqr, Sheikh-Jabbari:2026uol}. To achieve this, we consider a generic 2d CFT with a 3d holographic description, which we assume to be well-described by pure Einstein-AdS$_3$ gravity in the bulk. We study the holographic RG flow for the 2d CFT action and show that the renormalization group (RG) corrected action at an arbitrary energy scale contains a 2d scalar-tensor gravity theory. In the simplest case, the flow induces Jackiw-Teitelboim (JT) gravity, where the bulk radial lapse function seeds the dynamical dilaton field of the JT gravity. We show that the standard T$\bar{\text{T}}$ deformation of the 2d CFT is recovered as a special case in the Fefferman-Graham limit where the lapse is fixed. We further establish the robustness of the RG induced gravity picture by verifying its consistency under holographic renormalization and by generalizing the result to a one-parameter family of boundary conditions. Our results provide a first-principles derivation of the JT gravity at a finite cutoff as an intrinsic manifestation of the holographic RG flow in a non-Fefferman-Graham gauge

Block tensor decomposition (BTD) and canonical polyadic decomposition (CPD) are combined into a unified $O(N^3)$-scaling framework for second-order perturbation theory (PT2), demonstrated on MP2 and renormalized PT2 (rPT2). BTD constructs the tensor hyper-contraction kernel at $O(N^3)$ via a dual-grid scheme; CPD factorizes the exchange channel through a block-based two-stage ALS. An asymmetric half-kernel design applies bare Coulomb to one vertex and coupling-constant-averaged screening to the other, capturing the SOSEX component of rPT2 without a frequency-dependent CPD. For MP2, BTD-CPD reproduces canonical RI-MP2 to 0.058~kcal/mol per heavy atom. For rPT2@PBE0 on the S66x8 benchmark, the mean absolute error is 0.36~kcal/mol (ME $-$0.19, RMSE 0.46) over 528 data points. The CPD-compressed intermediates yield $O(N^2)$ storage alongside $O(N^3)$ scaling.

We develop IV Fréchet regression (IVFR), an instrumental-variable (IV) method for settings where the outcome is an entire distribution. Framing the problem as an IV regression in 2-Wasserstein space, IVFR extends global Fréchet regression to the case with endogenous covariates. IVFR projects IV-weighted quantile curves onto the space of valid distributions and then recovers the corresponding regression coefficient functions. The projection provably reduces the estimation error in finite samples and guarantees valid fitted distributions. We show that the IVFR estimator converges weakly to a mean-zero Gaussian process and establish the validity of a multiplier bootstrap procedure for uniform inference. In simulations, the projection reduces the integrated mean squared error (IMSE) by up to 63% relative to existing methods. Revisiting the effects of Chinese import competition on the wage distribution within commuting zones, the proposed method produces 9-10% narrower confidence bands than existing methods. Using our novel uniform confidence bands, we find no evidence that import competition reduced wages at the very bottom of the distribution, but only between the 10th and 35th quantile. We also revisit the effect of county food stamp programs on the county's birth weight distribution and find no significant effects.

The wormhole contribution to the gravitational path integral may be interpreted as smooth remnant of correlations among the erratic large-$N$ behaviors of dual CFTs. In this work, we investigate this idea in (2+1)-dimensional gravity. We show that one-sided boundary gravitons are intrinsically incomplete in the sense that the associated observable algebra has a nontrivial center regardless of choices of boundary conditions. Based on asymptotic symmetries, we bootstrap a general Poisson bracket to construct completions of the boundary gravitons. In the simplest completion, the commutant of the boundary graviton observable algebra is given by an observable algebra of monodromy data which we interpret as an effective description of one-sided black holes. We show that, to describe Lorentzian multi-boundary wormholes, only the monodromy data with a positivity restriction is needed. The positivity restriction results in emergent erratic large-$N$ behaviors for some observables. We filter out the erratic observables by restricting to a subspace on which they act trivially. The monodromy observables generate nonlocal symmetries lack of corresponding local currents. We show that gauging the nonlocal symmetries is equivalent to filtering out the erratic observables. For one CFT, gauging the nonlocal symmetries at the quantum level removes all black hole states. Filtering the partition function of CFTs leads to an apparent ensemble averaging. For two CFTs, a Hilbert subspace describing wormholes survives after gauging global part of the nonlocal symmetries. The filtered partition function of the two CFTs is an ensemble average over quantum gates entangling the monodromy degrees of freedom the two CFTs. The correlation between the erratic observables of the two CFTs is preserved, which contributes to the filtered partition function as a wormhole term.

Split Ga vacancies are the dominant native acceptor in $β$-$Ga_2O_3$; however, their role in $α$ and $κ$ phases has been largely overlooked or assumed to be unfavorable. A detailed understanding of these defects is critical for tailoring the electrical conductivity and optical properties and optimising $Ga_2O_3$-based devices. In this work, we used machine learning interatomic potentials (MLIPs) to accelerate the discovery of non-local defect reconstructions, followed by HSE06 hybrid DFT to accurately quantify defect properties of single vacancy $V_{\text{Ga}}$, split vacancy $V_{\text{Ga}}^{\text{i}}$ and substitutional donors ($\mathrm{Hf_{Ga}}$ and $\mathrm{Si_{Ga}}$) across a wide range of experimentally relevant conditions for the oxygen chemical potential. We find that split vacancies are the ground-state vacancy for all studied polymorphs ($β$, $α$, and $κ$). Split vacancies are more stable than simple vacancies by ~0.75 eV ($β$), ~0.41 eV ($α$), and ~0.14 eV ($κ$). Notably, MLIPs correctly identified the specific split-vacancy ground states and yielded an energetic ordering of symmetry-inequivalent defect configurations in excellent agreement with HSE06 results. While Hf and Si show low formation energy and act as shallow donors, especially under oxygen-poor conditions, their efficiency is limited by split-vacancy compensation. The growth under oxygen-poor conditions is a universal requirement to suppress these defects and achieve high n-type conductivity across the $Ga_2O_3$ polymorph.

We show that there does not exist a complex $d\times n$ equiangular tight frame with \[ d^2-d+1<n<d^2. \] The proof, which originated from an internal model at OpenAI, mimics the relationship between real equiangular tight frames and strongly regular graphs.

The correct gravitational representation of the supersymmetric index is a smooth complex solution, rather than the na\"ıve Euclidean continuation of the Lorentizan BPS black hole. We construct such saddles for black holes with \(\mathrm{AdS}_3\times S^3\) boundary conditions in the STU model. We arrive at the same finite-temperature BTZ \(\times S^3\) geometries in two independent ways: from two-center four-dimensional BPS solutions with complex dipole charges, and from six-dimensional black strings after imposing the BPS relation among conserved charges. We analyze the resulting smoothness and periodicity conditions and show that they are precisely those required for globally well-defined supersymmetry and for the thermodynamic potentials of the supersymmetric index.