Accurate performance prediction is essential for optimizing scientific applications on modern high-performance computing (HPC) architectures. Widely used performance models primarily focus on cache and memory bandwidth, which is suitable for many memory-bound workloads. However, it is unsuitable for highly arithmetic intensive cases such as the sum-factorization with tensor $n$-mode product kernels, which are an optimization technique for high-order finite element methods (FEM). On processors with relatively high single instruction multiple data (SIMD) instruction latency, such as the Fujitsu A64FX, the performance of these kernels is strongly influenced by loop-body splitting strategies. Memory-bandwidth-oriented models are therefore not appropriate for evaluating these splitting configurations, and a model that directly reflects instruction-level efficiency is required. To address this need, we develop a dependency-chain-based analytical formulation that links loop-splitting configurations to instruction dependencies in the tensor $n$-mode product kernel. We further use XGBoost to estimate key parameters in the analytical model that are difficult to model explicitly. Evaluations show that the learning-augmented model outperforms the widely used standard Roofline and Execution-Cache-Memory (ECM) models. On the Fujitsu A64FX processor, the learning-augmented model achieves mean absolute percentage errors (MAPE) between 1% and 24% for polynomial orders ($P$) from 1 to 15. In comparison, the standard Roofline and ECM models yield errors of 42%-256% and 5%-117%, respectively. On the Intel Xeon Gold 6230 processor, the learning-augmented model achieves MAPE values from 1% to 13% for $P$=1 to $P$=14, and 24% at $P$=15. In contrast, the standard Roofline and ECM models produce errors of 1%-73% and 8%-112% for $P$=1 to $P$=15, respectively.

We investigate a driven particle system, a multilane asymmetric exclusion process, where the particle number in every lane is conserved, and stationary state is fully uncorrelated. The phase space has, starting from three lanes and more, an umbilic manifold where characteristic velocities of all the modes but one coincide, thus allowing us to study a weakly hyperbolic system with arbitrarily large degeneracy. We then study space-time fluctuations in the steady state, at the umbilic manifold, which are expected to exhibit universal scaling features. We formulate an effective mode-coupling theory (MCT) for the multilane model within the umbilic subspace and test its predictions. Unlike in the bidirectional two-lane model with an umbilic point studied earlier, here we find a robust $z=3/2$ dynamical exponent for the umbilic mode. The umbilic scaling function, obtained from Monte-Carlo simulations appears to have a universal shape for a range of interaction parameters and depends only on umbilic mode degeneracy. Remarkably, the shape and dynamic exponent of the non-degenerate mode can be analytically predicted on the base of effective MCT, up to non-universal scaling factor. Our findings suggest the existence of novel universality classes with dynamical exponent $3/2$, appearing in long-lived hydrodynamic modes with equal characteristic velocities.

We define a nonlinear Fourier transform which maps sequences of contractive $n \times n$ matrices to $SU(2n)$-valued functions on the circle $\mathbb{T}$. We characterize the image of finitely supported sequences and square-summable sequences on the half-line, and construct an inverse for $SU(2n)$-valued functions whose diagonal $n \times n$ blocks are outer matrix functions. As an application, we relate this nonlinear Fourier transform with quantum signal processing over $U(2n)$ and multivariate quantum signal processing.

Replication packages are crucial for enabling transparency, validation, and reuse in software engineering (SE) research. While artifact sharing is now a standard practice and even expected at premier SE venues such as ICSE, the practical usability of these replication packages remain underexplored. In particular, there is a marked lack of studies that comprehensively examine the executability and reproducibility of replication packages in SE research. In this paper, we aim to fill this gap by evaluating 100 replication packages published in ICSE proceedings over the past decade (2015 - 2024). We assess the (1) executability of the replication packages, (2) efforts and modifications required to execute them, (3) challenges that prevent executability, and (4) reproducibility of the original findings for those that are executable. We spent approximately 650 person-hours in total to execute the artifacts and reproduce the study findings. Our analysis shows that only 40 of the 100 evaluated artifacts were fully executable. Among these, 32.5% ran without any modification. However, even executable artifacts required varying levels of effort: 17.5% required low effort, while 82.5% required moderate to high effort to execute successfully. We identified five common types of modifications and 13 challenges that lead to execution failure, encompassing environmental, documentation, and structural issues. Among the executable artifacts, only 35% (14 out of 40) reproduced the original results. These findings highlight a notable gap between artifact availability, executability, and reproducibility. Our study proposes three actionable guidelines to improve the preparation, documentation, and review of research artifacts, thereby strengthening the rigor and sustainability of open science practices in SE research.

This article provides a comprehensive review of the critical role of detection efficiency in demonstrating non-classicality across various device-independent and semi-device-independent scenarios. The central focus is the detection loophole, a challenge in which imperfect detectors can allow classical hidden variable models to mimic quantum correlations, thus masking genuine non-classicality. As a review, the article revisits the paradigmatic Bell scenario, detailing the efficiency requirements for the CHSH inequality, such as the 2/3 threshold for symmetric efficiencies, and traces the historical trajectory toward the first loophole-free tests. The analysis extends to other causal structures to explore how efficiency requirements are affected in different contexts. These include the instrumental scenario, which for binary variables has recently been shown to follow the same inefficiency bounds as the bipartite dichotomic Bell scenario; the prepare-and-measure scenario, where inefficiencies impact the certification of a quantum system's dimension and create security breaches in protocols such as Quantum Key Distribution (QKD); and the bilocality scenario, which exemplifies how employing multiple independent sources can significantly relax the required efficiencies to certify non-classical correlations.

The continuous growth of China's private passenger vehicle fleet has intensified material demand and embodied carbon emissions, underscoring the need for effective decarbonization pathways. This study develops a transferable, dynamic material flow analysis framework to assess vehicle stocks, metal flows (steel, aluminum, and copper), and embodied emissions from 2000 to 2070, and to quantify the contributions of demand-side and technology-side efficiency measures. The results reveal that: (1) The vehicle fleet is projected to peak at 327-507 million vehicles by mid-century, with new energy vehicles dominating both in-use stocks and end-of-life flows by the 2040s. (2) Cumulative metal demand is projected to reach 1914-2990 million tonnes over the upcoming five decades, with 879-1320 million tonnes supplied from secondary sources under baseline conditions. Technology-oriented measures substantially enhance recycling performance, enabling secondary steel to fully meet manufacturing demand and allowing aluminum and copper cycles to approach near closure by 2070. (3) Correspondingly, cumulative embodied carbon emissions from vehicle metals by 2070 range from 4958 to 9218 megatonnes of carbon dioxide, with technological upgrading reducing emissions by 1051-1619 megatonnes. In collaborative scenarios, demand management accounts for 64.3% of total emission reductions, while technology-oriented measures become increasingly important over the medium to long term. Overall, the findings demonstrate that unmanaged demand growth can substantially offset technological mitigation gains, highlighting the necessity of integrated demand- and technology-oriented strategies. This study provides a systemic and transferable framework to guide circular economy development and deep decarbonization transitions in vehicle fleets in China and other emerging economies.

The Krasnoselskii-Mann iteration is an important algorithm in optimization and variational analysis for finding fixed points of nonexpansive mappings. In the general case, it produces a sequence converging \emph{weakly} to a fixed point provided the parameter sequence satisfies a divergent-series condition. In this paper, we show that \emph{strong} convergence holds provided the underlying nonexpansive mapping is \emph{linear}. This improves on a celebrated result by Baillon, Bruck, and Reich from 1978, where the parameter sequence was assumed to be constant as well as on recent work where the parameters were bounded away from $0$ and $1$.

In this paper we study two families of three-dimensional quartics in the complex projective space ${\mathbb P}^4$: hypersurfaces with a unique quadratic singularity of rank 3, which is resolved by two blowups, and hypersurfaces with two quadratic singularities of rank 3 and 4, respectively. Both families have codimension 3 in the natural parameter space. For a Zariski general quartic in each of these families we prove factoriality and birational rigidity and describe its group of birational self-maps.

We give an elementary proof of some identities that express the squares of Riemann zeta function at integer points in terms of the series involving hyperbolic functions, digamma function, Bernoulli numbers etc. In this version, inaccuracies in the text have been corrected and one of the bibliographic references has been updated.

We present a string theory construction in which the particle physics contributions to the one-loop vacuum energy exactly cancel, whilst the gravitational contributions are suppressed in the size of one or two large extra dimensions. This provides an ultraviolet realisation of the Dark Dimension and Supersymmetric Large Extra Dimensions scenarios, with, moreover, an explanation as to why the Standard Model contributions to the vacuum energy cancel without the need of eV mass-splittings. Gravity propagates in micron sized dark dimension(s), whilst the visible and hidden sectors are supported on D-branes. Supersymmetry is broken in the dark dimension(s) à la Scherk-Schwarz, whereas supersymmetry is broken at the string scale, à la Brane Supersymmetry Breaking, in the D-branes sector, without inducing tadpoles, similarly to a different construction proposed a long time ago by Angelantonj and Antoniadis. Vacuum energy from the visible sector is cancelled by the vacuum energy of the hidden sector branes. We also discuss moduli stabilization in this set-up, finding that the interplay between the Scherk-Schwarz one-loop contribution and non-perturbative effects can fix the size of the dark dimension(s) to be exponentially large in the inverse string-coupling, leading to an exponentially small total vacuum energy, with all moduli stabilised in a dS saddle.

Accurate single photoelectron (SPE) characterization of photosensors is essential for controlling systematic uncertainties in low-light neutrino and dark matter detectors. We present a compact laboratory setup for the characterization of photosensors under controlled, low-light conditions. Specifically, we demonstrate its use with photomultiplier tubes (PMTs) operated at the SPE-level, using picosecond laser pulses and waveform digitization to determine key PMT properties. Measurements as a function of supply voltage and temperature ($-50^\circ$C to $+20^\circ$C) are performed on ET Enterprises 9821(Q)B tubes and a Hamamatsu R9980 assembly, which show exponential gain-voltage behavior and device-to-device variation. Cooling increases the gain by $\sim 0.1\,\%/^\circ$C, while the transit time spread (TTS) and peak-to-valley ratio (P/V) exhibit no clear temperature dependence. TTS decreases with voltage. Late pulses remain at the percent level and prepulses at the sub-percent level. Cable length affects both apparent gain and TTS. A model-independent, data-driven self-convolution method is introduced to quantify double photoelectron contributions from pulse charge spectra. The procedures provide a reproducible, practice-oriented reference for SPE-level PMT characterization and can be extended to other photosensor types.

In the center-of-mass frame, the spin density matrix for octet baryon-antibaryon pairs produced in polarized electron-positron annihilation is unambiguously determined within the one-photon-exchange approximation. The formalism simultaneously incorporates parity ($P$) and combined parity-charge conjugation ($CP$) violation arising from the coupling of the intermediate virtual photon to the baryon pair. The finite electron mass is explicitly accounted for as a correction to these $P$ and $CP$ violating effects. Built on the spin projection operator, the derived full and compact spin density matrix provides a natural starting point for evaluating other quantities of physical interest -- particularly angular distributions of sequential decays and the quantum entanglement of hyperon pairs.

We investigate many-body effects on the spin-split electron bands in altermagnets by computing the electron self-energy arising from interactions with magnons, phonons, and hybridized magnon-phonon modes. These interactions lead to band broadening, which can obscure the intrinsic spin-splitting in spectroscopic measurements. We consider a $d$-wave Lieb lattice altermagnet as a representative example. Our results reveal that the spin-splitting remains spectroscopically resolvable and provide theoretical estimates of lifetime effects relevant for experimental detection. For electron-magnon coupling, we find a distinct difference between spectral function broadening for up and down spins close to the Fermi surface, which is not present in the case of electron-phonon coupling. We relate it to the spin splitting of the magnon modes in altermagnets. The results, including magneto-elastic coupling, are very similar to the pure magnon case. This provides insights into quasiparticle dynamics in altermagnets and contributes to the broader understanding of many-body interactions in spin-split systems. By including the temperature dependence of the self-energies, we also quantify how thermal fluctuations influence the broadening of the electronic states.

For each $ω\in (0, 1)^{\mathbb N}$, we may construct a Cantor set $E(ω)\subset [0, 1]$ called a generalized Cantor set for $ω$. We study the moduli space of $ω$ denoted by $\mathcal M(ω)\subset (0, 1)^{\mathbb N}$. It is the set of $ω'$ so that $E(ω')$ is quasiconformally equivalent to $E(ω)$. In this paper, we show that the set $\mathcal M(ω)$ is measurable in $(0, 1)^{\mathbb N}$ and we give a necessary condition for $ω'$ to belong to $\mathcal M(ω)$. By using this condition, we show that there are uncountably many moduli spaces in $(0, 1)^{\mathbb N}$. We also show that except for at most one moduli space, the volume of the moduli space with respect to the standard product measure of $(0, 1)^{\mathbb N}$ vanishes.

LISA can observe cosmological millihertz (mHz) gravitational wave (GW) backgrounds that may offer a decisive test for asteroid-mass primordial black hole (PBH) dark matter (DM). In standard scenarios, failing to detect a scalar-induced gravitational wave (SIGW) background would exclude the last viable window for PBH DM formed through critical collapse. We show that this conclusion becomes much weaker in the presence of astrophysical foregrounds and strongly non-Gaussian primordial density perturbations, by studying how these phenomena affect the link between SIGWs and PBHs, and reevaluate LISA's sensitivity to asteroid-mass PBHs. In addition, we analyse the interplay between PBHs and SIGWs to gain further insights into the nature of primordial non-Gaussianity. We find that uncertainties in $f_{\rm NL}$ can induce substantial uncertainties in the PBH abundance, which ultimately limits LISA's capacity to fully probe the asteroid-mass PBH DM window.

In this paper, we present a comprehensive catalog of short bursts from magnetars based on eight years of NICER observations. A total of 1130 bursts were identified from 14 sources, with the sample dominated by SGR 1935+2154, which accounts for 76% of all detected bursts. We analyzed burst durations, spectral properties, and their correlations across multiple sources. Bursts from SGR 1935+2154 exhibit significantly longer durations, with a distribution peak at 316 ms, compared to a peak of 23 ms for bursts from other magnetars. Two μs-scale bursts were detected for the first time, originating from 1E 1048.1-5937 and CXOU J010043.1-721134. Spectral analysis in the 0.5-8 keV range using both blackbody and power-law models shows that bursts with higher fluences have harder spectra. In contrast, correlations between burst duration and spectral parameters are weak or absent. This catalog provides a valuable dataset for studying magnetar short bursts, enabling future modeling efforts and improving our understanding of the diversity and physical mechanisms of magnetar bursts.

We prove that any convex flat subset in a complete Euclidean building is contained in an apartment of the maximal system of apartments.

We report validation tests of a calcium atomic-beam source fabricated via Laser Powder Bed Fusion (L-PBF). The surface quality and elemental composition of the printed component were quantitatively assessed, allowing us to establish reference parameters for reliable operation in an ultra-high-vacuum environment. Safe operating conditions of the atomic oven were determined through a combination of simulations and experimental measurements. The ability of the device to deliver an atomic beam to the main experimental region -- the electron/ion trap -- was verified using atomic fluorescence imaging. Fluorescence spectroscopy was further employed to characterize the beam divergence, yielding an emission-cone half-angle of approximately 19 degrees for atoms near the beam axis. A current of atoms on the order of $10^8$ s$^{-1}$ was estimated in the electron-trapping region, which is more than sufficient for anticipated electron-trapping and ion-trapping experiments.

Given a connected reductive algebraic group $G$ with a Borel subgroup $B$ and a quasiaffine spherical $G$-variety $X$, we prove that every $G$-orbit $Y$ contained in the regular locus of $X$ can be connected by a $B$-normalized additive one-parameter group action with any minimal $G$-orbit in $X$ containing $Y$ in its closure. As a consequence, we show that the regular locus of $X$ is transitive for the subgroup in the automorphism group of $X$ generated by $G$ and all $B$-normalized additive one-parameter subgroups.

We derive decomposition formulas for supercharacters of quantum affine ortho-symplectic superalgebras and twisted quantum affine superalgebras into supercharacters of their finite-type quantum sub-superalgebras, by employing Cauchy-type identities for supersymmetric Schur functions. These formulas are obtained via a folding (reduction) procedure applied to the supercharacters of the finite-dimensional general linear Lie superalgebra $\mathfrak{gl}(M|N)$. As a special case, our results provide explicit character formulas for a class of Kirillov--Reshetikhin modules of quantum affine algebras (and their Yangian counterparts), thereby proving a previously proposed conjecture derived from Bethe ansatz analysis (arXiv:2309.16660).

Topological photonic phases are typically identified through band reconstruction, steady-state transmission, or real-space imaging of edge modes. In this work, we present a framework for spectroscopic readout of chiral photonic topology in a single driven optical cavity containing a spin-orbit-coupled Bose-Einstein condensate. We demonstrate that the cavity transmission power spectral density provides a direct and measurable proxy for a momentum- and frequency-resolved photonic Chern marker, enabling topological characteristics to be inferred from spectral data without the need for bulk-band tomography. In the loss-dominated regime, where cavity decay exceeds atomic dissipation, the power spectral density exhibits Dirac-like gapped hybrid modes with a vanishing Chern marker, indicating a trivial phase. When the dissipation imbalance is reversed, a bright, gap-spanning spectral ridge emerges, co-localized with peaks in both the Chern marker and Berry curvature. The complex spectrum reveals parity-time symmetric coalescences and gain-loss bifurcations, marking exceptional points and enabling chiral, gap-traversing transport. By linking noise spectroscopy to geometric and non-Hermitian topology in a minimal cavity-QED architecture, this work provides a framework for spectroscopic detection of topological order in driven quantum systems. This approach offers a pathway to compact, tunable topological photonics across a broad range of light-matter platforms, providing a method for the study and control of topological phases in hybrid quantum systems.

In a $k$-critical bifiltration, every simplex enters along a staircase with at most $k$ steps. Examples with $k>1$ include degree-Rips bifiltrations and models of the multicover bifiltration. We consider the problem of converting a $k$-critical bifiltration into a $1$-critical (i.e. free) chain complex with equivalent homology. This is known as computing a free resolution of the underlying chain complex and is a first step toward post-processing such bifiltrations. We present two algorithms. The first one computes free resolutions corresponding to path graphs and assembles them to a chain complex by computing additional maps. The simple combinatorial structure of path graphs leads to good performance in practice, as demonstrated by extensive experiments. However, its worst-case bound is quadratic in the input size because long paths might yield dense boundary matrices in the output. Our second algorithm replaces the simplex-wise path graphs with ones that maintain short paths which leads to almost linear runtime and output size. We demonstrate that pre-computing a free resolution speeds up the task of computing a minimal presentation of the homology of a $k$-critical bifiltration in a fixed dimension. Furthermore, our findings show that a chain complex that is minimal in terms of generators can be asymptotically larger than the non-minimal output complex of our second algorithm in terms of description size.

Stabilizer simulation of Clifford quantum circuits - error-correction circuits, Clifford subroutines, etc. - on classical computers has played a central role in our understanding of circuit performance. The stabilizer description, however, restricts the accessible noise one can incorporate into the simulation to Pauli-type noise. More general noise, including coherent errors, may have more severe impact on circuit performance than Pauli noise; yet, such general noise have been difficult to access, much less investigate fully, in numerical simulations. Here, through the use of stratified importance sampling, we show how general noise can be simulated within the stabilizer formalism in reasonable time, with non-unitary noise being nearly as cheap as Pauli noise. Unitary (or coherent) noise can require an order of magnitude more time for the simulation, but nevertheless completes in very reasonable times, a drastic improvement over past approaches that typically fail to converge altogether. Our work thus enables detailed beyond-Pauli understanding of circuit performance in the presence of real device noise, which is rarely Pauli in nature. Among other examples, we present direct simulation results for the performance of the popular rotated planar surface codes under circuit-level general noise, previously available only in limited situations and/or through mappings to efficiently simulatable physical models.

In the standard random graph process, edges are added to an initially empty graph one by one uniformly at random. A classic result by Ajtai, Komlós, and Szemerédi, and independently by Bollobás, states that in the standard random graph process, with high probability, the graph becomes Hamiltonian exactly when its minimum degree becomes $2$; this is known as a \emph{hitting time} result. Johansson extended this result by showing the following: For a graph $G$ with $δ(G) \geq (1/2+\varepsilon)n$, in the random graph process constrained to the host graph $G$, the hitting times for minimum degree $2$ and Hamiltonicity still coincide with high probability. In this paper, we extend Johansson's result to Berge Hamilton cycles in hypergraphs. We prove that if an $r$-uniform hypergraph $H$ satisfies either $δ_1(H) \geq (\frac{1}{2^{r-1}} + \varepsilon)\binom{n-1}{r-1}$ or $δ_2(H) \geq \varepsilon n^{r-2}$, then in the random process generated by the edges of $H$, the time at which the hypergraph reaches minimum degree $2$ coincides with the time at which it contains a Berge Hamilton cycle with high probability. In addition, we prove an analogous result for weak Berge Hamilton cycles. This generalizes the work of Bal, Berkowitz, Devlin, and Schacht, who established the result for the case where $H$ is a complete $r$-uniform hypergraph.

In this work we derive analytic expressions and numerical recipes for finding the effective observed position of sources close enough on sky that their Point Spread Functions (PSF), modelled as Gaussian profiles, overlap. In particularly we derive these for an elongated PSF, with a long and short axis, such as we would see from an instrument with a rectangular or elliptical mirror (relevant, for example, for the Gaia mission). We show that in this case the problem can be reduced to a one dimensional brightness profile with extrema along the line connecting the two sources, with an effective PSF width that depends on the relative orientation of the PSF and its degree of elongation. The problem can then be expressed in units of this effective width to be a function of the relative separation and light ratio alone (thus reducing to a rescaling of the un-elongated case). We derive the minimum light ratio, for a given separation and effective width, above which two sources will be resolved. We map out numerical procedures for finding the positions of these extrema across all possible cases. Finally we derive the positional offset and deviance associated with observing a fixed pair of blended sources from a variety of orientations, showing that this can be a significant source of excess noise.

Time-delay cosmography leverages strongly lensed quasars to measure the Universe's current expansion rate, H_0, independently from other methods. While the latest TDCOSMO results relied mainly on quadruply lensed quasars, doubly lensed systems are far more common and offer precise time delays, potentially enlarging the usable sample by a factor of five and enabling percent-level constraints on H_0. We present the first TDCOSMO analysis of a doubly imaged source, HE1104-1805, including the measurement of the four necessary ingredients. First, by combining 17 years of data from the SMARTS, Euler and WFI telescopes, we measure a time delay of 176.3\pm 10.8 days. Second, using MUSE data, we extract stellar velocity dispersion measurements in three radial bins with up to 5% precision. Third, employing F160W HST imaging for lens modelling and marginalising over various modelling choices, we measure the Fermat potential difference between the images. Fourth, using wide-field imaging, we measure the convergence added by objects not included in the lens modelling. Hence, we measure the time delay distance and the angular diameter distance to the deflector, favouring a power-law mass model over a baryonic and dark matter composite model. The measurement was performed blindly and yielded H_0 = 64.2^{+5.8}_{-5.0} x $λ_{int} km s^{-1} Mpc^{-1}, where λ_{int} is the internal mass sheet degeneracy parameter. This is in agreement with the TDCOSMO-2025 milestone and its precision for λ_{int}=1 is comparable to that obtained with the best-observed quadruply lensed quasars (4-6%). This work is a stepping stone towards a precise measurement of H_0 using a large sample of doubly lensed quasars, supplementing the current sample. The next TDCOSMO milestone paper will include this system in its hierarchical analysis, constraining λ_{int} and H_0 jointly with multiple lenses.

Symplectic slice theorems elucidate the local structure of symplectic manifolds carrying Hamiltonian actions of compact Lie groups. We generalize these theorems in two natural settings. The first is based on the idea that complex reductive algebraic groups are the natural complex-geometric counterparts of compact Lie groups. Using new definitions of Poisson and symplectic slices, we prove analogues of the classical symplectic slice theorems for Hamiltonian actions of complex reductive algebraic groups. These analogues have versions in the complex-algebraic and holomorphic categories, and make extensive use of Slodowy slices and decomposition classes in complex reductive Lie algebras. The starting point for our second setting is the fact that Hamiltonian Lie group actions are special cases of Hamiltonian symplectic groupoid actions. We generalize the classical symplectic slice theorems to the latter case.

We study constrained versions of the Ingleton inequality in the entropic setting and quantify its stability under small violations of conditional independence. Although the classical Ingleton inequality fails for general entropy profiles, it is known to hold under certain exact independence constraints. We focus on the regime where selected conditional mutual information terms are small (but not zero), and the inequality continues to hold up to controlled error terms. A central technical tool is a structural lemma that materializes part of the mutual information between two random variables, implicitly capturing the effect of infinitely many non-Shannon--type inequalities. This leads to conceptually transparent proofs without explicitly invoking such infinite families. Some of our bounds recover, in a unified way, what can also be deduced from the infinite families of inequalities of Matúš (2007) and of Dougherty--Freiling--Zeger (2011), while others appear to be new.

We discuss Euclidean geometries in AdS$_3$ whose Lorentzian slicing gives rise to closed baby universes with a spatial geometry given by genus $g\geq 2$ surfaces. Our setup only involves a two-dimensional holographic CFT defined on a higher genus Riemann surface and thus provides a well-posed alternative to shell states whose microscopic duals are less well understood. We find that geometries giving rise to baby universes are always subdominant. It follows that the baby universe does not provide a semi-classical description of the state since it is encoded in an exponentially suppressed part of the wave function. We then apply a prescription developed in \cite{Belin:2025wju} to make the baby universe geometry the leading saddle. In the process, the CFT state becomes mixed, in agreement with the qualitative gravitational picture. We show that the fluctuations in the baby universe are small, even at fixed central charge, making the geometry reliable in the semi-classical limit. Finally, we discuss the interpretation of this mixed state in pure gravity from the perspective of the Virasoro TQFT.

Interferometric Particle Imaging (IPI) is a powerful technique to characterize aerosol particles, which so far has been applied only to particles larger than about 100 wavelengths. We extend its applicability to smaller ice crystals, combining rigorous modelling of particle shapes with the Phase Field Modelling and light-scattering simulations with the Discrete Dipole Approximation (DDA). Even for particles with the largest dimension of 11.5 wavelengths (and the smallest one comparable to the wavelength), the 2D Fourier transform of the interferometric image remains linked to the 2D autocorrelation of the particle shape at various viewing angles, validating the general measurement principle. However, the sensor must necessarily have wide viewing angle, which complicates interpretation of apparent particle shape, when such particles are observed from the edge. IPI is, thus, shown to be a powerful optical technology for characterizing ice particles down to a few micrometers in the atmosphere. Meanwhile, DDA is a versatile method for such synthetic experiments and can further supply large datasets for development of various inversion methods.