This work examines approaches to making computational models reversible. Broadly speaking, transforming a computational model into a reversible one, i.e. reversibilizing it, means extending its operational semantics conservatively in a way that each term of the model is interpretable as a bijection. We recall that the most common strategy to reversibilize a computational model yields operational semantics that halts computations whenever a computational state cannot be uniquely determined from its successor state, thereby allowing terms to be interpreted as partial bijective functions. We are interested in reversible computational models whose terms can be interpreted as total bijective functions. This is essential for studying aspects of computational complexity related to reversible computational models. We introduce SCORE, a language designed for manipulating variables and stacks. Notably, common reversibilization strategies naturally lead to interpreting the functions for stack manipulation as partial bijections. According to our interests, we demonstrate how to interpret SCORE in a state space where, using a proof-assistant, we certify that stack operations are total bijections. It follows that all SCORE terms can be interpreted as total bijections.

This theoretical work is devoted to investigating the magnon-magnon interaction effect in a two-dimensional Heisenberg-Kitaev honeycomb ferromagnet with Dzyaloshinskii-Moriya interaction (DMI). Based on the first-order Green function formalism, we calculate the thermal-fluctuation-induced temperature-dependent self-energy corrections of magnons. Our calculations reveal that the critical temperature for temperature-induced topological phase transitions monotonically approaches the Curie temperature with increasing DMI strength. Furthermore, it is shown that the critical temperature for topological phase transitions is correlated with Dzyaloshinskii-Moriya interaction and magnetic field strength.

Topological Anderson insulators represent a class of disorder-induced, nontrivial topological states of matter. In this study, we propose a feasible strategy to unveil and design topological Anderson insulators protected by latent symmetries. These are not visible in the original system, but become obvious after performing an isospectral reduction. Using this technique, we design a family of disordered multi-atomic chains that exhibit latent chiral symmetry or mirror (inversion) symmetry. Using topological invariants, bulk polarization, and the divergence of localization length of the topological bound edge states in the reduced disordered system, we show how to identify the gapped and ungapped topological Anderson states in the original systems. Our work thus extends the concept of topological Anderson insulating phases protected by geometric symmetries and tenfold-way classification to the various types of latent symmetry cases. Overall, our work paves the way for exploiting topological Anderson insulators in terms of latent symmetries.

We report the emergence of Majorana flat bands (MFBs) in the vortex line of superconducting (SC) time-reversal-symmetry-breaking Weyl semimetals. By considering a Weyl semimetal as a stack of Chern insulators with varying Chern numbers along one ($z$) direction, we decompose the vortex bound states of SC Weyl semimetals into those of $k_{z}$-resolved SC Chern insulators. Through analytical and numerical calculations of the topological phase diagram of the SC Chern insulators, we explain the appearance of MFBs and determine the exact boundaries of them. Notably, the tuning of chemical potential or pairing strength results in the MFBs along the entire $k_{z}$ axis. To characterize the MFBs, we propose a $k_{z}$-resolved $Z_{2}$ Chern-Simons invariant as the topological indicator. Finally, we take an attractive Hubbard interaction into consideration, and the aforementioned SC Weyl semimetal with BCS pairing can be realized under appropriate parameters.

Realistic metric spaces (such as road/transportation networks) tend to be much more algorithmically tractable than general metrics. In an attempt to formalize this intuition, Abraham et~al.\ (SODA 2010, JACM 2016) introduced the notion of highway dimension. A weighted graph $G$ has highway dimension $h$ if for every ball $B$ of radius $\approx4r$, there is a hitting set of size $h$ hitting all the shortest paths of length $>r$ in $B$. Unfortunately, this definition fails to incorporate some very natural metric spaces such as the grid graph, and the Euclidean plane. We relax the definition of highway dimension by demanding to hit only approximate shortest paths. In addition to generalizing the original definition, this new definition also incorporates all doubling spaces (in particular the grid graph and the Euclidean plane). We then construct a PTAS for TSP under this new definition (improving a QPTAS w.r.t.\ the original more restrictive definition of Feldmann et~al.\ (SICOMP 2018)). Finally, we develop a basic metric toolkit for spaces with small highway dimension by constructing padded decompositions, sparse covers/partitions, and tree covers. An abundance of applications follow.

This paper presents an energy and thermal management system for electric race cars, where we tune a lift-off-throttle signal for the driver in real-time to respect energy budgets and thermal constraints. First, we compute the globally optimal state trajectories in a real-time capable solving time, optimizing a 47-kilometer horizon in 2.5 seconds. Next, for safe operation with a human driver, we simplify it to a maximum-power-or-coast operation in full-throttle regions (straights). Thereby, both the positions from which the vehicle should start coasting and the optimal throttle map are subject to tuning. To this end, we define the coasting sections with a threshold on the co-state trajectory of the kinetic energy from the optimal solution. We devise an online implementable bisection algorithm to tune this threshold and adapt it using PI feedback. Finally, we validate the proposed approach for an electric endurance race car and compare three variants with varying implementation challenges: one re-optimizing and updating the kinetic co-state trajectory online, one applying only the bisection algorithm online, and one relying exclusively on feedback control. Our results show that, under typical racing disturbances, our energy management can achieve stint times ranging from less than 0.056\% to 0.22\% slower compared to offline optimization with a priori knowledge of disturbances, paving the way for on-board implementations and testing.

We measure the cross-correlation between cosmic shear from the third-year release of the Dark Energy Survey, thermal Sunyaev-Zel'dovich (tSZ) maps from Planck, and X-ray maps from ROSAT. We investigate the possibility of developing a physical model able to jointly describe both measurements, simultaneously constraining the spatial distribution and thermodynamic properties of hot gas. We find that a relatively simple model is able to describe both sets of measurements and to make reasonably accurate predictions for other observables (the tSZ auto-correlation, its cross-correlation with X-rays, and tomographic measurements of the bias-weighted mean gas pressure). We show, however, that contamination from X-ray AGN, as well as the impact of non-thermal pressure support, must be incorporated in order to fully resolve tensions in parameter space between different data combinations. We obtain simultaneous constraints on the mass scale at which half of the gas content has been expelled from the halo, $\mathrm{log}_{10}(M_c)=14.83^{+0.16}_{-0.23}$, on the polytropic index of the gas, $Γ=1.144^{+0.016}_{-0.013}$, and on the ratio of the central gas temperature to the virial temperature $α_T=1.30^{+0.15}_{-0.28}$.

We extend the classical coding of measured $\mathbb R$-trees by continuous excursion-type functions to càdlàg excursion-type functions through the notion of parametric representations. The main feature of this extension is its continuity properties with respect to the Gromov-Hausdorff-Prokhorov topology for $\mathbb R$-trees and Skorokhod's $M_1$ topology for càdlàg functions. As a first application, we study the $\mathbb R$-trees $\mathcal T_{x^{(α)}}$ encoded by excursions of spectrally positive $α$-stable Lévy processes for $α\in (1,2]$. In a second time, we use this setting to study the large-scale effects of a well-known bijection between plane trees and binary trees, the so-called rotation. Marckert has proved that the rotation acts as a dilation on large uniform trees, and we show that this remains true when the rotation is applied to large critical Bienaymé trees with offspring distribution attracted to a Gaussian distribution. However, this does not hold anymore when the offspring distribution falls in the domain of attraction of an $α$-stable law with $α\in (1,2)$, and instead we prove that the scaling limit of the rotated trees is $\mathcal T_{x^{(α)}}$.

Semi-topological Galois theory associates a canonical finite splitting covering to a monic Weierstrass polynomial. The inverse limit of the corresponding deck groups defines the absolute semi-topological Galois group, $\PiST(X,x)$. This paper develops a cohomology theory for $\PiST(X,x)$ with discrete torsion coefficients, establishing its fundamental properties and canonical comparison maps to singular cohomology. A Lyndon-Hochschild-Serre spectral sequence is used to yield an obstruction theory for semi-topological embedding problems. We prove several structural and vanishing results, including ST-fullness for free fundamental groups and triviality for finite fundamental groups. As applications, we provide a criterion for lifting finite projective monodromy to linear monodromy, formulate the $π_1$-detectable Weierstrass realizability conjecture for divisor classes and show that this conjecture is true for abelian varieties, smooth complex projective curves and ruled surfaces over positive-genus curves.

The issue of general covariance in effective quantum gravity models within the Hamiltonian framework is addressed. The previously proposed equations for the covariance condition in spherically symmetric models are explicitly derived. By solving this equation, a new effective Hamiltonian constraint is obtained, incorporating free functions that can account for quantum gravity effects. The resulting spacetime structure is analyzed by specifying the free functions. Remarkably, in this model, the classical singularity is replaced by a region where the metric asymptotically approaches a Schwarzschild-de Sitter one with negative mass. Thus, this new quantum-corrected black hole model avoids the Cauchy horizons presented typically in previously studied models. The covariant approach is also applicable to matter coupling in the models.

We analyze Szöllősi's recent construction of a conjecturally optimal five-dimensional kissing configuration and produce a new such configuration, the fourth to be discovered. We construct five-dimensional sphere packings from these configurations, which augment Conway and Sloane's list of conjecturally optimal packings. We also construct a new kissing configuration in nine dimensions. None of these constructions improves on the known records, but they provide geometrically distinct constructions achieving these records.

The energy demand of modern cloud services, particularly those related to generative AI, is increasing at an unprecedented pace. To date, carbon-aware computing strategies have primarily focused on batch process scheduling or geo-distributed load balancing. However, such approaches are not applicable to services that require constant availability at specific locations due to latency, privacy, data, or infrastructure constraints. In this paper, we explore how the carbon footprint of energy-intensive services can be reduced by adjusting the fraction of requests served by different service quality tiers. We show that adapting this quality of responses with respect to grid carbon intensity can lead to additional carbon savings beyond resource and energy efficiency. Building on this, we introduce a forecast-based multi-horizon optimization that reaches close-to-optimal carbon savings and is able to automatically adapt service quality for best-effort users to stay within an annual carbon budget. Our approach can reduce the emissions of large-scale LLM services, which we estimate at multiple 10,000 tons of CO2 annually, by up to 10%.

Large plume-like features within the Greenland Ice Sheet disrupt radiostratigraphy and complicate the use of isochrones in reconstructions of past ice dynamics. Here we use numerical modeling to test the hypothesis that convection is a viable mechanism for the formation of the large (>1/3 ice thickness) englacial plume-like features observed in north Greenland. Greater horizontal shear and snow accumulation impede formation of convection plumes, while stable and softer ice encourages them. These results potentially explain the dearth of basal plumes in the younger and higher-accumulation southern ice sheet. Leveraging this mechanism to place bounds on ice rheology suggests that -- for north Greenland -- ice viscosity may be ~9-15 times lower than commonly assumed. Softer-than-assumed ice there implies significantly reduced basal sliding compared to standard models. Implementing a softer basal ice rheology in numerical models may help reduce uncertainty in projections of future ice-sheet mass balance.

We study the property $P_{\text {naive }}$ of mapping class groups of surfaces of infinite type, that is, for any finite collection of non-trivial elements $h_{1},h_{2}, \cdots, h_{n}$, there exists another element $g\neq 1$ of infinite order such that for all $i$, $\langle g, h_{i}\rangle \cong \langle g \rangle * \langle h_{i} \rangle$.

In the evolving digital landscape, network flow models have transcended traditional applications to become integral in diverse sectors, including supply chain management. This research develops a robust network flow model for semiconductor wafer supply chains, optimizing resource allocation and addressing maximum flow challenges in production and logistics. The model incorporates the stochastic nature of wafer batch transfers and employs a dual-layer optimization framework to reduce variability and exceedance probabilities in finished goods. Empirical comparisons reveal significant enhancements in cost efficiency, productivity, and resource utilization, with a 20% reduction in time and production costs, and a 10% increase in transportation and storage capacities. The model's efficacy is underscored by a 15% decrease in transportation time and a 6700 kg increase in total capacity, demonstrating its capability to resolve logistical bottlenecks in semiconductor manufacturing. This study concludes that network flow models are a potent tool for optimizing supply chain logistics, offering a 23% improvement in resource utilization and a 13% boost in accuracy. The findings provide valuable insights for supply chain logistics optimization.

In this paper we provide a detailed study on effective versions of the celebrated Bilu's equidistribution theorem for Galois orbits of sequences of points of small height in the $N$-dimensional algebraic torus, identifying the quantitative dependence of the convergence in terms of the regularity of the test functions considered. We develop a general Fourier analysis framework that extends previous results obtained by Petsche (2005), and by D'Andrea, Narváez-Clauss and Sombra (2017).

This study investigates the nucleation, dynamics, and stationary configurations of Abrikosov vortices in hybrid superconductor-ferromagnetic nanostructures exposed to inhomogeneous magnetic fields generated by a ferromagnetic nanodot. Using time-dependent Ginzburg-Landau simulations and Maxwell's equations, we observe and provide an explanation for the evolution of curved vortex structures that undergo creep-like deformation while reaching a steady state. Spatial variations in the Lorentz force, along with the interaction between geometric constraints and vortex interactions, give rise to unusual stationary vortex configurations that gradually change with increasing field strength, a behavior not seen in homogeneous magnetic fields. These findings reveal complex pinning mechanisms, providing valuable insights for the optimization and further advancement of nanoscale superconducting systems.

High harmonic generation is a resource of extremely broad frequency combs of ultrashort light pulses. The non-classical nature of this new quantum source has been recently evidenced in semiconductors by showing that high harmonic generation generates multimode squeezed states of light. Applications in quantum information science require the knowledge of the mode structure of the created states, defining how the quantum properties distribute over the spectral modes. To achieve that, an effective Schmidt decomposition of the reduced photonic state is performed on a tripartite harmonic set by simultaneously measuring the second- and third-order intensity correlation function. The Schmidt number is estimated which indicates an almost single-mode structure for each harmonic, a useful resource in quantum technology. By modelling our data with a displaced squeezed state, we retrieve the dependencies of the measured correlation as a function of the high harmonic driving laser intensity. The effective high-harmonic mode distribution is retrieved, and the strength of the contributing squeezing modes is estimated. Additionally, we demonstrate a significant violation of a Cauchy-Schwarz-type inequality for three biseparable partitions by multiple standard deviations. Our results confirm non-classicality of the high-harmonic generation process in semiconductors. The source operates at room temperature with compact lasers, and it could become a useful resource for future applications in quantum technologies.

This paper presents a study of the generalized Davis-Wielandt radius of Hilbert space operators. New lower bounds for the generalized Davis-Wielandt radius and numerical radius are provided. An alternative of the triangular inequality for operators is also derived.

This paper presents a discrete homotopy theory and a discrete homology theory for finite posets. In particular, the discrete and classical homotopy groups of finite posets are always isomorphic. Moreover, this discrete homology theory is related to the discrete homotopy theory through a discrete analogue of the Hurewicz map.

We prove that any mild solution in the Koch--Tataru space to the incompressible Navier--Stokes equation with initial data in $\mathrm{BMO}^{-1}$ is weak*-continuous in time, valued in $\mathrm{BMO}^{-1}$. We also show that the global mild solution vanishes in $\mathrm{BMO}^{-1}$ at infinity in time.

This paper explores team formation when workers differ in skills and their desire to out-earn co-workers. I cast this question as a two-dimensional assignment problem with imperfectly transferable utility and show that equilibrium sorting optimally trades off output maximisation with the need to match high-skill workers to co-workers with weak relative concerns. This can lead to positive (negative) assortative matching in skill even with submodular (supermodular) production functions. Under supermodular production, this heterogeneity in preferences benefits all workers and reduces wage inequality. With submodular production, the distributional consequences are ambiguous, and some workers become worse off. The model reveals that skill-biased technological change (SBTC) incentivises domestic outsourcing, as firms seek to avoid detrimental social comparisons between high- and low-skill workers, thus providing a compelling explanation for the long-term increase in outsourcing. Finally, the benefits of SBTC can trickle down to low-skill workers-but only those whose relative concerns are weak.

Exchange coupling parameters $J_{ij}$ in the Heisenberg model are crucial for describing magnetic behavior at the atomic level. In magnetic materials, spin fluctuations can be accompanied by a self-consistent electronic response -- including charge and magnetization redistribution and changes in orbital occupations -- reflecting electron--spin coupling in the sense of electronic feedback to finite spin rotations. However, the quantitative importance of this coupling in extracting reliable $J_{ij}$ has not been fully clarified. Here, using fully self-consistent, nonperturbative evaluations, we show that finite-angle spin rotations induce such electronic feedback and quantify how strongly it renormalizes the extracted $J_{ij}$. We examine systems of both fundamental and practical interest, including perovskite SrMnO$_3$, Nd-based permanent-magnet compounds (Nd$_2$Fe$_{14}$B and Nd$_2$Co$_{14}$B), and elemental $3d$ transition metals.The nonperturbative approach yields exchange couplings that remain consistent over a wide range of rotation angles. Moreover, spin models parameterized in this way give reasonable agreement with experimental magnetic phase-transition temperatures, underscoring the quantitative role of electron--spin coupling. Overall, our results provide a practical route to constructing quantitatively reliable spin models for predictive finite-temperature simulations and magnetic-materials design.

We prove a superposition theorem for input-to-output stability (IOS) of a broad class of nonlinear infinite-dimensional systems with outputs including both continuous-time and discrete-time systems. It contains, as a special case, the superposition theorem for input-to-state stability (ISS) of infinite-dimensional systems and the IOS superposition theorem for systems of ordinary differential equations known from the literature. To achieve this result, we introduce and examine several novel stability and attractivity concepts for infinite-dimensional systems with outputs: We prove criteria for the uniform limit property for systems with outputs, several of which are new already for systems with full-state output, we provide superposition theorems for systems which satisfy both the output Lagrange stability (OL) and IOS, give a sufficient condition for OL and characterize ISS in terms of IOS and input/output-to-state stability. Finally, by means of counterexamples, we illustrate the challenges appearing on the way of extension of the superposition theorems from the literature to infinite-dimensional systems with outputs.

For an $n$-valued self-map $f$ of a closed manifold $X$, we prove an averaging formula for the Reidemeister trace of $f$ in terms of the Reidemeister coincidence traces of single-valued maps between finite orientable covering spaces of $X$. We then derive analogous formulas for the Lefschetz and Nielsen numbers of $f$. In the special case where $X$ is an infra-nilmanifold, we obtain explicit formulas for the Lefschetz and Nielsen numbers of any $n$-valued map on $X$.

We develop the theory of local operations and classical communication (LOCC) for bipartite quantum systems represented by commuting von Neumann algebras. Our central result is the extension of Nielsen's Theorem, stating that the LOCC ordering of bipartite pure states is equivalent to the majorization of their restrictions, to arbitrary factors. As a consequence, we find that in bipartite system modeled by commuting factors in Haag duality, a) all states have infinite single-shot entanglement if and only if the local factors are not of type I, b) type III factors are characterized by LOCC transitions of arbitrary precision between any two pure states, and c) the latter holds even without classical communication for type III$_{1}$ factors. In the case of semifinite factors, the usual construction of pure state entanglement monotones carries over. Together with recent work on embezzlement of entanglement, this gives a one-to-one correspondence between the classification of factors into types and subtypes and operational entanglement properties. In the appendix, we provide a self-contained treatment of majorization on semifinite von Neumann algebras and $σ$-finite measure spaces.

When treatments are non-randomly assigned, continuous, and yield heterogeneous effects at the same intensity, causal identification becomes particularly challenging. In such contexts, existing approaches often fail to provide policy-relevant estimates of the relationship between treatment intensity and outcomes, especially in the presence of limited common support. To fill this gap, we introduce the Clustered Dose-Response Function (Cl-DRF), a novel estimator designed to uncover the continuous causal relationship between treatment intensity and the dependent variable across distinct subgroups. Our approach leverages both theoretical and data-driven sources of heterogeneity, relying on relaxed versions of the conditional independence and positivity assumptions that are plausible across various observational settings. We apply the Cl-DRF estimator to estimate subgroup-specific dose-response relationships between European Cohesion Funds and economic growth. In contrast to much of the literature, higher funding increases growth in more developed regions without diminishing returns, while limited absorptive capacity prevents other regions from fully benefiting.

This study discusses the mechanism of the emergence of nearly constant mean angular momentum profiles, which are widely observed in curved turbulent flows including the bulk region of Taylor--Couette (TC) flows. For high-Reynolds-number TC flows where the inner and outer cylinders are weakly counter-rotating and co-rotating, both the bulk and boundary layers become turbulent without Taylor rolls, referred to as the featureless ultimate regime (UR). Thus, we utilize the Reynolds-averaged Navier--Stokes (RANS) equations to explain the mechanism of the nearly constant mean angular momentum. High-Reynolds-number experiments of TC turbulence are performed for reference, where the angular velocity ratio $a = -ω_\mathrm{out}/ω_\mathrm{in}$ is in the range $-0.5 \le a \le 0.1$. Verification of the RANS based on the conventional algebraic Reynolds stress model suggests that convection of the Reynolds stress is essential for predicting the angular momentum profile. This indicates that the physical origin of the nearly constant angular momentum is the history effect of the Reynolds stress. To rigorously incorporate the convection effect into the Reynolds stress, we employ the Jaumann derivative as a covariant time derivative. The model that takes into account the history effect involving the normal stress difference successfully predicts the nearly constant mean angular momentum in the co-rotating cases. This study suggests the significance of the history effects for understanding curved or rotating turbulent flows in terms of the statistical analysis.

Diffusion model-based generative image steganography (DM-GIS) is an emerging paradigm that leverages the generative power of diffusion models to conceal secret messages without requiring pre-existing cover images. In this paper, we identify a fundamental trade-off between stego image quality, steganographic security, and extraction reliability within the DM-GIS framework. Drawing on this insight, we propose \textbf{PA-B2G}, a \textbf{P}rovable and \textbf{A}djustable \textbf{B}it-to-\textbf{G}aussian mapping. Theoretically, PA-B2G guarantees the reversible encoding of arbitrary-length bit sequences into pure Gaussian noise; practically, it enables fine-grained control over the balance between image fidelity, security, and extraction accuracy. By integrating PA-B2G with probability-flow ordinary differential equations (PF-ODEs), we establish a theoretically invertible mapping between secret bitstreams and stego images. PA-B2G is model-agnostic and can be seamlessly integrated into mainstream diffusion models without additional training or fine-tuning, making it also suitable for diffusion model watermarking. Extensive experiments validate our theoretical analysis of the inherent DM-GIS trade-offs and demonstrate that our method flexibly supports arbitrary payloads while achieving competitive image quality and security. Furthermore, our method exhibits strong resilience to lossy processing in watermarking applications, highlighting its practical utility.

We consider a lattice model in which a tracer particle moves in the presence of randomly distributed immobile obstacles. The crowding effect due to the obstacles interplays with the quasi-confinement imposed by wrapping the lattice onto a cylinder. We compute the velocity autocorrelation function and show that already in equilibrium the system exhibits a dimensional crossover from two- to one-dimensional as time progresses. A pulling force is switched on and we characterize analytically the stationary state in terms of the stationary velocity and diffusion coefficient. Stochastic simulations are used to discuss the range of validity of the analytic results. Our calculation, exact to first order in the obstacle density, holds for arbitrarily large forces and confinement size.