We study the moduli space $B\textrm{Diff}^+(M)$, for $M$ a reducible, oriented 3-manifold with irreducible prime factors $P_1,\ldots,P_n$. A programme of César de Sá-Rourke, Hendriks-Laudenbach, and Hendriks-McCullough studies the homotopy type of $\textrm{Diff}^+(M)$ in terms of the $\textrm{Diff}^+(P_i)$. Inspired by a delooping proposed by Hatcher, we construct a map from $B\textrm{Diff}^+(M)$ to $B\textrm{Diff}^+(P_1 \sqcup \dots \sqcup P_n)$, called the splitting map, that yields a prime decomposition fibre sequence. The fibre $H_g(P_1, \dots, P_n)$ is a space of $1$-handle attachments which we describe geometrically as a homotopy colimit of certain configuration spaces on the $P_i$. Firstly, this allows us to show that for $n>0$ the fibre is equivalent to a finite, connected cell complex. Secondly, this makes the fibre sequence an effective tool for computations, which we illustrate by computing the rational cohomology ring of $B\textrm{Diff}^+\!\left((S^1\times S^2)^{\sharp 2}\right)$.

In this contribution, I will present some properties of nuclear matter (NM) by using the chiral-scale effective field theory that is anchored on the chiral, scale and hidden local flavor symmetries of QCD. We show that the sound velocity (SV) of the compact star matter can saturate the conformal limit, the SV exhibits a peak configuration in the intermediate density. To extend the chiral-scale effective field theory to both dense and tnermal systems, we setup a chiral-scale density counting (CSDC) rule and explore the contributions up to $\mathcal{O}(k_c^{12})$.

Modern data analysis requires speed for massive datasets. Progressive Data Analysis and Visualization (PDAV) emerged as a discipline to address this problem, providing fast response times while maintaining interactivity with controlled accuracy. Yet it remains difficult to implement and reproduce. To lower this barrier, we present ProVega, a Vega-Lite-based grammar that simplifies PDAV instrumentation for both simple visualizations and complex visual environments. Alongside it, we introduce Pro-Ex, an editor designed to streamline the creation and analysis of progressive solutions. We validated ProVega by reimplementing 11 exemplars from the literature-verified for fidelity by 39 users-and demonstrating its support for various progressive methods, including data-chunking, process-chunking, and mixed-chunking. An expert user study confirmed the efficacy of ProVega and the Pro-Ex environment in real-world tasks. ProVega, Pro-Ex, and all related materials are available at https://github.com/XAIber-lab/provega

Near-surface wind fields on Mars are profoundly modulated by complex topography, yet fine-scale wind field characteristics remain poorly resolved for key geomorphological units such as deltas, valleys, and impact craters, due to the spatial constraints of lander-based wind observations. To address this, we identified three dominant wind directions using measured near-surface wind data from the Perseverance rover at Jezero Crater and then integrated in-situ wind measurements with high-resolution numerical modeling. We established a high-resolution three-dimensional (3D) terrain model encompassing key local geomorphic units, including the delta, an impact crater, and nearby mesas, and performed Computational Fluid Dynamics (CFD) simulations under the above-mentioned three dominant wind directions. The results reveal a robust coupling mechanism between local topography and near-surface wind field structures. We demonstrate that wind speed is significantly enhanced over windward slopes but evidently attenuated within depressions and crater floors. Crucially, significant wind direction deflection angles were particularly evident in areas characterized by steeper slopes. For instance, wind flow exhibited a symmetrical deflection pattern along the opposing inner walls of the modeled impact crater, but stabilizing on the crater floor. Spatial comparisons indicate that wind deflection is most pronounced over steeper slopes, while sector-based distributions within the impact crater reveal a consistent symmetry between opposing wall and floor regions. These findings offer new and critical insights into the intimate connection between Martian surface aeolian erosion/deposition processes and local topographic evolution, which is vital for interpreting the sedimentary history of Jezero Crater.

We study a restriction of Ramsey's theorem for 2-coloring of triples, in which homogeneous sets for color~1 are of bounded size ($\mathsf{BRT}^3_2$). We prove that the computational content of this statement is very close to Ramsey's theorem for pairs ($\mathsf{RT}^2_2)$, in that it satisfies the same known computability-theoretic upper bounds, but that $\mathsf{BRT}^3_2$ is not computably-reducible to $\mathsf{RT}^2_2$, even when allowing multiple applications of $\mathsf{RT}^2_2$.

Given a strict partial order $Δ$ on a set $Λ$ and an arbitrary ring $R$ with $1\neq 0$, the corresponding McLain group $M(Δ)$ has been studied in depth. We construct a larger family of McLain groups $G(Δ)$, where $Δ$ is neither asymmetric nor transitive, while satisfying two weaker axioms. Structural properties common to all members~$G(Δ)$ of this new family are investigated, including a group presentation, a description of the factors of its descending central series, a canonical form for its elements relative to any total order on~$Δ$, and a recursive determination of its upper central series. In addition, we prove the natural isomorphism $G(Δ)/G(Γ)\cong G(Δ\setminusΓ)$, where $Γ$ is a normal subset $Γ$ of $Δ$, and $G(Γ)$ and $G(Δ\setminusΓ)$ are extended McLain groups on their own right. This result has no parallel in the classical context.

Analytical treatments of polymer dynamics have mostly been restricted to linear response theory around some steady state obtained via perturbative field theory. Here, I derive an analytical framework that yields unified access to the evolution of conformations, contact probabilities, and fluctuations within a dynamical mean-field theory. Starting with the Langevin equation of a hydrodynamically coupled and self-avoiding heteropolymer, the key idea is to focus on the two-point correlator as the lowest-order relevant observable. Truncating higher-order correlations via a Gaussian closure leads to a self-consistent diffusion equation for the chain correlations. The theory is validated by contrasting coiled, globular, and self-avoiding polymers within a single dynamical framework, and predicts hyper-compacted fractal states in hydrodynamically coupled active polymers such as chromatin.

The Quantum Approximate Optimization Algorithm (QAOA) is a leading hybrid heuristic for combinatorial optimization, but efficiently handling hard constraints remains a significant challenge. XY-mixers successfully confine quantum state evolution to a feasible subspace, such as the Hamming-weight-1 sector for one-hot constraints. On the contrary, warm-starting biases the search toward promising regions based on preliminary solutions. Combining these two techniques requires maintaining the essential alignment between the initial state and the mixer Hamiltonian to preserve convergence guarantees. Previous work demonstrated warm-starting with XY-mixers via a biased initial state, but relying only on standard mixer Hamiltonians. Consequently, the initial state is no longer a ground state of the mixer. In this work, we overcome these limitations by formulating a warm-started XY-mixer Hamiltonian for one-hot constraints and proving its ground-state properties. Furthermore, we provide a shallow circuit implementation suitable for NISQ implementations. We embed the warm-starting into a classical heuristic that iteratively updates the bias based on previous samples, called Iterative Warm-Starting (IWS). Extensive numerical simulations on Max-$k$-Cut and Traveling Salesperson Problem instances demonstrate that IWS-QAOA significantly accelerates the solution-finding process, increasing the probability of sampling optimal solutions by orders of magnitude compared to standard XY-QAOA. Finally, we validate our approach on the ibm_boston QPU using hardware-tailored 144-qubit problem instances. By coupling IWS-QAOA with a greedy steepest-descent post-processing strategy to repair infeasible measurements caused by hardware noise, we successfully identify optimal solutions on actual quantum devices.

Quantum information processing, communication, and sensing networks are being developed with various qubit platforms that use different encoding schemes. Connecting quantum network nodes to distribute entanglement requires matching photon qubit basis encoding. In this work, we implement an interconversion protocol which converts photon qubit encoding from the polarization basis to the time-bin basis, transmits the photons through a transport fiber with large fluctuations in polarization, and converts back to polarization encoding for ease of measurement. This interconversion scheme faithfully transmits a polarization Bell state across the transport fiber by converting sources of infidelity to changes in transmission rate. These results illustrate a practical approach for interfacing distinct qubit platforms to enable modular and flexible operation in heterogeneous quantum networks.

We provide an approximate version of a rigidity result by Randrianantoanina: for a large class of Orlicz sequence spaces, almost isometric embeddings almost preserve disjointness. In specific cases, we can even prove that such embeddings almost preserve basic vectors. As a consequence, we prove that some Orlicz sequences spaces are guarded Fraïssé but not $ω$-categorical; moreover, they do not contain copies of $\ell_2$ and their age is not closed. This answers a question of Cúth-de Rancourt-Doucha.

CI/CD pipelines are central to DevOps practices, yet their growing complexity makes them increasingly difficult to interpret, analyze, and systematically evolve. Existing tooling primarily offers execution logs and static graph representations, providing limited support for structured analysis of pipeline behavior, failures, and version-to-version evolution. This paper presents a model-driven Digital Twin (DT) for CI/CD pipelines that leverages BPMN as a model-ing backbone to transform raw CI configurations into structured, higher-level process representations. The proposed DT architecture enables visual abstraction of pipeline structure, failure tracing, and systematic version comparison, supporting both monitoring and evolution analysis of DevOps processes. Building upon validated DT architectural principles and prior work on build optimization and anomaly detection, the framework provides a modular, extensible foundation for integrating advanced analytical and prescriptive services into software delivery processes. The approach is validated using open-source CI/CD projects, and ongoing work targets the integration of additional improvement services and the extension of the DT to broader DevOps lifecycle processes.

Chance-constrained correlated equilibrium enables coordination of noncooperative agents under cost uncertainty through probabilistic incentive-compatibility guarantees. However, computing such equilibria becomes intractable in large-scale systems due to the exponential growth of the joint action space. We develop an approximation method for computing chance-constrained correlated equilibria by showing that these equilibria admit a representation as convex combinations of a finite set of chance-constrained pure Nash equilibria, enabling tractable computation without solving the full correlated equilibrium program. Numerical experiments on large-scale multi-airline coordination scenarios demonstrate substantial reductions in computation time while achieving lower system delay costs compared to current operational practice. Under cost uncertainty, the proposed method consistently achieves lower deviation rate compared to the full formulation while achieving comparable coordination performance.

This paper presents a state- and control-dependent moving-horizon estimation (SCD-MHE) algorithm for nonlinear discrete-time systems. Within this framework, a pseudo-linear representation of nonlinear dynamics is leveraged utilizing state- and control-dependent coefficients, where the solution to a moving-horizon estimation problem is iteratively refined. At each discrete time step, a quadratic program is executed over a sliding window of historical measurements. Moreover, system matrices are consecutively updated based upon prior iterates to capture nonlinear regimes. In contrast to the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), nonlinearities and bounds are accommodated within a structured optimization framework, thereby circumventing the reliance on local Jacobian matrices. Furthermore, theoretical analysis is presented to establish the convergence of the iterative sequence, and bounded estimation errors are mathematically guaranteed under uniform observability conditions. Finally, comparative numerical experiments utilizing a quadrotor vertical kinematics system demonstrate that the SCD-MHE achieves superior estimation accuracy relative to the EKF, the UKF, and a fully nonlinear moving-horizon estimator, while reducing per-step computational latency by over an order of magnitude.

Distributed applications need identifiers that satisfy storage efficiency, chronological sortability, origin metadata embedding, zero-lookup verifiability, confidentiality for external consumers, and multi-century addressability. Based on our literature survey, no existing scheme provides all six of these identifier properties within a unified system. This paper introduces Source Known Identifiers (SKIDs), a three-tier identity system that projects a single entity identity across trust boundaries, addressing all six properties. The first tier, Source Known ID (SKID), is a 64-bit signed integer embedding a timestamp with a 250-millisecond precision, application topology, and a per-entity-type sequence counter. It serves as the database primary key, providing compact storage (8 bytes) and natural B-tree ordering for optimized database indexing. The second tier, Source Known Entity ID (SKEID), extends the SKID into a 128-bit Universally Unique Identifier (UUID) compatible value by adding an entity type discriminator, an epoch selector, and a BLAKE3 keyed message authentication code (MAC). SKEIDs enable zero-lookup verification of identifier origin, integrity, and entity type within trusted environments, with a big-endian byte layout that preserves chronological ordering in lexicographic UUID string comparisons. The third tier, Secure SKEID, encrypts the entire SKEID using AES-256 symmetric encryption as a single-block pseudorandom permutation, producing ciphertext indistinguishable from random bytes while remaining compatible with standard UUID data-type parsers in string representation. Deterministic bidirectional transformations connect all three tiers.

One of the characteristic features of categorical systems theory is that the behavior of systems can be characterized by certain morphisms into them. In other words, behaviors form a representable covariant functor to Set. And more generally, in the compositional setting, behaviors form a representable double functor to Span. Clock systems are convenient because behavior functors represented by clock systems are automatically well-behaved. It was previously not known whether stochastic and non-deterministic systems theories have clock systems. In this paper, we show that indeed they do have clock systems. Moreover, the clock systems for non-deterministic systems point to generalized notions of behavior for non-linear time.

A burgeoning literature in economics studies how people form beliefs about the causal structures linking economic variables, and what happens when those beliefs are mistaken. We survey this research and connect it to a rich literature in cognitive science. After providing an accessible introduction to causal Directed Acyclic Graphs, the dominant modeling approach, we review theory and evidence addressing three nested questions: how individuals reason within a fully parameterized causal structure, how they estimate its parameters, and how they learn such structures to begin with. We then discuss methodological challenges and review applications in microeconomics, macroeconomics, political economy, and business.

The classification of phases using categorical symmetries has greatly expanded the landscape of gapped and gapless phases. So far, however, these developments have largely been restricted to phases with unitary (higher-)categorical symmetries over $\mathbb{C}$. In this work, we incorporate anti-unitary symmetries, such as time-reversal symmetry $\mathbb{Z}_2^T$, and show that the relevant physical structures are naturally described by fusion categories over $\mathbb{R}$. A class of real fusion categories, which we call Galois-real fusion categories, provides the correct categorical model for anti-unitary symmetries. A simple example is the time-reversal symmetry $\mathbb{Z}_2^T$ itself. We discuss the basic structures of real fusion categories and present a range of examples, including the group-theoretical categories $(G^T)^ω$ and $\mathsf{Rep}(G^T)$ associated to anti-linear groups $G^T$, as well as non-invertible time-reversal symmetries described by a real analogue of Tambara--Yamagami fusion categories. We then classify gapped phases enriched with anti-linear symmetries in terms of module categories over Galois-real fusion categories. We furthermore apply the categorical formulation to prove dualities (i.e. gauge or Morita equivalences) of anti-linear symmetries generated by gauging subgroups. Complementing this, we also develop a Symmetry Topological Field Theory (SymTFT) framework, in which Galois-real fusion categories arise as boundary conditions of a $\mathbb{Z}_2^T$-enriched SymTFT. Morita equivalent anti-linear symmetries are shown to arise as different boundaries of the same $\mathbb{Z}_2^T$-enriched SymTFT.

In 2022, Gao, Huo, Liu, and Ma proved that every graph with minimum degree at least $k+1$ contains $k$ admissible cycles, where a set of $k$ cycles is said to be admissible if their lengths form an arithmetic progression with common difference one or two. In this paper, we provide a sharp size analogue of their result and characterize the extremal graphs attaining the lower bound. In 2016, Verstraëte conjectured that every $n$-vertex graph $G$ containing no $k$ cycles of consecutive even lengths has at most $(2k+1)(n-1)/2$ edges, with equality only if every block of $G$ is a clique of order $2k+1$. We prove this conjecture for $2k+2\leq n\leq 4k+1$, and in fact obtain a stronger result in this range.

We present results from directed searches for continuous gravitational waves from a sample of 15 nearby supernova remnants, likely hosting young neutron star candidates, using data from the first eight months of the fourth observing run (O4) of the LIGO-Virgo-KAGRA Collaboration. The analysis employs five pipelines: four semi-coherent methods -- the Band-Sampled-Data directed pipeline, Weave and two Viterbi pipelines (single- and dual-harmonic) -- and PyStoch, a cross-correlation-based pipeline. These searches cover wide frequency bands and do not assume prior knowledge of the targets' ephemerides. No evidence of a signal is found from any of the 15 sources. We set 95\% confidence-level upper limits on the intrinsic strain amplitude, with the most stringent constraints reaching $\sim 4 \times 10^{-26}$ near 300 Hz for the nearby source G266.2$-$1.2 (Vela Jr.). We also derive limits on neutron star ellipticity and $r$-mode amplitudes for the same source, with the best constraints reaching $\lesssim 10^{-7}$ and $\lesssim 10^{-5}$, respectively, at frequencies above 400 Hz. These results represent the most sensitive wide-band directed searches for continuous gravitational waves from supernova remnants to date.

Applying a rule-based holographic method, we investigate the reconstruction of dual gravity theories from the quantum field theory (QFT) data, specifically entanglement entropy. We first derive a three-dimensional black hole geometry from the entanglement entropy of a two-dimensional thermal system. Using the reconstructed solution, we extract various thermodynamic quantities with small numerical errors. Moreover, we explore how to reconstruct the dual gravity theory beyond the geometry itself. For an undeformed conformal field theory (CFT), we show that the dual gravity theory can be constructed analytically from the analytic form of the entanglement entropy. In particular, we demonstrate how to reconstruct the analytic dual geometry by applying the Abel transformation. Finally, we investigate the numerical reconstruction of the dual gravity theory from numerical entanglement entropy data for a relevantly deformed CFT. After reconstructing the dual gravity, we show that additional information about the renormalization group (RG) flow, for instance, the $\b$-function and the $c$-function, can be extracted for the considered relevantly deformed CFT.

Given a group $G$ acting faithfully on a set $S$, one gets a simple group denoted $SV_G$, called a twisted Brin--Thompson group. In this paper we drop the faithfulness assumption, and get an abstract version of a twisted Brin--Thompson group $SV_G$. While the resulting group is not simple, since $SV_G$ surjects onto $SV_{G/\ker(G \curvearrowright S)}$, we prove that every proper normal subgroup of $SV_G$ lies in the kernel of this surjection, so $SV_G$ is ``relatively simple''. The advantage is that now we can prove that every finitely presented simple group embeds in a finitely presented abstract twisted Brin--Thompson group intersecting this kernel trivially. In particular, if the Boone--Higman conjecture is true, then so is a related conjectural characterization of groups with solvable word problem, arising purely in the world of twisted Brin--Thompson groups. We also prove a variety of additional results about abstract twisted Brin--Thompson groups, some of which are new even in the faithful case: they are all uniformly perfect, have property NL and property FW$_\infty$, are boundedly acyclic and $\ell^2$-invisible, and are $C^*$-simple as soon as they have trivial amenable radical. Along the way we formulate a new general criterion for $\ell^2$-invisibility that is interesting in its own right.

We construct asymptotically good nested Calderbank-Shor-Steane (CSS) code pairs from Hsu-Anastasopoulos codes and MacKay-Neal codes. In the fixed-degree regime, we prove that the coding rate stays bounded away from zero and that the relative distances on both sides stay bounded away from zero with probability tending to one as the blocklength grows. Moreover, within an explicit low-degree search window, we determine exactly which even regular degree choices in our construction attain the classical Gilbert-Varshamov (GV) bound on both constituent sides, and consequently the CSS GV bound at fixed finite degree.

Nonlocal interaction is shown to be an appropriate tool for controlling coherence resonance in ensembles of non-excitable oscillators. The constructive role of nonlocal coupling is demonstrated through numerical simulations on an example of coupled generalized Van der Pol oscillators close to the saddle-node bifurcation of limit cycles. In particular, increasing the coupling radius is found to enhance coherence resonance, which manifests itself in the evolution of power spectra and dependencies of the correlation time on the noise intensity. Nonlocal coupling is interpreted as an intermediate topology between local and global coupling, both of which are also examined as mechanisms for controlling coherence resonance.

Neural networks are increasingly used as surrogates in optimization problems to replace computationally expensive models. However, embedding ReLU neural networks in mathematical programs introduces significant computational challenges, particularly for deep and wide networks, due to both the formulation of the ReLU disjunction and the resulting large-scale optimization problem. This work investigates how pruning techniques can accelerate the solution of optimization problems with embedded neural networks, focusing on the mechanisms underlying the computational gains. We provide theoretical insights into how both unstructured (weight) and structured (node) pruning affect the ReLU big-M formulation, showing that pruning monotonically tightens preactivation bounds. We conduct comprehensive empirical studies across multiple network architectures using an illustrative test function and a realistic chemical process flowsheet optimization case study. Our results show that pruning achieves speedups of up to three to four orders of magnitude, with computational gains attributed to three key factors: (i) reduction in problem size, (ii) decrease in the number of integer variables, and (iii) tightening of big-M bounds. Weight pruning is particularly effective for deep, narrow networks, while node pruning performs better for shallow, wide or medium-sized networks. In the chemical engineering case study, pruning enabled convergence within seconds for problems that were otherwise intractable. We recommend adopting pruning as standard practice when developing neural network surrogates for optimization, especially for engineering applications requiring repeated optimization solves.

Video steganography based on block structure, which embeds secret information by modifying Coding Unit (CU) block structure of I-frames, is currently a research hotspot. However, the existing algorithms still suffer from the limitation of poor anti-steganalysis, which results from significantly disrupting the original CU block structure after embedding secret information. To overcome this limitation, this paper proposes a video steganography algorithm based on multiple CU size and block structure distortion. Our algorithm introduces three key innovations: 1) a CU Block Structure Stability Metric (CBSSM) based on CU block structure restoration phenomenon to reveal the reasons for the insufficient anti-steganalysis performance of current algorithms. 2) a novel mapping rule based on multiple CU size to reduce block structure change and enhance embedding capacity. 3) a three-level distortion function based on block structure to better guide the secret information embedding. This triple strategy ensures that the secret information embedding minimizes disruption to the original CU block structure while concealing it primarily in areas where block structure changes occur after recompression, ultimately enhancing the algorithm's anti-steganalysis. Comprehensive experimental results highlight the crucial role of the proposed CBSSM in evaluating anti-steganalysis performance even at a low embedding rate. Meanwhile, compared to State-of-the-Art video steganography algorithms based on block structure, our proposed steganography algorithm exhibits greater anti-steganalysis, as well as further improving visual quality, bitrate increase ratio and embedding capacity.

Primordial non-Gaussianity is one of the most powerful probes of the inflationary epoch. The particle spectrum relevant to inflation, including masses and spins, is encoded in the precise form of statistical correlations of the adiabatic modes. Yet, in the presence of nonlinear structure formation, the optimal approach to measuring these signals remains unclear. Accurate modeling becomes crucial as late-time non-Gaussianty can become degenerate with primordial physics. Moreover, scale-dependent bias shows that information can move from non-Gaussian initial conditions to the amplitude of the Gaussian fluctuations. In this paper, we aim to clarify how primordial information is encoded in maps of galaxies. We use the field-level Cramer-Rao bound to investigate the ultimate limit of what can be extracted from realistic maps of the Universe. For local non-Gaussianity, we show that multi-tracer scale-dependent bias can exceed the sensitivity of conservative higher-point analyses. However, as expected, the multi-tracer analysis falls short of the optimal constraint when all the modes at the scale of the dark matter halos are included. We then forecast the potential reach of future surveys for equilateral and local non-Gaussianity. Equilateral in particular is highly sensitive to priors and modeling assumptions and can benefit dramatically from theoretical input such as the redshift evolution of the bias.

The vast majority of extensions of the Standard Model affecting the number of effective relativistic neutrino species ($N_{\rm eff}$) do so additively, namely, they enhance this quantity with some light state contributing to dark radiation. In this work, we consider precisely the opposite case: new physics scenarios that can lead to $N_{\rm eff} < 3$ that are consistent with all known cosmological, astrophysical, and laboratory data. We are motivated by three main reasons: 1) a recent measurement from ACT and SPT in combination with Planck that leads to $N_{\rm eff} = 2.81\pm0.12$, 2) by a new and powerful measurement of the primordial helium abundance, which anchors $N_{\rm eff}$ to be very close to the Standard Model value one second after the Big Bang, 3) by the deployment of the Simons Observatory which will provide precise tests of the radiation content in the Universe and which may detect with a high significance cosmologies with $N_{\rm eff}<3$. We survey the main theoretical possibilities and find that only a few simple scenarios can consistently give $N_{\rm eff}=2.81\pm0.12$. One class consists of thermal electrophilic relics with masses $m\sim 8\!-\!13\,{\rm MeV}$. Another consists of out-of-equilibrium particles decaying to $e^+e^-$ or $γγ$, with a rather particular lifetime $0.05\,{\rm s}\lesssim τ\lesssim 3\,{\rm min}$, mass $250\,{\rm MeV}\lesssim m \lesssim 600\,{\rm MeV}$, and abundance $ρ/ρ_γ\sim 0.1$ at decay. Thermal electrophilic particles are especially interesting because they can account for the dark matter in the Universe and can be tested in experiments such as SENSEI, DAMIC-M, and Oscura, and their portals to the visible sector at experiments such as NA64 and LDMX. We conclude that if the Simons Observatory confirms that $N_{\rm eff} \simeq 2.8$, it will point to very specific extensions of the Standard Model.

Dynamical and variational frameworks have long been viewed as distinct paradigms. In particular, in quantum embedding (QE) frameworks, dynamical mean-field theory (DMFT) captures nonperturbative dynamical correlations through a frequency-dependent self-energy, while the Gutzwiller approximation (GA) is formulated in terms of a variationally optimized ground-state wavefunction. Here we bridge these perspectives, proving that the ghost-Gutzwiller approximation (ghost-GA), which also admits a density-matrix-matching QE formulation known as ghost density matrix embedding theory (ghost-DMET), becomes strictly equivalent to DMFT in the limit of infinitely many auxiliary bath modes. This formal unification has immediate consequences. In particular, it yields a rigorous finite-temperature extension of ghost-GA and shows that the physical Green's function can be determined from static expectation values of the embedding Hamiltonians, providing a route to computational studies of competing phases in strongly correlated matter with DMFT-level accuracy, while bypassing the need to calculate dynamical spectra with conventional impurity solvers. More broadly, it shows that the variational ghost-GA, the density-matrix-matching ghost-DMET formulation, and the dynamical DMFT description are not separate constructions, but complementary formulations of the same QE structure, thereby providing a concrete formal basis for future controlled extensions beyond DMFT.

Motivated by the recent work of Deaconu, Mousavand and Paquette on the connection between infinite string bricks for certain gentle algebras and Sturmian words, we develop a decorated version of a deterministic automaton, called a multi-entry inverse automaton (MIA, for short) that accepts pointed words. We then associate an MIA $\mathsf M_{Λδ}$ over $\{0,1\}$ to a string algebra $Λ$, and show that strings over $Λ$ can be viewed as certain equivalence classes of the pointed words accepted by $\mathsf M_{Λδ}$. By defining (weak) brick words over this MIA, we show that a finite/infinite string module (resp. band module) is a brick if and only if every word in the associated equivalence class of pointed binary words is a brick word (resp. a weak brick word) over $\mathsf M_{Λδ}$. The result of Deaconu et al. follows as an immediate consequence.

We study the problem of reconstructing interaction kernels in systems of interacting agents from macroscopic measurements when posed as an optimization problem. The reconstruction procedure depends on the formulation of the forward model, which may be given either by a finite-dimensional coupled ODE system tracking individual agent trajectories or by a mean-field PDE describing the evolution of the agent density. We investigate the similarities and differences between these two formulations in the mean-field regime. While the first variation derived from the particle system does not provide an unbiased estimator of the first variation associated with the limiting PDE, we prove that, under mild assumptions, the two are close in a weak sense with a convergence rate $\mathcal{O}(N^{-1/2})$. This rate is further confirmed by numerical evidences.