We propose a precise and efficient physics-augmented neural network (PANN) to model strain-induced crystallization in rubbery polymers. We demonstrate that the model can be flexibly employed for both unfilled and filled natural rubber (NR). The approach is based on a two potential framework, similar to the concept of generalized standard materials (GSMs). To describe the material behavior, neural network-based free energy and dissipation potentials are employed. The evolution of crystallinity is derived from the two potentials. To ensure boundedness of the crystallinity, a novel constrained GSM-type evolution problem is proposed. To this end, two additional Lagrange multipliers together with the corresponding Karush-Kuhn-Tucker conditions are introduced. As a result, it is guaranteed that crystallinity can be interpreted as a variable of concentration type. The neural network-based potentials ensure all physically desirable properties by construction. Most importantly, objectivity, material symmetry and thermodynamic consistency are automatically fulfilled. In addition, an alternative derivation of the governing model equations in time-discrete form is presented based on an incremental variational framework, which also serves as the basis for a finite element implementation. We demonstrate the predictive capability of the PANN using three different experimental data sets from literature, considering both stress and crystallinity evolution at material point level as well as the corresponding field distributions in a notched specimen. Moreover, we show that model parameterization is also possible when experimental crystallinity data is not available, still enabling suitable stress predictions.

We present a track-finding algorithm for the Belle II experiment that specifically targets so-called kinks: signatures of charged particles decaying or scattering in-flight in the detector material, resulting in a sudden and significant change of the particle's flight direction. Our benchmark studies of this Kink Finder show that the reconstruction efficiency for such signatures is about 40%, compared to a value of around 11% for the standard Belle II track-finding algorithm. Our studies also show that the Kink Finder significantly improves the resolution of the secondary track parameters, suppresses the number of cloned tracks, and reduces the PID misidentification rates for kaon and pions.

Given a circuit $G: \{0, 1\}^n \to \{0, 1\}^m$ with $m > n$, the *range avoidance* problem ($\text{Avoid}$) asks to output a string $y\in \{0, 1\}^m$ that is not in the range of $G$. Besides its profound connection to circuit complexity and explicit construction problems, this problem is also related to the existence of *proof complexity generators* -- circuits $G: \{0, 1\}^n \to \{0, 1\}^m$ where $m > n$ but for every $y\in \{0, 1\}^m$, it is infeasible to prove the statement "$y\not\in\mathrm{Range}(G)$" in a given propositional proof system. This paper connects these two problems with the existence of *demi-bits generators*, a fundamental cryptographic primitive against nondeterministic adversaries introduced by Rudich (RANDOM '97). $\bullet$ We show that the existence of demi-bits generators implies $\text{Avoid}$ is hard for nondeterministic algorithms. This resolves an open problem raised by Chen and Li (STOC '24). Furthermore, assuming the demi-hardness of certain LPN-style generators or Goldreich' PRG, we prove the hardness of $\text{Avoid}$ even when the instances are constant-degree polynomials over $\mathbb{F}_2$. $\bullet$ We show that the dual weak pigeonhole principle is unprovable in Cook's theory $\mathsf{PV}_1$ under the existence of demi-bits generators secure against $\mathbf{AM}$, thereby separating Jerabek's theory $\mathsf{APC}_1$ from $\mathsf{PV}_1$. $\bullet$ We transform demi-bits generators to proof complexity generators that are *pseudo-surjective* with nearly optimal parameters. Our constructions build on the recent breakthroughs on the hardness of $\text{Avoid}$ by Ilango, Li, and Williams (STOC '23) and Chen and Li (STOC '24). We use *randomness extractors* to significantly simplify the construction and the proof.

This article presents a novel encoding for quantum Lattice Boltzmann method algorithm using Carleman linearization. In contrast to previous articles \cite{Sanavio2024LatticeBC,sanavio2025carleman}, the encoding used allows for local collision rules while keeping a higher probability to obtain the right result, which is of the order of $10^{-2}$. The algorithm scales as $O(log_2^2(N)+Q^3)$ each time step with $N$ the number of lattice sites of the 2D lattice and $Q$ the number of channels with a constant number of qubits when using dynamical circuits.

We present a method for efficiently searching long-duration gravitational wave signals from compact binary coalescences (CBCs). The approach exploits the smooth frequency-domain behavior of ratios between neighboring waveform templates. The matched-filter signal-to-noise ratio (SNR) time series of a data segment is first computed for a reference template, and the SNRs of nearby templates are then reconstructed by convolving this reference SNR time series with the ratio waveforms, defined as the frequency-domain ratios between the reference and neighboring templates. The computational speedup arises because the ratio waveforms can be safely truncated: they are significant only over a short interval approximately equal to the duration difference between the templates. Storing these truncated ratio waveforms is practical and enables additional efficiency gains, in contrast to storing full templates, which is generally infeasible for long-duration, low-mass signals. We demonstrate the efficacy of the method with mock non-spinning CBC injections in the $1-3~M_\odot$ range. The reconstructed SNR time series agrees with that obtained from standard matched filtering to an accuracy of $O(10^{-4})$, while the relative computational cost is reduced by $\gtrsim 25\%$. With a truncation threshold of $10^{-3}$ applied to the ratio waveform amplitudes, the storage requirement is reduced by a factor of $\sim 60$ relative to storing the full template bank.

The measurement of the anomalous electron magnetic moment $g-2$ through quantum transitions of a single trapped electron is the most stringent test of quantum field theory. These experiments are now so precise that they must account for the effects of the cavity containing the electron. Classical calculations of this "cavity shift" must subtract the electron's divergent self-field, and thus require knowledge of the exact Green's function for the cavity's electromagnetic field. We perform the first fully quantum calculation of the cavity shift in a closed cavity, which instead involves subtracting linearly divergent cavity mode sums and integrals. Using contour integration methods, we find perfect agreement with existing classical results for both spherical and cylindrical cavities, justifying their current use. Moreover, our mode-based results can be naturally generalized to account for systematic effects, necessary to push future measurements to the next order of magnitude in precision.

Simulation of stabilizer circuits is a well-studied problem in quantum information processing, with a number of highly optimized algorithms available. Yet, we argue that further improvements can arise from the theoretical structure of stabilizer operations themselves. We focus on the subclass of stabilizer circuits composed of Calderbank-Shor-Steane (CSS)-preserving stabilizer operations, which naturally appear in fault-tolerant computations over CSS stabilizer codes. Using elementary circuit transformation techniques, we show that such circuits can be exactly rewritten as classical probabilistic circuits that reproduce measurement statistics. This rewriting introduces no computational overhead, in contrast to the general case of stabilizer circuits. To clarify the origin of this simplification, we introduce the standard quadratic form representation of general stabilizer operations (Clifford channels). It provides an efficient way to describe compositions of stabilizer operations and thus to simulate stabilizer circuits. CSS-preserving operations correspond to purely linear forms, which under a Walsh-Hadamard-Fourier transform yield a noncontextual hidden variable model, providing an alternative proof of the introduced rewriting. Finally, we develop a theory of reference frames for multiqubit systems, where frames are encoded by quadratic forms. This allows us to express stabilizer operations as probabilistic maps for proper reference frames. Non-CSS-preserving stabilizer circuits require dynamical modifications of reference frames, embodying a contextuality resource that leads to the computational overhead. This framework provides a new perspective on simulating stabilizer and near-stabilizer circuits within dynamically evolving quasiprobability models.

We introduce a notion of compact association schemes, which serves as a compact analogue of classical (finite) association schemes. Our definition is formulated in a way that closely parallels the finite case, naturally admits a Bose--Mesner algebra, and includes the compact strong continuous association schemes introduced by Voit [J. Aust. Math. (2019)] within the framework of hypergroups. This approach provides a new perspective that bridges the theory of association schemes with harmonic analysis on compact homogeneous spaces.

We study shortest-path routing in large weighted, undirected graphs, where expanding search frontiers raise time and memory costs for exact solvers. We propose \emph{SPHERE}, a query-aware partitioning heuristic that adaptively splits the problem by identifying \emph{source-target} ($s$--$t$) overlaps of hop-distance spheres. Selecting an anchor node $a$ within this overlap partitions the task into independent induced subgraphs for $s\to a$ and $a\to t$, each restricted to its own induced subgraph. If resulting subgraphs remain large, the procedure recurses on that specific subgraph. We provide a formal guarantee that by using the partition cut within the shared overlap, the resulting subpaths preserve feasibility, thereby avoiding the need for boundary repair. Furthermore, \emph{SPHERE} acts as a solver-agnostic framework that naturally exposes parallelism across subproblems. On million-scale road networks, \emph{SPHERE} achieves faster runtimes and smaller optimality gaps than contemporary state-of-the-art partitioning and community-based routing pipelines. Crucially, it also substantially mitigates heavy-tail runtime outliers suffered by standard exact methods, yielding highly stable and predictable execution times across varying queries.

Mode fluctuations with a long lifetime are essential for quantum information and logic operations in magnonic devices. We probe the broadband nonlinear magnetization dynamics of a high-quality ferromagnet under a strong microwave drive using microwave spectroscopy. We observe an \textit{unexpected} Fano resonance in the microwave transmission when the driven amplitude of the magnetization is large and the drive frequency $ω_d$ is close to but not at the ferromagnetic resonance. We interpret this Fano resonance by a scattering theory of photons considering the three-magnon interaction between the Kittel magnon and magnon pairs with opposite wave vectors of frequency $ω_d/2$. The theoretical model suggests that the microwave spectroscopy measures the dynamics of the fluctuation $δ\hatα$ of the Kittel magnon and $δ\hatβ_{\pm k}$ of the magnon pairs over the driven steady states, which are coupled coherently by the steady-state amplitudes. With the damping of $δ\hatβ_{\pm k}$ much smaller than that of $δ\hatα$, the theoretical calculation well reproduces the observed Fano resonance, indicating the magnon pairs hold a recorded long lifetime.

Short-time dynamics in the $2D$ Blume-Capel model, with a non-conserved order-parameter and short-ranged interactions, is analysed. For non-equilibrium dynamics, both at a critical point in the $2D$ Ising universality class and at the tricritical point, we reproduce the values $Θ=0.190({5})$ and $Θ=-0.542({5})$, respectively, of the critical initial slip exponent. These agree with more early estimates and with the Janssen-Schaub-Schmittmann scaling relation. In phase-ordering kinetics, after a quench into the ordered phase, we establish the validity of short-time dynamics. In the $2D$ Ising universality class, we find $Θ=0.39({1})$ in agreement with the scaling relation $λ=d-2Θ$.

It is a classical problem in algebraic topology to decide whether a given graded $\mathbb{Z}$-algebra can be realized as the cohomology ring of a space. In this paper, we introduce families of Stanley-Reisner algebras depending on graphs, and relate their realizability to the span coloring of the graph.

Platelet-enriched plasma and red blood cells (RBC) are needed in the treatment of blood-related diseases, including anaemia and blood cancer. These essential components must be separated from blood in well-designed experimental setups. If active techniques are used, the blood components are likely to be damaged or contaminated while handling. Passive techniques for component separation are preferred, and their design for effectiveness before manufacturing is the subject of this article. Specifically, the performance of a design consisting of a trifurcated microchannel is examined in the framework of 3D numerical simulation, following similar design ideas in recent experimental studies. The influence of geometrical parameters of the channel, such as width and separation arm angle, inlet extension, flow constriction, and flow parameters, including flow rates, hematocrit concentration, and temperature, is studied. The present study utilizes the diffusive flux model (DFM) to model the shear-driven migration of red blood cells (RBC) in a microchannel along with an appropriate rheology model. The physical mechanism driving separation is the formation of the cell-free layer near the walls, using which the separation efficiency and device effectiveness are quantified. It is found that a microchannel with a smaller width and an extended inlet, along with diluted blood samples of lower hematocrit, is effective for greater separation, while the device performance is less sensitive to the flow rates, flow constriction, and the separator angle.

Emerging altermagnets with zero net magnetic moment and moment-dependent spin splitting offer a promising avenue for antiferromagnetic spintronic devices, yet their integration into magnetic tunnel junctions has been hindered by reliance on ferromagnetic electrodes (introducing stray fields) or by limited functionality (non-tunable magnetoresistance without spin filtering). Here, we propose an all-altermagnetic tunnel junction (AAMTJ) paradigm composed exclusively of altermagnets, exemplified by experimentally feasible RuO2/NiF2/RuO2. By introducing an altermagnetic NiF2 barrier, the achieved tunneling magnetoresistances of 11,704%, 2,496% and 1,892% for RuO2/NiF2/RuO2 are much higher than that of 221% for RuO2/TiO2/RuO2 with a nonmagnetic TiO2 barrier. High spin filtering efficiencies of ~90% are also obtained. This architecture unlocks multistate high magnetoresistance and spin filtering via magnetization control of the electrodes and barrier, stemming from their synergistic and antagonistic alignments of momentum-dependent altermagnetic spin-splitting. Importantly, high tunneling magnetoresistances are still achieved in the AAMTJ with TiO2 spacer of RuO2/TiO2/NiF2/TiO2/RuO2. Our AAMTJ inherently exhibits low consumption and zero stray field, with nonrelativistic spin splitting and vanishing magnetic moment, combining the advantages of both ferromagnetic and antiferromagnetic tunnel junctions. This AAMTJ paradigm opens an interesting avenue within the area of high-performance altermagnet-based tunnel junctions.

We study time-evolving resonant states in an open double quantum-dot system, taking into account spin degrees of freedom as well as both on-dot and interdot Coulomb interactions. We exactly derived a non-Hermite effective Hamiltonian acting on the subspace of two quantum dots, where the non-Hermiticity arises from an effect of infinite external leads connected to the quantum dots. By diagonalizing the effective Hamiltonian, we identify four types of two-body resonant states. For the initial states of localized two electrons with opposite spins on the quantum dots, we exactly solve the time-dependent Schroedinger equation and obtain time-evolving two-body resonant states. The time-evolving resonant states are normalizable since their wave function grows exponentially only inside a finite space interval that expands in time with electron velocity. By using the exact solution, we analyze the survival and transition probabilities of localized two electrons on the quantum dots.

A development effort to improve the performance of superconducting radio-frequency half-wave resonators (SRF HWRs) is underway at the Facility for Rare Isotope Beams (FRIB), where 220 such resonators are in operation. Our goal was to achieve an intrinsic quality factor (Q0) of >= 2E10 at an accelerating gradient (Ea) of 12 MV/m. FRIB production resonators were prepared with buffered chemical polishing (BCP). First trials on electropolishing (EP) and post-EP low temperature baking (LTB) of FRIB HWRs allowed us to reach higher gradient (15 MV/m, limited by quench) with a higher quality factor at high gradient, but Q0 was still below our goal. Trapped magnetic flux during the Dewar test was found to be a source of Q0 reduction. Three strategies were used to reduce the trapped flux: (i) adding a local magnetic shield (LMGS) to supplement the ``global'' magnetic shield around the Dewar for reduction of the ambient magnetic field; (ii) performing a ``uniform cool-down'' (UC) to reduce the thermoelectric currents; and (iii) using a compensation coil to further reduce the ambient field with active field cancellation (AFC). The LMGS improved the Q0, but not enough to reach our goal. With UC and AFC, we exceeded our goal, reaching Q0 = 2.8E10 at Ea = 12 MV/m.

We study polynomial functors in the incompressible category $\text{Ver}_4^+$, which can be viewed as super polynomial functors in characteristic 2. Concretely, we classify additive, exact and simple polynomial functors, and describe how simple polynomial functors evaluate on arbitrary objects. We also determine which objects are not annihilated by any polynomial functors of a given degree and for which objects the symmetric group algebra acts faithfully via the braiding.

Artificial spin ices (ASIs) provide a versatile platform to explore magnetic frustration and emergent phenomena. However, in kagome ASI, experimental access to the ground state remains elusive due to dynamical freezing. Here, we demonstrate a deterministic and rewritable approach to attain the ground state using ultrafast, site-selective laser annealing. By engineering sublattice-dependent optical absorption through selective capping of the nanomagnets with Cr or utilizing different nanomagnet thicknesses, we achieve selective partial demagnetization of one sublattice under a sub-coercive magnetic field, driving the system into the ground state in a single switching step. Magnetic force microscopy reveals nearly perfect long-range ordering, while heat-transfer simulations confirm the sublattice-selective excitation mechanism. This work establishes an ultrafast method to attain the kagome ASI ground state, which does not require a modification of the geometry of the ASI or the materials used for the individual nanomagnets. Beyond ground-state writing, this site-selective activation provides an important tool for controlling the magnetic states, which is important for applications such as reconfigurable magnonic crystals, neuromorphic computing and programmable nanomagnetic logic.

Given a compact Riemannian surface $M$, with Laplace-Beltrami operator $Δ$, for $λ> 0$, let $P_{λ,λ^{-\frac{1}{3}}}$ be the spectral projector on the bandwidth $[λ-λ^{-\frac{1}{3}}, λ+ λ^{\frac{1}{3}}]$ associated to $\sqrt{-Δ}$. We prove a polynomial improvement on the $L^2 \to L^{\infty}$ norm of $P_{λ,λ^{-\frac{1}{3}}}$ for generic simple spheres of revolution (away from the poles and the equator) and for the Euclidean disk away from its center but up to the boundary. We use the Quantum Integrability of those surfaces to express the norm in terms of a joint basis of eigenfunctions for $\left(\sqrt{-Δ}, \frac{1}{i}\frac{\partial}{\partial θ}\right)$. Then, we use that those eigenfunctions are asymptotically Lagrangian oscillatory functions, each supported on a Lagrangian torus with fold-type caustic. Thus, studying the distribution of the caustics, and using BKW decay away from the caustics, we are able to reduce the problem to counting estimates.

Millisecond pulsars (MSPs) are the oldest but fastest pulsars known to date. In the 1980s, to explain how these pulsars could be formed, a new hypothesis was formulated: the recycling of pulsars, i.e the fact that a pulsar could accrete matter from a companion and been spun up. In this paper, we developed a population synthesis algorithm for pulsars which belong to a binary, in order to check whether most of the observed recycled pulsars were formed via an accretion mechanism and derive statistics about their properties, that are difficult to obtain through observations. We also make predictions for future surveys. Toward the presented objectives, we use the code Stellar EVolution for N-body (SEVN) to take into account all the binary processes and our own code to evolve each pulsar self-consistently by taking into account the secular evolution of a force-free magnetosphere, the magnetic field decay, gravitational braking and spatial evolution. Each pulsar is born in binary with a main sequence companion, and evolve to present time. The radio and $γ$-ray emission locations were modeled by the polar cap geometry and striped wind model, respectively. Our simulations seem to reproduce well the population of radio and $γ$-ray pulsars observed in the selected surveys. We also found that there should be less than $220$ unidentified pulsars in the Fourth Fermi-LAT catalogue of $γ$-ray sources (4FGL). High values of the viewing angle $ζ$ seem to be needed to be able to observe the recycled pulsars, and it also seems difficult to observe recycled pulsars with an aligned rotation axis and magnetic axis (i.e., $χ\leq 10$°). We find that only a small fraction, approximately $\sim 7.6\times10^{-3}$ %, of oxygen-neon white dwarfs (ONeWDs) in binary systems appear to contribute to the population of mildly recycled pulsars through accretion-induced collapse.

Decentralized prediction markets (DePMs) allow open participation in event-based wagering without fully relying on centralized intermediaries. We review the history of DePMs which date back to 2011 and includes hundreds of proposals. Perhaps surprising, modern DePMs like Polymarket deviate materially from earlier designs like Truthcoin and Augur v1. We use our review to present a modular workflow comprising eight stages: underlying infrastructure, market topic, share structure and pricing, market initialization, trading, market resolution, settlement, and archiving. For each module, we enumerate the design variants, analyzing trade-offs around decentralization, expressiveness, and manipulation resistance. We also identify open problems for researchers interested in this ecosystem.

Time series aggregation (TSA) aims to construct temporally aggregated optimization models that accurately represent the output space of their full-scale counterparts while using a significantly reduced temporal dimensionality. This paper presents a theoretical approach that achieves exact temporal aggregation of full-scale power system models -- even in the presence of energy storage time-coupling constraints -- by leveraging active constraint sets and dual information. This advances the state of the art beyond existing TSA methods, which typically cannot guarantee solution accuracy or rely on iterative procedures to determine the required number of representative periods. To bridge the gap between this theoretical analysis and practical application, we employ machine learning, i.e., classification and clustering, to inform TSA in models that co-schedule variable renewable energy sources and energy storage. Numerical results show substantially improved computational performance relative to the full-scale model, while maintaining a favorable trade-off between solution accuracy and complexity.

Synchronization is a ubiquitous phenomenon in complex systems. The Kuramoto model serves as a paradigmatic framework for understanding how coupled oscillators achieve collective rhythm. Conventional approaches focus on pairwise interactions, but real-world systems frequently involve higher-order couplings among multiple elements. Previous studies have shown that higher-order interactions enrich dynamics but generally shrink the attraction basin of synchronized states, making synchronization harder to achieve. Here, we demonstrate this picture is incomplete. Through systematic analysis of twisted states on ring networks, we identify a moderate coupling regime where higher-order interactions enhance stability without altering basin structure. The relative distribution among twisted states remains constant, yet quasipotential barriers deepen as coupling strengths increase. By measuring mean first passage times, we show both pairwise and higher-order couplings contribute synergistically to enhance stability, consistent with large deviation theory. These findings provide new insights into the role of higher-order interactions in synchronization.

As GPU-accelerated mathematical programming techniques mature, there is growing interest in utilizing them to address the computational challenges of power system optimization. This paper introduces ExaModelsPower.jl, an open-source modeling library for creating GPU-compatible nonlinear AC optimal power flow models. Built on ExaModels.jl, ExaModelsPower.jl provides a high-level interface that automatically generates all necessary callback functions for GPU solvers. The library is designed for large-scale problem instances, which may include multiple time periods and security constraints. Using ExaModelsPower.jl, we benchmark GPU and CPU solvers on open-source test cases. Our results show that GPU solvers can deliver up to two orders of magnitude speedups compared to alternative tools on CPU for problems with more than 20,000 variables and a solution precision of up to $10^{-4}$, while performance for smaller instances or tighter tolerances may vary.

In this paper, we introduce a general method to prove the non-degeneracy of the Hessian in the spinfoam vertex amplitude for quantum gravity and apply it to the spinfoam models with a cosmological constant ($Λ$-SF models). By reformulating the problem in terms of the transverse intersection of some submanifolds in the phase space of flat ${\rm SL}(2,\mathbb{C})$ connections, we demonstrate that the Hessian is non-degenerate for critical points corresponding to non-degenerate, geometric 4-simplices in de Sitter or anti-de Sitter space. Non-degeneracy of the Hessian is an important necessary condition for the stationary phase method to be applicable. With a non-degenerate Hessian, this method not only confirms the connection of the $Λ$-SF model to semiclassical gravity, but also shows that there are no dominant contributions from exceptional configurations as in the Barrett-Crane model. Given its general nature, we expect our criterion to be applicable to other spinfoam models under mild adjustments.

Uncontrolled geostationary satellites abandoned near an unstable equilibrium point of the equator experience irregular transitions between dynamical states (continuous circulation, long and short libration). They are caused by the interaction between the longitudinal dynamics, governed by the tesseral harmonics of the geopotential, and the orbital precession forced by Earth's oblateness and lunisolar perturbations. The transitions are extremely sensitive to small perturbations, making the long-term evolution unpredictable. Recently, a Monte Carlo analysis of trajectories starting in the immediate vicinity of the 165 degrees E unstable equilibrium point, revealed that the evolution to chaos is not gradual. It occurs via sudden episodes of disorder at specific points of the precession cycle, when the orbital inclination is minimal. Due to the high cost of the statistical analysis, the results were limited to a single initial longitude. This paper applies modified versions of the diameter Lagrangian descriptor to reduce the computational burden. This enables mapping the dynamical behavior over the complete range of longitudes where transitions between modes of motion are possible, considering both unstable equilibrium points (165 degrees E and 15 degrees W). It is found that the episodes of chaos remain linked to the orbital inclination cycle, but their timing depends on the initial spacecraft longitude. As the initial position moves farther away from the unstable point, the transitions take place at higher values of the orbital inclination. The longitudes where the transitions occur at maximum inclination correspond to the boundaries of the chaotic region.

Process mapping asks to assign vertices of a task graph to processing elements of a supercomputer such that the computational workload is balanced while the communication cost is minimized. Motivated by the recent success of GPU-based graph partitioners, we propose two GPU-accelerated algorithms for this optimization problem. The first algorithm employs hierarchical multisection, which partitions the task graph alongside the hierarchy of the supercomputer. The method utilizes GPU-based graph partitioners to accelerate the mapping process. The second algorithm integrates process mapping directly into the modern multilevel graph partitioning pipeline. Vital phases like coarsening and refinement are accelerated by exploiting the parallelism of GPUs. The first algorithm has, on average, about 12 percent higher communication costs than the state-of-the-art solver and thus remains competitive with it. However, in terms of speed, it vastly outperforms the competitor with a geometric mean speedup of 22 times and a maximum speedup of 934 times. The second approach is even faster, with a geometric mean speedup of 1454 times and a peak speedup of 12376 times. Compared to other algorithms that prioritize speed over solution quality, this approach has the same quality but much greater speedups. To our knowledge, these are the first GPU-based algorithms for process mapping.

Recent experiments in neuroscience reveal that task-relevant variables are often encoded in approximately orthogonal subspaces of neural population activity. These disentangled, or abstract, representations have been observed in multiple brain areas and across different species. These representations have been shown to support out of distribution generalization and rapid learning of novel tasks. The mechanisms by which these representations emerge remain poorly understood, especially in the case of supervised task behavior. Here, we show mathematically that abstract representations of latent variables are guaranteed to appear in the hidden layer of feedforward nonlinear networks when they are trained on tasks that depend directly on these latent variables. These learned abstract representations reflect the semantics of the input stimuli. To show this, we reformulate the usual optimization over the network weights into a mean field optimization problem over the distribution of neural preactivations. We then apply this framework to finite-width ReLU networks and show that the hidden layer of these networks will exhibit an abstract representation at all global minima of the task objective. Finally, we extend our findings to two broad families of activation functions as well as deep feedforward architectures. Together, our results provide an explanation for the widely observed abstract representations in both the brain and artificial neural networks. In addition, the general framework that we develop here provides a mathematically tractable toolkit for understanding the emergence of different kinds of representations in task-optimized, feature-learning network models.

Some applied researchers hesitate to use nonparametric methods, worrying that they will lose power in small samples or overfit the data when simpler models are sufficient. We argue that at least some of these concerns are unfounded when nonparametric models are strongly shrunk toward parametric submodels. We consider expanding a parametric model with a nonparametric component $r(x)$ that is heavily shrunk toward zero. This construction allows the model to adapt automatically: if the parametric model is correct, the nonparametric component disappears, recovering parametric efficiency, while if it is misspecified, the flexible component activates to capture the missing signal. We show that this adaptive behavior follows from simple and general conditions. Specifically, we prove that Bayesian nonparametric models anchored to linear regression, including variants of Gaussian process regression and Bayesian additive regression trees, consistently identify the correct parametric submodel when it holds and give asymptotically efficient inference for regression coefficients. In simulations, we find that the general BART model performs identically to correctly specified linear regression when the parametric model holds, and substantially outperforms it when nonlinear effects are present. This suggests a practical paradigm: defensive model expansion as a safeguard against model misspecification.

Quantum masking is a special type of secret sharing in which some information gets reversibly distributed into a multipartite system, leaving the original information inaccessible to each subsystem. This paper proposes a dynamical extension of quantum masking to the level of quantum channels. In channel masking, the identity of a channel becomes locally hidden but still globally accessible after its output is sent through a bipartite broadcasting channel. We first characterize all families of d-dimensional unitaries that can be isometrically masked, a condition that holds even in the presence of depolarizing noise. For the case of qubits, we identify which families of Pauli channels can be masked, and we prove that a qubit channel can be masked against the identity if and only if it is unital and has a pure-state fixed point. Masking against the identity describes a scenario in which channel noise becomes completely delocalized through a broadcast map and undetectable through subsystem dynamics alone.