A Hamiltonian bundle $M \hookrightarrow P \to X$ (with monotone compact fibers) induces via Floer theory a type of ``bundle of $A _{\infty}$ categories'' over $X$, with fiber given by the Fukaya category of $M$. Morita theory of $A _{\infty} $ categories, the above picture for $X=S ^{m}$, and geometric representation theory yield the following: if $G$ is a compact Lie group and $R$ is a commutative ring then there is a natural group homomorphism $π_{m} (BG) \to K ^{Cat}_{m}(R) $, where $K ^{Cat} _{m} (R)$ are a type of categorified algebraic $K$-theory groups of $R$, analogous to Toën's secondary $K$-theory. We also construct underlying maps of this type to classical algebraic $K$-theory of $R$. This framework gives a geometry-powered proof that $K ^{Cat} _{2} (\mathbb{Z} )$ is infinitely generated (with the details to appear in a future work). This is in contrast to Quillen's finite generation result for standard algebraic $K$-theory of $\mathbb{Z} $. Taking the Langlands dual of $G$, we explore a conjectural relationship between the images of the corresponding homomorphisms above.

Controlling the light emitted by individual molecules is instrumental to a number of novel nanotechnologies ranging from super-resolution bio-imaging and molecular sensing to quantum nanophotonics. Molecular emission can be tailored by modifying the local photonic environment, for example by precisely placing a single molecule inside a plasmonic nanocavity with the help of DNA origami. Here, using this scalable approach, we show that commercial fluorophores experience giant Purcell factors and Lamb shifts, reaching values on par with those recently reported in scanning tip experiments. Engineering of plasmonic modes enables cavity-mediated fluorescence far detuned from the zero-phonon-line (ZPL) - at detunings that are up to two orders of magnitude larger than the fluorescence linewidth of the bare emitter and reach into the near-infrared. Our results evidence a regime where the emission linewidth is dominated by the excited state lifetime, as required for indistinguishable photon emission, baring relevance to the development of nanoscale, ultrafast quantum light sources and to the quest toward single-molecule cavity-QED. In the future, this approach may also allow to design efficient quantum emitters at infrared wavelengths, where standard organic sources have a reduced performance.

This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex, while the non-smooth component is convex and block-separable. The proposed method is adaptive to all problem parameters, including smoothness and weak convexity constants, and allows each of its block proximal subproblems to be inexactly solved. Each iteration of our adaptive proximal ADMM consists of two steps: the sequential solution of each block proximal subproblem; and adaptive tests to decide whether to perform a full Lagrange multiplier and/or penalty parameter update(s). Without any rank assumptions on the constraint matrices, it is shown that the adaptive proximal ADMM obtains an approximate first-order stationary point of the constrained problem in a number of iterations that matches the state-of-the-art complexity for the class of proximal ADMM's. The three proof-of-concept numerical experiments that conclude the paper suggest our adaptive proximal ADMM enjoys significant computational benefits.

The aim of this paper is twofold. First, we introduce standard blenders (special hyperbolic sets) and their variations, and prove their fundamental properties on the generation of $C^1$-robust tangencies. In particular, these blenders appear after $C^r$-small perturbations of any diffeomorphism having a heterodimensional cycle of coindex 1. Next, as an application, we show that unfolding a homoclinic tangency to a hyperbolic periodic point can produce uncountably many $C^1$-robust homoclinic tangencies, provided that either this point is involved in a coindex-1 heterodimensional cycle, or the central dynamics near it is not essentially two-dimensional. The result answers a question posed by Bonatti and D{í}az in \citep{BonDia:12b}.

We report our discovery of a temperature independent anomalous Hall effect (AHE) from 15 mK to 300 K temperature occurring in a 68 nm thick transport device made out of pure bismuth. This surprising behaviour is accompanied with an expected temperature dependent longitudinal resistance consistent with semi-metallic bismuth, however it surprisingly showed no hint of a magnetoresistance for magnetic fields between $\pm30$ T. Even though bismuth is a diamagnetic material which {\it a priori} does not break time-reversal symmetry (TRS), our analysis of the reconstructed conductivities points towards the AHE to be of the intrinsic type, which does not emanate from magnetic impurities. Finally, as pure bismuth has been shown numerically to host a Berry curvature at its surface which breaks inversion symmetry, we propose it as a possible explanation for the temperature independent AHE observed here.

Quench dynamics of topological phases have been studied in the past few years and dynamical topological invariants are formulated in different ways. Yet most of these invariants are limited to minimal systems in which Hamiltonians are expanded by Gamma matrices. Here we generalize the dynamical 3-winding-number in two-band systems into the one in generic multi-band Chern insulators and prove that its value is equal to the difference of Chern numbers between post-quench and pre-quench Hamiltonians. Moreover we obtain an expression of this dynamical 3-winding-number represented by gapless fermions in phase bands depending only on the phase and its projectors, so it is generic for the quench of all multi-band Chern insulators. Besides, we obtain a multifold fermion in the phase band in (k, t) space by quenching a three-band model, which cannot happen for two band models.

Finding a set of empirical criteria fulfilled by any theory satisfying the generalized notion of noncontextuality is a challenging task of both operational and foundational importance. This work presents a methodology for constructing the noncontextual polytope while ensuring that the dimension of the polytope associated with the preparations remains constant regardless of the number of measurements and their outcome size. The facet inequalities of the noncontextual polytope can thus be obtained in a computationally efficient manner. We illustrate the efficacy of our methodology through several distinct contextuality scenarios. Our investigation uncovers several hitherto unexplored noncontextuality inequalities and demonstrates applications of quantum contextual correlations in certification of non-projective measurements, witnessing the dimension of quantum systems, and randomness certification.

Many important phenomena in biochemistry and biology exploit dynamical features such as multi-stability, oscillations, and chaos. Construction of novel chemical systems with such rich dynamics is a challenging problem central to the fields of synthetic biology and molecular nanotechnology. In this paper, we address this problem by putting forward a molecular version of a recurrent artificial neural network, which we call recurrent neural chemical reaction network (RNCRN). The RNCRN uses a modular architecture - a network of chemical neurons - to approximate arbitrary dynamics. We first prove that with sufficiently many chemical neurons and suitably fast reactions, the RNCRN can be systematically trained to achieve any dynamics. RNCRNs with relatively small number of chemical neurons and a moderate range of reaction rates are then trained to display a variety of biologically-important dynamical features. We also demonstrate that such RNCRNs are experimentally implementable with DNA-strand-displacement technologies.

Long-duration human missions to Mars will require autonomous systems capable of converting in situ resources into structural materials, tools, and functional components. More broadly, such systems represent a class of resource-limited bioprocesses relevant to extreme-environment manufacturing. Here, we investigate engineered autotrophic-heterotrophic consortia, inspired by lichen biology, as a platform for autonomous biofabrication from granular feedstocks. We experimentally screened filamentous fungi and paired them with diazotrophic cyanobacteria to identify mutually supportive consortia capable of sustained growth and biomineral production in the presence of Martian regolith simulant as the primary inorganic substrate, without external organic carbon or nitrogen inputs. Selected co-cultures exhibited evidence of metabolic coupling, and untargeted metabolomic analysis revealed coordinated reprogramming consistent with integrated carbon and nitrogen metabolism within the consortia. These systems facilitated mineral consolidation of regolith particles, demonstrating the feasibility of near-closed-loop biomineral production under resource-limited conditions. While integration with additive manufacturing remains conceptual, this study establishes a framework for engineering self-sustaining microbial consortia for biomaterials production and highlights opportunities for coupling metabolism with material synthesis in both extraterrestrial and terrestrial environments.

The concept of fluidic viscosity is ubiquitous in our everyday life and for it to arise the fluidic medium must necessarily form a continuum where macroscopic properties can emerge. While a powerful concept for tangible liquids, hydrodynamic manifestation of collective flow in electronic systems such as two-dimensional electron gases (2DEGs) has only been shown recently to occur in graphene and GaAs/AlGaAs. Here, we present nonlocal electronic transport measurements in concentric annular rings formed in high-mobility GaAs/AlGaAs 2DEGs and the resulting data strongly suggest that viscous hydrodynamic flow can occur far away from the source-drain current region. Our conclusion of viscous electronic transport is further corroborated by simulations of the Navier-Stokes equations that are found to be in agreement with our measurements below 1K temperature. Most importantly, our work emphasizes the key role played by viscosity via electron-electron (e-e) interaction when hydrodynamic transport is restricted radially, and for which a priori should not have played a major role.

We show that there is a type-preserving homomorphism from the fundamental group of the figure-eight knot complement to the mapping class group of the thrice-punctured torus. As a corollary, we obtain infinitely many commensurability classes of purely pseudo-Anosov surface subgroups of mapping class groups of closed surfaces. This gives the first examples of compact atoroidal surface bundles over surfaces.

We give a complete classification of finite groups acting symplectically on supersingular K3 surfaces of Artin invariant one. Using work of Dolgachev and Keum, this provides the full classification of tame finite symplectic automorphism groups on any K3 surface, and in particular of all finite symplectic automorphism groups on K3 surfaces in characteristic p>11.

Trust mechanisms diverge between centralized and decentralized exchanges, representing distinct sociotechnical governance paradigms. However, quantifying trust dynamics and their redistribution between these architectures remains empirically challenging, limiting understanding of how institutional shocks affect market behavior. The FTX collapse offers a natural experiment to bridge this gap. Through an interdisciplinary approach combining causal inference and computational text analysis, we find significant price declines and capital reallocation from centralized to decentralized exchanges following the event. While sentiment metrics showed no sharp discontinuities, topic modeling and network analysis of Discord communities reveal that seasonal holiday discourse obscured underlying trust concerns in centralized exchange forums. These findings underscore the fragility of institutional trust architectures and demonstrate how mixed methods can illuminate behavioral patterns during systemic crises, offering insights for exchange risk management and regulatory assessment.

We briefly review the main results of the IceCube Neutrino Observatory one decade after the discovery of cosmic neutrinos. We emphasize the importance of multimessenger observations, most prominently for the discovery of neutrinos from our own Galaxy. We model the flux from the Galactic plane produced by Galactic cosmic rays interacting with the interstellar medium and discuss the perspectives of understanding the TeV-PeV emission of the Galactic plane by combining neutrino and gamma-ray observations. We draw attention to the interesting fact that the neutrino flux from the Galaxy is not a dominant feature of the neutrino sky, unlike the case in any other wavelength of light. Finally, we review the attempts to identify PeVatrons by confronting the neutrino and gamma-ray emission of Galactic sources, including those observed by LHAASO. We end with a discussion of searches for neutrinos from LHAASO's extragalactic transient source gamma-ray burst 221009A.

The U.S. Census Bureau's 2020 Disclosure Avoidance System (DAS) bases its output on noisy measurements, which are population tabulations added to realizations of mean-zero random variables. These noisy measurements are observed for a set of hierarchical geographic levels, e.g., the U.S. as a whole, states, counties, census tracts, and census blocks. The Census Bureau released the noisy measurements generated in the DAS executions for the two primary 2020 Census data products, in part to allow data users to assess uncertainty in 2020 Census tabulations introduced by disclosure avoidance. This paper describes an algorithm that can leverage the hierarchical structure of the input data in order to compute very high dimensional least squares estimates in a computationally efficient manner. Afterward, we show that this algorithm's output is equal to the generalized least squares estimator, describe how to find the variance of linear functions of this estimator, and provide a numerical experiment in which we compute confidence intervals of tabulations based on this estimator. We also describe an accompanying Census Bureau experimental data product that applies this estimator to the publicly available noisy measurements to provide data users with the inputs required to derive confidence intervals for all tabulations that were included in the 2020 Redistricting Data File, for the U.S., state, county, and census tract geographic levels.

A recent psychology study found that people sometimes reject overly generous offers from people because they imagine hidden ''phantom costs'' must be part of the transaction. Phantom costs occur when a person seems overly generous for no apparent reason. This study aims to explore whether people can imagine phantom costs when interacting with a robot. To this end, screen or physically embodied agents (human or robot) offered to people either a cookie or a cookie + \$2. Participants were then asked to make a choice whether they would accept or decline the offer. Results showed that people did perceive phantom costs in the offer + \$2 conditions when interacting with a human, but also with a robot, across both embodiment levels, leading to the characteristic behavioral effect that offering more money made people less likely to accept the offer. While people were more likely to accept offers from a robot than from a human, people more often accepted offers from humans when they were physically compared to screen embodied but were equally likely to accept the offer from a robot whether it was screen or physically embodied. This suggests that people can treat robots (and humans) as social agents with hidden intentions and knowledge, and that this influences their behavior toward them. This provides not only new insights on how people make decisions when interacting with a robot but also how robot embodiment impacts HRI research.

In this paper, a restricted memory quasi-Newton bundle method for minimizing a locally Lipschitz continuous function over a Riemannian manifold is proposed. The curvature information of the objective function is approximated by applying a Riemannian version of the quasi-Newton updating formulas. A Riemannian subgradient aggregation technique is proposed and used to significantly reduce the computations in the quadratic programming subproblem when calculating the candidate descent direction. Moreover, a Riemannian line-search procedure is proposed to generate the stepsizes, and the process is finitely terminated under the assumption of a newly proposed Riemannian semismoothness. Global convergence of the proposed method is established: if the serious iteration steps are finite, then the last serious iterate is stationary; otherwise, every accumulation point of the serious iteration sequence is stationary. In addition, a modified algorithm with limited-memory quasi-Newton updates is presented to further reduce the computational cost. Finally, numerical experiments demonstrate that (i) the quasi-Newton updates accelerate the convergence of the bundle method, (ii) the aggregation technique significantly reduces the computational cost for solving the quadratic programming subproblem, and (iii) the proposed methods outperform the compared state-of-the-art Riemannian optimization methods for locally Lipschitz continuous functions.

Evaluating causal treatment effects in observational studies requires addressing confounding. While the back-door criterion enables identification through adjustment for observed covariates, it fails in the presence of unmeasured confounding. The front-door criterion offers an alternative by leveraging variables that fully mediate the treatment effect and are unaffected by unmeasured confounders of the treatment-outcome pair. We develop novel one-step and targeted minimum loss-based estimators for both the average treatment effect and the average treatment effect on the treated under front-door assumptions. Our estimators are built on multiple parameterizations of the observed data distribution, including approaches that avoid modeling the mediator density entirely, and are compatible with flexible, machine learning-based nuisance estimation. We establish conditions for root-n consistency and asymptotic linearity by deriving second-order remainder bounds. We also develop flexible tests for assessing identification assumptions, including a doubly robust testing procedure, within a semiparametric extension of the front-door model that encodes generalized (Verma) independence constraints. We further show how these constraints can be leveraged to improve the efficiency of causal effect estimators. Simulation studies confirm favorable finite-sample performance, and real-data applications in education and emergency medicine illustrate the practical utility of our methods.

We establish universal relations between pattern formation and dissipation with a geometric approach to nonequilibrium thermodynamics of deterministic reaction-diffusion systems. We first provide a way to systematically decompose the entropy production rate (EPR) based on the orthogonality of thermodynamic forces, in this way identifying the amount of dissipation caused by each factor. This enables us to extract the excess EPR that genuinely contributes to the time evolution of patterns. We also show that a similar geometric method further decomposes the EPR into detailed contributions, e.g., the dissipation from each point in real or wavenumber space. Second, we relate the excess EPR to the details of the change in patterns through two types of thermodynamic trade-off relations for reaction-diffusion systems: thermodynamic speed limits and thermodynamic uncertainty relations. The former relates dissipation and the speed of pattern formation, and the latter bounds the excess EPR with partial information on patterns, such as specific Fourier components of concentration distributions. In connection with the derivation of the thermodynamic speed limits, we also extend optimal transport theory to reaction-diffusion systems, which enables us to measure the speed of the time evolution. This extension of optimal transport also solves the minimization problem of the dissipation associated with the transition between two patterns, and it constructs energetically efficient protocols for pattern formation. We numerically demonstrate our results using chemical traveling waves in the Fisher-Kolmogorov-Petrovsky-Piskunov equation and changes in symmetry in the Brusselator model. Our results apply to general reaction-diffusion systems and contribute to understanding the relations between pattern formation and unavoidable dissipation.

The Kitaev spin liquid, stabilized as the ground state of the Kitaev honeycomb model, is a paradigmatic example of a topological $\mathbb{Z}_2$ quantum spin liquid. The fate of the Kitaev spin liquid in presence of an external magnetic field is a topic of current interest due to experiments, which apparently unveil a $\mathbb{Z}_2$ topological phase in the so-called Kitaev materials, and theoretical studies predicting the emergence of an intermediate quantum phase of debated nature before the appearance of a trivial partially polarized phase. In this work, we employ hierarchical mean-field theory, an algebraic and numerical method based on the use of clusters preserving relevant symmetries and short-range quantum correlations, to investigate the quantum phase diagram of the antiferromagnetic Kitaev's model in a [111] field. By using clusters of 24 sites, we predict that the Kitaev spin liquid transits through two intermediate phases characterized by stripe and chiral order, respectively, before entering the trivial partially polarized phase, differing from previous studies. We assess our results by performing exact diagonalization and computing the scaling of different observables, including the many-body Chern number and other topological quantities, thus establishing hierarchical mean-field theory as a method to study topological quantum spin liquids.

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

Electrically connected and plasmonically enhanced molecular junctions combine the optical functionalities of high field confinement and enhancement (cavity function), and of high radiative efficiency (antenna function) with the electrical functionalities of molecular transport. Such combined optical and electrical probes have proven useful for the fundamental understanding of metal-molecule contacts and contribute to the development of nanoscale optoelectronic devices including ultrafast electronics and nanosensors. Here, we employ a self-assembled metal-molecule-metal junction with a nanoparticle bridge to investigate correlated fluctuations in conductance and tunneling-induced light emission at room temperature. Despite the presence of hundreds of molecules in the junction, the electrical conductance and light emission are both highly sensitive to atomic-scale fluctuations -- a phenomenology reminiscent of picocavities observed in Raman scattering and of luminescence blinking from photo-excited plasmonic junctions. Discrete steps in conductance associated with fluctuating emission intensities through the multiple plasmonic modes of the junction are consistent with a finite number of randomly localized, point-like sources dominating the optoelectronic response. Contrasting with these microscopic fluctuations, the overall plasmonic and electronic functionalities of our devices feature long-term survival at room temperature and under an electrical bias of a few volts, allowing for measurements over several months.

In this paper we consider the problem of recovering a signal $x \in \mathbb{R}^N$ from its power spectrum assuming that the signal is sparse with respect to a generic basis for $\mathbb{R}^N$. Our main result is that if the sparsity level is at most $\sim\! N/2$ in this basis then the generic sparse vector is uniquely determined up to sign from its power spectrum. We also prove that if the sparsity level is $\sim\! N/4$ then every sparse vector is determined up to sign from its power spectrum. Analogous results are also obtained for the power spectrum of a vector in $\mathbb{C}^N$ which extend earlier results of Wang and Xu \cite{arXiv:1310.0873}.

In a recent work arXiv:2201.07655v2 we showed that there is a constant $λ>0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit undergoes at most $D$ diagonal gates, (iii) each qudit is destructively measured in the computational basis or bases unbiased to it, and (iv) each qudit is initialised within $λ^{-D}$ of a diagonal state according to a particular distance measure. In this work we explicitly compute $λ$ for any two qubit diagonal gate, thereby extending the computation of arXiv:2201.07655v2 beyond CZ gates. For any finite degree graph this allows us to describe a two parameter family of pure entangled quantum states (or three parameter family of thermal states) which have a non-trivial classically efficiently simulatable "phase" for the permitted measurements, even though other values of the parameters may enable ideal cluster state quantum computation. The main the technical tool involves considering separability in terms of "cylindrical" sets of operators. We also consider whether a different choice of set can strengthen the algorithm, and prove that they are optimal among a broad class of sets, but also show numerically that outside this class there are choices that can increase the size of the classically efficient regime.

We theoretically calculate the fundamental noise that is present in gaseous (dilute fluid) flow in channels in the classical and degenerate quantum regime, where the Fermi-Dirac and Bose- Einstein distribution must be considered. Results for both regimes are analogous to their electrical counterparts. The quantum noise is calculated for a two terminal system and is a complicated function of the thermal and shot noise with the thermal noise dominating when $2k_BT >> mΔP$ and vice versa. The cumulant generating function for mass flow, which generates all the higher order statistics related to our mass flow distribution, is also derived and is used to find an expression for the third cumulant of flow across a fluidic channel.

This article presents MuMFiM, an open source application for multiscale modeling of fibrous materials on massively parallel computers. MuMFiM uses two scales to represent fibrous materials such as biological network materials (extracellular matrix, connective tissue, etc.). It is designed to make use of multiple levels of parallelism, including distributed parallelism of the macro and microscales as well as GPU accelerated data-parallelism of the microscale. Scaling results of the GPU accelerated microscale show that solving microscale problems concurrently on the GPU can lead to a 1000x speedup over the solution of a single RVE on the GPU. In addition, we show nearly optimal strong and weak scaling results of MuMFiM on up to 128 nodes of AiMOS (Rensselaer Polytechnic Institute) which is composed of IBM AC922 nodes with 6 Volta V100 GPU and 2 20 core Power 9 CPUs each. We also show how MuMFiM can be used to solve problems of interest to the broader engineering community, in particular providing an example of the facet capsule ligament (FCL) of the human spine undergoing uniaxial extension.

Traditional Insurance, a popular approach of financial risk management, has suffered from the issues of high operational costs, opaqueness, inefficiency and a lack of trust. Recently, blockchain-enabled "parametric insurance" through authorized data sources (e.g., remote sensing and IoT) aims to overcome these issues by automating the underwriting and claim processes of insurance policies on a blockchain. However, the openness of blockchain platforms raises a concern of user privacy, as the private user data in insurance claims on a blockchain may be exposed to outsiders. In this paper, we propose a privacy-preserving parametric insurance framework based on succinct zero-knowledge proofs (zk-SNARKs), whereby an insuree submits a zero-knowledge proof (without revealing any private data) for the validity of an insurance claim and the authenticity of its data sources to a blockchain for transparent verification. Moreover, we extend the recent zk-SNARKs to support robust privacy protection for multiple heterogeneous data sources and improve its efficiency to cut the incurred gas cost by 80%. As a proof-of-concept, we implemented a working prototype of bushfire parametric insurance on real-world blockchain platform Ethereum, and present extensive empirical evaluations.

In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. Towards this, we proposed the concepts of class obstruction, parametric obstruction, and universal obstruction as combinatorial objects that determine the approximate behaviour of a graph parameter. In this work, we explore its potential as a unifying framework for classifying graph parameters. Under this framework, we survey existing graph-theoretic results on many known graph parameters. Additionally, we provide some unifying results on their classification.

We outline a strategy to efficiently include the electromagnetic interactions of the sea quarks in QCD+QED. When computing iso-spin breaking corrections to hadronic quantities at leading order in the electromagnetic coupling, the sea-quark charges result in quark-line disconnected diagrams which are challenging to compute precisely. An analysis of the variance of stochastic estimators for the relevant traces of quark propagators helps us to improve the situation for certain flavour combinations and space-time decompositions. We present preliminary numerical results for the variances of the corresponding contributions using an ensemble of $N_\mathrm{f}=2+1$ domain-wall fermions generated by the RBC/UKQCD collaboration.

We prove that an HNN extension of a torsion-free nilpotent group is left-orderable. We also construct examples of non-left-orderable HNN extensions of left-orderable groups