Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a streamlined approach that decouples the control problem from the training process, rendering these additional layers of complexity unnecessary. In particular, our analysis and computational experiments demonstrate that a simple neural operator architecture, such as DeepONet, coupled with an unconstrained optimization routine, can solve tracking-type partial differential equation (PDE) constrained control problems with a single physics-informed training phase and a subsequent optimization phase. We achieve this by adding a penalty term to the cost function based on the differential equation residual to penalize deviations from the PDE constraint. This allows gradient computations with respect to the control using automatic differentiation through the trained neural operator within an iterative optimization routine, while satisfying the PDE constraints. Once trained, the same neural operator can be reused across different tracking targets without retraining. We benchmark our method on scalar elliptic (Poisson's equation), nonlinear transport (viscous Burgers' equation), and flow (Stokes equation) control problems. For the Poisson and Burgers problems, we compare against adjoint-based solvers: for the time-dependent Burgers problem, the approach achieves competitive accuracy with iteration times up to four times faster, while for the linear Poisson problem, the adjoint method retains superior accuracy, suggesting the approach is best suited to nonlinear and time-dependent settings. For the flow control problem, we verify the feasibility of the optimized control through a reference forward solver.

Large Language Models (LLMs) enhanced with Retrieval-Augmented Generation (RAG) have shown improved performance in generating accurate responses. However, the dependence on external knowledge bases introduces potential security vulnerabilities, particularly when these knowledge bases are publicly accessible and modifiable. While previous studies have exposed knowledge poisoning risks in RAG systems, existing attack methods suffer from critical limitations: they either require injecting multiple poisoned documents (resulting in poor stealthiness) or can only function effectively on simplistic queries (limiting real-world applicability). This paper reveals a more realistic knowledge poisoning attack against RAG systems that achieves successful attacks by poisoning only a single document while remaining effective for complex multi-hop questions involving complex relationships between multiple elements. Our proposed AuthChain address three challenges to ensure the poisoned documents are reliably retrieved and trusted by the LLM, even against large knowledge bases and LLM's own knowledge. Extensive experiments across six popular LLMs demonstrate that AuthChain achieves significantly higher attack success rates while maintaining superior stealthiness against RAG defense mechanisms compared to state-of-the-art baselines.

Software vulnerabilities such as buffer overflows and SQL injections are a major source of security breaches. Traditional methods for vulnerability detection remain essential but are limited by high false positive rates, scalability issues, and reliance on manual effort. These constraints have driven interest in AI-based approaches to automated vulnerability detection and secure code generation. While Large Language Models (LLMs) have opened new avenues for classification tasks, their complexity and opacity pose challenges for interpretability and deployment. Sparse Autoencoder offer a promising solution to this problem. We explore whether SAEs can serve as a lightweight, interpretable alternative for bug detection in Java functions. We evaluate the effectiveness of SAEs when applied to representations from GPT-2 Small and Gemma 2B, examining their capacity to highlight buggy behaviour without fine-tuning the underlying LLMs. We found that SAE-derived features enable bug detection with an F1 score of up to 89%, consistently outperforming fine-tuned transformer encoder baselines. Our work provides the first empirical evidence that SAEs can be used to detect software bugs directly from the internal representations of pretrained LLMs, without any fine-tuning or task-specific supervision. Code available at https://github.com/rufimelo99/SAE-Java-Bug-Detection

Generating high-quality, photorealistic textures for 3D human avatars remains a fundamental yet challenging task in computer vision and multimedia field. However, real paired front and back images of human subjects are rarely available with privacy, ethical and cost of acquisition, which restricts scalability of the data. Additionally, learning priors from image inputs using deep generative models, such as GANs or diffusion models, to infer unseen regions such as the human back often leads to artifacts, structural inconsistencies, or loss of fine-grained detail. To address these issues, we present SMPL-GPTexture (skinned multi-person linear model - general purpose Texture), a novel pipeline that takes natural language prompts as input and leverages a state-of-the-art text-to-image generation model to produce paired high-resolution front and back images of a human subject as the starting point for texture estimation. Using the generated paired dual-view images, we first employ a human mesh recovery model to obtain a robust 2D-to-3D SMPL alignment between image pixels and the 3D model's UV coordinates for each views. Second, we use an inverted rasterization technique that explicitly projects the observed colour from the input images into the UV space, thereby producing accurate, complete texture maps. Finally, we apply a diffusion-based inpainting module to fill in the missing regions, and the fusion mechanism then combines these results into a unified full texture map. Extensive experiments shows that our SMPL-GPTexture can generate high resolution texture aligned with user's prompts.

In genome-scale constraint-based metabolic models, gene deletion strategies are essential for achieving growth-coupled production, where cell growth and target metabolite synthesis occur simultaneously. Despite the inherently networked nature of genome-scale metabolic models, existing computational approaches rely primarily on sequential data and lack graph representations that capture their complex relationships, as both well-defined graph constructions and learning frameworks capable of exploiting them remain largely unexplored. To address this gap, we present a twofold solution. First, we introduce a systematic pipeline for constructing graph representations from constraint-based metabolic models. Second, we develop a deep learning framework that integrates these graph representations with gene and metabolite sequence data to predict growth-coupled gene deletion strategies. Across three metabolic models, our approach consistently outperforms established baselines, with improvements in overall accuracy of 14.04%, 16.26%, and 13.18% over a deep feedforward neural network baseline, 6.17%, 4.96%, and 5.31% over a sequence-learning baseline, and 5.10%, 4.36%, and 4.70% over a topology-aware graph aggregation baseline on the same metabolite graph, respectively. The source code and example datasets are available at: https://github.com/MetNetComp/GraphGDel.

Rendering realistic human-object interactions (HOIs) from sparse-view inputs is a challenging yet crucial task for various real-world applications. Existing methods often struggle to simultaneously achieve high rendering quality, physical plausibility, and computational efficiency. To address these limitations, we propose HOGS (Human-Object Rendering via 3D Gaussian Splatting), a novel framework for efficient HOI rendering with physically plausible geometric constraints from sparse views. HOGS represents both humans and objects as dynamic 3D Gaussians. Central to HOGS is a novel optimization process that operates directly on these Gaussians to enforce geometric consistency (i.e., preventing inter-penetration or floating contacts) to achieve physical plausibility. To support this core optimization under sparse-view ambiguity, our framework incorporates two pre-trained modules: an optimization-guided Human Pose Refiner for robust estimation under sparse-view occlusions, and a Human-Object Contact Predictor that efficiently identifies interaction regions to guide our novel contact and separation losses. Extensive experiments on both human-object and hand-object interaction datasets demonstrate that HOGS achieves state-of-the-art rendering quality and maintains high computational efficiency.

The estimation of underwater sound velocity distribution serves as a critical basis for facilitating effective underwater communication and precise positioning, given that variations in sound velocity influence the path of signal transmission. Conventional techniques for the direct measurement of sound velocity, as well as methods that involve the inversion of sound velocity utilizing acoustic field data, necessitate on--site data collection. This requirement not only places high demands on device deployment, but also presents challenges in achieving real-time estimation of sound velocity distribution. In order to construct a real-time sound velocity field and eliminate the need for underwater onsite data measurement operations, we propose a self-attention embedded multimodal data fusion convolutional neural network (SA-MDF-CNN) for real-time underwater sound speed profile (SSP) estimation. The proposed model seeks to elucidate the inherent relationship between remote sensing sea surface temperature (SST) data, the primary component characteristics of historical SSPs, and their spatial coordinates. This is achieved by employing CNNs and attention mechanisms to extract local and global correlations from the input data, respectively. The ultimate objective is to facilitate a rapid and precise estimation of sound velocity distribution within a specified task area. Experimental results show that the method proposed in this paper has lower root mean square error (RMSE) and stronger robustness than other state-of-the-art methods.

Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations observed in practical large-scale diffusion models. Offset noise has been proposed as an empirical solution to this issue, yet its theoretical basis remains insufficiently explored. In this paper, we propose a novel diffusion model that naturally incorporates additional noise within a rigorous probabilistic framework. Our approach modifies both the forward and reverse diffusion processes, enabling inputs to be diffused into Gaussian distributions with arbitrary mean structures. We derive a loss function based on the evidence lower bound and show that the resulting objective is structurally analogous to that of offset noise, with time-dependent coefficients. Experiments on controlled synthetic datasets demonstrate that the proposed model mitigates brightness-related limitations and achieves improved performance over conventional methods, particularly in high-dimensional settings.

As the rapid development of computer vision and the emergence of powerful network backbones and architectures, the application of deep learning in medical imaging has become increasingly significant. Unlike natural images, medical images lack huge volumes of data but feature more modalities, making it difficult to train a general model that has satisfactory performance across various datasets. In practice, practitioners often suffer from manually creating and testing models combining independent backbones and architectures, which is a laborious and time-consuming process. We propose Flemme, a FLExible and Modular learning platform for MEdical images. Our platform separates encoders from the model architectures so that different models can be constructed via various combinations of supported encoders and architectures. We construct encoders using building blocks based on convolution, transformer, and state-space model (SSM) to process both 2D and 3D image patches. A base architecture is implemented following an encoder-decoder style, with several derived architectures for image segmentation, reconstruction, and generation tasks. In addition, we propose a general hierarchical architecture incorporating a pyramid loss to optimize and fuse vertical features. Experiments demonstrate that this simple design leads to an average improvement of 5.60% in Dice score and 7.81% in mean interaction of units (mIoU) for segmentation models, as well as an enhancement of 5.57% in peak signal-to-noise ratio (PSNR) and 8.22% in structural similarity (SSIM) for reconstruction models. We further utilize Flemme as an analytical tool to assess the effectiveness and efficiency of various encoders across different tasks. Code is available at https://github.com/wlsdzyzl/flemme.

Data fusion modeling can identify common features across diverse data sources while accounting for source-specific variability. Here we introduce the concept of a \textit{coupled generator decomposition} and demonstrate how it generalizes sparse principal component analysis (SPCA) for data fusion. Leveraging data from a multisubject, multimodal (electro- and magnetoencephalography (EEG and MEG)) neuroimaging experiment, we demonstrate the efficacy of the framework in identifying common features in response to face perception stimuli, while accommodating modality- and subject-specific variability. Through split-half cross-validation of EEG/MEG trials, we investigate the optimal model order and regularization strengths for models of varying complexity, comparing these to a group-level model assuming shared brain responses to stimuli. Our findings reveal altered $\sim170ms$ fusiform face area activation for scrambled faces, as opposed to real faces, particularly evident in the multimodal, multisubject model. Model parameters were inferred using stochastic optimization in PyTorch, demonstrating comparable performance to conventional quadratic programming inference for SPCA but with considerably faster execution. We provide an easily accessible toolbox for coupled generator decomposition that includes data fusion for SPCA, archetypal analysis and directional archetypal analysis. Overall, our approach offers a promising new avenue for data fusion.

Finance, especially option pricing, is a promising industrial field that might benefit from quantum computing. While quantum algorithms for option pricing have been proposed, it is desired to devise more efficient implementations of costly operations in the algorithms, one of which is preparing a quantum state that encodes a probability distribution of the underlying asset price. In particular, in pricing a path-dependent option, we need to generate a state encoding a joint distribution of the underlying asset price at multiple time points, which is more demanding. To address these issues, we propose a novel approach that uses a Matrix Product State (MPS), which can be encoded into a state of qubits, as a generative model for time series generation. We focus on the training of such an MPS and present its procedure in detail. To validate our approach, taking the Heston model as a target, we conduct numerical experiments to generate time series in the model. Our findings demonstrate the capability of the MPS model to generate paths in the Heston model, highlighting its potential for path-dependent option pricing on quantum computers.

AI and robotics technologies have witnessed remarkable advancements in the past decade, revolutionizing work patterns and opportunities in various domains. The application of these technologies has propelled society towards an era of symbiosis between humans and machines. To facilitate efficient communication between humans and intelligent robots, we propose the "Avatar" system, an immersive low-latency panoramic human-robot interaction platform. We have designed and tested a prototype of a rugged mobile platform integrated with edge computing units, panoramic video capture devices, power batteries, robot arms, and network communication equipment. Under favorable network conditions, we achieved a low-latency high-definition panoramic visual experience with a delay of 357ms. Operators can utilize VR headsets and controllers for real-time immersive control of robots and devices. The system enables remote control over vast physical distances, spanning campuses, provinces, countries, and even continents (New York to Shenzhen). Additionally, the system incorporates visual SLAM technology for map and trajectory recording, providing autonomous navigation capabilities. We believe that this intuitive system platform can enhance efficiency and situational experience in human-robot collaboration, and with further advancements in related technologies, it will become a versatile tool for efficient and symbiotic cooperation between AI and humans.

Three generations of software have transformed the role of artificial intelligence in society. In the first, programmers wrote explicit logic; in the second, neural networks learned programs from data; in the third, large language models turn natural language itself into a programming interface. These shifts have consequences that reach far beyond computer science, reshaping how societies generate knowledge, make decisions, and govern themselves. While generative adversarial networks introduced the era of deepfakes and synthetic media, large language models have added an entirely new class of systemic risks. This report applies a forensic-psychology profiling methodology to characterize AI based on nine documented features: hallucinations, bias and toxicity, sycophancy and echo chambers, fabrication and credulity, knowledge without understanding, discontinuity and the inability to learn from experience, jagged intelligence and scaling limits, shortcuts and fractured representations, and cognitive atrophy. The resulting profile reveals an "entity" that confabulates fluently, mirrors its users' biases, possesses encyclopedic recall without causal understanding, and erodes the competence of those who depend on it. The implications extend to institutional erosion across law, academia, journalism, and democratic governance. To address these challenges, this report proposes a three-pillar framework for AI resilience: cognitive sovereignty, which preserves the capacity for independent judgment; measurable control, which translates ethical commitments into enforceable standards and red lines; and partial autonomy, which maintains human agency at critical decision points. This report is an updated and extended version of arXiv:1912.08786v1.

A new approach to producing multidisciplinary lists of highly cited researchers is described and used for compiling a multidisciplinary list of highly cited researchers. This approach is essentially related to the recently discovered law of the constant ratios (Podlubny, 2004) and gives a better-balanced representation of different scientific fields.

Let $K$ be a field of characteristic $p>0$, $A=K[[Y]]$ be a power series ring in one variable and $Q(A)$ be the field of fraction of $A$. Suppose that $R=A[X_1,\ldots,X_n]$ is a standard $\mathbb{N}^n$-graded polynomial ring over $A$, i.e., $\operatorname{deg} (A)=\underline{0}\in \mathbb{N}^n$ and $\operatorname{deg}(X_j)=e_j\in \mathbb{N}^n$. Assume that $M=\bigoplus_{\underline{u}\in \mathbb{Z}^n} M_{\underline{u}}$ is a $\mathbb{Z}^n$-graded $\mathcal{F}$-finite, $\mathcal{F}$-module over $R$. In this article we prove that, $\displaystyle M_{\underline{u}}\cong E(A/YA)^{a(\underline{u})}\oplus Q(A)^{b(\underline{u})}\oplus A^{c(\underline{u})}$ for some finite numbers $a(\underline{u}), b(\underline{u}), c(\underline{u})\geq 0$. Let for a subset of $U$ of $\mathcal{S}=\{1, \ldots, n\}$, define a block to be the set $\displaystyle\mathcal{B}(U)=\{\underline{u} \in \mathbb{Z}^n \mid u_i \geq 0 \mbox{ if } i \in U \mbox{ and } u_i \leq -1 \mbox{ if } i \notin U \}$. Note that $\bigcup_{U\subseteq \mathcal{S}}\mathcal{B}(U)=\mathbb{Z}^n$. We prove that the sets $\{a(\underline{u})\mid \underline{u}\in \mathbb{Z}^n\}$, $\{b(\underline{u})\mid \underline{u}\in \mathbb{Z}^n\}$ and $\{c(\underline{u})\mid \underline{u}\in \mathbb{Z}^n\}$ are constant on $\mathcal{B}(U)$ for each subset $U$ of $\{1,\ldots,n\}$. In particular, these results holds for composition of local cohomology modules of the form $ H^{i_1}_{I_1}(H^{i_2}_{I_2}(\dots H^{i_r}_{I_r}(R)\dots)$ where $I_1,\ldots,I_r$ are $\mathbb{N}^n$-graded ideals of $R$. This provides a positive characteristic analogue of the results proved in \cite{TS-23} by the authors in characteristic zero.

Recent cosmological data reveal tension between parameters inferred from measurements of the cosmic microwave background (CMB), baryon acoustic oscillations (BAO), and supernovae (SN) under $Λ$CDM. Typical dynamical dark energy parameterizations (such as $w_0w_a$) that seek to jointly resolve these tensions have an equation of state parameter that crosses into the phantom regime, leading to potential instabilities for physical models. We show that the BAO (early-time) and SN (late-time) sides of the tension can instead be treated independently. Early dark energy (EDE) can reduce the tension between CMB-BAO data by changing the calibration of the sound horizon at the drag epoch $r_d$, with a $Δχ^2 = -{9.4}$ relative to $Λ$CDM, raising $H_0$ to 70.87 $\rm km s^{-1}Mpc^{-1}$. EDE alone cannot bring consistency between CMB, BAO, and SN data, but combining with a thawing-quintessence component of dark energy reduces tensions between the three datasets, with $Δχ^2=-12.6$ relative to $Λ$CDM without a phantom component, vs. $Δχ^2=-15.8$ for $w_0 w_a$ with one. We consider different SN datasets, using the most recent DES Dovekie catalog as our default while assessing differences with the original DESY5 and Pantheon+ catalogs. While the significance of adding thawing quintessence changes, the EDE solution to the CMB-BAO tension remains nearly unaffected. Moreover, though we do not include direct Hubble constant measurements in these $Δχ^2$ values, the EDE solution reduces the Hubble tension with the Local Distance Network value from $7σ$ in $Λ$CDM to $2-3σ$ depending on the SN dataset, nominally the equivalent of an extra $Δχ^2 \sim -40$ or more.

We study closed-loop stability and suboptimality for MPC and infinite-horizon optimal control solved using a surrogate model that differs from the real plant. We employ a unified framework based on quadratic costs to analyze both finite- and infinite-horizon problems, encompassing discounted and undiscounted scenarios alike. Plant-model mismatch bounds proportional to states and controls are assumed, under which the origin remains an equilibrium. Under continuity of the model and cost-controllability, exponential stability of the closed loop can be guaranteed. Furthermore, we give a suboptimality bound for the closed-loop cost recovering the optimal cost of the surrogate. The results reveal a tradeoff between horizon length, discounting and plant-model mismatch. The robustness guarantees are uniform over the horizon length, meaning that larger horizons do not require successively smaller plant-model mismatch.

We lay the foundations for a quantum formalism describing the real-time evolution of particles in the Glasma phase of a heavy-ion collision, focusing on the implications of gauge invariance in the definition of the momentum of a particle in a classical background field. We first establish the correspondence between the classical Wong's equations and the Heisenberg equations of motion for a particle in a classical non-Abelian background field. Using this correspondence, we obtain equations of motion for both the kinetic momentum -- the gauge invariant, physically measurable quantity -- and the canonical momentum, which is conjugate to the coordinates in the Hamiltonian. In particular, the kinetic momentum broadening receives non-trivial contributions from the transverse field components, even in the eikonal limit. Finally, we demonstrate that imposing a transverse Coulomb gauge condition at the initial time significantly reduces the accumulation of numerical errors, thereby providing an optimized framework for the forthcoming quantum implementation.

Fresnel zone plates (FZPs), with patterns of $1\,μ$m resolution, allow the formation of clean, diffraction-limited foci -- but have a static phase profile. Spatial light modulators (SLMs) allow dynamic control of spatial beam intensity and phase -- but are bulky and currently limited to roughly $10\,μ$m pixel sizes and $1\,$Mega-pixel formats. Here, we present a new `best-of-both' kind of FZP, scalable to large area rings currently incompatible with direct SLM generation. It is equivalent to a plano-convex donut lens, whereby light's local intensity and global phase at the FZP map directly onto the image plane. The same FZP under different SLM illumination can generate: rings and arcs, double-rings, phase windings and ring lattices (or dynamic combinations thereof). The smooth and adaptable near-field waveguide this enables will be ideal for Sagnac interferometry with ultracold atoms.

The study of repeated interactions between a learner and a utility-maximizing optimizer has yielded deep insights into the manipulability of learning algorithms. However, existing literature primarily focuses on independent, unlinked rounds, largely ignoring the ubiquitous practical reality of budget constraints. In this paper, we study this interaction in repeated second-price auctions in a Bayesian setting between a learning agent and a strategic agent, both subject to strict budget constraints, showing that such cross-round constraints fundamentally alter the strategic landscape. First, we generalize the classic Stackelberg equilibrium to the Budgeted Stackelberg Equilibrium. We prove that an optimizer's optimal strategy in a budgeted setting requires time-multiplexing; for a $k$-dimensional budget constraint, the optimal strategy strictly decomposes into up to $k+1$ distinct phases, with each phase employing a possibly unique mixed strategy (the case of $k=0$ recovers the classic Stackelberg equilibrium where the optimizer repeatedly uses a single mixed strategy). Second, we address the intriguing question of non-manipulability. We prove that when the learner employs a standard Proportional controller (the "P" of the PID-controller) to pace their bids, the optimizer's utility is upper bounded by their objective value in the Budgeted Stackelberg Equilibrium baseline. By bounding the dynamics of the PID controller via a novel analysis, our results establish that this widely used control-theoretic heuristic is actually strategically robust.

Understanding the mechanisms that limit high-fidelity readout in circuit quantum electrodynamics is essential for its optimization. Multi-photon resonances are understood to be a limiting factor, causing population transfer from the computational states to higher-energy states under drive. This effect, known as measurement-induced state transitions, has been extensively studied for the transmon qubit. While this exploration has begun for the fluxonium qubit, a systematic study of this effect is lacking. Here, we bridge this gap by theoretically studying measurement-induced state transitions in the fluxonium qubit over a wide range of parameters, comprising essentially all experimentally explored ranges. We find that lighter fluxoniums are less susceptible to these state transitions when compared to their heavier counterparts. We attribute this effect to the combination of lower density of multi-photon resonances, a smaller requisite coupling for a given dispersive shift, and a more harmonic-like structure of the charge operator. We confirm the validity of our analysis by performing time-dependent readout simulations. Finally, we consider the impact of the superinductor's array modes on measurement-induced state transitions over a large range of parameters.

Our study investigates the relationship between accessibility symbols and emerging technologies in supporting disability disclosure. We conducted twenty three remote design creation sessions with semi structured interviews to examine participants awareness of existing symbols, how they use symbols across online and offline contexts, and barriers to adoption and interpretation. Through participant sketching and future oriented storyboard probes, participants proposed ways to integrate symbols into wearable devices, mobile interfaces, and portable tools, emphasizing customizable and context sensitive disclosure. Our findings suggest symbols are most effective when paired with technologies that provide user control over visibility and optional pathways for explanation, helping reduce misinterpretation while supporting agency in disclosure moments. By reimagining symbol based assistance as part of a broader disclosure system where meaning depends on the symbol, its carrier, and context, this work informs more inclusive accessibility supports across diverse settings.

Recently, it has been shown that wave function coefficients (WFCs) admit a natural description in terms of the orthogonal Grassmannian, furnishing homogeneous solutions to the three-dimensional conformal Ward identities in spinor-helicity variables. This, however, presents a challenge for WFCs of conserved currents, which satisfy inhomogeneous Ward identities; correspondingly, the Grassmannian construction reproduces only their \textit{discontinuities}. In this paper, we show that $\mathcal{N}=2$ supersymmetry, by relating spinning and non-spinning WFCs, leads to a Grassmannian formula augmented by a kinematic prefactor that captures the full WFC. Moreover, we show that the positive and negative branches of the Grassmannian formula admit a natural interpretation in terms of supersymmetric invariants, and give rise to distinct helicity amplitudes in the flat-space limit.

Modified theories of gravity often introduce geometric structure beyond general relativity in order to address unresolved problems in the gravitational sector without invoking ad hoc matter fields. Mimetic gravity, for example, generates an effective cosmological dark sector by isolating the conformal mode of the metric, while Horava--Lifshitz gravity attains power-counting renormalizability by endowing spacetime with a preferred dynamical foliation. Although chronology protection was not the original motivation for either theory, both enforce it classically through stable causality. This suggests that chronology protection itself may be elevated from a derived property to a guiding principle for constructing modified gravitational theories, especially if its implementation at the quantum-gravitational level leaves infrared imprints in the effective action. Motivated by this possibility, we introduce a toy metric--affine gravity model that modifies only the geometric sector. The model realizes stable causality by dynamically generating a global time function via breaking of projective invariance. We further show that mimetic gravity is recovered as a special case, while a broader dark sector emerges naturally.

Recent advances in single-cell technologies have advanced our understanding of gene regulation and cellular heterogeneity at single-cell resolution. Single-cell data contain both gene expression levels and the proportion of expressing cells, which makes them structurally different from bulk data. Currently, methodological work on causal mediation analysis for single-cell data remains limited and often requires specific distributional assumptions. To address this challenge, we present QuasiMed, a mediation framework specialized for single-cell data. Our proposed method comprises three steps, including (i) screening mediator candidates through penalized regression and marginal models (similar to sure independence screening), (ii) estimation of indirect effects through the average expression and the proportion of expressing cells, (iii) and hypothesis testing with multiplicity control. The key benefit of QuasiMed is that it specifies only the mean functions of the mediation models through a quasi-regression framework, thereby relaxing strict distributional assumptions. The method performance was evaluated through the real-data-inspired simulations, and demonstrated high power, false discovery rate control, and computational efficiency. Lastly, we applied QuasiMed to ROSMAP single-cell data to illustrate its potential to identify mediating causal pathways. R package is freely available on GitHub repository at https://github.com/sjahnn/QuasiMed.

We study the non-Gaussian features of the gravitational wave (GW) background generated by a population of inspiraling supermassive black hole (SMBH) binaries. We show that the SMBH GW amplitude distribution (GWAD) features a universal heavy power-law tail $\propto A^{-4}$, while the low-amplitude tail depends on the SMBH merger rate and the energy-loss mechanisms of the binaries. The distribution of the induced timing residuals inherits this heavy tail. As a result, the ensemble averaged statistical moments of order three and higher diverge, limiting their usefulness as measures of non-Gaussianity, and the GW background from SMBH binaries exhibits the single loud source principle, according to which the strongest signals are more likely to be caused by a small number of loud sources. We confirm that the variance-averaged Gaussian approximation accurately describes the timing residual statistics. This approximation justifies a factored likelihood structure that combines standard Gaussian-process PTA posteriors with the non-Gaussian population prior, enabling consistent incorporation of non-Gaussian effects into SMBH model inference. We provide a fast and flexible Python implementation to compute the distribution of timing residuals from a given SMBH merger rate or GWAD.

The family $\mathcal{P}_{d}^{λ_{d-1}}$ of all probability measures on $[0,1]^d$ whose $(d-1)$-dimensional marginals are all equal to the Lebesgue measure $λ_{d-1}$ on $[0,1]^{d-1}$ contains remarkably pathological elements: Working with Iterated Function Systems with Probabi\-lities (IFSPs) we construct measures $μ\in \mathcal{P}_{d}^{λ_{d-1}}$ of the following two types: (i) $μ$ has self-similar fractal support; (ii) $μ$ has self-similar support and models the situation of complete/functional dependence in each direction.As our main results concerning type (i) we prove, firstly, that for every $d\geq 3$ the set $\mathcal{D}_d$ of Hausdorff dimensions of the supports of elements in $\mathcal{P}_{d}^{λ_{d-1}}$ is dense in $[d-1,d]$; and, secondly, that the subset of elements in $\mathcal{P}_{d}^{λ_{d-1}}$ having fractal support is dense in $\mathcal{P}_{d}^{λ_{d-1}}$ with respect to the Wasserstein metric. Moreover, we show the existence of an element in $\mathcal{P}_{3}^{λ_{2}}$ of type (ii) whose support is a Sierpinski tetrahedron and study some generalizations.

We study Schrödinger operators on metric and discrete decorated graphs. The values taken by the integrated density of states (IDS) on spectral gaps are called gap labels. A natural question is which gap labels can occur. We answer this for graphs arising from uniquely ergodic one-dimensional dynamical systems by proving Johnson-Schwartzman gap-labelling theorems in both the metric and discrete settings. Our results extend Johnson-Schwartzman gap labelling beyond the standard one-dimensional setting. Unlike in one dimension, these graphs may contain cycles, which prevent the use of Sturm oscillation theory and require different spectral methods. We also analyze discontinuities of the IDS for certain graph families and show that not every admissible label corresponds to an open spectral gap. This reveals a mechanism of gap closing driven by graph geometry rather than by the underlying dynamics.

We analyse the effects of a non-standard evolution of the Universe during the reheating epoch on the spectrum of scalar-induced gravitational waves (SIGWs) accounting for the presence of primordial non-Gaussianity. We show that given values of $w$ and $c_s^2$ leave characteristic features in the spectrum which can be detectable by third generation interferometers like LISA. In addition, we argue that the specific reheating dynamics can suppress or even enhance the spectrum, with crucial consequences for its detectability. We perform a Fisher forecast for different values of $w$ and different scans to assess the detectability of the signal when different values of the amplitude and central frequency are considered.

Gromov's theorem states that a finitely generated group has polynomial growth if and only if it is virtually nilpotent. A key ingredient in its proof is the small doubling property. In this work, we study entropy analogues of this property for random walks on groups. We show that if a finitely supported symmetric random walk $R_n$ satisfies \[ \mathrm{H}(R_{2n}) \le \mathrm{H}(R_n) + \log K \] at some sufficiently large scale $n$, then the underlying group is virtually nilpotent, with bounds depending on $K$ and $μ_{\min}$. Our approach adapts Tao's entropy Balog--Szemerédi--Gowers argument to unimodular locally compact groups, combined with structural results on approximate groups. As applications, we obtain entropy-based criteria for polynomial growth. We also deduce an entropy gap phenomenon: if $G$ is not virtually nilpotent, then the entropy of random walks on $G$ grows faster than a universal superlogarithmic function.