Papers

Single-molecule affinity mapping enables measurement of individual proteins and proteoforms, but imperfect and nonspecific probe binding means that affinity traces may be compatible with multiple proteoforms. Accurate abundance estimation therefore requires probabilistically weighting ambiguous traces rather than assigning each trace to a single candidate. We developed ProteoEM, an expectation-maximization framework for weighted proteoform quantification, inspired by transcript abundance estimation methods for RNA-seq and released as an open-source Python package. ProteoEM evaluates each observed affinity trace against all candidate proteoforms using fixed, pre-calibrated probe-response rates that are separate from abundance estimation. It estimates the abundance of each proteoform and reports proteoforms that the probes cannot tell apart as a single group. Because some proteoforms are observed more readily than others, ProteoEM also corrects for these observation yields to estimate the composition of the source sample. We show that grouping traces that carry the same evidence into equivalence classes reduces the EM's work sevenfold without changing the estimates. In simulations, ProteoEM recovered the true molecular composition, whereas approaches that reduced each affinity trace to a hard yes/no call introduced substantial errors. Performance was robust to moderate, uniform calibration error but was biased by informative missing data and by proteoforms absent from the reference set. When observation yields were known, ProteoEM also recovered source-sample composition from observed molecular counts. ProteoEM is an open-source, reproducible framework for quantitative analysis of single-molecule affinity measurements and provides a basis for validation using experimental molecule-level data.

Large language model agents increasingly rely on natural-language skills to solve complex tool-use tasks. However, such tasks often admit multiple valid solution paths, making it inappropriate to improve skills by forcing failed trajectories to match a fixed successful trajectory. Moreover, failed trajectories are rarely entirely wrong: an agent may first collect useful evidence and make meaningful progress, but later deviate into an erroneous suffix. We therefore argue that skill self-evolution should identify where productive problem solving begins to break down, rather than reflect coarsely over the entire failure. Based on this insight, we propose SkillPivot, a deviation-point-guided framework for skill self-evolution. SkillPivot detects the transition from a useful prefix to an erroneous suffix using execution validity, goal progress, and action diversity. A stronger teacher then continues from the same prefix and produces a successful alternative under the same interaction history. By contrasting the student's failed suffix with the teacher's successful suffix, SkillPivot generates localized skill updates while preserving already effective guidance. Experiments on ToolQA, LogicBench, and WildClawBench show that SkillPivot consistently outperforms competing skill-evolution methods, improves multiple agent models, and produces compact, transferable skill updates.

For every integer $n \ge 2$, we construct explicit tetrahedral counterexamples showing that repeated longest-edge (LE) n-section refinement does not, in general, preserve shape regularity, contrary to long-standing conjectural expectations. For $n = 2$, the construction disproves the finite-family conjecture put forward by Adler in 1983 and the non-degeneracy conjecture for tetrahedral longest-edge bisection formulated by Rivara and Levin in 1992. It also shows that the sharper higher-dimensional diameter decay suggested by Stynes in 1983,following his 1980 planar finite-similarity result, cannot hold for arbitrary tetrahedra. For $n = 3$, it disproves the published non-degeneracy conjecture for tetrahedral longest-edge trisection formulated in 2011 by Suárez, Abellón, Abad and Plaza on the basis of numerical experiments. The resulting infinite descendant sequences violate both the minimum and maximum angle conditions. For $n \ge 3$, the selected edge is always the unique longest edge at every refinement step. The two-step recurrence used in the construction exhibits two distinct degeneration behaviors: a flat-tetrahedron regime for $2 \le n \le 5$ and a skinny-tetrahedron regime for $n \ge 6$. The degenerating sequences can also be realized within conforming partitions generated by the conforming LE n-section algorithm. For both the classical and the conforming LE n-section algorithms, the maximal element diameter tends to zero as the number of refinement steps tends to infinity, regardless of which longest edge is chosen. Thus diameter convergence, and even conformity, do not prevent shape degeneration. These algorithms should therefore be used with care in applications requiring uniform shape regularity.

We develop compactness and defect-of-compactness results for Banach-valued evolution classes with Morrey control in time. For \[ \begin{aligned} \mathbb W_M^{p,\lambda}(0,T;E_0,E_1) =\{u\in\mathcal M^{p,\lambda}(0,T;E_0):\;& u'\in\mathcal M^{p,\lambda}(0,T;E_1)\},\\[-1mm] &0<\lambda<1. \end{aligned} \] the exact trace exponent \[ \theta=1-\frac{1-\lambda}{p} \] governs both continuity and compactness. If $E_0\hookrightarrow\!\hookrightarrow E\hookrightarrow E_1$, bounded sets are compact in the same Morrey space $\mathcal M^{p,\lambda}(0,T;E)$, not merely in $L^p(0,T;E)$. In contrast, compactness in $C([0,T];E)$ holds if and only if the exact trace space $(E_1,E_0)_{\theta,\infty}$ embeds compactly into $E$. We also obtain compact lower-order Hölder embeddings and a sharp Hilbert-triple threshold. On unbounded domains we prove a tightness criterion for global Morrey compactness. In the Hilbert-valued case we establish, by a direct time-averaging argument, cocompactness modulo spatial translations and a translation profile decomposition whose remainder vanishes in every strictly subcritical time-Morrey–Sobolev target; a uniform little-Morrey condition removes the loss in the time exponent. At the doubly critical endpoint, heat and whole-space Stokes dynamics force balanced parabolic profiles, and the remainder vanishes in $\mathcal M_t^{2,\lambda}L_x^{2^*}$. Finally, in three-dimensional Navier–Stokes we show that the classical nonlinear profile decomposition has a scale-sensitive Morrey refinement: the remainder is small in $\mathcal M_t^{p,1-p/4}L_x^6$ for every $2\le p<4$, and orthogonal profiles have vanishing interaction in the corresponding Morrey forcing space.

Earth-observation (EO) foundation models provide reusable embeddings, yet downstream task accuracy does not reveal whether these representations encode geographic information, which may be beneficial for location-aware applications but potentially detrimental when representations invariant to geographic location are desired. We therefore evaluate the geographic coordinate robustness of Tessera v1, Tessera v1.1, and AlphaEarth by testing whether coordinates can be predicted from the embedding representations using 284 quality-verified European solar farms from 2024. We assessed geographic information content information through the association between cosine and geodesic distances and through prediction of projected coordinates in EPSG:3035. Embeddings from all three EO foundation models contain recoverable geographic information. All prediction models significantly outperform training-range uniform random sampling baselines, with AlphaEarth exhibiting the strongest distance association and lowest mean geodesic error. Both Tessera variants also yielded higher geographic distance correlations than the Sentinel-2 controls. These findings motivate geographic information content as an additional criterion for auditing EO foundation models.

This paper investigates the joint optimization of the transmit precoder and the transmission/reflection coefficients of a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) to maximize the weighted sum rate (WSR) in a multi-user downlink. We propose a particle-swarm-assisted gradient meta-learning (PSA-GML) algorithm for this non-convex problem. The original problem is first equivalently transformed via an amplitude-split parameterization and a collapsed precoder representation, which automatically satisfy the energy-conservation constraint and reduce the search dimension. Particle swarm optimization (PSO) then performs a global search over the STAR-RIS coefficients to yield a high-quality, initialization-robust warm start, with the transmit precoder obtained in closed form. Departing from conventional alternating optimization (AO), a coordinate-wise long short-term memory (LSTM) meta-optimizer trained by first-order gradient meta-learning further refines the coefficients and precoder jointly, learning per-coordinate adaptive update rules from data. The meta-optimizer is trained offline and applied to unseen channels without further adaptation. Numerical results show that PSA-GML attains an 11.06 bits/s/Hz WSR at 10 dB with N=32 elements and K=4 users, exceeding AO by 13.1% (and by 6.2% even with multiple random restarts) and the random-phase scheme by 35.1%. In the interference-limited regime it reaches 83.9% of the hand-designed Adam refinement without manual hyper-parameter tuning, and it transfers zero-shot across regimes, indicating that the learned update rule captures the intrinsic WSR landscape structure.

This paper investigates a fundamental question in stripeless erasure coding based on symmetric balanced incomplete block designs (SBIBDs): how many replicas per object are precisely required to guarantee recovery from any set of at most $p$ node failures? We refine the known sufficient recovery guarantee for the generalized SBIBD $(v,k,\lambda)$ construction. One replica is necessary and sufficient for $p=1$, and $q=\lambda(p-1)+2$ replicas ($q\le k$) guarantee recovery for $p\ge2$. Recovery takes one round for $p=2$ and at most two rounds in general. To study the tightness of this count, we define the universal replica threshold $q^\ast(A,p)$ for a fixed zero-diagonal SBIBD representative~$A$. We determine $q^\ast(A,p)$ for $p=1$ and $p=2$. For $p\ge3$, we identify pairwise separated sets and private target permutations as the structures determining whether the sufficient count is tight or can be further reduced. These conditions give exact thresholds for all but the case where $\lambda>1$ and $A$ contains no pairwise separated set of size~$p$. We improve the bounds for this remaining case and leave its exact threshold open. Finally, we give sufficient conditions for pairwise separated sets and show how affinity relabeling can realize private target permutations.

We establish an exact trace theorem for vector-valued time-Morrey spaces and complementary continuity theorems for time-BMO evolution classes. For a Banach couple $X_1\hookrightarrow X_0$, $1<p<\infty$ and $0<\lambda<1$, we prove that the trace of the class $u\in\mathcal M^{p,\lambda}(X_1)$, $u_t\in\mathcal M^{p,\lambda}(X_0)$ is exactly $(X_0,X_1)_{\theta,\infty}$, where $\theta=1-(1-\lambda)/p$. A constructive extension realizes every admissible trace, and counterexamples establish optimality of both the smoothness exponent and the weak fine index. Time-BMO control yields continuous finite-index interpolation traces and, under a mixed boundedness hypothesis, a logarithmic time modulus whose base-space logarithm is necessary. For the quadratic viscous Hamilton–Jacobi equation on the torus, we characterize the bounded initial data generating Morrey-regular solutions by the exact Besov condition $u_0\in B_{2,\infty}^{2\theta}$. The proof uses Hopf–Cole linearization and a direct composition argument, and requires no smallness assumption. Lacunary nonlinear solutions realize the sharp trace threshold. A forced Hamilton–Jacobi example exhibits genuinely logarithmic time regularity, and a forward–backward mean-field-game system illustrates initial and terminal trace compatibility. \par\smallskip\noindentKeywords: Morrey spaces; trace spaces; real interpolation; Hamilton–Jacobi equations; bounded mean oscillation.

We prove global well-posedness of the one-dimensional defocusing cubic nonlinear Schrödinger equation in the modulation space $M^{\infty,1}(\mathbb{R})$. This space imposes no spatial decay and contains $C_b^2(\mathbb{R})$ as well as all absolutely convergent sums of plane waves. The result applies to arbitrary data in this space, including large smooth quasiperiodic profiles and their localized perturbations. The proof constructs a nonnegative density satisfying a local conservation law from forward Weyl ratios, which are defined through half-line square-integrable solutions of the associated spectral problem. A suitable nonlinear combination of localized integrals of this density controls the modulation norm. Finally, choosing the spatial localization scale and NLS scaling in a coordinated way makes the accumulated boundary flux small enough to continue every mild solution globally.

Bangla, the seventh most spoken language in the world, remains under-resourced for neural text-to-speech. Public Bangla speech corpora are dominated by short read-prompt utterances collected for speech recognition, leaving long-form prosody and consistent single-speaker narration uncovered. We present BanglaKontho, a single-speaker Bangla TTS corpus of 20 hours derived from professional audiobook recordings: 7,050 segmented utterances with verified transcripts at 24 kHz. We also release a reusable Bangla text normalizer covering Bangladeshi-style digit grouping, currency and date expressions, Danda punctuation and Unicode normalization, together with the full preprocessing pipeline. An MB-iSTFT-VITS baseline trained from scratch reaches 9.5% WER and 4.46 naturalness MOS, against 16.0% and 3.16 for the same architecture retrained on the 12-hour IndicTTS-Bn corpus. The corpus is released openly under CC BY-NC 4.0.

A generative search answer can cite a supported passage yet omit a source relationship that changes its interpretation. We specify a claim-gated audit of the query-source-answer tuple. An omission is resolved only when relationship evidence, answer adoption, materiality, and disclosure are all observed; incomplete evidence remains unresolved rather than being treated as independence. The specification separates this endpoint from citation support and review priority, and binds decisions to versioned evidence spans. A reference checker makes the record contract executable. On an exhaustive synthetic suite, it reproduces all 81 three-state predicate combinations and rejects 192 deliberately malformed records. Common-guard baselines and predicate ablations isolate endpoint logic from missing-evidence handling, while controlled transitions check support separation and evidence removal. These are finite contract-conformance results, not detector accuracy or evidence of improved user outcomes. We define the independent annotation, held-out evaluation, and paired utility tests still required to establish semantic validity and deployment benefit.

Persistent memory lets language-model agents improve prompts and skills without updating model weights. We show that matching retrieval scope to certification scope enables these edits to support reliable repeated adaptation across recurring task families. We study frozen-model agents on ProcStream-RSI, a 12-round code-repair stream, using Orthogonal Regression Control (ORC), an execution-grounded gate for persistent skill edits. In an intervention that holds proposals and gate decisions fixed, retrieving each accepted skill only for its originating family raises mean hidden trajectory utility from 0.713 under global memory to 0.816 and changes harmful deployments from six of eight to none. In 27 paired randomized-order streams, Scoped-ORC improves mean trajectory utility by 0.063 [0.037, 0.094] over Global-ORC, accepts 63 rather than 12 updates, and produces multiple accepted updates in 19/27 streams, with 0/63 harmful acceptances. The global control reaches 0.713, below the static agent's 0.775, because locally valid edits can interfere with unrelated families. These results establish scope matching as a complementary control for persistent agent memory: certification determines whether an edit is supported, while retrieval scope determines where that evidence authorizes its use.

AI-moderated interviews are emerging as a scalable market-research method for generating consumer insights and building consumer "digital twins." Yet it remains unclear whether they match human-moderated interviews and whether they improve on simpler, static data collection methods. In a pre-registered study with three industry partners, the authors randomly assign participants to AI-moderated interviews (N = 139), static interviews (N = 154), or interviews conducted by professional human moderators (N = 24). AI moderation matches human moderation in depth, covers more themes, and, at equal budget, recovers more customer needs than either alternative, although participants sound more emotionally engaged with a human interviewer. The authors then build a digital twin of each participant and evaluate it against the participant's own held-out responses to six real-world marketing stimuli. Twins built from AI-moderated interviews predict consumer responses better than demographics-only personas, but no better than twins built from static interviews: the richer conversation does not necessarily yield more accurate predictions. Comparing the open-ended explanations provided by participants and their twins shows that prediction errors arise when twins reason differently than the people they represent and when questions fall far outside what the interview covered. AI moderation thus pays off most for discovering customer needs, and less for predicting customer responses.

Direct On-Policy Distillation (Direct-OPD) transfers reinforcement-learning-induced policy improvements from a small model to a larger student by using the token-level log-ratio between post-RL and pre-RL checkpoints as dense supervision on the student's own rollouts. This transfer rewards the policy shift at every state, yet the log-ratio measures only relative change: it can stay fixed even as the probability mass that both checkpoints assign to the student's candidate tokens vanishes. Through an exact construction, we show that the Direct-OPD reward and its update can remain unchanged while the Jensen-Shannon divergence (JSD) and both KL directions between the checkpoints vanish with this mass, and we note that a small JSD bounds how much the teacher's behavior changed. Motivated by this analysis, we propose Selective Supervision for Direct-OPD (S$^2$D-OPD), which ranks student-sampled states by their teacher-reference JSD and masks Direct-OPD supervision at low-divergence states, retaining only the top 10% of states per response. Across two teacher pairs and four student models ranging from 1.7B to 8B parameters, S$^2$D-OPD improves held-out accuracy over dense Direct-OPD on AIME and HMMT benchmarks in seven of eight settings and matches it in the eighth, without extra forward passes.

We give a deterministic polynomial kernel for Odd Cycle Transversal, derandomizing the randomized kernel of Kratsch and Wahlström (TALG 2014). Our algorithm uses a deterministic polynomial-time construction of almost multilinear representations of gammoids. Such a representation assigns a block of columns to each element so that, for every subset of elements, the normalized matrix rank approximates its matroid rank to within a prescribed additive error $\delta$. The construction builds on recent breakthroughs in NC algorithms for matching. Our kernelization algorithm then computes the required representative families from these representations.

Repeated evaluation can estimate a benchmark score accurately while still requiring replication to certify narrow uncertainty. We characterize that requirement on a fixed grid of $M$ tasks with $L$ binary paths per task under the hard budget $(M+t)K$, where each path costs at most $K$ responses or episodes. For fixed $L \ge 3$ and $0 < \alpha \le 1/12$, the optimal expected width on the worst pure cohort is $\Theta_{\alpha,L}([M(t+1)]^{-1/2})$ when every task is observed and $\Theta_{\alpha,L}([M(t+\sqrt{M})]^{-1/2})$ when omission is allowed. The lower bounds cover adaptive hard-budget policies, and fixed random-subset designs attain both rates through disagreement certificates. A joint mean/disagreement interval turns the task-covering law into practical finite-budget inference. In an equal-budget LiveCodeBench replay with 16 models, 880 tasks, and five outputs per task, the task-covering design reduces median point-estimation MSE by 87.0% relative to pooled uniform sampling, while the Joint certificate produces narrower confidence intervals in 15/16 panels and reduces median interval width by 30.6%. Finite-regime analyses identify task coverage as the effective choice at the evaluated scale and characterize how cohort size and within-task agreement determine the useful operating region. Together, the sharp laws and fixed-budget evidence make replication and task coverage explicit design variables for information-efficient repeated evaluation.

Type IIP supernovae (SNe IIP) are the most common subclass of core-collapse SNe in observations. However, SNe IIP with short plateaus of the order of tens of days are rarely observed. The progenitors for this kind of SN can help to address the red supergiant issue in stellar evolution. In this article, we report optical photometry and spectroscopy of SN\,2025aedz, a rapidly post-peak declining SN IIP with a typical short plateau. It exhibits a peak absolute magnitude of $M_r=-17.16\pm0.03$\,mag. The $r$-band light curve shows a steep early post-peak decline of $\sim5\,\mathrm{mag}\,(100\,\mathrm{d})^{-1}$ followed by a relatively short plateau, with a plateau duration of $\sim50\pm3$\,d. The overall spectral evolution is consistent with that of normal SNe~IIP, showing a blue continuum with prominent Balmer P-Cygni profiles during the photospheric phase, followed by the gradual strengthening of hydrogen and metal lines as the ejecta cools down, although the metal lines remain weak and the expansion velocities decline rapidly. SN\,2025aedz is similar to the short-plateau SN\,2018gj in its overall evolution, whereas its pronounced early decline resembles that of SN\,2023ufx, which has the shortest plateau duration known so far. The radioactive tail of the bolometric light curve implies a synthesized $^{56}$Ni mass of $\sim0.03\pm0.01\,M_\odot$. Motivated by the steep early decline, we performed radiation hydrodynamic simulations by exploring different circumstellar material configurations to reproduce its early bolometric light curve. These simulations indicate that SN\,2025aedz originated from a progenitor with a relatively low-mass hydrogen envelope, possibly produced through enhanced mass loss or binary interaction, while the steep early decline is likely explained by additional luminosity from circumstellar interaction.

Frozen self-supervised (SSL) speech encoders are strong, low-cost front ends for audio deepfake detection, and recent comparisons agree that large, multilingual, discriminative encoders generalize best out of domain. These comparisons fail to control for encoder capacity, pretraining objective, and multilingual coverage together, identifying which encoder wins without isolating why. We present a controlled decomposition with a fixed pipeline and trainable capacity. We vary multilingual coverage on four wav2vec2-family encoders, matched to ~315M parameters. We isolate the pretraining objective on two encoders matched on identical data. Coverage does not help monotonically, as out-of-domain error drops sharply at the ~100-language scale (XLS-R) but does not improve further at the 1406-language extreme (MMS). We find that a mid-coverage encoder is strongest on farther out-of-domain sets, matching or surpassing a 577M-parameter model at 315M. Its lead on these far sets, statistically significant under paired bootstrap, and on the official ASVspoof 5 cost metric holds under two backends. Separately, masked-prediction pretraining generalizes better than contrastive on identical data (In-the-Wild EER 26.5% vs. 46.8%). Within this fixed frozen-encoder recipe, we find that broader and larger models are not reliably better.

We study the roles of broken spectra and exceptional points in finite-time driven non-Hermitian fermionic dynamics. We compute the Nambu biorthogonal correlation matrix for this purpose. The imbalanced-pairing Kitaev chain serves as our concrete realization. Transient passage through a broken-spectrum region amplifies preparation memory. The effect survives when the final Hamiltonian returns to a real-spectrum regime. Negative imbalance forces spectral nonpositivity in the static endpoint state. We isolate the genuine drive history by subtracting out this baseline, leaving an excess that is strictly controlled by the accumulated imaginary-energy action and persists over the entire post-ramp time window. A connected longitudinal correlation mirrors this physics. Its slow-ramp growth tracks the corresponding doubled action. Unstable sectors instead continue amplifying post-ramp if the drive halts inside the broken-spectrum region. Exceptional points yield distinct physics. The finite-time propagator and subsystem correlation matrix remain entirely regular near an exceptional endpoint, even as the quasiparticle gap exhibits its characteristic square-root closing. This finite-time regularity reflects the analyticity of the matrix evolution in the endpoint parameter; a diagonalizable endpoint is strictly not required. A diverging long-time crossover eventually reveals the exceptional scale. We halt the drive exactly at the exceptional point to find that the correlation projector and the connected longitudinal correlation share an identical ballisti front. The subsystem saturation length establishes a distinct but comparable spatial scale. Memory and exceptional-endpoint scalings show no divergence across the tested negative-imbalance range. Memory scaling is fixed by the drive and remains insensitive to the specific choice of real-spectrum final endpoint.

The centers of galaxies harbor the densest stellar environments, where a massive black hole (MBH) accelerates stars to such high velocities that direct collisions can result in high-energetic phenomena, such as gravitational wave sources, kilonovae, and supernova-like transients. These collisions can reshape the cluster's density profile and release gas that can be subsequently accreted by the MBH. However, the evolving rates of such phenomena from self-consistent dynamics around mass-growing MBHs remain largely unexplored. In this work, we simulate nuclear star clusters (NSCs) across a range of masses and density profiles by employing the GNC Monte Carlo code, that self-consistently models stellar dynamics and the subsequent accretion of released gas. We find that stellar collisions flatten the density cusp in the innermost regions ($r \lesssim 10^{-3}-10^{-2}$ pc) within $\sim 0.1-1$ Gyr. While high initial collision rates in steep cusps quickly decline due to stellar depletion, the interplay between collisions and MBH growth is important only in massive NSCs ($M_\star \sim 10^9 M_\odot$). As MBH grows, increased stellar velocities shift the balance toward destructive collisions of which relative velocities can be $\gtrsim 2500 {\rm \,km\,s^{-1}}$. Consequently, present-day destructive collision rates in massive clusters remain high ($10^{-4}\sim 10^{-3}{\rm yr}^{-1}$), whereas they are smaller in Milky Way-like NSCs or negligible in smaller NSCs. Our results highlight a crucial synergy between stellar dynamics and MBH growth, identifying massive galaxies as prime targets for observing transients from destructive stellar collisions.

Chiral anomalies in baryon and lepton number currents in the GUT-inspired $SO(5) \times U(1) \times SU(3)$ gauge-Higgs unification model in the Randall-Sundrum (RS) warped space are examined. Total anomalies including contributions of all Kaluza-Klein (KK) excited modes of fermions running along internal triangular loops are expressed in terms of the values of wave functions of gauge-boson KK towers at the ultraviolet (UV) and infrared (IR) branes in the RS space. The covariant divergence of 5D baryon number current picks up an anomaly term proportional to ${\rm Tr} \,F_{\mu\nu} \tilde F^{\mu\nu} |_{SU(2)_L} - {\rm Tr} \, F_{\mu\nu} \tilde F^{\mu\nu} |_{SU(2)_R}$ at the UV and IR branes where $SU(2)_L \times SU(2)_R$ is a subgroup of $SO(5)$.

This paper investigates the following May–Nowak type model for viral infection in a bounded domain $\Omega \subset \mathbb{R}^n$, $n \ge 2$: $\begin{cases} u_t = \Delta u - \chi \nabla \cdot (u \nabla v) + \kappa - u - uw - \mu \dfrac{u^{1+\alpha}}{\ln^k(u+e)}, \\[1mm] \gamma v_t = \Delta v - v + uw, \\[1mm] w_t = \Delta w - w + v, \end{cases}$ where $\chi \in \mathbb{R}$, $\mu > 0$, $k \in [0,1)$, $\alpha > 0$, and $\gamma \in \{0,1\}$. We establish the global existence and uniform-in-time boundedness of classical solutions for suitably regular initial data under one of the following conditions: (A) $\gamma = 1$, $n = 2$, $k \in [0,1)$, $\alpha = 1$, and $\mu > 0$; (B) $\gamma = 1$, $3 \le n \le 5$, $k = 0$, $\alpha = 1$, and $\mu $ is sufficiently large; (C) $\gamma = 1$, $n \ge 6$, $k = 0$, $\alpha > \frac{n-2}{4}$, and $\mu > 0$; (D) $\gamma = 0$, $n \ge 2$, $k = 0$, $\alpha > \frac{n+2}{2}$, and $\mu>0$. In particular, in the physically relevant dimensions $n = 2,3$, both subquadratic and quadratic damping are sufficient to prevent blow-up. Moreover, in the fully parabolic case ($\gamma = 1$), our results improve upon recent findings by relaxing the condition $\alpha > \frac{n}{2}$ to weaker assumptions within the above parameter regimes.

At a fixed threshold, relative utility (RU) measures the net-benefit gain of a prediction model over the better of treat-all and treat-none relative to the corresponding gain under perfect outcome classification. We illustrate that RU equal to 1 therefore represents perfect outcome classification at that fixed threshold, not perfect probabilistic prediction. However, even when every predicted probability equals the true probability, observed RU can equal 0. In a simple constant-risk setting, this occurs with probability approaching 1 as the sample size increases. Consequently, the distance from observed RU to 1 should not in general be interpreted as improvement achievable by a better prediction for binary probabilities.

Jellyfish-inspired robots offer a compliant and efficient approach to underwater locomotion, but achieving large deformation together with repeatable actuation and closed-loop control remains challenging. In this work, we present a tendon-driven robotic jellyfish with constrained soft actuation. Each actuator combines a flexible substrate with discrete constraints, enabling bending up to \(150^\circ\) with an approximately linear tendon displacement-bending relationship. Eight actuators driven by four servos allow the robot to perform stable swimming, attitude adjustment, and self-righting. Based on the linear actuation, a reinforcement-learning controller is further developed, enabling closed-loop depth regulation in both simulation and physical experiments. These results show that mechanical constraints can improve the controllability of soft actuation while preserving compliant jellyfish-like motion, providing a route toward manoeuvrable and autonomous jellyfish robots.

Internet texts are replete with format tags that carry structural, semantic, and functional meaning. Current large language model (LLM)-based translation systems struggle to balance translation fluency with tag fidelity when processing tagged text. We argue that resolving this tension requires a systematic approach at three interconnected levels: data synthesis, capability building, and multi-objective alignment. At the data level, we identify and formalize a fundamental trade-off between structural tag diversity and translation naturalness in synthetic data generation; existing methods optimize for one at the expense of the other. We propose a hybrid synthesis strategy (Hy-LST) combining LLM-based synthesis tag method and Two-Stage LLM-based synthesis tag method to produce both diverse and natural tagged data. At the capability level, we decompose tag-aware translation into four sub-tasks of increasing difficulty in a multi-task supervised fine-tuning framework, enabling targeted capability acquisition and knowledge transfer. At the alignment level, we design three complementary reward functions under a group relative policy optimization framework, each targeting a distinct objective (fluency, tag fidelity, and tag-scoped translation quality), and show that joint optimization consistently outperforms single-reward alternatives. Experiments on six language directions (en2zh, en2ja, en2de, en2fr, en2ru, de2fr) demonstrate that each level contributes measurable improvements, and the complete system significantly outperforms existing methods. Qualitative analysis reveals specific error patterns and their mitigation after training with our method.

Short claims such as not-phishing or official can change how a large language model (LLM) judges a domain name, without explicit prompt-injection commands. We study this manipulation as ClaimMirage: a name under inspection claims its own safety or approval. We analyze 622,080 judgments across 64 brands and five LLMs, comparing ten claims with length- and hyphen-matched controls in constructed brand-like names. Self-claims can substantially reduce or increase alerts, depending on the LLM and input setting. In one setting, risk-denial terms inside the registrable name reduce alerts by 45.3 percentage points even with a basic safeguard: the prompt supplies the potentially impersonated brand and its official domain for comparison. Without these references, endorsement terms at that position increase alerts by 65.6 points in the same LLM. References and component annotation remove some alert reductions but leave others or make them larger. These findings motivate testing resistance to self-claims and seeking independent evidence before treating a domain name under inspection as safe or authorized.

Programming tutorial videos on YouTube are an important information resource for software developers and students, and their comment sections have evolved into active spaces where viewers ask follow-up questions. The volume of these questions, however, often exceeds what content creators can address, leaving learners without the clarifications they need. We present VidTutorAssistant, a web platform that automates responses to viewer questions on programming video tutorials. VidTutorAssistant implements a retrieval-augmented generation pipeline that extracts a video's transcript, then segments it and embeds it. It then classifies each viewer comment as being a question or non-question, retrieves the most relevant transcript segments to each identified question via cosine similarity, and then generates an answer to the question using an LLM (GPT-4), while grounding the response using the retrieved transcript segments as context. We validate VidTutorAssistant through a study on a subset of 440 user comments selected from a larger dataset of 105,553 comments extracted from 7,522 Python and Java tutorials. VidTutorAssistant is evaluated on various criteria: a) its ability to identify the programming language in a video, achieving a 0.99 accuracy; b) its ability to classify comments into questions and non-questions, reaching a 0.96 accuracy; and c) its ability to produce correct and complete answers to questions, producing 98% correct and 99.5% complete responses, compared with 89% and 90% for the original creators' answers.

We propose a bio-inspired approach that uses the inner-hair-cell (IHC) response of the Cascade of Asymmetric Resonators with Fast-Acting Compression (CARFAC) model to efficiently extract cyclic modulation from acoustic signals. We further investigate the contribution of IHC processing by comparing the CARFAC-IHC response with the CARFAC basilar-membrane (BM) filtering. Furthermore, the CARFAC-IHC and CARFAC-BM approach are benchmarked against conventional FFT Accumulation Method (FAM), Integrated Cyclic Modulation Coherence (ICMC), and Detection of Envelope Modulation On Noise (DEMON) approaches using the Case Western Reserve University (CWRU) bearing dataset and a real ShipsEar work-vessel recording dataset. The results demonstrate reliable recovery of characteristic cyclic components while substantially reducing the computational burden of conventional cyclostationary analysis.

In this paper, we conduct a systematic study of quandle colorings and quandle coloring quivers for pretzel links using the dihedral quandle $\mathbb{Z}_{n}$. First, we systematically investigate all possible colorings of 3-pretzel links, determining the number of distinct colorings in each case as well as the structure of their quandle coloring quivers. In order to obtain more general conclusions, we impose restrictions on $n$ based on the properties of the coefficient matrix of the system of congruence equations. So we examine the number of quandle colorings and the quandle coloring quivers for 4-pretzel links in the case where $n$ is prime. Finally, Combining the results of 4-pretzel links we rigorously derive both the coloring numbers and quandle coloring quivers for general $m$-pretzel links in the case where $n$ is prime, with full proofs provided.

Autonomous security-testing agents can spend much of a fixed action budget repeating earlier tool selections. We evaluate a reward-free scheduler inspired by mushroom-body novelty processing in Drosophila. It combines sparse state encoding with decaying habituation counters over structural URL classes and tool families. The counters penalize repeated clean or error outcomes without updating weights from scalar reward. Four matched campaigns motivated this design by exposing reward-accounting errors and tool-failure loops; reward-driven components did not improve the tested primary outcomes over the reward-free MB condition. A pre-registered pilot and two confirmatory stages then evaluated repeated (tool, URL) selections. In the second confirmatory stage, 8 of 10 screened lab targets remained measurable after two error-heavy slow-XSS exclusions. The habituation-enabled scheduler lowered duplicate-action ratios in all 6 non-tied target pairs (exact one-sided p=0.015625), with two ties; the largest reduction was 51 to 18 duplicate steps within a 60-step budget. This is evidence for the complete scheduler on the measurable budget-hold population, not an isolated habituation ablation or a vulnerability-discovery gain. A complementary study on a 13,498-neuron MaleCNS-derived circuit (501,267 synaptic edges with weight at least 5) found no action selectivity from the five tested local-plasticity approaches under a fixed readout; readout plasticity produced qualified positive results in synthetic tasks without establishing a biological-topology advantage. We report the population bounds, remaining input-integrity dependencies, and an internal AI-assisted review protocol alongside the results.