Since Choo and Siow (2006), a burgeoning literature has analyzed matching markets when utility is perfectly transferable and the joint surplus is separable. We take stock of recent methodological developments in this area. Combining theoretical arguments and simulations, we show that the separable approach is reasonably robust to omitted variables and/or non-separabilities. We conclude with a caveat on data requirements and imbalanced datasets.

We prove that for a generic family of circle diffeomorphisms every parameter value that corresponds to an irrational rotation number is approximated by parameter values for which the diffeomorphisms have arbitrarily large finite numbers of periodic orbits. This phenomenon implies that families where irrational rotation numbers appear are not weakly structurally stable. Moreover, we prove that any locally residual set of one-parameter families with nonconstant rotation number yields a continuum of weak equivalence classes of families.

This paper addresses the numerical optimization of proportional-integral-derivative (PID) controllers for linear time-invariant systems with delays, where the derivative action is implemented using a low-pass filter. While performance assessment is often based on the spectral abscissa of the ideal PID-controlled system, the inclusion of a derivative filter fundamentally alters the closed-loop spectral properties and cannot be treated as a post-processing step. In particular, the spectral abscissa of the filtered closed-loop system may differ significantly from that of its unfiltered counterpart, potentially affecting both stability and performance. We propose a systematic numerical design framework in which the PID gains and the filter constant are optimized simultaneously by directly minimizing the spectral abscissa of the filtered closed-loop system. Treating the filter as an integral part of the control design allows us to reconcile robustness at high frequencies, in the sense of mitigating fragility issues due to approximate identities, with performance at low frequencies, in addition to counter measurement noise amplification. At the end of the presentation, numerical examples illustrate the proposed approach and highlight the benefits of controller-filter co-design. The results apply to general linear systems with input and/or state delays and are valid for both single-input single-output (SISO) and multi-input multi-output (MIMO) configurations.

In the winter semester of 1890--1891 Adolf Hurwitz delivered a lecture course at the Albertina University in Königsberg entitled -Theorie der algebraischen Gleichungen-. These lectures contain a particularly clear presentation of the ideas of Evariste Galois and, in particular, a proof of the fundamental theorem of Galois theory formulated in the language of substitutions. The present paper analyzes Hurwitz's treatment of this result on the basis of his lecture notes preserved in the ETH Library in Zurich (Hs 582:66), together with material from his Mathematisches Tagebuch 23 (Hs 582:23). After placing the Königsberg lectures in their historical context, we give an overview of their mathematical content and reconstruct in detail Hurwitz's argument leading to the fundamental theorem.

Test-time augmentation (TTA) has become a promising approach for mitigating data sparsity in sequential recommendation by improving inference accuracy without requiring costly model retraining. However, existing TTA methods typically rely on uniform, user-agnostic augmentation strategies. We show that this "one-size-fits-all" design is inherently suboptimal, as it neglects substantial behavioral heterogeneity across users, and empirically demonstrate that the optimal augmentation operators vary significantly across user sequences with different characteristics for the first time. To address this limitation, we propose AdaTTA, a plug-and-play reinforcement learning-based adaptive inference framework that learns to select sequence-specific augmentation operators on a per-sequence basis. We formulate augmentation selection as a Markov Decision Process and introduce an Actor-Critic policy network with hybrid state representations and a joint macro-rank reward design to dynamically determine the optimal operator for each input user sequence. Extensive experiments on four real-world datasets and two recommendation backbones demonstrate that AdaTTA consistently outperforms the best fixed-strategy baselines, achieving up to 26.31% relative improvement on the Home dataset while incurring only moderate computational overhead

Magnetic textures are central to emerging spintronic and unconventional computing technologies due to their rich dynamics, topological properties and nanoscale dimensions. A major challenge remains achieving tunable, reversible, and spatially resolved control over these textures and their evolution as a function of external stimuli, by spatially reprogramming the magnetic energy landscape that governs their nucleation and stability. Here, we exploit a focused laser-assisted local field cooling technique that establishes a fast, non-contact and scalable platform for grayscale spin texture engineering. By non-destructively controlling the exchange-bias anisotropy with nanoscale resolution in thin-film heterostructures, this approach enables grayscale, reprogrammable control of the local energy profile, which we use to create magnetic patterns with highly controlled hysteresis, field-dependent readability and tunable switching thresholds. Leveraging this capability, we demonstrate information encoding with magnetic field-gated readability, and artificial spin metamaterials, stabilizing spin lattices with field-reconfigurable symmetries and creating artificial Moiré spin textures via the geometric superposition of twisted magnetic potentials. These results establish a versatile, reprogrammable platform that bridges the gap between application-oriented magnetic memory and fundamental studies of emergent order in artificial lattices.

We consider an iterative eigensolver for Schrödinger equations that constructs low-rank approximations of eigenfunctions with accuracy-adapted ranks, with particular focus on fermionic Schrödinger equations in second-quantized form and on matrix product state approximations enforcing particle number conservation. We provide a complete analysis of a solver based on preconditioned inverse iteration combined with rank truncation and propose a generalization to subspace iteration for the joint approximation of several eigenspaces. The practical performance of the method is illustrated by numerical tests for several model problems.

The paradigm shift towards local and on-device inference under stringent resource constraints is represented by the tiny machine learning (TinyML) domain. The primary goal of \gls{tml} is to integrate intelligence into tiny, low-cost devices under strict resource, energy, and latency constraints. However, the ultra-resource-constrained nature of these devices can lead to increased inference execution time, which can be detrimental in latency critical applications. At the same time, TinyML applications are often associated with sensitive data. As such, latency optimization approaches that rely on training samples are infeasible when such data is unavailable, proprietary, or sensitive, highlighting a pressing need for optimization approaches that do not require access to the training dataset and can be applied directly to pre-trained models. Replacing costly multiplications with more hardware-efficient operations, such as shifts and additions, has been proposed as an effective method for reducing inference latency. However, post-training power-of-two (Po2) approaches are scarce and, in many cases, lead to unacceptable accuracy loss. In this work, we propose a framework that applies approximate matrix decomposition to a given CNN in order to optimize hardware implementations subject to strict constraints and without any need of re-training or fine-tuning steps. The genetic algorithm-driven framework explores different matrix decompositions and resulting multiplier-less CNN accelerator designs for FPGA targets. A comprehensive evaluation of different TinyML benchmarks demonstrates our framework's efficacy in generating latency-optimized implementations that satisfy strict accuracy and resource constraints, achieving an average 33% latency improvement with an average accuracy loss of 1.3% compared to typical systolic array-based FPGA accelerators.

The decomposition of complex structures into simpler substructures is a powerful technique with a wide range of applications. We study the computation of decompositions in the context of programmable matter. The amoebot model is a well-established model for programmable matter, which places $n$ tiny robots called amoebots on the triangular grid. We consider the reconfigurable circuit extension of the geometric amoebot model, which allows amoebots to interconnect via so-called circuits. Amoebots can then instantaneously transmit simple beeps to all amoebots connected by the same circuit. Using reconfigurable circuits, previous papers have described a linear-time triangulation algorithm, and a logarithmic-time decomposition algorithm into so-called tunnel regions. Both algorithms only work on a restricted class of amoebot structures. In this paper, we define a decomposition into $O(|\mathcal H|)$ simple, geodesically convex regions for arbitrary amoebot structures, and show how it can compute such a decomposition in $O(\log n)$ rounds, where $|\mathcal H|$ denotes the number of holes in the amoebot structure. As a byproduct, we also improve the global maxima algorithm of Padalkin et al. (Nat. Comput., 2024) for special cases and with that also their spanning tree algorithm to $O(\log n)$ rounds w.h.p.

We propose a concept of dissipative weak (DW) solutions for the Navier-Stokes-Korteweg (NSK) system and prove conditional convergence of a structure-preserving finite volume scheme towards such a solution. DW solutions provide a generalized solution concept in computational fluid dynamics and have recently attracted significant attention. They provide an extension of the famous Lax Equivalence Theorem to nonlinear problems, i.e. consistency and stability of a numerical scheme imply convergence. Our work builds on recent advances where convergence towards DW solutions of structure-preserving schemes has been established for the Euler and Navier-Stokes equations. Indeed, we prove convergence of a recently proposed FV scheme by leveraging its conservation and dissipation properties as well as its consistency.

We revisit the constrained log-subtracted two-point Padé (LSTP) ensemble for thermal $\mathcal{N}=4$ supersymmetric Yang--Mills (SYM) thermodynamics in four spacetime dimensions after upgrading the weak-coupling truncation from $\mathcal{O}(λ^2)$ to the exact $\mathcal{O}(λ^{5/2})$ coefficient. We keep the interpolation ansatz unchanged and shift the weak-side matching points to the regime where the new term is numerically significant. The admissible set collapses from $9$ nominal survivors ($3$ distinct curves) to a single distinct curve, the crossover range shrinks to a unique value, and the pointwise band width drops to zero within numerical resolution. The Hermite-Padé (HP) central curve does not coincide with the unique LSTP survivor, so the exact weak-coupling coefficient removes the LSTP scan uncertainty but not the difference between the two routes. The next step is to compute the unknown $\mathcal{O}(λ^{-3})$ strong-coupling coefficient.

In a double-slit experiment with a bipartite system, the visibility of interference fringes depends on the availability of which-way information. Here, we report the formation of a Bell-like state of photoelectron and residual ion in the multiphoton dissociative ionization of the D$_2$ molecule. Evidence for entanglement is provided by the correlated emission directions of photoelectron and ion, which is observed using a COLTRIMS reaction microscope. In the presence of this correlation, the holographic interference fringes contained in the photoelectron momentum distributions are suppressed, indicating the existence of which-way information. We show that the which-way information is erased, and the interference pattern is restored, when a single ionic state is selected. The experimental observations and conclusions are fully supported by the numerical solution of the electronic-nuclear time-dependent Schrödinger equation. Our work demonstrates that coincidence spectroscopy of ions and electrons is a powerful method for studying fundamental concepts of quantum information science within the context of ultrafast light-matter interactions.

We establish an isoperimetric type inequality for the level sets of functions in fractional Sobolev spaces. This answers a question posed by the first author in a previous paper. To obtain it, we work out a slight modification of some estimates for nonlocal interaction functionals established by Savin and Valdinoci. We also show how said isoperimetric inequality leads to the Hölder continuity of functions in (weak) fractional De Giorgi classes.

We find an exact nonequilibrium steady state of an open dissipatively driven XXZ spin-1/2 chain with source or sink spin bath at one end and an arbitrary boundary field at the other end.

We propose a quantum-resistant quantum teleportation (QRQT) framework protected by post-quantum cryptography (PQC) to secure the classical correction channel, which is vulnerable to quantum adversaries. By applying PQC to the classical control bits, QRQT eliminates the classical attack surface of quantum teleportation. Our analysis reveals that quantum memory is a hidden bottleneck linking physical and computational security: its finite coherence time simultaneously limits communication distance, constrains tolerable PQC overhead, and restricts the adversary attack window. Under realistic parameters (1 ms coherence, fiber-optic propagation), the maximum secure teleportation distance ranges from 191 km (FrodoKEM-1344) to 199 km (Kyber512). We show that the joint classical-quantum attack probability exhibits a non-monotonic, Bell-shaped profile due to the opposing time dependencies of classical cryptanalysis and quantum decoherence, establishing a bounded optimal attack window beyond which adversarial success decays exponentially. We further analyze how leakage of classical correction bits affects teleportation security under four stochastic leakage models: independent exponential, sequential, burst, and correlated leakage, also accounting for amplitude damping on the shared Bell pair. For each scenario, we derive closed-form expressions for the average Holevo quantity and teleportation fidelity as functions of time, providing measurement-independent upper bounds on extractable information and guiding the design of leakage-resilient quantum communication protocols.

The observed solar photospheric magnetic fields and Doppler velocities are frequently used to quantify the Poynting flux and helicity flux. Multiple methods have been developed for this purpose, but their estimates of the Poynting flux and helicity flux often differ from one another. Here we study the performance of three widely used methods on NOAA active region 12673: "PTD-Doppler-FLCT Ideal" (PDFI), "Differential Affine Velocity Estimator for Vector Magnetograms" (DAVE4VM), and an extension of the latter with Doppler velocity constraint (DAVE4VMwDV). We find that the values of the accumulated energy and helicity differ significantly between the three methods, even in signs. Using the Helmholtz-Hodge decomposition, we show that Doppler velocity can contribute significantly to the Poynting flux and helicity flux through the non-inductive (curl-free) electric field. The different, ad hoc treatments of the Doppler and transverse velocities in three methods are directly responsible for the discrepancies. We discuss the desired future observations that can better constrain these methods.

Swarm protocols are a recently introduced formalism for specifying, implementing, and verifying peer-to-peer systems called swarms. A swarm consists of distributed agents called machines that communicate by asynchronous event propagation. Following a local-first model, each machine can progress without requiring continuous connectivity to other machines. Existing models of swarms are not compositional, making the modular development of large and complex swarm applications as well as the reuse of code difficult. We address these issues by presenting novel theory and techniques for the compositional specification, verification, and implementation of swarms. These results enable the correct compositional reuse of pre-existing swarm protocols and machine implementations. We implement these contributions in a companion software artifact which enables the automatic integration of independently designed and verified swarm components.

We show that the Hilbert space of the Koopman--von Neumann formulation of Landau--Ginzburg theory is parametrised by a real Monge--Ampère domain, which carries a natural pre-Frobenius. Restricting to finite-dimensional (dually flat) exponential families, the parameter space becomes a Monge--Ampère domain and a pre-Frobenius manifold. Our main theorem proves that for every Berglund--Hübsch--Krawitz mirror pair of Calabi--Yau orbifolds arising from an invertible polynomial, this Monge--Ampère domain (the open probability simplex) is the base of a Lagrangian torus fibration on both the original and the mirror hypersurface, with dual fibres in the sense of Strominger--Yau--Zaslow. The construction recovers the SYZ picture from the Landau--Ginzburg--Koopman--von Neumann framework. In particular, this proves the Kontsevich--Soibelman conjecture (2001) for all Berglund--Hübsch--Krawitz mirror pairs: the base of the SYZ fibration is a Monge--Ampère domain (the open simplex), and the torus fibrations on the mirror pair are dual. A toy model of cones of positive definite matrices illustrates the geometric structures.

Thermodynamics provides a useful interpretation of scalar-tensor gravity, in which the effective imperfect fluid admitted by the nonminimal coupling features a temperature that is associated with the departure from general relativity. However, in this construction, certain thermodynamical quantities are defined with respect to a particular conformal frame. In the present work, we show that the originally proposed effective temperature assigned to nonminimally coupled scalar field theories is not frame invariant, and can thus be arbitrarily tuned by a change of frame. This raises the question of whether temperature can be viewed as an intrinsic property of a scalar-tensor theory rather than a particular representation of it. Working instead with the frame invariant formulation of scalar-tensor gravity, we find that the frame invariant effective fluid is perfect with identically vanishing temperature. The departure from general relativity is then governed not by temperature, but rather by a frame invariant chemical potential, similar to minimal theories. Therefore, general relativity can be interpreted as a state of diffusive equilibrium for any scalar-tensor theory, regardless of whether it is minimal or nonminimal.

Off-nuclear tidal disruption events (TDEs) provide a rare probe of massive black holes (MBHs) outside galactic nuclei. Only a handful are known, including five X-ray-selected candidates and two optically selected events. We present observations of TDE 2025abcr, the second optically selected off-nuclear TDE, discovered at a projected offset of $9.08 \pm 0.02$ kpc from the nucleus of its host galaxy. We analyze X-ray, UV, optical, and infrared (IR) data from Swift, Keck, ZTF, and JWST. Broad H and He emission lines in the optical and IR confirm a TDE-H-He classification. From luminosity scaling relations and MOSFiT modeling, we infer a BH mass of $10^{6}$-$10^{7}\,M_{\odot}$, substantially smaller than the $10^{8.35 \pm 0.41}\,M_{\odot}$ BH inferred for the host-galaxy nucleus. We observe velocity evolution in the N III + He II emission complex, shifting from $-500$ km s$^{-1}$ at day $-7$ to $+1000$ km s$^{-1}$ by day $+29$, which we interpret as radiative transfer effects in an evolving reprocessing layer. The IR SED deviates from a thermal blackbody, with $νL_ν \propto λ^{-2.13 \pm 0.04}$, significantly shallower than the Rayleigh-Jeans slope of $λ^{-3}$. We rule out dust as the source of this IR excess. Two possibilities remain: free-free emission from reprocessing gas, or an unresolved stellar cluster at the TDE location. Reprocessed emission provides a natural explanation for the IR excess but an underlying stellar cluster of mass $\log(M_{*}/M_{\odot}) = 7.57 \pm 0.02$ and age $<$2 Gyr is also consistent with the data. If interpreted as a stellar cluster, the inferred mass suggests a stripped remnant of a satellite galaxy. The wandering MBH most likely originated in a minor merger with a smaller galaxy, although dynamical ejection from the host nucleus cannot yet be ruled out.

The evolution of 6th generation (6G) networks increasingly relies on satellite-based Non-Terrestrial Networks (NTNs) to extend broadband connectivity to remote and unserved regions, and to support public safety. In this paper we compare two representative and conceptually different satellite constellation architectures, namely Starlink and IRIS 2. Starlink is a commercial private Internet constellation by SpaceX, based on dense Low Earth Orbit (LEO) satellites. It is primarily designed to deliver high-capacity broadband services for civil applications, with performance targets comparable to those of terrestrial networks. In contrast, IRIS 2 is a planned public initiative to be deployed by the European Union, based on a multi-layer combination of LEO, Medium Earth Orbit (MEO), and Geo-stationary Earth Orbit (GEO) satellites. It is primarily designed to provide a secure, resilient, and sovereign infrastructure for government and critical communications. After describing the main technical characteristics of Starlink and IRIS 2, we run a comprehensive simulation campaign to evaluate the design tradeoffs between the two. Specifically, we evaluate the per-cell and per-user achievable capacity, the impact of satellite mobility and handover, and identify the capability of each architecture to support global and reliable connectivity. We also provide design suggestions for possible future IRIS 2 deployment extensions.

Using the LP algebraic toolkit, Conway's original topograph is rethought of as a cluster construction, paving the way for a wider topography based on mutation-type local rules. As a remarkable application of such cluster-driven upgrade, both the process of analytic continuation for Painlevé VI and the reduction algorithm for quadratic forms are endowed with the Laurent phenomenon. En passant, the rattlesnake is defined so to complete the bijection between snake graphs and rationals to the whole of $\mathbb{Q}$.

We present a geometric framework for reconstruction problems based on Vaisman foliations and Atiyah--Molino sequences. Independent projections induce transverse foliations and dual connections; vanishing torsion and curvature duality guarantee unique, path-independent reconstruction, while obstructions yield non-associative quasigroupoids. Toric symmetry provides equivariant uniqueness. Applications to generative AI imputation and cryo-electron microscopy demonstrate the framework's practical power, unifying differential geometry with data-driven inverse problems.

The interconnection network is a key component of Supercomputers and Data centers, and its design must cope with the increasing communication demands of current applications and services; otherwise, it may become a system bottleneck. The most challenging network design issues are the topology, routing algorithm, flow control, and power efficiency. However, even the most efficient interconnection networks may suffer severe performance degradation due to congestion, especially under specific network traffic patterns generated by communication operations in high-performance computing~(HPC), deep learning training, or online data-intensive services. In this context, characterizing and modeling these communication operations and the network traffic patterns they generate is a fundamental challenge for studying their impact on network performance. This paper presents a methodology, based primarily on the VEF Traces framework, to characterize, model, and simulate the communication patterns of representative computing- and data-intensive applications. More precisely, we have extended the VEF traces framework with tools that enable us to characterize network congestion, either directly from VEF traces or via simulations. We have analyzed a set of VEF traces obtained from runs of NEST, GROMACS, LAMMPS, and PATMOS on several Supercomputers. In these studies, we identify potential congestion scenarios that arise in realistic network configurations when certain collective operations are performed.

The relic abundance of Dark Matter (DM) produced via thermal freeze-in is sensitive to the thermal history during and after cosmic reheating. In minimal models, this opens up the possibility to make predictions for collider observables by combining the requirement to match the DM relic abundance with observations of the Cosmic Microwave Background (CMB). We assess the impact of thermal corrections to the rate of cosmic reheating and the rate of thermal DM production on CMB observables and the relic abundance. We find that such corrections are generally small in the regime where they can be computed by means of finite-temperature field theory. We construct counter-examples where this general rule is violated.

We present Veritas-RPM, a provenance-guided multi-agent architecture comprising five processing layers: VeritasAgent (ground-truth assembly), SentinelLayer (anomaly detection), DirectorAgent (specialist routing), six domain Specialist Agents, and MetaSentinelAgent (conflict resolution and final decision). We construct a 98-case synthetic taxonomy of false-positive scenarios derived from documented RPM patterns. Synthetic patient epochs (n = 530) were generated directly from taxonomy parameters and processed through the pipeline. Ground-truth labels are known for all cases. Performance is reported as True Suppression Rate (TSR), False Escalation Rate (FER), and Indeterminate Rate (INDR).

In most split-tunnel VPN/ZTNA deployments, installing an internal route authorizes the entire device, not a specific application, to use it. An unprivileged malicious process can therefore reach internal services by reusing routes intended for corporate applications. We present ProcRoute, a system that restricts internal-route access to explicitly authorized applications. ProcRoute models route access as an access-control problem: application identities are principals, destination prefixes with port and protocol constraints are resources, and a total, default-deny decision function mediates every connect() and UDP sendmsg() to an internal destination. Processes without a grant retain external access but are denied internal routes under our threat model. We describe ProcRoute's formal model, a Linux prototype built on cgroup v2 and eBPF socket-address hooks, and two complementary evaluations. In a two-machine WireGuard deployment, ProcRoute matches the WireGuard baseline and 13% faster than an nftables cgroup-matching configuration, with a p50 connect latency of 93 $μ$s (+3.6 $μ$s over baseline), flat policy scaling to 5,000 prefixes, and sub-millisecond revocation. Single-machine loopback microbenchmarks confirm low hook overhead: 2.7 $μ$s on the internal-allow path, 82/82 unauthorized pivot attempts blocked, and zero transient allows across 1.2 million connection attempts during policy reload.

In this article, we derive explicit combinatorial formulas, depending only on $q$, for the Wedderburn decomposition of the rational group algebras of the finite linear groups $\operatorname{SL}_2(q)$ and $\operatorname{PSL}_2(q)$. Furthermore, we also determine the number of pairwise non-isomorphic simple $\mathbb Q G$-modules of each possible dimension for $G$ being either $\operatorname{SL}_2(q)$ or $\operatorname{PSL}_2(q)$.

We compute the real part of the semi-classical limit of the sequence of quantum hyperbolic invariants (QHI) of the figure-eight knot complement $M$. We show that it is rigid, in the sense that it does not depend on the choice of holonomy representation of $M$, and it is either $0$ or equal to the hyperbolic volume of $M$ divided by $2π$, depending on a parity condition satisfied by logarithms of the holonomy eigenvalues on the canonical longitude, where the logarithms are parameters of the QHI of $M$. Along the way we also survey some relevant general features of the QHI.

We study the patient zero problem in epidemic spreading processes in the independent cascade model and propose a geometric approach for source reconstruction. Using Johnson-Lindenstrauss projections, we embed the contact network into a low-dimensional Euclidean space and estimate the infection source as the node closest to the center of gravity of infected nodes. Simulations on Erdős-Rényi graphs demonstrate that our estimator achieves meaningful reconstruction accuracy despite operating on compressed observations.