Papers

We study smooth fibred two-knots whose fundamental quandle is the prism quandle of order fifty-six. The candidates arise from framed circle surgery along a section of a mapping torus, using the two possible normal-framing classes. We prove that both ambient homotopy four-spheres are diffeomorphic to the standard four-sphere. The candidates have the same knot group and diffeomorphic exteriors, but they are inequivalent even as topological pairs. Every smooth fibred realization of this quandle in a homotopy four-sphere is equivalent, up to knot orientation, to exactly one of these two knots. Standardness follows from a Whitehead-link model for the orbit orbifold together with circle-action recognition. Inequivalence is detected by the third cyclic branched covers, on which a spin-bordism secondary invariant takes different values. Thus the parameter-seven prism quandle admits smooth fibred realizations in the standard four-sphere.

We study the relaxation dynamics of a one-dimensional system of hard rods at the level of one-body fields using superadiabatic dynamical density functional theory, and compare the results with Brownian dynamics simulations. The theory uses the exact equilibrium excess free energy functional and incorporates superadiabatic effects from first principles via an adiabatic closure relation at the three-particle level. The predicted superadiabatic response shows very good agreement with simulation data, provided that initial-state ensemble differences between theory and simulations remain small. Furthermore, we evaluate an approximate power functional theory based on a velocity-gradient expansion, which also yields an accurate superadiabatic response, although requiring a memory kernel extracted from simulation data.

We introduce PUBG Ally, an embodied agent for PUBG: BATTLEGROUNDS that can reason, act autonomously, and play alongside players as a voice-enabled teammate. Building such a teammate requires combining two difficult capabilities: it must perceive and respond to a constantly changing game world under strict latency constraints while interacting naturally with players, keeping its speech synchronized with its actions. Ally therefore combines agentic tool use with real-time game control. A language-model agent uses a controlled interface to inspect game information, interpret player speech, maintain context, decide what to say, and issue high-level action choices that steer a faster control layer for movement, combat, and recovery. Because the player's and Ally's speech and actions continually shape each other and the course of the match, training requires data from actual gameplay. We therefore collect data across nearly 39k sessions in which real players play alongside Ally, recording gameplay, player speech, agent decisions, tool use, actions, and player feedback, and use these records for iterative training. To evaluate teammate quality, we use player feedback and preference comparisons to identify gaps between offline evaluations and player preferences, and iteratively refine the evaluation criteria. Deploying Ally in live service further requires low-latency on-device execution and safeguards for player-facing communication, which we address through model compression, context compaction, targeted safety training, runtime guardrails, and memory redaction. During the live service, we surveyed players in 141 countries. Among respondents whose play with Ally was confirmed in game records, positive responses exceeded negative responses by 25.1 percentage points when asked whether they would recommend Ally, with players describing Ally not only as a tool but also as a teammate or companion.

While 2D Vision Foundation Models offer a pathway to automate 3D semantic pseudo-labelling, translating these priors into robust 3D representations typically requires complex heuristics or multi-model ensembles. We introduce SplatLabel, an automated pipeline that leverages a 4D Gaussian representation to extract LiDAR segmentation with predictive confidence, as well as semantic occupancy grids at arbitrary voxel resolutions. At its core, SplatLabel handles dynamic environments through an explicit temporal manifold that models the trajectories and lifespans of individual 3D primitives. This allows the system to accurately track moving actors and strictly define when objects appear and disappear, completely eliminating the need for pre-annotated 3D bounding boxes. To robustly support this dynamic tracking, the representation is grounded by structural and semantic priors: we guide scene geometry in unobserved regions by integrating 360-degree LiDAR via virtual depth maps, and rather than relying on domain-specific prompt engineering, we directly distill continuous soft probabilities from 2D models to inherently resolve semantic ambiguities over time and space. Finally, to accurately reflect the real-world trade-off between precision and recall, we reframe pseudo-label evaluation as a selective classification task using a generalized risk-recall metric. Experiments on SemanticKITTI demonstrate that SplatLabel consistently outperforms state-of-the-art baselines across multiple recall levels, establishing a highly robust framework for both 3D LiDAR segmentation and occupancy prediction.

LiDAR provides precise geometric information for spatial perception tasks such as object detection in autonomous driving and outdoor robotics. However, recognizing and localizing individual objects is not sufficient to answer questions that require composing spatial relations and grounding the intended target. Motivated by recent advances in large language models (LLMs) for autonomous driving, we leverage their language priors to interpret complex spatial questions and ground the referred target in LiDAR geometry. To support this spatial grounding capability, we introduce SpatialLiDAR-QA, which combines single- and multi-step relational grounding with complementary spatial understanding tasks. We further propose SpatialLiDAR-LM, which aligns LiDAR point features with an LLM and grounds target coordinates through language-conditioned, position-aware proposal retrieval and local point refinement. This design derives target coordinates directly from local LiDAR geometry rather than through textual language decoding. Experiments demonstrate substantial improvements over representative LiDAR–language models and multi-camera VLMs on precise coordinate prediction tasks. Our dataset and model training code will be publicly released.

A fixed coarse-grained description need not uniquely determine the underlying microscopic rules. Variations in these rules can alter collective behaviour while leaving the retained observables unchanged. Here we develop a method to identify and use such variations for collective-state design. We construct families of microscopic models with exactly matched coarse observables and use the response derivative within each family to identify independent first-order output changes. In a nonreciprocal active mixture, the largest first-order change in interfacial growth rate under a pointwise kernel budget also determines the leading minimax error of predictions based only on the matched data. Near a Hopf bifurcation, this response map gives an initial turning-kernel design, which is refined by jointly solving for the periodic kinetic state and the kernel. Fixed-kernel integrations realize prescribed oscillation powers and frequencies while preserving the selected angular relaxation rates. In a reaction-diffusion family, cubic amplitude equations guide the design of stripe and hexagon amplitudes while the full linear operator remains fixed. Additional constraints reduce the available response even when its rank is unchanged, whereas the matched angular moments retain their exact relaxation rates. These results provide a constructive route to collective-state design within a prescribed coarse-grained description.

Adaptive algorithms increasingly make decisions while reshaping the dynamics that generate their future data. We establish a shrinking-tube concentration bound for projected stochastic approximation driven by an adaptive Markov chain. The bound guarantees, with high probability, that every iterate after a chosen time remains within a tolerance around the target that tightens over time. The probability of any exit after the chosen time admits a polynomially decaying upper bound, and a matching lower bound shows that its polynomial exponent cannot be improved in general under finite second moments. The result therefore identifies a sharp tradeoff between how quickly the tolerance shrinks and how rapidly the probability of any future exit decreases. We also extend the analysis to recursions with additional martingale-difference noise and predictable bias, showing how growth in the martingale-difference noise scale slows the decay of the exit-probability bound while predictable bias restricts the admissible tube shrinkage. The proof combines backward kernel replacement, a finite-time mean-squared-error bound, and a blockwise maximal first-exit argument. We apply the theory to inventory learning with stockout-dependent demand and fixed stockout costs, and quantify how numerical gradient accuracy affects the all-future reliability of the resulting policies.

A new method for multi-input flight maneuver design for system identification is presented. The method consists of injecting "full-harmonic" orthogonal multisine signals into the flight control system. Orthogonality is achieved by repeating maneuvers with changing multisine polarities. The multisines can contain the same frequency content, which can simplify frequency response estimation and allow for long flight maneuvers to be split into several shorter maneuvers while maintaining the same frequency resolution and minimum frequency. An input allocation scheme is presented that augments the multisines to size the vehicle response amplitude about a specific degree of freedom. The developed approach was demonstrated through flight testing of a small octocopter in near-hover conditions. The input allocation scheme was utilized successfully to increase excitation about the yaw axis. Electrical power, motor speed, and rigid-body dynamic models were identified and are shown to predict the vehicle and motor responses accurately. The models are parameterized primarily by rotor thrust and torque coefficients, making them suitable for analysis of aircraft flight dynamics and individual rotor aerodynamics. The results demonstrate that the near-hover flight dynamics can be modeled accurately by neglecting rotor hub moments, variations in rotor coefficients, gyroscopic moments in roll and pitch, and aerodynamic interaction effects.

We relate the theory of $q$-rational and $q$-real numbers introduced by Morier-Genoud and Ovsienko to the classical theory of Kleinian groups and their Teichmüller spaces. This provides a geometric point of view on several recent results about realisations of $q$-rationals for particular values of $ q \in \mathbb{C} $. As an application we resolve a conjecture of Bapat, Becker, and Licata on the topology of the $q$-deformed Farey tessellation.

We present a systematic study of the sensitivity of quasifission dynamics to the nuclear symmetry energy in the $^{48}$Ca~+~$^{249}$Cf system, the reaction used for the synthesis of oganesson ($Z = 118$), spanning the full range of target orientations and angular momenta. Employing time-dependent Hartree-Fock (TDHF) calculations with four Skyrme parameterizations from the SV family that systematically vary the symmetry energy at saturation ($a_{\text{sym}} = 28$–$34$~MeV), we perform over 500 TDHF trajectories spanning angular momenta $L = 0$–$100\hbar$ and twelve orientations of the prolate-deformed $^{249}$Cf target ($\beta = 0^{\circ}$–$165^{\circ}$ in $15^{\circ}$ steps). Shell effects in the quasifission fragments are dominated by a deformed–deformed channel: the light fragment clusters near the prolate-deformed $Z \approx 40$, $N \approx 58$ shell region (Zr/Sr), and the complementary heavy fragment populates the shape-coexistence region near $Z \approx 78$, $N \approx 121$ (Os/Pt). This channel accounts for $34$–$48\%$ of quasifission events and is geometrically incompatible with the spherical $Z = 82$, $N = 126$ closures, which are populated only at shorter contact times. The balance between the deformed and near-spherical channels depends on the symmetry energy parameterization. These results demonstrate that quasifission observables in superheavy element formation reactions carry quantifiable sensitivity to the isovector sector of the nuclear energy density functional.

We describe a fiber-based dual-beam trap for dielectric nanospheres with the ability to transfer the trapped particles into a retro-reflective standing-wave trap within micron-range distances of a metallic mirror surface. We illustrate its capability for three dimensional scanning force sensing over a several square micron area of an ultra-thin gold-coated silicon nitride mirror-membrane with a total thickness of approximately 370~nm. We also demonstrate three-dimensional laser feedback cooling and zeptonewton force resolution in high-vacuum at micron range from the membrane, showing promise for future improved tests of gravity at short distances and other surface force investigations. By using charged nanospheres, we expect the method may be useful for studying fluctuating patch potentials and electric field noise in the vicinity of a surface in the $\sim$ kHz to $\sim 100$ kHz frequency regime.

We present ChunkRank, an open-source Python library that derives chunk boundaries from a target model's tokenizer and context window, and selects an answer among candidates produced independently per chunk. It ships a validated registry of 90 models across 15 providers and six answer-selection methods, and needs only three core dependencies. For chunking, ChunkRank avoids context-window overflow automatically from the model name, whereas character-based splitters overflow or waste the budget, and a fidelity study across 11 languages shows why token-exact budgets matter beyond English. For answer selection we report a negative result: on NaturalQuestions, TriviaQA and HotpotQA, with extractive and generative readers, no content-based ranker reliably beats taking the first non-empty answer. The reason is reader abstention on chunks that lack the answer, not answer position. A long-context baseline shows that chunking matches single-call reading on single-hop questions, so ChunkRank targets small-window and beyond-window settings. Code, registry and evaluation harness are released.

Accurate tide forecasts are essential for coastal management, navigation, flood-risk reduction, and infrastructure protection. Observed sea level can be decomposed into astronomical and non-astronomical components, the latter mainly driven by meteorological effects. This study investigates a hybrid framework for hourly sea-level forecasting that combines harmonic analysis (HA) for the astronomical component with data-driven models for the non-astronomical contribution. The approach is evaluated at six tide-gauge stations with different tidal regimes: Venice, Trieste, Saint-Malo, Vardø, Nikiski, and Nagasaki. Four data-driven model classes are considered: (i) linear parametric models, represented by autoregressive models with exogenous variables; (ii) functional parametric models, based on functional autoregressive models with exogenous variables; (iii) semiparametric and nonlinear models, including generalized additive models and autoregressive neural networks; and (iv) a semi-functional non-standard k-nearest-neighbours approach combining similarity in recent non-astronomical trajectories and meteorological conditions. Results reveal that hybrid models reduce forecast errors by 52.9-54.9% on average relative to HA. The generalized additive model is the most competitive across locations, while k-nearest neighbours performs best at Saint-Malo and the autoregressive model with exogenous variables is favoured in Nagasaki. For Venice, an economic decision-making case study assesses the operational use of sea-level forecasts in managing the MoSE flood-barrier system.

We establish that the ellipticity of the minimal surface integrand is the sharp threshold for $\mathrm{W}^{1,1}$-regularity of solutions to the Dirichlet problem on $\mathrm{BV}$. Here, we particularly deal with the autonomous case of convex linear growth functionals.

Patient-specific 4D myocardial reconstruction from cine MRI supports quantitative functional assessment, regional motion analysis, and simulation-based modeling. However, routinely acquired short-axis (SAX) cine MRI is sparsely sampled along the through-plane direction, making dense and anatomically consistent surface reconstruction challenging. In this study, we propose an anatomy-aligned surface learning framework that parameterizes the epicardial and endocardial surfaces on a shared circumferential-longitudinal UV domain. This formulation converts irregular 3D reconstruction into structured coordinate-field completion with explicit correspondence across subjects and cardiac phases. Sparse SAX contours are encoded as UV observation fields, coverage-aware sampling improves robustness to incomplete slice coverage, and topology- and distortion-aware learning preserves circumferential continuity and local surface quality. Experiments on three public cine MRI datasets showed that the proposed method consistently outperformed representative mesh-based and implicit reconstruction approaches, achieving overall Chamfer distances of $2.887$~mm on ACDC, $2.641$~mm on M&Ms, and $2.810$~mm on M&Ms-2. The reconstructed sequences also preserved ventricular function, with end-diastolic volume and ejection fraction errors of $3.3$~mL and $1.1 \%$, respectively. These results demonstrate that anatomy-aligned UV learning provides an accurate, efficient, and correspondence-aware representation for sparse cine MRI reconstruction and myocardial modeling. The source code will be available at https://github.com/yuan-xiaohan/SAX2MyoSurf.

We formulate a generalized Saito criterion for complex projective plane curves, building on a recent generalized Saito criterion for plus-one generated arrangements of hyperplanes due to Junyan Chu.

What, if anything, makes Minkowski spacetime a privileged local reference geometry in General Relativity? Recent work by \cite{WeatherallFletcher} argues: nothing. In response, I proposed a criterion of “$\delta$-flatness”, which bounds the magnitude of tidal acceleration within a tubular neighborhood by $\delta$, and showed that Minkowski uniquely saturates the bound. Here I ask how $\delta$-flatness generalises, and distinguish two kinds of extension. Reference-metric generalisations compare physical tidal acceleration with a reference tidal-force term constructed from another metric. Lorentzian signature obstructs every such comparison in which the reference fails to share the lightcones of the physical metric. Criterion modifications instead build the criterion from the physical geometry alone. The space of such modifications is wide, and I focus on those closest to $\delta$-flatness, where one bounds the deviation of tidal acceleration from a non-zero target. The minimal candidate, which I call $\delta$-MSS, has a singular limit that picks out the maximally symmetric spacetimes (Minkowski, de Sitter, Anti-de Sitter) via Schur's theorem. A restricted variant, which compares $g$ with a conformal rescaling of itself, either collapses to $\delta$-MSS or fails to pick out a unique geometry. The chief result is that $\delta$-flatness distinguishes Minkowski with no free parameter. $\delta$-MSS, a weaker variant, picks out the maximally symmetric family at the cost of an externally supplied scalar.

Robotic imitation learning often relies on external cameras, yet local interaction cues such as object proximity, contact onset, and grasp state are difficult to observe near the fingertips because of occlusion and limited temporal resolution. We study how to effectively incorporate complementary fingertip sensing into imitation learning using pressure-sensitive tactile and reflective proximity sensors, along with pretrained sensor encoders. The two modalities provide information at different manipulation phases: proximity sensing is informative before contact, whereas tactile sensing becomes informative after contact. However, naively adding these signals to a policy does not consistently improve performance and can even underperform vision-only policies, suggesting that sparse, phase-dependent sensor signals are difficult to exploit from limited demonstrations. We therefore propose a proprioception-anchored pretraining method, PROprioceptive-and-PRoactive Anchoring (PROPRA), which independently aligns each fingertip sensor history with proprioceptive and action segments. This provides a continuously available sensorimotor reference, allowing each sensor to be aligned independently during its informative phases. Experiments on real-world manipulation tasks show that our pretraining method improves average success rates over vision-only policies and image-anchored pretraining baselines. Representation analysis further shows that it preserves richer information about pre-contact states, enabling more effective use of complementary fingertip sensing. Please refer to our project page: https://tomohiromotoda.github.io/nia.propra/

We study exact one-center optimization for axis-parallel segments using axis-parallel squares under endpoint-based coverage, where a segment is \emph{$1$-covered} if the square contains at least one of its endpoints. In the monochromatic problem, we seek a minimum-side-length square that $1$-covers all $n$ input segments. We obtain $O(n\log n)$-time algorithms for both unrestricted and segment-constrained centers. The unrestricted bound matches the known bound implied by the two-representative color-spanning-square problem, whereas the segment-constrained result is new. We also prove matching $\Omega(n\log n)$ lower bounds for both center models in the fixed-order algebraic decision-tree model. In the bichromatic problem, an admissible square must fully contain all $m$ blue segments, minimize the number of red segments with an endpoint in its interior, and, subject to this minimum, maximize its side length within a prescribed bounding box. We give deterministic $O(m+n\log^2 n)$-time and $O(m+mn\log n)$-time algorithms for unrestricted and blue-segment-constrained centers, respectively.

Imagined speech decoding from electroencephalography (EEG) has gained increasing attention as a potential communication pathway for individuals with severe motor impairments, yet reported performance often relies on evaluation protocols that do not clearly reflect cross-subject generalization. This study presents a transparent baseline investigation of a multi-class imagined speech EEG dataset under a strictly subject-independent evaluation framework. Two preprocessing and feature extraction pipelines were compared: a time-domain statistical feature approach and a frequency-domain spectral bandpower approach, evaluated using subject-wise cross-validation and trial-level majority voting with a random forest classifier. The spectral pipeline achieved a significantly higher mean trial-wise accuracy than the statistical pipeline (49.03 $\pm$ 4.18% vs. 37.97 $\pm$ 3.79%) for coarse-level classification across subjects. Forward feature selection further indicated that a limited subset of frequency bands captured most of the discriminative information. Overall, this work provides a strong basis for future brain-computer interface studies targeting improved cross-subject generalization in EEG-based imagined speech decoding.

In large-scale participatory budgeting, citizens cannot inspect the full proposal pool, so the order in which proposals are shown becomes a form of agenda-setting power. We argue that fair exposure should therefore be treated as a democratic-design goal. We study Consul Democracy, a widely deployed open-source digital-democracy platform, and show that its proposal feeds are typically ordered by popularity, recency, or comment activity. Building on this diagnosis, we propose FairFeed, a feed-ranking design for PB that uses transparently declared preferences, boosts under-exposed proposals, and admits a rate-limited reject channel for crowd-sourced vetting. We evaluate the design in a simulation anchored in Munich's 2025 PB process and compare it with random, newest, and most-commented feeds. In this simulation, FairFeed broadens proposal discovery, distributes visibility more evenly across the eligible pool, increases cross-cutting support, and improves resistance to manipulation relative to comment-based ranking. We conclude by outlining the human-subjects evaluation needed to test whether onboarding can recover voter preferences accurately enough for deployment in practice.

We study the stability of the log–log blow-up regime for the focusing mass-critical nonlinear Schrödinger equation under small $H^s$ perturbations. Previously, stability was established for every $0<s<1$ in dimension two by Colliander and Raphaël [Math. Ann. (2009)] and subsequently extended to dimensions $d\geq3$ under the restriction $s>1/(1+\min\{1,4/d\})$ by Sun and the fourth author [J. Math. Pures Appl. (2020)]. We remove this restriction and establish stability throughout the full subcritical range $0<s<1$.

Autocorrelation functions play a key role in the theoretical characterization of the dynamical properties of interacting many-body quantum systems. Recently, bringing together the eigenstate thermalization hypothesis and hydrodynamics, it was theoretically predicted that the relaxation of autocorrelators can be described by the relaxation-overlap inequality, which, when saturated, predicts a hierarchy of relaxation exponents for a set of operators that are easily identified and constructed. Here, we employ a trapped-ion quantum simulator to experimentally demonstrate it in the diffusive regime; to do so, we have extended the theory of the overlap-relaxation inequality to systems with multiple conservation laws. Our study thus opens the path to a thorough characterization of the relaxation to equilibrium and appearance of hydrodynamic behavior in quantum matter.

Recent years have witnessed major progress in joint audio-video generation. Existing models still suffer from limited per-modality fidelity, insufficient text-modality alignment and weak cross-modal synchronization. While reinforcement-learning post-training offers a promising remedy, directly adapting it to joint audio-video generation is challenging. Heterogeneous multimodal rewards entangle learning signals and complicate credit assignment. Joint optimization of two modality towers is computationally expensive given their divergent dynamics. Moreover, synchronization evaluation difficulty depends on paired samples, preventing fair reward comparisons. We propose AV-GRPO, a modality-anchored online diffusion RL framework, and 5DAV, a decoupled, difficulty-controllable training dataset. AV-GRPO includes three key modules: (1) modality-anchored rollouts to disentangle learning signals and stabilize difficulty; (2) trajectory-locked frozen-tower optimization to reduce cost and reassign credit; (3) adaptive objectives and perturbation strengths tailored to modality-specific dynamics. This converts coupled multimodal preference learning into unimodal subproblems for precise reward attribution and better synchronization. Our 5DAV dataset decouples samples across five dimensions for systematic training. Experiments on JavisBench and VABench demonstrate AV-GRPO outperforms LTX-2.3 in generation quality, semantic alignment and cross-modal synchronization under LoRA and full fine-tuning. Ablations confirm our designs. Code and data: https://github.com/zhiyuxu03/AV-GRPO

Sequential recommendation aims to predict users' future interests from their historical interactions. Although Large Language Models (LLMs) capture rich item semantics, existing methods often struggle to align collaborative signals with textual semantic knowledge. As a result, the learned item representations fail to capture the complementary strengths of both signals, leading to suboptimal recommendation quality. To address this limitation, we propose Latent Semantic Fusion for Sequential Recommendation via Flow-based Conditional Variational Autoencoders (LSF-SR), a novel framework that uses a Conditional Variational Autoencoder (CVAE) with Normalizing Flows to fuse item ID embeddings and LLM-generated semantic signals. At the core of LSF-SR is a conditional fusion module augmented with planar or radial flows. This module learns a flexible latent space that encourages items with similar semantic profiles to cluster together within the latent manifold. Through extensive experiments on five public benchmark datasets, we demonstrate that LSF-SR consistently outperforms state-of-the-art baselines, achieving gains of up to 12.98% and 14.13% in Recall@20 and NDCG@20, respectively.

Tabular foundation models (TFMs) provide a promising route to time-series classification, but their effectiveness depends on how sequential data are converted into tabular representations. Existing representations face two challenges: global aggregation can lose the order of temporal evolution, while features computed in independently fitted coordinate systems may not have consistent meanings across sequences. We therefore view representation design for TFMs as a problem in its own right: the representation should preserve local temporal transitions while maintaining a shared feature definition across samples. We propose SwitchPFN, which learns a shared projection and regime codebook from the training sequences, making local dynamic operators and transition features directly comparable across samples. Across the evaluated benchmarks, SwitchPFN achieves the highest mean accuracy among the evaluated methods, improving over the strongest baseline by 4.47% relatively. Ablation studies, parameter sensitivity analyses, and reduced-training-data experiments further examine the contributions of the representation, its main design choices, and its behavior when labeled data are limited.

We present S2Planner, a trajectory planner that combines three front-facing cameras with ego-motion history and the current driving command. A fine-tuned DINOv3 backbone and a Spatial Tuning Adapter produce multi-scale image features; a coarse-to-fine decoder then uses trajectory self-attention and camera-projected cross-attention to refine candidate waypoints. The contribution is the integration of ego-conditioned trajectory initialization with iterative, geometry-guided sampling of multi-scale image features, rather than a new visual backbone or attention operator. On the NAVSIM v1 non-reactive evaluation, the previously reported navtest run obtained 88.03 PDMS. Because that run was selected using navtest performance, this number is exploratory and cannot be interpreted as an unbiased test estimate. Validation-selected evaluation on unexposed data, repeated runs, and computational measurements are needed to establish generalization and efficiency.

Looped Transformers have attracted substantial attention as a parameter-efficient approach to increasing computational depth through repeated application of shared Transformer blocks. However, their practical advantages over conventional Transformers remain under debate: each additional loop incurs another Transformer pass and requires caching another set of KV states, causing inference FLOPs and KV-cache memory to grow continuously with loop depth. This overhead becomes particularly severe at large loop counts and long context, preventing the parameter efficiency of Looped Transformers from translating into practical inference efficiency. In this paper, we find that much of the additional computation and storage introduced by looping is redundant. As recurrence proceeds, state changes become increasingly concentrated on a small subset of tokens; attention-output differences are dominated by a sparse and stable subset of key columns; and KV residuals between adjacent loops become progressively more amenable to low-bit quantization. Building on these observations, we introduce FlashLoop, a training-free inference framework that reduces cross-loop redundancy through token-sparse updates, sparse attention, and KV-residual quantization. Across several Looped Transformers models, FlashLoop delivers lossless accuracy while achieving up to 1.64$\times$ end-to-end speedup and up to 6$\times$ KV-cache memory reduction, substantially improving the practicality of scaling Looped Transformers to greater computational depths and longer context.

A fracton model of a complex medium has been constructed to study physicochemical processes for radiation-technological purposes that occur under intense irradiation. The possibility of shock-wave generation, as well as of percolation phenomena involving fractal aggregates, has been studied in the search for an ideal thermal insulator.

Piezoelectricity is a key phenomenon in solid-state physics and has significant technological relevance. In teaching, however, it is often treated either without a historical context or an explicit link to the microscopic crystal structure, meaning that a crucial level of understanding remains untapped. This study combines the history of the discovery of piezoelectricity with its physical description within a didactically coherent framework. Building on the work of the brothers, Jacques and Pierre Curie (1880 - 1882), it demonstrated how investigations into pyroelectricity led to the identification of polarization induced by mechanical compression in hemihedral crystals such as tourmaline and quartz. The development from early qualitative experiments towards the first quantitative determination of piezoelectric constants is traced in a structured manner. Using low quartz as an example, the microscopic cause of piezoelectricity was attributed to the asymmetric displacements of silicon and oxygen ions within the orthosilicate ion tetrahedral network. This leads to the formation of macroscopic polarization owing to uncompensated dipole moments in the crystal lattice. The direct and reciprocal piezoelectric effects are qualitatively distinguished and discussed in the context of mechanical-electrical coupling. The article is aimed at students in physics and engineering as well as lecturers. It was conceived as a didactic review article (tutorial article) and serves as a structured introduction to the physical and historical foundations of piezoelectricity.