In the field of 3D content generation, single image scene reconstruction methods still struggle to simultaneously ensure the quality of individual assets and the coherence of the overall scene in complex environments, while texture editing techniques often fail to maintain both local continuity and multi-view consistency. In this paper, we propose a novel system ZeroScene, which leverages the prior knowledge of large vision models to accomplish both single image-to-3D scene reconstruction and texture editing in a zero-shot manner. ZeroScene extracts object-level 2D segmentation and depth information from input images to infer spatial relationships within the scene. It then jointly optimizes 3D and 2D projection losses of the point cloud to update object poses for precise scene alignment, ultimately constructing a coherent and complete 3D scene that encompasses both foreground and background. Moreover, ZeroScene supports texture editing of objects in the scene. By imposing constraints on the diffusion model and introducing a mask-guided progressive image generation strategy, we effectively maintain texture consistency across multiple viewpoints and further enhance the realism of rendered results through Physically Based Rendering (PBR) material estimation. Experimental results demonstrate that our framework not only ensures the geometric and appearance accuracy of generated assets, but also faithfully reconstructs scene layouts and produces highly detailed textures that closely align with text prompts.

Despite being trained on vast amounts of data, most LLMs are unable to reliably generate well-designed UIs. Designer feedback is essential to improving performance on UI generation; however, we find that existing RLHF methods based on ratings or rankings are not well-aligned with with designers' workflows and ignore the rich rationale used to critique and improve UI designs. In this paper, we investigate several approaches for designers to give feedback to UI generation models, using familiar interactions such as commenting, sketching and direct manipulation. We first perform an evaluation with 21 designers where they gave feedback using these interactions, which resulted in 1500 design annotations. We then use this data to finetune a series of LLMs to generate higher quality UIs. Finally, we evaluate these models with human judges, and we find that our designer-aligned approaches outperform models trained with traditional ranking feedback and all tested baselines, including GPT-5.

The substantial data volumes encountered in modern particle physics and other domains of fundamental physics research allow (and require) the use of increasingly complex data analysis tools and workflows. While the use of machine learning (ML) tools for data analysis has recently proliferated, these tools are typically special-purpose algorithms that rely, for example, on encoded physics knowledge to reach optimal performance. In this work, we investigate a new and orthogonal direction: Using recent progress in large language models (LLMs) to create a team of agents -- instances of LLMs with specific subtasks -- that jointly solve data analysis-based research problems in a way similar to how a human researcher might: by creating code to operate standard tools and libraries (including ML systems) and by building on results of previous iterations. If successful, such agent-based systems could be deployed to automate routine analysis components to counteract the increasing complexity of modern tool chains. To investigate the capabilities of current-generation commercial LLMs, we consider the task of anomaly detection via the publicly available and highly-studied LHC Olympics dataset. Several current models by OpenAI (GPT-4o, o4-mini, GPT-4.1, and GPT-5) are investigated and their stability tested. Overall, we observe the capacity of the agent-based system to solve this data analysis problem. The best agent-created solutions mirror the performance of human state-of-the-art results.

We propose a Buckley James (BJ) Boost Q learning framework for estimating optimal dynamic treatment regimes from right censored survival outcomes in longitudinal randomized clinical trials, motivated by the clinical need to support patient specific treatment decisions when follow up is incomplete and covariate effects may be nonlinear. The method combines accelerated failure time modeling with iterative boosting using flexible base learners, including componentwise least squares and regression trees, within a counterfactual Q learning framework. By modeling conditional survival time directly, BJ Boost Q learning avoids the proportional hazards assumption, yields clinically interpretable time scale contrasts, and enables estimation of stage specific Q functions and individualized decision rules under standard potential outcomes assumptions. In contrast to Cox based Q learning, which relies on hazard modeling and can be sensitive to nonproportional hazards and model misspecification, our approach provides a robust and flexible alternative for regime learning. Simulation studies and analyses of the ACTG175 HIV trial and the CALGB 8923 two stage leukemia trial show that BJ Boost Q learning improves treatment decision accuracy and produces more stable within participant counterfactual contrasts, particularly in multistage settings where estimation error and bias can compound across stages.

In recent years, 3D generation has made great strides in both academia and industry. However, generating 3D scenes from a single RGB image remains a significant challenge, as current approaches often struggle to ensure both object generation quality and scene coherence in multi-object scenarios. To overcome these limitations, we propose a novel three-stage framework for 3D scene generation with explicit geometric representations and high-quality textural details via single image-guided model generation and spatial layout optimization. Our method begins with an image instance segmentation and inpainting phase, which recovers missing details of occluded objects in the input images, thereby achieving complete generation of foreground 3D assets. Subsequently, our approach captures the spatial geometry of reference image by constructing pseudo-stereo viewpoint for camera parameter estimation and scene depth inference, while employing a model selection strategy to ensure optimal alignment between the 3D assets generated in the previous step and the input. Finally, through model parameterization and minimization of the Chamfer distance between point clouds in 3D and 2D space, our approach optimizes layout parameters to produce an explicit 3D scene representation that maintains precise alignment with input guidance image. Extensive experiments on multi-object scene image sets have demonstrated that our approach not only outperforms state-of-the-art methods in terms of geometric accuracy and texture fidelity of individual generated 3D models, but also has significant advantages in scene layout synthesis.

Hardware-efficient circuits employed in Quantum Machine Learning are typically composed of alternating layers of uniformly applied gates. High-speed numerical simulators for such circuits are crucial for advancing research in this field. In this work, we numerically benchmark universal and gate-specific techniques for simulating the action of layers of gates on quantum state vectors, aiming to accelerate the overall simulation of Quantum Machine Learning algorithms. Our analysis shows that the optimal simulation method for a given layer of gates depends on the number of qubits involved, and that a tailored combination of techniques can yield substantial performance gains in the forward and backward passes for a given circuit. Building on these insights, we developed a numerical simulator, named TQml Simulator, that employs the most efficient simulation method for each layer in a given circuit. We evaluated TQml Simulator on circuits constructed from standard gate sets, such as rotations and CNOTs, as well as on native gates from IonQ and IBM quantum processing units. In most cases, our simulator outperforms equivalent Pennylane's default.qubit simulator by up to a factor of 10, depending on the circuit, the number of qubits, the batch size of the input data, and the hardware used.

The scarcity of high-quality multimodal biomedical data limits the ability to effectively fine-tune pretrained Large Language Models (LLMs) for specialized biomedical tasks. To address this challenge, we introduce MINT (Multimodal Integrated kNowledge Transfer), a framework that aligns unimodal large decoder models with domain-specific decision patterns from multimodal biomedical data through preference optimization. While MINT supports different optimization techniques, we primarily implement it with the Odds Ratio Preference Optimization (ORPO) framework as its backbone. This strategy enables the aligned LLMs to perform predictive tasks using text-only or image-only inputs while retaining knowledge learnt from multimodal data. MINT leverages an upstream multimodal machine learning (MML) model trained on high-quality multimodal data to transfer domain-specific insights to downstream text-only or image-only LLMs. We demonstrate its effectiveness through two key applications: (1) Rare genetic disease prediction from texts, where MINT uses a multimodal encoder model, trained on facial photos and clinical notes, to generate a preference dataset for aligning a lightweight Llama 3.2-3B-Instruct. Despite relying on text input only, the MINT-derived model outperforms models trained with SFT, RAG, or DPO, and even outperforms Llama 3.1-405B-Instruct. (2) Tissue type classification using cell nucleus images, where MINT uses a vision-language foundation model as the preference generator, containing knowledge learnt from both text and histopathological images to align downstream image-only models. The resulting MINT-derived model significantly improves the performance of Llama 3.2-Vision-11B-Instruct on tissue type classification. In summary, MINT provides an effective strategy to align unimodal LLMs with high-quality multimodal expertise through preference optimization.

In both neuroscience and artificial intelligence, popular functional frameworks and neural network formulations operate by making use of extrinsic error measurements and global learning algorithms. Through a set of conjectures based on evolutionary insights on the origin of cellular adaptive mechanisms, we reinterpret the core meaning of sensory signals to allow the brain to be interpreted as a negative feedback control system, and show how this could lead to local learning algorithms without the need for global error correction metrics. Thereby, a sufficiently good minima in sensory activity can be the complete reward signal of the network, as well as being both necessary and sufficient for biological learning to arise. We show that this method of learning was likely already present in the earliest unicellular life forms on earth. We show evidence that the same principle holds and scales to multicellular organisms where it in addition can lead to division of labour between cells. Available evidence shows that the evolution of the nervous system likely was an adaptation to more effectively communicate intercellular signals to support such division of labour. We therefore propose that the same learning principle that evolved already in the earliest unicellular life forms, i.e. negative feedback control of externally and internally generated sensor signals, has simply been scaled up to become a fundament of the learning we see in biological brains today. We illustrate diverse biological settings, from the earliest unicellular organisms to humans, where this operational principle appears to be a plausible interpretation of the meaning of sensor signals in biology, how this relates to current neuroscientific theories and findings, and how it can be applied to solve body control.

Generative AI is transforming education by enabling personalized, on-demand learning experiences. However, current AI systems lack awareness of the learner's cognitive state, limiting their adaptability. Meanwhile, electroencephalography (EEG)-based neuroadaptive systems have shown promise in enhancing engagement through real-time physiological feedback. This paper presents NeuroChat, a neuroadaptive AI tutor that integrates real-time EEG-based engagement tracking with generative AI to adapt its responses. NeuroChat continuously monitors a learner's cognitive engagement and dynamically adjusts content complexity, tone, and response style in a closed-loop interaction. In a within-subjects study (n=24), NeuroChat significantly increased both EEG-measured and self-reported engagement compared to a non-adaptive chatbot. However, no significant differences in short-term learning outcomes were observed. These findings demonstrate the feasibility of real-time cognitive feedback in LLMs, highlighting new directions for adaptive learning, AI tutoring, and deeper personalization in human-AI interaction.

Linear bandits have long been a central topic in online learning, with applications ranging from recommendation systems to adaptive clinical trials. Their general learnability has been established when the objective is to minimise the inner product between a cost parameter and the decision variable. While this is highly general, this reliance on an inner product structure belies the name of \emph{linear} bandits, and fails to account for problems such as Optimal Transport. Using the Kantorovich formulation of Optimal Transport as an example, we show that an inner product structure is \emph{not} necessary to achieve efficient learning in linear bandits. We propose a refinement of the classical OFUL algorithm that operates by embedding the action set into a Hilbertian subspace, where confidence sets can be built via least-squares estimation. Actions are then constrained to this subspace by penalising optimism. The analysis is completed by leveraging convergence results from penalised (entropic) transport to the Kantorovich problem. Up to this approximation term, the resulting algorithm achieves the same trajectorial regret upper bounds as the OFUL algorithm, which we turn into worst-case regret using functional regression techniques. Its regret interpolates between $\tilde{\mathcal O}(\sqrt{T})$ and ${\mathcal O}(T)$, depending on the regularity of the cost function, and recovers the parametric rate $\tilde{\mathcal O}(\sqrt{dT})$ in finite-dimensional settings.

As early as 1949, Weaver defined communication in a very broad sense to include all procedures by which one mind or technical system can influence another, thus establishing the idea of semantic communication. With the recent success of machine learning in expert assistance systems where sensed information is wirelessly provided to a human to assist task execution, the need to design effective and efficient communications has become increasingly apparent. In particular, semantic communication aims to convey the meaning behind the sensed information relevant for Human Decision-Making (HDM). Regarding the interplay between semantic communication and HDM, many questions remain, such as how to model the entire end-to-end sensing-decision-making process, how to design semantic communication for the HDM and which information should be provided for HDM. To address these questions, we propose to integrate semantic communication and HDM into one probabilistic end-to-end sensing-decision framework that bridges communications and psychology. In our interdisciplinary framework, we model the human through a HDM process, allowing us to explore how feature extraction from semantic communication can best support HDM both in theory and in simulations. In this sense, our study reveals the fundamental design trade-off between maximizing the relevant semantic information and matching the cognitive capabilities of the HDM model. Our initial analysis shows how semantic communication can balance the level of detail with human cognitive capabilities while demanding less bandwidth, power, and latency.

Purpose: The credibility of Artificial Intelligence (AI) models for medical imaging continues to be a challenge, affected by the diversity of models, the data used to train the models, and applicability of their combination to produce reproducible results for new data. In this work, we aimed to explore whether emerging Virtual Imaging Trials (VIT) methodologies can provide an objective resource to approach this challenge. Approach: The study was conducted for the case example of COVID-19 diagnosis using clinical and virtual computed tomography (CT) and chest radiography (CXR) processed with convolutional neural networks. Multiple AI models were developed and tested using 3D ResNet-like and 2D EfficientNetv2 architectures across diverse datasets. Results: Model performance was evaluated using the area under the curve (AUC) and the DeLong method for AUC confidence intervals. The models trained on the most diverse datasets showed the highest external testing performance, with AUC values ranging from 0.73-0.76 for CT and 0.70-0.73 for CXR. Internal testing yielded higher AUC values (0.77-0.85 for CT and 0.77-1.0 for CXR), highlighting a substantial drop in performance during external validation, which underscores the importance of diverse and comprehensive training and testing data. Most notably, the VIT approach provided objective assessment of the utility of diverse models and datasets, while offering insight into the influence of dataset characteristics, patient factors, and imaging physics on AI efficacy. Conclusions: The VIT approach enhances model transparency and reliability, offering nuanced insights into the factors driving AI performance and bridging the gap between experimental and clinical settings.

In this paper, we provide a precise mathematical model of crystal-to-crystal response which is used to generate the white image - a necessary compensation model needed to overcome the physical limitations of the PET scanner. We present a closed-form solution, as well as several accurate approximations, due to the complexity of the exact mathematical expressions. We prove, experimentally and analytically, that the difference between the best approximations and real crystal-to-crystal response is insignificant. The obtained responses are used to generate the white image compensation model. It can be written as a single closed-form expression making it easy to implement in known reconstruction methods. The maximum likelihood expectation maximization (MLEM) algorithm is modified and our white image model is integrated into it. The modified MLEM algorithm is not based on the system matrix, rather it is based on ray-driven projections and back-projections. The compensation model provides all necessary information about the system. Finally, we check our approach on synthetic and real data. For the real-world acquisition, we use the Raytest ClearPET camera for small animals and the NEMA NU 4-2008 phantom. The proposed approach overperforms competitive, non-compensated reconstruction methods.

Following the recent success of Machine Learning tools in wireless communications, the idea of semantic communication by Weaver from 1949 has gained attention. It breaks with Shannon's classic design paradigm by aiming to transmit the meaning, i.e., semantics, of a message instead of its exact version, allowing for information rate savings. In this work, we apply the Stochastic Policy Gradient (SPG) to design a semantic communication system by reinforcement learning, separating transmitter and receiver, and not requiring a known or differentiable channel model -- a crucial step towards deployment in practice. Further, we derive the use of SPG for both classic and semantic communication from the maximization of the mutual information between received and target variables. Numerical results show that our approach achieves comparable performance to a model-aware approach based on the reparametrization trick, albeit with a decreased convergence rate.

Current bounds on the tensor-to-scalar ratio imply that the energy scale of inflation may lie below the grand-unified scale. In this paper, we show that in a broad class of single-field inflation models with sufficiently small energy scales, an extremely efficient tachyonic instability develops at the end of inflation. This instability rapidly drives the system into a nonlinear regime before coherent oscillations can be established, leading to a first-order phase-transition--like phenomenon without tunneling or barrier crossing. The resulting ultra-relativistic shock fronts surrounding the bubble interiors expand to near the Hubble scale, corresponding to the most strongly enhanced tachyonic modes, and collide with one another, producing energetic inflaton particles and gravitational waves. As a result, the post-inflationary dynamics can differ significantly from the conventional high-scale inflationary scenario. Interestingly, inflation at MeV--EeV energy scales can be probed via gravitational-wave observations, including pulsar timing arrays, ground-based detectors, and future space-based experiments. Recent limits from the LIGO--KAGRA--Virgo collaboration already constrain EeV-scale inflation, while pulsar timing array results may be interpreted as evidence for gravitational waves generated by GeV-scale inflation. We also briefly discuss further implications of the resulting tachyonic shocks.

We derive and study expansions of and over the Askey--Wilson polynomials. We study these expansions and examine some limits to the continuous dual $q$-Hahn, Al-Salam--Chihara, continuous big $q$-Hermite and continuous $q$-Hermite polynomials and their $q^{-1}$-analogues. The Poisson kernel for the infinite discrete orthogonality relation for the $q^{-1}$-Al-Salam--Chihara polynomials is derived which in a special case reduces to the Gupta--Masson biorthogonal rational ${}_4ϕ_3$-functions. This Poisson kernel implies new infinite series connection relations for the Askey--Wilson polynomials involving these rational ${}_4ϕ_3$-functions. We also consider various interesting limits.

We develop finite free information theory for real-rooted polynomials, establishing finite free analogues of entropy and Fisher information monotonicity, as well as the Stam and entropy power inequalities. These results resolve conjectures by Shlyakhtenko and Gribinski and recover inequalities in free probability in the large-degree limit. Equivalently, our results may be interpreted as potential-theoretic inequalities for the zeros of real-rooted polynomials under differential operators which preserve real-rootedness. Our proofs leverage a new connection between score vectors and Jacobians of root maps, combined with convexity results for hyperbolic polynomials.

Radial oscillations provide a clean dynamical test of the high-density stiffness of neutron-star equations of state. We study spherically symmetric pulsations of nonrotating relativistic stars built from cold, charge-neutral, $β$-equilibrated pure nucleonic matter described within relativistic mean-field theory. As a baseline we adopt the UCIa parameter set [Astron. Astro-phys. 689, A242 (2024)], and we implement high-density stiffening via the $σ$-cut scheme by adding a regulator potential $U_{\rm cut}(σ)$ [Phys. Rev. C 92, no.5, 052801 (2015), Phys. Rev. C 106, no.5, 055806 (2022)]. For representative choices $f_s=0$ (no cutoff) and $f_s=0.58$ (stiffened), we solve the Tolman-Oppenheimer-Volkoff and tidal perturbation equations to obtain equilibrium sequences, mass-radius relations, and tidal deformabilities. We then derive and solve the linear general-relativistic radial pulsation equations to compute the eigenfrequencies and eigenfunctions of the fundamental and overtone modes. The $σ$-cutoff suppresses the growth of the scalar field at supranuclear density, increases the pressure, and shifts the maximum mass, radii, and $Λ_{1.4}$ accordingly, while systematically raising the radial-mode frequencies at fixed mass. Using the sign change of $ω_0^2$ as a stability criterion, we identify stiffened models that remain radially stable up to the observed $\sim 2M_\odot$ mass scale and are consistent with current multimessenger constraints, demonstrating how radial spectra complement static EoS tests.

The goal of this paper is twofold. In addition to the results stated in the next paragraph, we present some classical results on absoluteness relevant to functional analysis that are well known to logicians but not nearly as well advertised as they should be. We show that the theory of separable C*-algebras can be developed in ZF (that is, without using any Choice). This includes proving the Gelfand-Naimark representation theorems as well as the Spectral Mapping Theorem for polynomials and developing continuous functional calculus for commuting normal elements. Some of our proofs are modifications of the standard ones, obtained by avoiding the use of Choice. Some other proofs require new ideas in order to avoid the use of Choice. Yet another batch of proofs proceeds by using the set-theoretic Shoenfield Absoluteness Theorem. This result (well known to logicians but regrettably not as well advertised as it deserves) implies that statements about standard Borel spaces of low quantifier complexity that are provable in ZFC, or even ZFC together with the Continuum Hypothesis are provable in ZF. One of the main objectives of this paper is to present these results in a convenient form that can be utilized by analysts not familiar with set theory. We also show that in the absence of Choice (more precisely, assuming the existence of a Russell set) there is a concretely representable unital commutative \cstar-algebra that is not isomorphic to C(X) for any compact Hausdorff space X. Finally, from the model-theoretic point of view, while the property of having a tracial state is provably axiomatizable in ZFC, it is not provably axiomatizable in ZF+DC.

In this article we use Gaussian measure on $\mathbb{R}^N$ to define the coefficients of an elliptic diffusion on an open cone of $\mathbb{R}^2$. We prove the existence and uniqueness of a stationary distribution for this diffusion. In a companion article, we show that the diffusion constructed in this work is the inviscid limit of the laws of the ``enstrophy-energy'' process of a stationary $N$-dimensional Galerkin-Navier-Stokes type evolution with Brownian forcing and random stirring (the strength of which can be made to go to zero in the inviscid limit). In the present work, owing to the special properties of the coefficients constructed with the Gaussian measure, we bound the distance to $1$ of the ratio of the expected energy to the expected enstrophy (this ratio is at most $1$ with our normalization). Together with our companion article, this shows that for suitable Brownian forcings an inviscid condensation inducing an attrition of all but the lowest modes takes place.

Reconfigurable intelligent surfaces (RISs) offer programmable control of radio propagation for future wireless systems. For configuration, geometry-driven analytical approaches are appealing for their simplicity and real-time operation, but their performance in challenging environments such as industrial halls with dense multipath and metallic scattering is not well established. To this end, we present a measurement-based evaluation of geometry-driven RIS beam steering in a large industrial hall using a 5 GHz RIS prototype. A novel RIS configuration is proposed in which four patch antennas are mounted in close proximity in front of the RIS to steer the incident field and enable controlled reflection. For this setup, analytically computed, quantized configurations are implemented. Two-dimensional received power maps from two measurement areas reveal consistent, spatially selective focusing. Configurations optimized near the receiver produce clear power maxima, while steering to offset locations triggers a rapid 20-30 dB reduction. With increasing RIS-receiver distance, elevation selectivity broadens due to finite-aperture and geometric constraints, while azimuth steering remains robust. These results confirm the practical viability of geometry-driven RIS beam steering in industrial environments and support its use for spatial field control and localization under non-ideal propagation.

This paper explores a new perspective on the universality of the vertical lift in tangent categories by presenting a categorification of the dimension of smooth manifolds. The universality of the vertical lift is a key part of the axioms of a tangent category as presented in [4]. The categorical dimension presented in this paper provides insight into the nature of this property. The main result is Theorem 3.7, showing that if it exists, the dimension of the tangent bundle must fulfill an equation relating the dimension of the tangent bundle to the dimension of the base. In particular, when the dimension function is a strong tangent dimension, Theorem 3.8 shows that the dimension of the tangent bundles is either twice the dimension of the base, or equal to the dimension of the base. Many examples of dimension functions are provided to demonstrate the utility of the definition. In particular, a consequence of Theorem 3.7 is that there are limitations on which functors may be tangent bundle endofunctors for a category. We show that this means that there are no non-trivial tangent structures on sets, as an example.

Microwave synthesizers are central to test and measurement systems across applications including wireless communications, radar, spectroscopy, and time and frequency metrology. State-of-the-art microwave sources, however, are fundamentally constrained by trade-offs between frequency tunability and spectral purity. Electro-optic frequency division (eOFD) is an emerging technique for dividing down the purity of optical sources to the microwave domain. Previously reported eOFD-based synthesizers generally have limited tunability due to feedback stabilization requirements. Here we demonstrate a feed-forward eOFD architecture in which the frequency tunability of a microwave source is preserved while optical spectral purity is divided through feed-forward cancellation, without any downstream electronic frequency synthesis. By canceling the phase noise of the microwave source without feedback, this eOFD approach removes loop bandwidth and source noise constraints observed in prior eOFD architectures. We achieve octave-spanning tunability, including the entire X-band, with phase noise below -140 dBc/Hz at kilohertz offsets and a high-frequency noise floor between -155 dBc/Hz and -145 dBc/Hz for carrier frequencies from 8 to 16 GHz. This performance corresponds to single-femtosecond integrated timing jitter, enabling, to our knowledge, the first demonstration of coherent, optically referenced microwave synthesis under wide tuning with this level of spectral purity.

In this article we consider a stationary $N$-dimensional Galerkin-Navier-Stokes type evolution with Brownian forcing and random stirring (of arbitrarily small strength). We show that the stationary diffusion in an open two-dimensional cone constructed in a companion article, stands as the inviscid limit of the laws of the ``enstrophy-energy'' process of the $N$-dimensional diffusion process considered here, this regardless of the strength of the stirring. With the help of the quantitative condensation bounds of the companion article, we infer quantitative inviscid condensation bounds, which for suitable forcings show an attrition of all but the lowest modes in the inviscid limit.

In this paper, we develop and introduce a Casorati inequality for Riemannian submersions involving the Casorati curvatures of both the vertical and horizontal distributions. A general form of the inequality is derived for Riemannian submersions between Riemannian manifolds, and the corresponding equality cases are completely characterised. As applications, we obtain the inequality for Riemannian submersions whose total spaces are real, complex, generalised Sasakian, Sasakian, cosymplectic, Kenmotsu, and almost $c(α)$-space forms. For each theorem, we present illustrative examples. Some of these examples achieve equality, while others do not. Furthermore, these inequalities are derived for invariant, anti-invariant, slant, semi-slant, hemi-slant, and bi-slant Riemannian submersions.

21cm radiation from neutral hydrogen serves as a direct probe of the Epoch of Reionization. However, both its detection and physical interpretation are severely hindered by contamination from astrophysical foreground emission and instrumental noise that are several orders of magnitude brighter than the signal of interest. A promising way to tackle these challenges is to cross-correlate the 21cm signal with other independent tracers of large-scale structure, most notably high-redshift galaxies. Besides validating putative 21cm detections, such joint analyses are expected to provide independent insights into the properties of ionizing sources and the evolving morphology of ionized regions during reionization. The 21cm signal, however, is intrinsically highly non-Gaussian, limiting the effectiveness of conventional two-point cross-correlation statistics, which capture information only up to the second order. In this work, we therefore investigate the utility of k-nearest-neighbour cumulative distribution functions (kNN CDF), which encode information from the joint clustering at all orders, as an alternative framework for probing 21cm-galaxy cross-correlations. Using self-consistently simulated mock 21cm fields and a catalog of line-emitting galaxies at z = 7, we conducted a proof-of-concept study comparing the kNN CDF formalism and the two-point cross-correlation approach. We find that the kNN CDF statistics outperform the two-point statistics in detecting 21cm-galaxy cross-correlations, even in the presence of instrumental noise and aggressive foreground filtering. Moreover, at a fixed global ionized fraction, it is even able to differentiate between reionization models that remain indistinguishable using two-point statistics. These results demonstrate the power and unexplored potential of exploiting higher-order statistics for extracting maximal information from 21cm-galaxy synergies.

A deformation of Heisenberg algebra induces among other consequences a loss of Hermiticity of some operators that generate this algebra. Therefore, these operators are not Hermitian, nor is the Hamiltonian operator built from them. In the present paper, we propose a position deformation of Heisenberg algebra with both maximal length and minimal momentum uncertainties. By using a pseudo-similarity transformation to the non-Hermitian operators, we prove their Hermiticity with a suitable positive-definite pseudo-metric operator. We then construct Hilbert space representations associated with these pseudo-Hermitian operators. Finally, we study the eigenvalue problem of a free particle in this deformed space and we show that this deformation curved the quantum levels allowing particles to jump from one state to another with low energy transitions.

In this paper, we provide a complete mathematical theory for the entanglement of mixtures of Dicke states. These quantum states form an important subclass of bosonic states arising in the study of indistinguishable particles. We introduce a tensor-based parametrization where the diagonal entries of these states are encoded as a symmetric tensor, enabling a direct translation between entanglement properties and well-studied convex cones of tensors. Our results bridge multipartite entanglement theory with semialgebraic geometry and the theory of completely positive and copositive tensors. This dictionary maps separability to completely positive tensors, the PPT property to moment tensors, entanglement witnesses to copositive tensors, and decomposable witnesses to sum of squares tensors. Using this framework, we construct explicit PPT entangled states in three or more qutrits. In this class of states, we establish that PPT entanglement exists for all multipartite systems with three qutrits or more, disproving a recent conjecture in [J. Math. Phys. 66, 022203 (2025)]. We also show that, for mixtures of Dicke states, the PPT condition with respect to the most balanced bipartition implies PPT with respect to any other bipartition. We further connect bosonic extendibility of mixtures of Dicke states to the duals of known hierarchies for non-negative polynomials, such as the ones by Reznick and Polya. We thus provide semidefinite programming relaxations for separability and entanglement testing in the Dicke subspace.

We study the lattice $\mathbf{tors}(A)$ of torsion pairs in the category $\mathrm{mod}(A)$ of finitely generated modules over an artinian ring $A$. It was shown by the authors in previous work that $\mathbf{tors}(A)$ is isomorphic to a lattice formed by certain closed sets, called maximal rigid, in the Ziegler spectrum of the unbounded derived category $\mathrm{D}(A)$ of $A$. Moreover, the structure of this lattice is described by an operation on maximal rigid sets which encompasses (the dual of) silting mutation. In this paper we provide an explicit description of this operation and we discuss how it is reflected in the lattice $\mathbf{tors}(A)$. We establish a bijection between the wide intervals in $\mathbf{tors}(A)$ and the closed rigid sets in the Ziegler spectrum of $\mathrm{D}(A)$. Moreover, we show that the arrows in the Hasse quiver of $\mathbf{tors}(A)$ correspond to the closed rigid sets that are almost complete, or equivalently, that can be completed to a maximal rigid set in exactly two ways. Our results are most interesting in the case when $A$ is a finite dimensional algebra. In fact, we generalise results by Adachi, Iyama and Reiten, with an important difference: not every point in a maximal rigid set is mutable. We use the topology on the Ziegler spectrum to determine the mutable points. In the last section of the paper we illustrate our results by the example of a finite dimensional algebra arising from a triangulation of an annulus.

Graham conjectured in 1971 that for any prime $p$, any subset $S\subseteq \mathbb{Z}_p\setminus \{0\}$ admits an ordering $s_1,s_2,\dots,s_{|S|}$ where all partial sums $s_1, s_1+s_2,\dots,s_1+s_2+\dots+s_{|S|}$ are distinct. We prove this conjecture for all subsets $S\subseteq \mathbb{Z}_p\setminus \{0\}$ with $|S|\le p^{1-α}$ and $|S|$ sufficiently large with respect to $α$, for any $α\in (0,1)$. Combined with earlier results, this gives a complete resolution of Graham's rearrangement conjecture for all sufficiently large primes $p$.