The relative entropy between two states is a key concept in quantum information theory and quantum field theory. In the setting of quantum field theory, its computation requires the handling of relative modular Hamiltonians, which are typically very difficult to compute explicitly. In this paper, we exploit locality properties of general algebraic QFTs to estimate relative modular Hamiltonians between two states, $ω$ and $\tildeω$, and hence also their relative entropy, in terms of the modular Hamiltonian of a reference state $\hatω$, which might be better understood. For suitable pairs of states we can estimate the relative modular Hamiltonian for the algebra of a region $V_2$ from above, resp. from below, in terms of the modular Hamiltonian of $\hatω$ on a larger region $V_3$, resp. a smaller region $V_1$. Pairs of states and choices of regions which are susceptible to our scheme are related to the presence of superluminal signalling in the sense of Sorkin's paradox. If $ω=\hatω$, then there exists a unitary that maps $ω$ to $\tildeω$ on $V_3$ and that does not allow superluminal signalling from the spacelike complement $V_3'$ to $V_2$, resp. from $V_1$ to $V_2'$, if our upper, resp. lower, bound applies. To investigate the strength of our estimates we consider coherent states for CCR systems, focussing particularly on free scalar fields. Our estimates apply even if the relative modular Hamiltonian cannot be computed exactly. For sufficiently regular excitations we recover an exact result by squeezing. Our method thus yields an independent proof for the relative entropy formula in cases where the relative modular Hamiltonian cannot be computed exactly. For massless fields we establish the analogous result also for double cone regions. These results indicate that our estimates do not lose too much information.

In this paper, we introduce and study shifted twisted quantum affine algebras which provide a twisted counterpart of the theory of shifted quantum affine algebras. The shifted twisted quantum affine algebra $\U_q^{μ_+,μ_-}(\hgs)$ is obtained from the Drinfeld current presentation of twisted quantum loop algebras by shifting the Cartan--Drinfeld currents $ϕ_i^\pm(z)$ according to a coweight pair $(μ_+,μ_-)$. We prove that it admits a triangular decomposition and that, up to isomorphism, they depend only on the total shift $μ=μ_+ + μ_-$. For each shift $μ$, we define a category $\mathcal O_μ$ of representations of $\U_q^μ(\hgs) = \U_q^{0,μ}(\hgs)$ and prove a rationality theorem for the Cartan currents: on every weight space, the two currents $ϕ_i^+(z)$ and $ϕ_i^-(z)$ are expansions of the same rational operator-valued function, whose degree is prescribed by $α_i(μ)$. As a consequence, we classify the simple objects of $\mathcal O_μ$ by rational $\ell$-weights of the corresponding degrees. We then construct a deformed Drinfeld coproduct and use it to define a fusion product on the direct sum $\mathcal{O}^{sh}$ of the categories $\mathcal O_μ$. This fusion product is compatible with $q$-characters. We also classify finite-dimensional simple modules in $\mathcal{O}^{sh}$ in terms of dominant rational $\ell$-weights, with a separate treatment of type $A_{2n}^{(2)}$. Finally, we construct restriction representations relating representations of twisted quantum affine Borel algebras to representations of shifted twisted quantum affine algebras, and establish a $q$-characters formula for simple finite-dimensional representations of shifted twisted quantum affine algebras in terms of the $q$-characters of the corresponding simple representations of the twisted quantum affine Borel algebra $\U_q(\bs)$.

This study investigates the cosmological dynamics of an accelerating universe within the framework of teleparallel gravity using an exponential f(T) functional form. To obtain exact cosmological solutions, a hybrid scale factor is employed to model the smooth transition from an early decelerated phase to the present accelerated expansion of the Universe. The physical consistency of the model is analyzed through classical energy conditions and cosmographic parameters. By constraining the model parameters using 31 Hubble data points, we find that the resulting matter-energy density and pressure evolution remain consistent with the observed cosmic acceleration. Diagnostic analysis confirms that the model remains within the quintessence regime and asymptotically approaches the ΛCDM scenario.

We study order parameters in one-dimensional quantum lattice models with finite invertible or non-invertible symmetry. We investigate what properties a string operator must satisfy in order to acquire a non-vanishing expectation value in a given gapped phase. We deduce that multiplets of string order parameters organise into a Lagrangian algebra in the Drinfel'd centre of the symmetry category. In particular, we highlight the role of the multiplication rule as governing the fusion of the twisted sector local operators that constitute the string operator in the infrared limit. Our derivations exploit the tensor network approach to the classification of gapped phases and its reformulation in terms of module categories over the symmetry category. Within this framework, a gapped phase is associated with a pattern of spontaneous symmetry breaking wherein a Morita class of algebras of topological lines is preserved in the ground state subspace. The crux of the proof is to show that the expectation value of any string operator explicitly depends on the tube algebra module associated with the Lagrangian algebra, which is realised as the full centre of the corresponding module category. Finally, we demonstrate that these techniques extend to phases of symmetric mixed states.

Automata acceptance can, in several situations of interest, be captured game-theoretically via acceptance games. The existence of a winning strategy for Verifier then captures the existence of a winning run-tree of a given automaton over a model. However, such acceptance is rigid, in that it does not allow a measurable defect budget, which can be a challenge in software verification. In this paper, we draw inspiration from how bisimulation distance can be defined as an extension of bisimilarity to define epsilon-acceptance games. Our main theorem shows that a tree T is epsilon-accepted iff there is a tree T' that is accepted in the traditional (rigid) sense and the bisimulation distance of T' and T is at most epsilon. Our work also suggests a strong connection with measure theory, of which we give a preliminary exploration via appropriate examples. Our framework is defined over binary trees with leaves and infinite branches, and strictly contains the case in which binary nodes are seen as probabilistic choice and the defect measures the probability of the set of rejected branches.

Quantum state tomography (QST) is a fundamental task in quantum information science that aims to reconstruct unknown quantum states from measurement data. However, the exponential growth of Hilbert-space dimension with system size makes full tomography of general quantum states statistically and computationally prohibitive. This challenge has motivated extensive research on structured quantum state tomography, where prior structure, such as low-rankness, tensor-network representations, shallow quantum circuits, and neural quantum states, can substantially reduce the effective degrees of freedom and enable scalable recovery. In this review, we provide a unified perspective on QST for structured quantum states through three closely related themes: compact state representations, measurement design, and computational algorithms. After reviewing common models for structured quantum states, we survey existing work on geometric preservation properties of measurement frameworks, ranging from informationally complete POVMs to randomized measurements, and their implications for sample complexity. On the algorithmic side, we review optimization methods for reconstructing structured quantum states from empirical measurements. By connecting QST with broader principles from compressive sensing, matrix sensing, and structured inverse problems, this survey highlights common theoretical foundations underlying sample complexity, measurement efficiency, and scalable recovery.

We give a new proof of vanishing result of Esnault for the cohomology of constructible sheaves in the tower of ``mock'' Frobenius covers of projective space. The key idea is to use (a global form of) the perversity of nearby cycles.

The application of two-dimensional (2D) semiconductors, such as monolayer MoS2, is limited by the high contact resistance commonly attributed to interfacial barriers at metal contacts. Furthermore, the dependence of electrical conductivity on MoS2 thickness is still unsettled, as both increasing and decreasing trends with layer number have been reported. By showing the contrast between electrical transport of mono- and multilayer MoS2 exfoliated on Au under ultra-high vacuum (UHV) and ambient conditions, we experimentally prove that, contrary to the prevailing view in the literature, the intrinsic MoS2/Au junction is highly conductive and exhibits ohmic behaviour. Our results indicate that interfacial contamination is responsible for the high contact resistances reported to date and affects the thickness dependence of electrical transport, explaining the discrepancies observed in the literature. We rationalize those findings using electrical transport simulations. Lastly, we show that local force-mediated lamination on lightly contaminated contacts can recover pristine, ohmic contacts, offering a route towards nanoscale patterning.

Bayesian dynamic borrowing methods incorporate historical control data into current clinical trial analyses while allowing the degree of borrowing to depend on the compatibility between historical and current data. Although many methods have been proposed, the degree of borrowing is often difficult to interpret, especially when multiple historical control sources are available. This scoping review focuses on posterior quantification of borrowing from multiple historical controls. We discuss overall borrowing summaries based on effective historical sample size, together with method-specific source-level summaries of borrowing, information contribution, or compatibility arising from power priors, unit information priors, multisource exchangeability models, Dirichlet process mixture models, and potential bias models. We distinguish posterior borrowing measures from quantities describing prior information allocation or source-specific conflict. Two case studies, one with a binary endpoint and one with a continuous endpoint, illustrate that methods with broadly similar posterior treatment effect estimates may differ in both the overall amount and source-specific pattern of borrowing. These examples show that large overall borrowing may reflect selective borrowing from compatible historical sources rather than uniform borrowing from all sources. We recommend reporting treatment effect estimates together with overall and source-specific borrowing summaries, when available, to improve transparency in posterior inference.

This paper investigates the new notion of $2$-word-$π$-repre\-sentable graphs: the nodes of the graph correspond to the letters of the two words and there exists an edge between two nodes if the projections of any two letters of both words are equal. The benefit of not only using one word for a representation as introduced by Kitaev and Pyatkin is that every graph is $2$-word-$π$-representable. We present an algorithm that returns two representing words for any graph. Aside, we show that every permutation graph is representable by two $1$-uniform words and give constructions how graph operations on $2$-word-$π$-representable graphs can be realised on their representing words which give further insights into the representation of cographs.

In general, the pricing of variable annuities with guarantees can be done by solving the corresponding optimal stochastic control problem if the contract withdrawal strategy is assumed to be optimal. This is typically solved as a dynamic programming problem using deterministic grid methods, which become computationally infeasible for more than a few state variables. In such situations, one needs to rely on simulation methods. The least-squares Monte Carlo (LSMC) method has become a popular simulation method for solving optimal stochastic control problems in quantitative finance over the last decades. In principle, the LSMC, originally developed for pricing Bermudan options, cannot be used directly for pricing variable annuities without simplifying assumptions because the underlying state variables are affected by the control decisions. This paper presents modifications of the LSMC algorithm that makes the pricing of general variable annuities feasible. For numerical illustrations, the pricing of variable annuities with guaranteed minimum withdrawal benefit under optimal withdrawal strategies is obtained with and without stochastic interest rates, using either polynomial regression or neural network regression in the LSMC algorithm. We found that the classical polynomial LSMC can give very accurate prices, at the cost of manual feature engineering, and with a standard deviation of the estimator that increases greatly when interest rates are made stochastic. By contrast, neural network LSMC gives slightly less accurate prices, requires more training time, but does not require manual feature engineering, and making interest rates stochastic makes no visible difference to its accuracy, suggesting a more stable and robust pricing performance of deep LSMC for higher-dimensional pricing problems.

We investigate photon-assisted thermoelectric transport in four--quantum-dot nanostructures featuring ring and ring--chord geometries coupled to ferromagnetic leads. Focusing on the interplay between microwave-induced Floquet sidebands and geometry-driven Fano interference, we employ the nonequilibrium Green's function formalism combined with Floquet theory and a self-consistent Hartree treatment of electron-electron interactions within the linear response regime. The inclusion of a longitudinal interdot chord bridging the lead-coupled dots introduces a discrete interference pathway that competes with the continuum of ring-mediated states, giving rise to pronounced Fano resonances. Microwave irradiation dynamically reshapes these resonances through photon absorption and emission processes, enabling tunable control of electrical conductance, thermopower, and electronic thermal conductance. Quantitatively, at an intermediate temperature of $T=0.3Γ_0$ (where $Γ_0$ denotes the dot-lead coupling strength), the microwave-driven ring-chord geometry exhibits an exceptional thermoelectric figure of merit of ZT $\approx$ 12 and an optimal efficiency--power trade-off, reaching nearly $62\%$ of the Carnot efficiency with an output power of $6.24~\mathrm{fW}$. Crucially, the combination of spin-polarized injection from the leads and Zeeman splitting within the dots induces a robust spin-dependence within this Floquet--Fano interference. This cooperative interplay results in an enhanced spin Seebeck response and a maximum spin thermoelectric figure of merit of nearly $Z_sT \approx 18$. Our findings establish microwave-driven engineering of Fano interference as an effective strategy for modulating spin-caloritronic behavior in multi-quantum-dot devices.

We report on the impact of the stoichiometry of superconducting MoSi thin films on the performance of superconducting nanowire single-photon detectors (SNSPDs). Specifically, we investigate the relation between the film parameters critical temperature Tc , sheet resistance Rs and superconductor thickness d and observe a universal scaling behavior. To benchmark the performance of SNSPDs fabricated from films having different stoichiometry, we measure the bias dependent count rate curves, while the detector is illuminated with wavelengths between 780 nm and 1550 nm. The detector performance as a function photon energy for different nanowire widths reveals a linear relation between the detection current and the photon energy. Furthermore, we determine the interfacial thermal boundary conductance $β$ between the superconducting thin film and the substrate, by measuring the return current of the SNSPD and find an increase of $β$ with increasing Mo concentration. The highest sensitivity amongst all compared devices is achieved for Mo$_{0.53}$Si$_{0.47}$, with low Tc (4.1 K) and high Rs (397$Ω$/sq) at a film thickness of 5.4 nm.

The study of complex nitrogen (N)-bearing molecules is essential for probing the physical and chemical evolution of star-forming regions. In this paper, we present the identification of rotational emission lines from several complex N-bearing species such as methyl cyanide (CH$_{3}$CN), ethyl cyanide (C$_{2}$H$_{5}$CN), vinyl cyanide (C$_{2}$H$_{3}$CN), cyanamide (NH$_{2}$CN), and formamide (NH$_{2}$CHO) toward the high-mass protostar S255IR NIRS3 using ALMA band 4 observations. In addition, the vibrationally excited transitions of cyanoacetylene (HC$_{3}$N, $ν_{7}$ = 2) were detected. The column densities and excitation temperatures of these molecules were derived through LTE spectral modelling, yielding excitation temperatures in the range of 175$-$220 K. The high excitation temperatures (175$-$220 K) indicate that the identified N-bearing molecules arise from the warm inner regions ($T \geq 100$ K) of the source. The fractional abundances were further estimated relative to H$_{2}$, CH$_{3}$OH, and CH$_{3}$CN. A Pearson correlation heat map of the abundances reveals a strong positive correlation ($r > 0.7$) among three molecules in the cyanide family, such as CH$_{3}$CN, C$_{2}$H$_{3}$CN, and C$_{2}$H$_{5}$CN, suggesting that these N-bearing molecules may be chemically linked. Comparison with three-phase warm-up chemical models shows that the observed abundances of CH$_{3}$CN, C$_{2}$H$_{5}$CN, C$_{2}$H$_{3}$CN, NH$_{2}$CN, NH$_{2}$CHO, and HC$_{3}$N ($ν_{7}$ = 2) relative to H$_{2}$ are consistent with model predictions within factors of 1.04, 0.67, 1.28, 0.76, 0.72, and 0.96, respectively. Finally, we discuss the potential formation pathways of the identified N-bearing molecules in the context of gas-grain chemistry within S255IR NIRS3.

Quadratically regularized optimal transport (QOT) is an alternative to entropic regularization that yields sparse couplings and avoids numerical instabilities due to exponential scaling. From an optimization viewpoint, the dual QOT objective is concave but features a positive part function which prevents strong concavity and reduces smoothness of optimizers. Consequently, standard arguments for linear convergence of algorithms do not apply. In this paper, we nevertheless establish a quantitative curvature property for the QOT dual. Under mild assumptions covering both continuous and semi-discrete transport problems, we prove a local error bound and a Polyak-Lojasiewicz (PL) inequality, with explicit constants depending only on the problem primitives. These results are obtained by functional-analytic techniques exploiting that near the optimum, the argument of the positive part function is positive on the interior of the support of the optimal coupling. As applications, we derive linear convergence of the gradient ascent, coordinate ascent, and coordinate gradient ascent algorithms on the dual problem, with explicit contraction rates.

A graph $G$ is called $k$-factor-critical if after deleting any $k$ vertices the remaining subgraph still has a perfect matching. Fan and Lin [Adv. in Appl. Math. 174 (2026) 103019] posed an adjacency spectral condition for a graph with minimum degree to be $k$-factor-critical. A graph $G$ is fractional $k$-factor-critical if after deleting any $k$ vertices the remaining subgraph still has a fractional perfect matching. Clearly, the fractional $k$-factor-criticality of a graph is a necessary property for a graph to be $k$-factor-critical. Jia, Fan and Liu [Discrete Appl. Math. 386 (2026) 255-263] proposed a tight sufficient condition in terms of the spectral radius for a graph with fractional $k$-factor-criticality to be $k$-factor-critical. A natural question arises: can we derive analogous sufficient conditions by incorporating the minimum degree parameter of graphs? We first establish a lower bound on the size to ensure that a $(k+1)$-connected graph with fractional $k$-factor-criticality is $k$-factor-critical, where $k$ is a positive integer with $k\geq1$. Moreover, we provide a sufficient condition in terms of the spectral radius for a $(k+1)$-connected graph with fractional $k$-factor-criticality to be $k$-factor-critical. Our results generalize the result of Jia, Fan and Liu to $(k+1)$-connected graphs. Furthermore, our spectral conditions apply to a broader family of connected graphs compared with the results of Fan and Lin, as well as Jia et al.

In latent-position random graph models (LPMs), latent vertex positions $U_{1},\ldots,U_{n}$ are sampled from some distribution on a latent space $Ω$, then edges of an observed graph $G = ([n],E)$ are sampled with some probability $\mathbb{P}[(i,j) \in E ]=w(U_i,U_j)$ that depends on the unobserved latent positions. LPMs are ubiquitous in the statistical analysis of networks, offering models that have good empirical performance, strong theoretical guarantees, and tractable algorithms. The special case $Ω= [0,1]$ is important, as it corresponds to graphs with temporal or preference-based structure. In this paper, we study three problems related to LPMs with latent space $[0,1]$: \textit{ordering} the vertices according to the latent positions, \textit{estimating} the generating graphon $w$, and \textit{testing} whether an observed graph $G$ could have come from an LPM with state space $[0,1]$. Our results on the ordering problem greatly generalize two observations of Janssen/Smith (2022): (i) for \textit{some} families of graphons, the best estimate of the ordering converges much faster than the usual statistical rate of $\frac{1}{\sqrt{n}}$, and (ii) this occurs even though, for the same families of graphons, the best estimate of the latent positions still occurs at the usual $\frac{1}{\sqrt{n}}$ rate. As a main consequence, we develop a computationally-efficient graphon-estimation algorithm and show that it has the same convergence rate as the non-explicit optimal algorithm of Gao et al (2015). We also derive and analyze a testing procedure.

Right to be Forgotten (RTBF) in one of the oldest and prominent of the legal data rights. While its legal intention is straight forward (for example, the GDPR describes it in just 417 words), the computing community has found it challenging to implement this in practice. For example, regulators have issued 205 RTBF violations in the first five years of GDPR i.e., an RTBF failure once every 9 days, on average. In this work, we identify the uncertainties and risks in supporting RTBF from a computing perspective. Then, to mitigate these challenges, we propose a two-phase approach that bridges an intrinsic dichotomy between law and computing. We demonstrate the effectiveness of our technique by showing how it could have fully avoided 80% of RTBF violations that occurred in the year-6 of GDPR. We also discover six long-standing practices of computing and data management that have become anti-patterns for RTBF. Finally, to ground our research, we introduce RTBF capability into Elasticsearch, a popular open-source search engine.

Motivated by Refs.[1, 2], we investigate whether quantum chromodynamics (QCD)-inspired matter at finite quark chemical potential can dynamically support \emph{regular} black-hole interiors during gravitational collapse. To this end, we couple two effective equations of state, namely a three-flavor chiral quark model at finite temperature and chemical potential and a cold-QGP mean-field model with a dynamical gluon mass, to a spherically symmetric advanced Eddington--Finkelstein geometry. The matter source is treated as an effective anisotropic fluid. Rather than assuming a regular mass profile a priori, we determine the radial temperature dependence from the local conservation law and reconstruct the mass function from the Einstein equations. In the chiral model, the conservation equation admits an exact Lambert-function solution, but the physical coefficients select a singular near-center branch. In the cold-QGP model, the exact implicit temperature-radius relation drives the temperature to diverge near the center, causing the thermodynamic source terms and the reconstructed mass function to become incompatible with the regular-center condition. We therefore find that, within the effective framework adopted here, finite quark chemical potential reshapes the thermodynamics of the collapse phase but does not by itself provide a self-regularizing black-hole core. Any regular completion must invoke an additional inner vacuum-like phase or further microphysics beyond the two QCD-inspired equations of state considered in this work.

We investigate the zero-temperature phase diagram of a one-dimensional constrained quantum spin chain realized in coherently driven Rydberg-atom arrays with competing local Rabi driving and dipole-dipole exchange interactions. Projecting onto the blockade-constrained Hilbert space yields an effective model in which local and nonlocal quantum fluctuations compete on equal footing. Combining exact diagonalization, the density-matrix renormalization group, and variational uniform matrix-product-state calculations, we establish a complete phase diagram comprising a Luttinger liquid, an antiferromagnetic ordered phase, and a polarized paramagnet. We identify two distinct mechanisms for the destruction of antiferromagnetic order: a conventional Ising transition at strong driving and a continuous quantum melting into the Luttinger liquid at weak driving, characterized using entanglement-based diagnostics and finite-entanglement scaling. In addition, we uncover an exact ground-state factorization line embedded within the ordered phase, providing an analytically tractable zero-entanglement reference point for experiments with programmable Rydberg quantum simulators.

This paper addresses a novel weighted Riesz--Kolmogorov theorem and the extrapolation of multilinear compact operators in the context of weighted variable Lebesgue spaces. We establish the latter result via our Riesz--Kolmogorov theorem which yields a weighted interpolation theorem for multilinear compact operators in the variable Lebesgue setting. In proving this, we also show a weighted interpolation theorem in mixed-norm variable Lebesgue spaces. By means of our extrapolation result, we obtain new weighted compactness estimates for the commutators of multilinear $ω$-Calderón--Zygmund operators, multilinear fractional integrals and multilinear Fourier multipliers on weighted variable Lebesgue spaces. Our work generalizes several recent ones, including but not limited to those of Cao, Olivo and Yabuta in the setting of multilinear operators acting on the classical weighted Lebesgue spaces as well as the previous result by the authors in the setting of bilinear operators and variable Lebesgue spaces.

Fast prediction of the synthesizability conditions of materials remains challenging, even assuming synthesis under thermodynamic equilibrium. Approaches solely based on convex stability hulls neglect finite-temperature effects, while phonon-based phase diagram calculations are computationally demanding. Here, we demonstrate high-throughput generation of phase predominance diagrams as a function of temperature and partial pressures of gaseous reactants, helping bridge the gap between computational predictions and experimental synthesis. We employ fitting of elemental phase reference energies to zero-temperature total energies for improved calculation of formation enthalpies, along with machine-learned interatomic potentials for rapid determination of vibrational entropy and heat capacity. The resulting predominance diagrams can be intuitively understood by experimentalists and can be used to translate energies above stability hulls into synthesis conditions. Predominance diagrams are generated for selected oxide, nitride, sulfide, and phosphide systems, as well as for 48 more complex ternary metal phosphosulfide systems. The calculated predominance diagrams generally show good agreement with the experimental synthesis literature, with a drastic reduction in computational cost compared to a conventional approach relying on DFT-based phonon calculations. We identify several compounds predicted to be stable under well-defined thermodynamic windows, even though they appear as metastable in a zero-temperature stability hull picture. The method can be applied to rapidly estimate synthesis conditions for any inorganic material.

Stars of intermediate mass (~4-8Msun) evolve to the stage of white dwarfs through the asymptotic giant branch (AGB) stage: stationary hydrogen shell burning and helium thermal pulses, wind mass loss and planetary nebula ejection. Almost the totality of the mass lost (the initial mass minus the remnant white dwarf mass) is heavily processed `hot bottom burning' (HBB), as plain convection reaches the outer edge of the H-burning shell. This phase has been subject of intense investigations in the latest 25 years, in connection to three main research subjects: 1) the chemical evolution of proton-capture elements cycled in these stars, and their intrinsic uncertainties due to the uncertainty in the description of the AGB models; 2) the role of AGBs in the formation of multiple populations in globular clusters; 3) the possible AGB role in the composition of hot gas with high N/O in some primordial galaxies, particularly in those hosting a massive black holes. We here summarize some main achievements and problems in these research fields.

In this work, we establish a direct connection between supplemented Dyck language and the signed expectation value of chains of second quantization operators relatively to the physical vacuum and relatively to a one-determinant state. Inspired by the fact that Dyck language provides an example of the emergence of the Catalan numbers in linguistic framework analysis, we show that these numbers are central when numbering the terms remaining when eliminating vanishing contributions detected by our application of Dyck language to fermionic second quantization. From the translation of creation and annihilation operator - or of pairs of operators - into a bracket alphabet, we derive simple and intuitive sufficient conditions for the nullity of expectation values that does not require an explicit application of Wick's theorem. This is done here with respect to the physical vacuum or relatively to a one-determinant state. We also extend this translation into a diagrammatic framework that allows a visual determination of the signature of fully contracted terms, reproducing the results of Wick's theorem. This approach has been extended to the case of (nested) commutators of pairs of fermionic second quantization including at least one excitation or deexcitation operator. Our results have been implemented in a software, MobiDyck, whose source code is freely available on the web. The algorithmic approach inspired by our work on Dyck language is detailed in this paper. Finally, a comparison of our diagrammatic approach with Goldstone diagrams is provided and closes the article.

Social and behavioral science runs thousands of experiments each year, yet their findings rarely accumulate into a coherent map of what is known, what conflicts, and what remains missing. We introduce ExAtlas, a framework for turning an archive of experiments into an atlas: a structured map in which studies link, conflict, or leave bridgeable gaps. Given a target study, ExAtlas searches for prior studies that are locally close in treatment and outcome space and asks whether their observed effects can be composed to predict the target effect. This yields three cases. If the composition succeeds and agrees with the observed result, ExAtlas links the target to consistent prior evidence. If composition succeeds but disagrees, ExAtlas reconciles the conflict and proposes candidate moderators or higher-level theories that could explain it. If composition fails, ExAtlas proposes bridge experiments to close the gap. We provide an error bound for composition under local smoothness of the treatment-effect surface. On held-out targets certified as locally supported, ExAtlas recovers effect direction in 98.6% of cases. Human evaluations further suggest that its proposed bridge experiments are plausible and exhibit connectedness, and that its conflict explanations are useful for theory generation. These results suggest that the archive of social experiments contains more latent structure than current practice extracts -- and that making this structure explicit can guide both future theory and future experimentation.

The goal of this paper is to describe the birational geometry of the blowup of $\mathbb{P}^n$ at $n+4$ points in very general position. To achieve this, we follow an idea of Mukai and explore a special instance of Gale duality, namely, a correspondence between configurations of $n+4$ points in the projective spaces $\mathbb{P}^n$ and $\mathbb{P}^2$. We first prove that the blowup $X$ of $\mathbb{P}^n$ at $n+4$ general points is isomorphic to a certain Gieseker moduli space of rank $2$ vector bundles on the surface $S$ obtained by blowing up $\mathbb{P}^2$ at the $n+4$ Gale dual points. We then study the variation of these moduli spaces as we vary the polarization $L$ on $S$, and translate this variation into a partial Mori chamber decomposition of $\overline{Eff}(X)$, describing to some extent the birational geometry of $X$.

This work studies spectral properties of Schrödinger operators in the context of aperiodic order, using weighted Delone sets to explore the interplay between the underlying dynamics and spectral properties. We study parameter-dependent families interpolating between periodic and aperiodic regimes, whose spectra form so-called spectral butterflies. These reflect fractal and self-similar structures of the spectra. We review existing results, introduce additional examples, and establish new connections between works in the literature. The framework is largely dimension-independent and extends to non-Abelian groups and more general settings.

Radio continuum emission has the potential to be an extinction-free tracer of star formation. However, the relation between radio continuum luminosity and star formation rate, the radio-SFR relation, is affected by various effects such as cosmic-ray transport, free-free absorption, and cosmic-ray electron energy losses. We aim to calibrate the radio-SFR relation in a sample of nearby galaxies ranging from dwarf to spiral galaxies covering nearly five orders of magnitude in SFR range. We include, both, global (individual galaxies) and local (kiloparsec sized) measurements. We measured radio continuum luminosities at $144\,\rm MHz$ using observations with the LOw Frequency ARray (LOFAR) and measure radio spectral indices using ancillary $1.4\,\rm GHz$ data. Selecting 70 nearby (distance $d < 30\,\rm Mpc$) galaxies, 15 of which were used for local measurements, with rich ancillary data we present a study of the radio-SFR relation using total infrared, mid-infrared, H$α$, and far-ultraviolet as complementary SFR tracers. About one third of our sample are at least moderately star-forming edge-on galaxies with the remaining ones chosen to be a representative sample of a wide range of morphological types and SFR values. For the first time, we show that the radio luminosity ($L_{144}$), the star-formation rate (SFR), and the radio spectral index ($α$) define a 'fundamental plane' in the [$\log(L_{144})$, $\log(\rm SFR)$, $α$] space. This allows us to define a unified radio-SFR relation that works both for global and local data when using the radio spectral index as a second parameter. A unified radio-SFR relation for, both, global and local data may serve as a litmus test for galaxy simulations that include the effect of cosmic rays and magnetic fields. It also strengthens the case for using the radio-SFR relation as an extinction-free tracer of star formation.

We give a more space-efficient implementation of adaptive mergesort: Virtual-Memory Powersort. Using internal buffering techniques, we significantly reduce the memory consumption of the algorithm; specifically, for sorting $n$ objects the required buffer area is reduced from space for $n/2$ objects to $O(\sqrt{n \log n})$ objects. While this space-efficiency can be achieved (indeed reduced to $O(1)$) conceptually very easily with known inplace merging algorithms, using these as a drop-in replacement for the standard merge algorithm incurs a substantial slow-down. Virtual-Memory Powersort, by contrast, uses the same number of moves and comparisons as previous Powersort implementations up to an additive $O(n)$ term. We report on an empirical running-time study comparing our implementation against other Powersort variants and state-of-the-art stable sorting methods, demonstrating that almost in-place stable sorting can be achieved with negligible overhead in many scenarios.

The ordinary subdiffusion equation, with a fractional time derivative of at most first order, describes a process in which the propagation velocity of diffusing molecules is unlimited. To avoid this non-physical property different forms of the Cattaneo subdiffusion equation have been proposed. We define the Cattaneo effect as a delay of the ordinary subdiffusion flux activation by a random time. By incorporating this effect into the flux equation we get a Cattaneo--type subdiffusion equation (CTSE). We consider a subdiffusion process in which the Cattaneo effect is generated by the time-delay probability distribution controlled by the Mittag-Leffler function. Then, CTSE differs from the ordinary subdiffusion equation by a term with a fractional time derivative, whose order can be independent of the subdiffusion exponent. The influence of the Cattaneo effect on the solutions to the CTSE is discussed. We show that the process described by CTSE is subdiffusion in the entire time domain even though the temporal evolution of the mean square displacement of diffusing particle in the short-time limit is typical for superdiffusion. The delay in the flux activation in the subdiffusion equation should also cause a flux delay in a boundary condition. As an example, we study subdiffusion with the Cattaneo effect in a system with a partially absorbing wall at which the Robin boundary condition is assumed. We also propose a method for experimentally identifying the Cattaneo effect in a subdiffusive system.