We develop an analytical framework to predict the one-point probability distribution function (PDF) of dispersion measures (DMs) for fast radio bursts (FRBs) within the baryonification (BFC) model. BFC provides a computationally efficient alternative to expensive hydrodynamical simulations for modelling baryonic effects on cosmological scales. By applying the halo mass function and halo bias, we convolve contributions from individual halos across a range of masses and redshifts to derive the large-scale structure contribution to the DM PDF. We validate our analytical predictions against consistency-check simulations and compare them with the IllustrisTNG hydrodynamical simulation over the redshift range $ z = 0$ to $z = 5$, demonstrating excellent agreement. We demonstrate that our model produces consistent results when fitting gas profiles and predicting the PDF, and vice versa. We show that the BFC parameters controlling the gas profile, particularly the halo mass scale ($M_\mathrm{c}$), mass-dependent slope ($μ$), and outer truncation ($δ$), are the primary drivers of the PDF shape. Additionally, we investigate the validity of the log-normal approximation commonly used for DM distributions, finding that it provides a sufficient description for a few hundred FRBs. Our work provides a self-consistent model that links gas density profiles to integrated DM statistics, enabling future constraints on baryonic feedback processes from FRB observations.

Heterogeneous nucleation from defects dominates the electric field required for polarization switching of ferroelectrics. Here, we consider the switching of a nominally non-switchable polar thin film of AlN due to the proximity effect arising from embedded ferroelectric nanoclusters of Al1-xScxN. Using a Landau-Ginzburg-Devonshire thermodynamic approach and finite element modeling, we study the influence of nanocluster shape on polarization switching and domain nucleation emerging in AlN. The ferroelectric nanocluster boundary is modeled as a thin layer transitioning from Al1-xScxN to AlN. We analyze the conditions under which polarization switching in the AlN film occurs at coercive fields significantly lower than its dielectric breakdown field. In the presence of spike-like Al1-xScxN nanoclusters, the proximity effect enables switching of the spontaneous polarization in AlN and significantly reduces the corresponding coercive field. The internal field, which is depolarizing inside the AlN (due to its larger spontaneous polarization) and polarizing within the ferroelectric Al1-xScxN nanoclusters (due to its smaller spontaneous polarization), lowers the potential barrier in the clusters and nucleates nanodomains at the Al1-xScxN-AlN interface, forming localized regions of reversed polarization. Proximity effect can thus provide a pathway towards "thawing" previously "frozen" ferroelectrics through engineered nucleation for memory, actuation and optical technologies.

Eclipse attacks isolate blockchain nodes by monopolizing their peer-to-peer connections. The attacks were extensively studied in Bitcoin (SP'15, SP'20, CCS'21, SP'23) and Monero (NDSS'25), but their practicality against Ethereum nodes remains underexplored, particularly in the post-Merge settings. We present the first end-to-end implementation of an eclipse attack targeting Ethereum (2.0 version) execution-layer nodes. Our attack exploits the bootstrapping and peer management logic of Ethereum to fully isolate a node upon restart. We introduce a multi-stage strategy that majorly includes (i) poisoning the node's discovery table via unsolicited messages, (ii) infiltrating Ethereum's DNS-based peerlist by identifying and manipulating the official DNS crawler, and (iii) hijacking idle incoming connection slots across the network to block benign connections. Our DNS list poisoning is the first in the cryptocurrency context and requires only 28 IP addresses over 100 days. Slots hijacking raises outgoing redirection success from 45\% to 95\%. We validate our approach through controlled experiments on Ethereum's Sepolia testnet and broad measurements on the mainnet. Our findings demonstrate that over 80\% of public nodes do not leave sufficient idle capacity for effective slots occupation, highlighting the feasibility and severity of the threat. We further propose concrete countermeasures and responsibly disclosed all findings to Ethereum's security team.

In this paper we generalise the notion of linearity (in the sense of Lawvere) to a category C equipped with a compatible sum structure and product structure. In this context, any morphism f from an n-fold sum to an n-fold product has a unique n by m matrix presentation, but a morphism for a given matrix does not necessarily exist. We define the sum and product to be compatible if there exists a natural transformation i from sum to product with matrix presentation the identity and define C to be partially linear if such an i is invertible. We establish a coherence theorem for partially linear categories. We generalise the notion of a central morphism to this setting, and show that the central morphisms of a partially linear category admit enrichment over monoids.

Low-temperature plasma processing is a promising technique for tailoring transition metal dichalcogenides (TMDs). For chalcogen substitution processing, a key challenge is to identify the ion energy window that enables selective chalcogen removal while preserving the metal lattice. Using ab-initio molecular dynamics (AIMD), we demonstrate that oxygen and fluorine functionalization widen the processing window by significantly lowering the sulfur sputtering energy threshold ($E_{\text{sputt,S}}$) of MoS${}_2$ from $\sim 30$ eV to $\sim 10$ eV via formation of sputtering products such as SO${}_2$ and SF${}_n$. Additionally, we show that experimentally relevant cryogenic temperatures strongly affect $E_{\text{sputt,S}}$. The dependence is confirmed via AIMD and also predicted by a mechanistic parameter-free theory, suggesting that $E_{\text{sputt}}(T)$ generalizes to other TMDs, functionalization, and surface impacts in general. Our results highlight oxygen/fluorine functionalization, ionic impact angle, and material temperature to be key control parameters for selective, damage-controlled chalcogen removal in TMD processing.

Gravitational-wave (GW) observatories have used template-based search to detect hundreds of compact binary coalescences (CBCs). However, template-based search cannot detect astrophysical sources that lack accurate waveform models, including core-collapse supernovae, neutron star glitches, and cosmic strings. Here, we present a novel approach for template-free search using coincident anomaly detection (CoAD). CoAD requires neither labeled training examples nor background-only training sets, instead exploiting the coincidence of events across spatially separated detectors as the training loss itself: two neural networks independently analyze data from each detector and are trained to maximize coincident predictions. Additionally, we show that integrated gradient analysis can localize GW signals from the neural-network weights, providing a path toward data-driven template construction of unmodeled sources, and further improving precision by frequency matching. Using the CodaBench dataset of real LIGO backgrounds with injected simulated CBCs and sine-Gaussian low-frequency bursts, CoAD achieves recall up to 0.91 and 0.85 respectively at a false-alarm rate of one event per year, and achieves recall above 0.5 at signal-to-noise ratios below 10. The fully-unsupervised nature of CoAD makes it especially well-suited for next-generation detectors with greater sensitivity and associated increases in GW event rates.

This paper develops a data-driven time-limited h2 model reduction method for discrete-time linear time-invariant systems. Specifically, we formulate and solve a regularized time-limited h2 model reduction problem using only noisy impulse response data. Furthermore, we show that the objective function and its gradient can be represented using only noisy impulse response data. Numerical experiments using SLICOT benchmarks demonstrate that the proposed regularized method achieves lower relative time-limited h2 errors than the tested alternatives and is effective in situations where the unregularized method may deteriorate under noise.

This paper explores option portfolio optimization when the underlying returns are skew-elliptical t-distributed. We use the variance and value at risk (VaR) to measure portfolio risk. The novelty of our work is the departure from the traditional normal returns setting, allowing investors to capture both heavy-tailed and skewed market dynamics. We provide explicit portfolio weights for the variance and VaR approximation. Our second contribution is the numerical representation of portfolio weights, obtained from numerical optimization for better VaR approximations. The effect of skewness on the portfolio weights is quantified by comparing our optimal skew t weights with those generated in the Student t setting. We also find that, as expected, a better VaR approximation risk measure yields optimal portfolio weights which are more different than the variance optimal weights.

Certain approaches to quantum gravity, such as the one based on the concept of purely virtual particles (fakeons), sacrifice the cause-effect relation at very small scales to reconcile renormalizability with unitarity. Other developments have also urged caution regarding the idea of causality as a fundamental principle. In this paper, we examine the problem from multiple perspectives, including locality and predictivity, and extend the existing skepticism in several directions. Emphasizing the impact of unruly "disruptors", we point out that the illusory arrow of time associated with causality and predictivity is inherently statistical. This renders the cause-effect relation strained at the microscopic level. We also show that causation is a borderline concept that demands belief in entities which can act on nature without being part of it. Ultimately, not only is renouncing microcausality a reasonable price to pay for a consistent and predictive theory of quantum gravity (as is the one based on the fakeon idea), but the very notion of causality is misleading. Resting as it does on metaphysical assumptions, it should therefore be abandoned in fundamental physics.

We derive threshold resummation of semi-inclusive deep-inelastic scattering (SIDIS), by building upon previous results by some of us for the resummation of the Drell-Yan process at fixed rapidity, which is related to SIDIS by crossing. We consider both a double-soft limit, in which both the Bjorken and the fragmentation scaling variables tend to their threshold value, and single soft limits in which either of them does. We show that in the former limit only soft radiation contributes, and in the latter limit only collinear radiation, and we derive resummed expressions for the coefficient functions in all cases. We determine explictly resummation coefficients in the nonsinglet channel up to next-to-next-to-leading log by comparing to recent fixed next-to-next-to-leading order results. Expanding out the single-soft resummation we reproduce recent next-to-leading power results.

Context. The solar atmosphere is gravitationally stratified and consists of several layers at temperatures different by orders of magnitude. Consequently, the solar atmospheric plasma changes from weakly ionized in the photosphere, partially ionized in the chromosphere, to eventually fully ionized in the corona. However, integrating ionization and recombination processes into multi-fluid solar plasma models with gravitational stratification remains nontrivial. Aims. We intend to provide a method for constructing multi-fluid-multi-species gravitational stratification that satisfies ionization equilibrium and hydrostatic equilibrium at the same time, avoiding causing non-physical disturbances and numerical instability due to initial in-equilibria. Methods. We assume that collisional interactions between fluids are sufficient for coupling all fluids when there is no high-frequency external driving force imposed. Ionization fractions can be (I) calculated assuming ionization in statistical equilibrium at any given temperature, or (II) extracted from other atmospheric models. A simple numerical integration routine is then designed and used to construct multi-fluid-multi-species gravitational stratifications. Results. A gravitational stratification constructed using the present numerical integration routine can be in hydrostatic equilibrium with any given ionization fractions of multi-species plasmas. Meanwhile, without any dynamic driving force, fluid decoupling appears, particularly in the transition region of the constructed stratification, while the total velocity of all fluids remains zero. Conclusions. A gravitational stratification constructed using the present routine can be used in multi-fluid-multi-species models to study specific dynamics without being affected by initial in-equilibria.

Approximation semantics capture the observable behaviour of λ-terms, with Böhm Trees and Taylor Expansion standing as two central paradigms. Although conceptually different, these notions are related via the Commutation Theorem, which links the Taylor expansion of a term to that of its Böhm tree. These notions are well understood in Call-by-Name λ-calculus and have been more recently introduced in Call-by-Value settings. Since these two evaluation strategies traditionally require separate theories, a natural next step is to seek a unified setting for approximation semantics. The Bang-calculus offers exactly such a framework, subsuming both CbN and CbV through linear-logic translations while providing robust rewriting properties. However, its approximation semantics is yet to be fully developed. In this work, we develop the approximation semantics for dBang, the Bang-calculus with explicit substitutions and distant reductions. We define Böhm trees and Taylor expansion within dBang and establish their fundamental properties. Our results subsume and generalize Call-By-Name and Call-By-Value through their translations into Bang, offering a single framework that uniformly captures infinitary and resource-sensitive semantics across evaluation strategies.

A colleague asked about the Adams filtrations of the homotopy classes in the homotopy of the fiber of a particular map between GEMs. The theorem proved in arXiv:2105.02601v3 [math.AT] proves to be effective in answering this (Theorem 4.4). We show that this and some related Adams spectral sequences all collapse at $E_3$ and we determine the value of $E_3 = E_\infty$. Notably, we do not need to determine the cohomology of the fiber or the $E_2$ term of the Adams spectral sequence to do this.

There is growing evidence from gravitational-wave observations that some merging black holes are created from previous mergers. Using the prediction that these hierarchically merged black holes have dimensionless spin magnitudes of $χ\approx 0.69$, we identify a subpopulation in the gravitational-wave data consistent with a hierarchical-merger origin in dense star clusters. This subpopulation's primary mass distribution peaks at $17.0^{+18.3}_{-4.4},\mathrm{M}_{\odot}$, which is approximately twice as large as its secondary mass distribution's mode ($10.5^{+29.7}_{-4.7},\mathrm{M}_{\odot}$), and its spin tilt distribution is consistent with isotropy. Our inferred secondary mass distributions imply that isolated binary evolution may still be needed to explain the entirety of the $9\,\mathrm{M}_{\odot}$ peak. Surprisingly, we find that the rate of hierarchical mergers may evolve more steeply with redshift than the rest of the population ($98.0\%$ credibility): the fraction of all binary black holes that are hierarchically formed at $z=0.1$ is $0.03^{+0.05}_{-0.02}$, compared to $0.09^{+0.11}_{-0.07}$ at $z=1$. This provides an explanation for the previously discovered broadening of the effective spin distribution with redshift. Our results have implications for star cluster formation histories, as they suggest the potential existence of a high-redshift population of massive, compact clusters.

Guo and Royle recently classified the connected cubic graphs without eigenvalues of their adjacency matrix in the open interval $(-1, 1)$, and raised the question of extending their classification to graphs of maximum degree at most $3$. They carried out a preliminary investigation of the subcubic case, exhibiting both infinite families and sporadic examples. In this paper, we complete this investigation by determining all connected subcubic graphs that are not cubic and have no eigenvalues in $(-1,1)$. We show that exactly two infinite families and seven sporadic examples occur, and that every sporadic graph has at most $18$ vertices. As a consequence, we prove that $(-1,1)$ is a maximal spectral gap set for the class of connected subcubic graphs. Guo and Royle, answering a question of Kollár and Sanark, established this maximality for connected cubic graphs. Our result generalizes their conclusion to the subcubic setting.

We prove $\ell^{1}\!\to\!\ell^{\infty}$ dispersive estimates for the discrete Klein--Gordon equation on $\mathbb Z$ with small real-analytic quasi-periodic potentials, showing that the time-decay rate persists as $(\tfrac13)^{-}$. As applications, we derive the corresponding Strichartz estimates and establish small-data global well-posedness for the associated nonlinear discrete Klein--Gordon equation.

Operating power amplifiers (PAs) at lower input back-off (IBO) levels is an effective way to improve PA efficiency, but often introduces severe nonlinear distortion that degrades transmission performance. Amplitude-phase-time block modulation (APTBM) has recently emerged as an effective solution to this problem. The intrinsic amplitude and phase constraints of each APTBM block can be leveraged to mitigate PA-induced nonlinear distortion via constraint-guided signal reconstruction. However, existing reconstruction methods apply these constraints only heuristically and statistically, limiting the achievable IBO reduction and PA efficiency improvement. This paper addresses this limitation by decomposing the nonlinear distortion into dominant and residual components, and accordingly develops a novel two-stage signal reconstruction algorithm consisting of coarse and fine reconstruction stages. The coarse reconstruction stage eliminates the dominant distortion by jointly exploiting the APTBM block structure and PA nonlinear characteristics. Subsequently, the fine reconstruction stage minimizes the residual distortion by casting it as a nonconvex optimization problem subject to explicit APTBM constraints, for which a closed-form solution is derived. The proposed algorithm is validated through comprehensive numerical simulations and testbed experiments. Results show that, without compromising transmission quality, the proposed algorithm enables an additional IBO reduction of approximately 5 dB in simulations and 2 dB in experiments over baseline methods, yielding relative PA efficiency improvements of 77.8\% and 30.9\%, respectively.

We theoretically and experimentally investigate spontaneous self-organization in a conservative (Hamiltonian) turbulent wave system, operating far from thermodynamic equilibrium. Our system is governed by two coherently coupled nonlinear Schrödinger equations, describing the polarization evolution of light in a dispersive nonlinear optical fiber. The analysis reveals the emergence of two fundamentally distinct turbulent regimes. In a first regime, the waves undergo a slow, irreversible thermalization process, which is accurately described by the wave turbulence kinetic equation and the associated H-theorem of entropy growth. In stark contrast with this expected irreversible process, we identify a second different regime, where strong phase-correlations spontaneously emerge, giving rise to a fast reversible oscillatory dynamics of the normal correlator and anomalous phase-correlator. Experimental observations confirm the occurrence of both irreversible thermalization and reversible dynamics mediated by the anomalous correlated fluctuations.

In this paper, we propose a simultaneous secrecy and covert communications (SSACC) scheme in a reconfigurable intelligent surface (RIS)-aided network with a cooperative jammer. The scheme enhances communication security by maximizing the secrecy capacity and the detection error probability (DEP). Under a worst-case scenario for covert communications, we consider that the eavesdropper can optimally adjust the detection threshold to minimize the DEP. Accordingly, we derive closedform expressions for both average minimum DEP (AMDEP) and average secrecy capacity (ASC). To balance AMDEP and ASC, we propose a new performance metric and design an algorithm based on generative diffusion models (GDM) and deep reinforcement learning (DRL). The algorithm maximizes data rates under user mobility while ensuring high AMDEP and ASC by optimizing power allocation. Simulation results demonstrate that the proposed algorithm achieves faster convergence and superior performance compared to conventional deep deterministic policy gradient (DDPG) methods, thereby validating its effectiveness in balancing security and capacity performance.

The rapid advancement of deep learning has turned models into highly valuable assets due to their reliance on massive data and costly training processes. However, these models are increasingly vulnerable to leakage and theft, highlighting the critical need for robust intellectual property protection. Model watermarking has emerged as an effective solution, with black-box watermarking gaining significant attention for its practicality and flexibility. Nonetheless, existing black-box methods often fail to better balance covertness (hiding the watermark to prevent detection and forgery) and robustness (ensuring the watermark resists removal)-two essential properties for real-world copyright verification. In this paper, we propose ComMark, a novel black-box model watermarking framework that leverages frequency-domain transformations to generate compressed, covert, and attack-resistant watermark samples by filtering out high-frequency information. To further enhance watermark robustness, our method incorporates simulated attack scenarios and a similarity loss during training. Comprehensive evaluations across diverse datasets and architectures demonstrate that ComMark achieves state-of-the-art performance in both covertness and robustness. Furthermore, we extend its applicability beyond image recognition to tasks including speech recognition, sentiment analysis, image generation, image captioning, and video recognition, underscoring its versatility and broad applicability.

We propose a renormalization group (RG) approach to compare and collapse eigenvalue densities of random matrix models of complex systems across different system sizes. The approach is to fix a natural spectral scale by letting the model normalization run with size, turning raw spectra into comparable, collapsed density curves. We demonstrate this approach on generalizations of two classic random matrix ensembles--Wigner and Wishart--modified to have power-law variance profiles. We use random matrix theory methods to derive self-consistent fixed-point equations for the resolvent to compute their eigenvalue densities, we define an RG scheme based on matrix decimation, and compute the Beta function controlling the RG flow as a function of the variance profile power-law exponent. The running normalization leads to spectral collapse which we confirm in simulations and solutions of the fixed-point equations. We expect this RG approach to carry over to other ensembles, providing a method for data analysis of a broad range of complex systems.

In this survey we talk about what is known as Invariance Principle in dynamical systems. It states that the disintegration of measures with zero center Lyapunov exponents admits some extra invariance by holonomies. We focus on explaining the basic definitions and ideas behind a series of results about the Invariance Principle and give some basic applications on how this is used in dynamical systems.

Simulation of fermionic Hamiltonians with gate-based quantum computers requires the selection of an encoding from fermionic operators to quantum gates, the most widely used being the Jordan-Wigner transform. Many alternative encodings exist, with quantum circuits and simulation results being sensitive to choice of encoding, device connectivity and Hamiltonian characteristics. Non-stochastic optimisation of the ternary tree class of encodings to date has targeted either the device or Hamiltonian. We develop a deterministic method which optimises ternary tree encodings without changing the underlying tree structure. This enables reduction in Pauli-weight without ancillae or additional swap-gate overhead. We demonstrate this method for a variety of encodings, including those which are derived from the qubit connectivity graph of a quantum computer. Numerical results for a suite of standard encoding methods applied to water in the STO-3G basis indicate that our method reduces qDRIFT circuit depths on average by 24.7% and 26.5% for untranspiled and transpiled circuits respectively.

In arXiv:2407.11958, a moduli stack parametrizing $I$--indexed diagrams of Higgs bundles over a base stack $X$ was constructed for any finite simplicial set $I$, inspiring speculations about extending the non-Abelian Hodge correspondence to these moduli stacks. In the present work, we formalize the de Rham side of this conjectural extension. We construct moduli stacks parametrizing diagrams of bundles with $λ$--connections over a base prestack $X$, where $λ$ can be a fixed number or a parameter. Taking $λ$ to be $1$ gives a moduli stack parametrizing diagrams of bundles with connection, while taking it to be a parameter gives a version of Simpson's non-Abelian Hodge filtration for digrams of bundles with connection. We show that when $X$ is a smooth and projective scheme over an algebraically closed field $k$ of characteristic $0$, these moduli stacks are algebraic and locally of finite presentation, and have affine diagonal.

Covering spaces are a fundamental tool in algebraic topology because of the close relationship they bear with the fundamental groups of spaces. Indeed, they are in correspondence with the subgroups of the fundamental group: this is known as the Galois correspondence. In particular, the covering space corresponding to the trivial group is the universal covering, which is a "1-connected" variant of the original space, in the sense that it has the same homotopy groups, except for the first one which is trivial. In this article, we formalize this correspondence in homotopy type theory, a variant of Martin-Löf type theory in which types can be interpreted as spaces (up to homotopy). Along the way, we develop an n-dimensional generalization of covering spaces. Moreover, in order to demonstrate the applicability of our approach, we formally classify the covering of lens spaces and explain how to construct the Poincaré homology sphere.

Smartphones handle sensitive tasks such as messaging and payment and may soon support critical electronic identification through initiatives such as the European Digital Identity (EUDI) wallet, currently under development. Yet the susceptibility of modern smartphones to physical side-channel analysis (SCA) is underexplored, with recent work limited to pre-2019 hardware. Since then, smartphone system on chip (SoC) platforms have grown more complex, with heterogeneous processor clusters, sub 10 nm nodes, and frequencies over 2 GHz, potentially complicating SCA. In this paper, we assess the feasibility of electromagnetic (EM) SCA on a Raspberry Pi 4, featuring a Broadcom BCM2711 SoC and a Fairphone 4 featuring a Snapdragon 750G 5G SoC. Using new attack methodologies tailored to modern SoCs, we recover ECDSA secrets from OpenSSL by mounting the Nonce@Once attack of Alam et al. (Euro S&P 2021) and show that the libgcrypt countermeasure does not fully mitigate it. We present case studies illustrating how hardware and software stacks impact EM SCA feasibility. Motivated by use cases such as the EUDI wallet, we survey Android cryptographic implementations and define representative threat models to assess the attack. Our findings show weaknesses in ECDSA software implementations and underscore the need for independently certified secure elements (SEs) in all smartphones.

We present a comprehensive first-principles investigation of carbon self-interstitial defects in diamond, ranging from mono- to hexa-interstitial complexes. By quantum mechanical density functional theory, empowered by interatomic potential models, we efficiently sample the complex configurational landscape and identify both known and previously unreported defect geometries. Our results reveal a pronounced energetic driving force for aggregation: the formation energy per interstitial decreases systematically from isolated split interstitials to compact multi-interstitial clusters, with the tetra-interstitial platelet emerging as a particularly stable structural motif. Additionally, charge analysis indicates that the predominantly covalent bonding in diamond becomes more polar within the defect centers. Analysis of defect energy levels shows that only the investigated mono-, di-, penta-, and hexa-interstitial complexes introduce in-gap electronic states, whereas the tri- and tetra-interstitial clusters are electronically inert. Vibrational spectroscopies further reveal that self-interstitials generate characteristic signatures. Short carbon-carbon bonds inside the defect cores give rise to high-frequency vibrational modes between 1375 and 1925 cm$^{-1}$, which are strongly IR-active but exhibit weak Raman activity. Through a systematic analysis of metastable configurations, we identify the 3H defect center as a neutral di-interstitial defect. Based on this identification, we further suggest that the TR12 center may arise from a 3H-containing defect like a metastable hexa-interstitial configuration. Taken together, these findings provide a coherent picture of the structural, electronic, and vibrational characteristics of carbon self-interstitials and establish a robust framework for their experimental identification.

A sharp change in apparent mobility at a characteristic temperature that depends on the observation time has been reported in experiments and simulations of hydrated proteins. Such behavior is often discussed in the context of the protein dynamical transition, yet its general physical origin remains unclear. Here we show that fluctuating diffusivity within a Langevin framework naturally gives rise to an observation-time-induced crossover in translational diffusion: the effective diffusion coefficient exhibits a temperature-dependent change whose crossover point systematically shifts with the observation time. Through analytical and numerical analyses, we elucidate the mechanism of this crossover and identify the minimal conditions required for its emergence. Our results establish observation-time-induced crossover as a generic non-equilibrium phenomenon in systems with slowly relaxing mobility fluctuations. While distinct from internal dynamical transitions probed in neutron scattering, this framework provides a unified perspective that encompasses related finite-time crossover phenomena observed in hydrated proteins and other complex soft-matter systems.

We study the effect of modular flow on correlation functions of fermions in the Sachdev-Ye-Kitaev (SYK) model coupled weakly to a bath, which we take to be another SYK model. The system and bath, together are prepared in the thermofield double (TFD) state, and we focus on the effect of modular flow generated by the reduced density matrix for the SYK system, obtained by tracing out the bath. We show, in the late time limit, that modular flowed correlators of two Majorana fermions, single-sided and two-sided, exhibit non-trivial singularities. Beyond a critical value of the modular parameter, the ``modular scrambling time", the singularity structure shows correlations being transferred from one boundary to the other. The calculations are performed by employing the replica trick in Euclidean time and appropriately analytically continuing to real time. Exploiting the connection between modular flow generators and SL$(2,{\mathbb R})$ boosts we use the microscopic picture to reconstruct the dual bulk modular flow in two-sided AdS$_2$ black hole spacetime. Fixed points of the flow allow to identify quantum extremal surfaces (QES) demarcating the entanglement wedge of the boundary system and the island. We show that bulk modular flow can move fermion insertions near the right boundary past the horizon leading to lightcone singularities in appropriately smeared boundary correlators, probing physics beyond the horizon.

Extending data-driven algorithms based on Willems' fundamental lemma to stochastic data often requires empirical and customized workarounds. This work presents a unified Bayesian framework for linear systems that provides a systematic and general method for handling stochastic data-driven tasks, including smoothing, prediction, and control, via maximum a posteriori estimation. This framework formulates a unified trajectory estimation problem for the three tasks by specifying different types of trajectory knowledge. Then, a Bayesian problem is solved that optimally combines trajectory knowledge with a data-driven characterization of the trajectory from offline data for correlated input-output uncertainties with elliptical distributions. Under specific conditions, this problem is shown to generalize existing data-driven prediction and control algorithms. Numerical examples demonstrate the performance of the unified approach for all three tasks against other data-driven and system identification approaches.