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Motivated by a question of L. Robert, asking whether $\rm L(T(A)) = Lsc_{C}(T(A))$ for any separable C*-algebra A, we introduce and initiate the study of \emph{tracially reflexive C*-algebras}. We first prove that commutative C*-algebras are tracially reflexive. We also prove that tracial reflexiveness satisfies permanence properties, such as being preserved under inductive limits. Subsequently, we expose two criteria for tracial reflexiveness, using the Cuntz semigroup and a weak version of the Schröder-Simpson theorem, respectively. In particular, separable topological dimension zero C*-algebras are tracially reflexive. We end the manuscript by closing remarks that could lead to further lines of investigation involving tracial reflexiveness.

Nociception is a protective biological mechanism that links harmful stimulation to a reaction. This paper investigates artificial nociception for a robotic arm with whole-body tactile sensing. We present a complete pipeline that maps pressure changes from sensitive skin on a robot manipulator to bio-inspired withdrawal motions. The system first converts skin pressure into a scalar pain gain using a nonlinear continuous model. We compare three reflexes: (i) uniform reflex moves four robot joints by a fixed amount, whereby the withdrawal is approximated by a movement of the arm "toward the base", independent of where the robot was touched; (ii) biologically motivated location-dependent joint-space withdrawal derived from human withdrawal reflex characteristics; (iii) Cartesian space withdrawal along the surface normal of the contacted skin pad. All behaviors are integrated in a reflex controller that interrupts the task, executes the withdrawal, and returns to a pre-contact pose. A user study with 15 participants compared the strategies using Godspeed questionnaire subscales, custom perceived-naturalness and safety items, forced-choice comparisons, and qualitative feedback. Interesti

This letter studies CSI denoising for MIMO--OFDM with variable NR resource block (RB) allocations. ReFLEX is a length-generalizable Transformer whose frequency attention uses a relative-frequency position bias (RFPB) generated from subcarrier offsets. A single checkpoint handles unseen RB lengths and can be applied to sparse DM-RS observations in the tested RB5/RB10 PUSCH setup without retraining. In a 3GPP~TR~38.901 UMa NLOS channel, ReFLEX achieves about $-9.6$~dB NMSE on unseen RB lengths. In NR PUSCH/UL-SCH simulations, ReFLEX denoising followed by time-frequency interpolation reduces the 10\% BLER threshold by about 2--3~dB.

Reinforcement learning has long struggled with poor sample efficiency. One promising approach to mitigate this problem is leveraging group-invariant Markov Decision Processes ($G$-invariant MDPs). Existing works in this direction have primarily focused on image-based RL and rotational symmetry such as $\mathrm{SO(2)}$, leaving state-based RL and reflection symmetry largely underexplored. In this work, we focus on state-based continuous control tasks and exploit reflection symmetry by introducing Reflex, a paradigm that seamlessly integrates with both on-policy and off-policy RL algorithms. We formalize two types of reflection-axial reflection and bilateral reflection, and characterize their corresponding transformations. Building on a theoretical analysis of symmetry-preserving optimal value functions and policies, Reflex integrates reflection symmetry into policy learning through principled symmetry regularization mechanisms. We integrate Reflex with PPO and SAC, and evaluate it on a suite of OpenAI Gym and DeepMind Control benchmarks, demonstrating superior performance over standard baselines while improving sample efficiency. Our code is available at https://github.com/TonyStark

Reflexive homology is the homology theory associated to the reflexive crossed simplicial group; one of the fundamental crossed simplicial groups. It is the most general way to extend Hochschild homology to detect an order-reversing involution. In this paper we study the relationship between reflexive homology and the $C_2$-equivariant homology of free loop spaces. We define reflexive homology in terms of functor homology. We give a bicomplex for computing reflexive homology together with some calculations, including the reflexive homology of a tensor algebra. We prove that the reflexive homology of a group algebra is isomorphic to the homology of the $C_2$-equivariant Borel construction on the free loop space of the classifying space. We give a direct sum decomposition of the reflexive homology of a group algebra indexed by conjugacy classes of group elements, where the summands are defined in terms of a reflexive analogue of group homology. We define a hyperhomology version of reflexive homology and use it to study the $C_2$-equivariant homology of certain free loop and free loop-suspension spaces. We show that reflexive homology satisfies Morita invariance. We prove that under ni

Large multimodal language models (LLMs) have emerged as powerful tools for guiding evolutionary search toward interpretable programmatic policies. However, existing frameworks rely on a monolithic model call to simultaneously interpret visual behavioral evidence and synthesize corrective code. This diagnosis-repair entanglement creates an opaque feedback loop, obscuring the rationale behind mutations and preventing the retention of algorithmic insights across independent runs. To achieve auditable and efficient policy search, we argue that visual diagnosis must be structurally decoupled from code generation. We present REFLEX, a train-free evolutionary framework that operationalizes this decoupling. In REFLEX, a vision-enabled Critic first distills task-specific behavioral evidence into structured, auditable diagnoses. Subsequently, a text-optimized Actor synthesizes child policies using these diagnoses alongside a persistent, self-evolving Skill Memory of reusable code snippets. This architecture not only provides transparent mutation traces but also enables cross-run programmatic knowledge transfer. Extensive evaluations across control benchmarks (Lunar Lander, Acrobot, Pendulum)

Mixture-of-experts (MoE) models increase parameter capacity by activating only a small subset of experts for each token. This conditional-computation paradigm has enabled autoregressive language models to scale model capacity without a proportional increase in per-token computation. In diffusion language models (DLMs), however, each denoising forward jointly revisits all token positions despite their sharply different refinement demands, while the default fixed token-choice routing assigns them a uniform expert budget, creating a mismatch between expert computation and refinement demand. We argue that MoE inference in DLMs should therefore be viewed as refinement-aware compute allocation across heterogeneous token refinement states. We propose REFLEX (\textbf{RE}finement-aware \textbf{FLEX}ible expert allocation), a training-free method that keeps the default router unchanged while reorganizing expert computation around the evolving refinement process. Specifically, REFLEX introduces a coarse-to-fine hierarchy for expert-budget allocation that aligns computation with block-relative refinement roles while using the Frontier-Progress Score to resolve active-block priorities. Across m

The unconditioned reflex (e.g., protective reflex), which is the innate reaction of the organism and usually performed through the spinal cord rather than the brain, can enable organisms to escape harms from environments. In this paper, we propose an online, highly-dynamic motion planning algorithm to endow manipulators the highly-dynamic unconditioned reflexes to humans and/or environments. Our method is based on a chained version of Signed Distance Functions (SDFs), which can be pre-computed and stored. Our proposed algorithm is divided into two stages. In the offline stage, we create 3 groups of local SDFs to store the geometric information of the manipulator and its working environment. In the online stage, the pre-computed local SDFs are chained together according the configuration of the manipulator, to provide global geometric information about the environment. While the point clouds of the dynamic objects serve as query points to look up these local SDFs for quickly generating escape velocity. Then we propose a modified geometric Jacobian matrix and use the Jacobian-pseudo-inverse method to generate real-time reflex behaviors to avoid the static and dynamic obstacles in the

Flow matching Vision-Language-Action (VLA) models promise precise continuous control, but their iterative denoising nature introduces fundamental incompatibilities with real-time robotics: global timestep injection invalidates KV-caching, forcing a choice between slow $O(N^2)$ re-computation or mathematically incorrect cache reuse. We present \textbf{Reflex}, a framework that enables \textit{real-time streaming inference} for flow matching policies by exploiting the \textit{Timestep-Invariance Property} -- that perception encoders are functionally independent of the denoising loop. Reflex partitions the attention context into static, sliding, and dynamic regions, enabling $O(1)$ incremental cache updates while preserving full-batch-equivalent attention outputs for fixed inputs. To ensure stability under continuous high-frequency inference, we introduce \textit{AdaRMSNorm}, an adaptive normalization layer that prevents BFloat16 numerical collapse by gating on flow phase. We further maximize throughput through an \textit{async pipeline} that decouples visual encoding from action generation, combined with \textit{operator fusion} that reduces kernel overhead. On LIBERO and Kinetix ben

Evaluating log summarization systems is challenging due to the lack of high-quality reference summaries and the limitations of existing metrics like ROUGE and BLEU, which depend on surface-level lexical overlap. We introduce REFLEX, a reference-free evaluation metric for log summarization based on large language model (LLM) judgment. REFLEX uses LLMs as zero-shot evaluators to assess summary quality along dimensions such as relevance, informativeness, and coherence, without requiring gold-standard references or human annotations. We show that REFLEX produces stable, interpretable, and fine-grained evaluations across multiple log summarization dataset, and more effectively distinguishes model outputs than traditional metrics. REFLEX provides a scalable alternative for evaluating log summaries in real-world settings where reference data is scarce or unavailable.

The prevalence of fake news on social media demands automated fact-checking systems to provide accurate verdicts with faithful explanations. However, existing large language model (LLM)-based approaches ignore deceptive misinformation styles in LLM-generated explanations, resulting in unfaithful rationales that can mislead human judgments. They rely heavily on external knowledge sources, introducing hallucinations and even high latency that undermine reliability and responsiveness, which is crucial for real-time use. To address these challenges, we propose REason-guided Fact-checking with Latent EXplanations (REFLEX), a self-refining paradigm that explicitly controls reasoning style anchored on verdict. REFLEX utilizes self-disagreement veracity signals between the backbone model and its fine-tuned variant to construct steering vectors, naturally disentangling fact from style. Experiments on the real-world dataset show REFLEX achieves state-of-the-art performance under LLaMA-series models with only 465 self-refined samples. Moreover, owing to its transferability, REFLEX yields up to a 7.54% gain on in-the-wild data. Our results further demonstrate that our method effectively mitiga

We establish some general principles and find some counter-examples concerning the Pontryagin reflexivity of precompact groups and P-groups. We prove in particular that: (1) A precompact Abelian group G of bounded order is reflexive iff the dual group $\hat{G}$ has no infinite compact subsets and every compact subset of G is contained in a compact subgroup of G. (2) Any extension of a reflexive P-group by another reflexive P-group is again reflexive. We show on the other hand that an extension of a compact group by a reflexive $ω$-bounded group (even dual to a reflexive P-group) can fail to be reflexive. We also show that the P-modification of a reflexive $σ$-compact group can be nonreflexive (even if the P-modification of a locally compact Abelian group is always reflexive).

The musculoskeletal humanoid has various biomimetic benefits, and it is important that we can embed and evaluate human reflexes in the actual robot. Although stretch reflex has been implemented in lower limbs of musculoskeletal humanoids, we apply it to the upper limb to discover its useful applications. We consider the implementation of stretch reflex in the actual robot, its active/passive applications, and the change in behavior according to the difference of parameters.

The nociceptive withdrawal reflex (NWR) is a mechanism to mediate interactions and protect the body from damage in a potentially dangerous environment. To better convey warning signals to users of prosthetic arms or autonomous robots and protect them by triggering a proper NWR, it is useful to use a biological representation of temperature information for fast and effective processing. In this work, we present a neuromorphic spiking network for heat-evoked NWR by mimicking the structure and encoding scheme of the reflex arc. The network is trained with the bio-plausible reward modulated spike timing-dependent plasticity learning algorithm. We evaluated the proposed model and three other methods in recent studies that trigger NWR in an experiment with radiant heat. We found that only the neuromorphic model exhibits the spatial summation (SS) effect and temporal summation (TS) effect similar to humans and can encode the reflex strength matching the intensity of the stimulus in the relative spike latency online. The improved bio-plausibility of this neuromorphic model could improve sensory feedback in neural prostheses.

Modelling perturbations of the Milky Way (MW) halo induced by the infall of the Large Magellanic Cloud (LMC) offers new avenues to constrain the dark matter (DM) distribution in our Galaxy. A key observable is the reflex motion of the MW disc with respect to the halo induced by the LMC's infall, which imprints a velocity dipole on kinematics of halo stars. Here we investigate how the dipole varies with Galactocentric radius, and study the sensitivity of the reflex motion signal to different DM outer-halo profiles. Using a suite of basis function expansion (BFE) simulations with truncated NFW profiles ($ρ\propto r^{-β}$ beyond $r=50$ kpc), our $N$-body models show that (i) The reflex motion amplitude varies with Galactocentric radius but is largely insensitive to the outer DM slope, implying that the MW-LMC mass ratio alone does not set the dipole strength. (ii) In contrast, the direction of the disc motion is very sensitive to the density distribution of the outer DM halo. (iii) The contraction of the MW halo induced by the LMC's gravitational pull also depends strongly on the outer DM halo profile. (iv) We find a halo instability whose oscillation frequency increases with $β$ prod

Protolanguage reconstruction is central to historical linguistics. The comparative method, one of the most influential theoretical and methodological frameworks in the history of the language sciences, allows linguists to infer protoforms (reconstructed ancestral words) from their reflexes (related modern words) based on the assumption of regular sound change. Not surprisingly, numerous computational linguists have attempted to operationalize comparative reconstruction through various computational models, the most successful of which have been supervised encoder-decoder models, which treat the problem of predicting protoforms given sets of reflexes as a sequence-to-sequence problem. We argue that this framework ignores one of the most important aspects of the comparative method: not only should protoforms be inferable from cognate sets (sets of related reflexes) but the reflexes should also be inferable from the protoforms. Leveraging another line of research -- reflex prediction -- we propose a system in which candidate protoforms from a reconstruction model are reranked by a reflex prediction model. We show that this more complete implementation of the comparative method allows

Objective: Reflex testing protocols allow clinical laboratories to perform second line diagnostic tests on existing specimens based on the results of initially ordered tests. Reflex testing can support optimal clinical laboratory test ordering and diagnosis. In current clinical practice, reflex testing typically relies on simple "if-then" rules; however, this limits their scope since most test ordering decisions involve more complexity than a simple rule will allow. Here, using the analyte ferritin as an example, we propose an alternative machine learning-based approach to "smart" reflex testing with a wider scope and greater impact than traditional rule-based approaches. Methods: Using patient data, we developed a machine learning model to predict whether a patient getting CBC testing will also have ferritin testing ordered, consider applications of this model to "smart" reflex testing, and evaluate the model by comparing its performance to possible rule-based approaches. Results: Our underlying machine learning models performed moderately well in predicting ferritin test ordering and demonstrated greater suitability to reflex testing than rule-based approaches. Using chart review

Achieving human-level dexterity in robotic grasping remains a challenging endeavor. Robotic hands frequently encounter slippage and deformation during object manipulation, issues rarely encountered by humans due to their sensory receptors, experiential learning, and motor memory. The emulation of the human grasping reflex within robotic hands is referred to as the ``bionic reflex". Past endeavors in the realm of bionic reflex control predominantly relied on model-based and supervised learning approaches, necessitating human intervention during thresholding and labeling tasks. In this study, we introduce an innovative bionic reflex control pipeline, leveraging reinforcement learning (RL); thereby eliminating the need for human intervention during control design. Our proposed bionic reflex controller has been designed and tested on an anthropomorphic hand, manipulating deformable objects in the PyBullet physics simulator, incorporating domain randomization (DR) for enhanced Sim2Real transferability. Our findings underscore the promise of RL as a potent tool for advancing bionic reflex control within anthropomorphic robotic hands. We anticipate that this autonomous, RL-based bionic re

Matlis duality for modules over commutative rings gives rise to the notion of Matlis reflexivity. It is shown that Matlis reflexive modules form a Krull-Schmidt category. For noetherian rings the absence of infinite direct sums is a characteristic feature of Matlis reflexivity. This leads to a discussion of objects that are extensions of artinian by noetherian objects. Classifications of Matlis reflexive modules are provided for some small examples.