Papers

3D digital assets are increasingly used in education, simulation, design, and immersive content creation, yet most remain behaviorally inert: they provide geometry and component structure but lack the semantic annotations, motion constraints, and executable behaviors needed to function as dynamic objects in Extended Reality (XR). Animating such assets therefore still requires manual rigging, object-specific templates, or substantial programming expertise. We introduce MotionAnimator, an intent-driven, part-aware XR animation authoring system that transforms semantically unlabeled, part-structured 3D assets into executable animations from natural-language instructions. Rather than generating code directly from text, MotionAnimator externalizes object understanding and motion reasoning into explicit semantic and motion representations. It grounds object identity, semantic parts, and functional directions, constructs a structured plan that coordinates object- and part-level motion, and translates the plan into executable Unity behavior. On a benchmark of 90 prompts across 30 objects, MotionAnimator demonstrated reliable semantic grounding and coordinated animation generation across diverse objects and animation intents. An exploratory user study further provided insights into users' experiences with MotionAnimator and highlighted its potential for part-aware XR animation authoring. These findings demonstrate how explicit semantic and motion representations can bridge high-level user intent and executable behavior, enabling existing part-structured assets to support coordinated XR animations beyond object-level transformations and predefined behaviors.

Physical flexibility plays a significant role not only in human motions but also in robot motions. For example, a humanoid robot with passive and flexible elements, which can be regarded as a rigid–soft hybrid-link system, has the advantages of storing energy and mitigating impact in a dynamic motion. However, the motion design and control of a hybrid-link system are challenging to achieve and have only been discussed in the literature. In this study, we propose the framework of inverse kinematics and compliance optimization-based control for a hybrid-link humanoid system that represents the continuous deformation of a flexible structure using the piece-wise constant strain (PCS) model. The proposed method was validated using forward dynamics simulations for standing, jumping, and walking motions. Then, we built an experimental setup using a biped humanoid robot with leaf-spring type prosthesis leg, in which the prosthesis deformation was measured by a motion capture system. Using this setup, we experimentally validated the proposed method for standing balance control in both double- and single-support cases.

In integrated sensing and communication (ISAC) systems, strict sensing requirements can substantially constrain the transmit power available for communication. A hybrid reconfigurable intelligent surface (HRIS) with passive reflection and active amplification capabilities mounted on an unmanned aerial vehicle (UAV) can enhance coverage and strengthen communication links in such power-limited regimes. Meanwhile, rate-splitting multiple access (RSMA) provides an effective transmission strategy for managing inter-user interference, particularly in dense multiuser wireless scenarios. Motivated by this, we analyze the performance of a UAV-mounted HRIS-assisted monostatic ISAC system employing RSMA scheme. We consider the imperfections in the channel state information and successive interference cancellation in the RSMA, which are inevitable in practical system implementations. We then derive highly accurate expressions for outage probability, ergodic rate, and throughput to evaluate communication performance over Nakagami-$m$ fading channels. These expressions reveal key insights into the diversity order and coding gain of the system in the high signal-to-noise ratio regime. To characterize the sensing performance, we derive expressions for the probability of detection, the probability of false alarm, and the Cramér-Rao lower bound. Numerical results validate the theoretical findings and highlight the performance gains of the proposed system over conventional multiple-access schemes and RIS-based systems.

Dwarf galaxies exhibit a large diversity in rotation curve shapes, challenging galaxy formation models within the $\Lambda$CDM paradigm. We present NIVARIA-LG, a new suite of cosmological simulations studying dwarf galaxy evolution in realistic Local Group environments. This intermediate-resolution pilot lays the groundwork for the full-scale NIVARIA project. The simulations combine constrained Local Group initial conditions from HESTIA with the NIHAO galaxy formation model. The simulated galaxies reproduce observed stellar-to-halo mass relations, match the Baryonic Tully-Fisher relation, and capture the distribution of stellar effective radii, including compact and diffuse galaxies. We analyse the structural and kinematic properties of isolated dwarf galaxies with $10^7 \lesssim M_\star/M_\odot \lesssim 10^{10}$, focusing on rotation curve diversity. NIVARIA-LG naturally produces a broad range of rotation curve shapes, including slowly rising systems underrepresented in previous simulations and steep rotation curves. We find that rotation curve diversity is primarily associated with gas extent and inner dark matter structure: more extended gas and shallower inner density profiles correspond to more slowly rising curves, while stellar effective radius shows little independent association. Individual galaxies show that rotation curve shapes change rapidly as gas is redistributed during assembly. Recent accretion events are also associated with more slowly rising curves in the most massive dwarfs. Together, these results suggest that rotation curve diversity is linked to the baryonic cycle, which shapes the inner dark matter distribution. The Local Group environment and its filaments influence this evolution by regulating gas accretion and redistribution, producing the observed diversity in rotation curve shapes.

This paper proposes a channel-knowledge-map (CKM)-based predictive beamforming framework for integrated sensing, communication, and powering (ISCAP) of a mobile energy-constrained node in non-line-of-sight (NLoS) multipath environments. The CKM provides location-dependent channel information for both predictive beamforming and EKF-based tracking, while resolved path parameters estimated from the sensing echoes are used as observations. Based on the predicted node location, the transmit covariance and power-splitting ratio are jointly optimized to maximize wireless power-transfer efficiency subject to communication, sensing, transmit-power, and tracking-quality constraints. A finite-battery model and an adaptive inter-frame energy-management policy are further introduced to balance decoding energy consumption and battery preservation. The resulting non-convex fractional problem is solved using Dinkelbach's method, alternating optimization, and semidefinite relaxation. Numerical results show that the proposed framework maintains reliable tracking, satisfies the prescribed position-uncertainty requirement, achieves near-oracle wireless power-transfer performance after the initial tracking transient, and preserves more battery energy while meeting the required communication quality of service.

Let $K>1$ be a real number and let $A\subsetneq \mathbb Z$ be a finite and nonempty subset. Suppose $|A+A|<K|A|$. A fundamental open problem is to characterize the size of higher iterated sumsets $nA = A+\cdots+A$ ($n$-fold sumset). In 2004, Terry Tao formally posed the problem of determining the optimal growth function governing iterated sumsets of small-doubling sets. In this manuscript, we give a solution to this long-standing open problem for large enough $n$.

Beeping Networks (BN) have become an established model of wireless communication and computation. They assume, however, that the communication interference caused by beeping nodes is binary (OR channel), while both artificial and nature-driven networks are based on varied signal strength and receiving thresholds. This work naturally extends the classic beeping networks to weighted beeping networks (WBN), by modeling signal strengths by weights on graph edges and receiving a beep if the accumulative signal strengths of transmitting neighbors are above receiving threshold. Under this generalized model, we study the fundamental Local Broadcast (LB) problem. Since edges with low weights may not even accumulate to a received beep, we only require that messages are delivered along sufficiently heavy edges, with weights above some given threshold $\sigma$. We design an LB algorithm that completes its task in $O(I_\sigma \log n \cdot (\mathcal{M}+\log n))$ beeping rounds, whp, where $n$ is the number of nodes, $I_\sigma$ is the maximum local interference on heavy edges, and $\mathcal{M}$ is the maximum length of messages sent locally. This result is nearly optimal, as, with probability $1$, $\Omega(I_\sigma)$ beeping rounds are necessary to solve LB. Finally, we show that any algorithm designed for the classic beeping networks and terminating in polynomial number of beeping rounds, can be emulated on any WBN with a logarithmic overhead, that is, it returns the same output as working on the classic beeping network isomorphic to the sub-graph of heavy edges.

We give a negative answer to the second question of Erdős Problem #1117: can the number $\nu_f(r)$ of maximum-modulus points of a nonzero, non-monomial entire function on $|z|=r$ tend to infinity as $r\to\infty$? Write $f(z)=z^m g(z)$ with $g(0)\ne0$, and let $k$ be the first positive exponent with a nonzero coefficient in the Taylor expansion of $g$. We prove that $\{r>0:\nu_f(r)>2k\}$ is locally finite in $(0,\infty)$, and that the constant $2k$ is sharp. In particular, $\liminf_{r\to\infty}\nu_f(r)\le2k<\infty$, without a growth assumption. The proof combines finite local parametrizations of a logarithmic-derivative correspondence with analytic continuation and a local description of stationary points.

Fix $0<\kappa<8$ and put $d=1+\kappa/8$. Recent work by OpenAI identifies an explicit exact Hausdorff gauge \( h_\kappa(r)=r^d\bigl(\log\log(1/r)\bigr)^{(2-d)/2} \) for sufficiently small $r$ for chordal $\mathrm{SLE}_\kappa$: the corresponding Hausdorff measure is almost surely positive and finite on every segment $\gamma([s,t])$ with $0<s<t<\infty$, and has finite expectation in bounded subsets of the plane. We show that this Hausdorff measure is a deterministic positive constant multiple of the occupation measure (natural length) constructed by Lawler and Rezaei.

Historically, phase I oncology trials were designed with the focus to find the highest tolerable dose. However, given the FDA's acknowledgment that the highest tolerable dose might not be the dose which is optimal biologically, there is an increased emphasis the development of designs that explore the dose-toxicity and dose-efficacy relationship. Backfill designs have emerged as a popular response to address this need by allocating participants to doses deemed safe while awaiting participants outcomes. Previous designs have explored how to assign participants to doses in backfill designs in a rigorous manner while providing simplicity and performance (a class of designs known as model-assisted) for single agents. Still, a research gap exists in the lack of model-assisted backfill designs for drug combinations. Frequently, the combinations two of cancer agents are explored in phase I trials, with the goal of identifying the highest tolerable combination. This paper incorporates and extends methodology based on previous model-assisted backfill designs to provide clinicians with a simple-to-use backfill design for phase I drug combination trials.

The world has seen several threats that include resource depletion, food security, poverty and inequality, difficulties associated with urbanization, migration, and environmental effects. The World Risk Index (WRI) is a metric that is used to measure the susceptibility of nations against natural disasters and related risks that is reported by the Humanitarian Data Exchange. The WRI is comprised of factors such as susceptibility, vulnerability to natural hazards, and coping mechanisms. The WRI index has allowed to recognize regions in advance in order to face threats and situations beforehand. This study was conducted by analyzing the data that was related to years from 2000 to 2025 using data visualization techniques. Python related libraries of Matplotlib, Seaborn, and Geopandas were used due to their efficiency and usability in analyzing WRI data. As per the analysis, it was identified that countries of Philippines, Mexico, Indonesia, and India were recorded with high WRI index values that showed these nations should be prepared for natural disasters and situations. Hence, this study has provided insights using data visualization techniques in understanding natural disasters and threats so that necessary measures can be taken

Randomized experiments are often linked to administrative data to measure outcomes, but coarse identifiers can leave multiple administrative records consistent with each experimental unit. We show that unbiased estimation of the sample average treatment effect is possible without resolving these ambiguous links or specifying an outcome model. Our key linkage requirement is that the true administrative outcome is contained among the candidate outcomes for each experimental unit. We characterize the precision cost of linkage ambiguity and study two complementary ways to mitigate it: regression adjustment and reweighting based on observed linkage characteristics. We establish finite-sample and asymptotic properties of these estimators and develop valid randomization-based and large-sample inference.

Supporting edge Artificial Intelligence (AI) inference as a network service is challenging because current mobile systems can transport tensors but do not expose or understand the inference context that gives those tensors operational meaning. Prior studies have addressed this gap through dynamic partitioning, collaborative inference, and split pipelines; however, these solutions remain application-bound, network-blind, or context-free. This work proposes Inference on Demand (IoD), an inference-on-demand abstraction that exposes split inference through a CAMARA-like Application Program Interface (API) and carries a split-aware tensor context in-band across the 5G user plane path. We evaluate the IoD on a programmable user plane function (UPF)-based testbed using a partitionable visual AI workload, showing that adaptive split selection can operate as a network-facing service while avoiding the rigid cost profile of static configurations. Including our findings, split inference becomes more than offloading when the service intent, runtime partitioning, and tensor transport are made visible to the mobile data plane. This opens a path toward network-native AI services, in which programmable telco infrastructure coordinates computation, context, and connectivity for user-facing applications.

Accurate and efficient analysis of dental radiographs has become increasingly important for disease diagnosis and clinical decision making. In particular, dental radiographs segmentation plays a critical role as it is challenging due to several reasons, such as low contrast, noise in the images, variations in the image quality, etc. Previous studies have primarily addressed these challenges using convolutional neural networks (CNN)-based models. However, direct comparison of these segmentation models is still challenging due to the variations among the experimental settings. Therefore, we mainly compared four segmentation models, including Pyramid Scene Parsing Network (PSPNet), DeepLabV3, UNet, and UNet++, through a fair, controlled experimentation setting under varying conditions such as image sizes and batch sizes. For this, we used 1269 dental radiography images, and prior to training, we implemented a series of preprocessing techniques. To assess the models, we used several metrics, including Dice coefficient (DICE), Intersection over Union (IoU), accuracy, precision, training and validation losses. According to our results, UNet++ demonstrated the highest IoU score of 0.6719, and a DICE value of 0.7869, showing superior results in terms of segmentation, specifically when configured with an image size of 300x300 and a batch size of 16. In addition, we also explored the effect of image resolutions and batch sizes on model performance and accuracy under different architectures. Therefore, this study provides insights into the strengths of different segmentation models and the potential of deep learning-based semantic segmentation methods for improving automated dental radiograph analysis.

An eV-scale sterile Majorana neutrino can suppress neutrinoless double-beta decay through destructive interference with the active-neutrino contribution, weakening the resulting constraints on sterile-neutrino parameters. We investigate how complementary beta-decay information restricts this cancellation in the 3+1 framework. Using updated oscillation parameters that include the first JUNO results, we determine the allowed sterile-neutrino mass and mixing regions for both normal and inverted ordering. We show that an upper limit on the effective beta-decay mass $m_\beta$ of the three light neutrinos strengthens the constraints from neutrinoless double-beta decay alone. The beta-decay bound restricts the light-neutrino masses and hence the cancellation between the active and sterile contributions to $m_{\beta\beta}$. We derive analytic expressions for the resulting boundaries and use complex-plane geometry to explain the allowed values of the sterile Majorana phase $\alpha_4$ for a finite $|m_{\beta\beta}|$ limit. For the mixing considered, normal ordering allows a broad range of $\alpha_4$ at small sterile masses, whereas inverted ordering favors values near $\pi$. The allowed phase range narrows as the sterile mass approaches its upper bound or the limit on $|m_{\beta\beta}|$ becomes more stringent.

Current state-of-the-art Speech Emotion Recognition (SER) systems rely on lots of training data, which is available only for a few languages such as English. For low-resource languages, using a cross-lingual model or adapting it to the target language might be an alternative to training a mono-lingual model from scratch. However, it is not clear what constitutes a "low-resource", i.e. where model adaptation loses its edge over the mono-lingual approach. We investigate this topic by training and adapting several SER models on English and Mandarin data, focusing on the emotional attributes of arousal, valence and dominance. Our results show that, for arousal, model adaptation is beneficial even with two hours of data, while for valence 10-20 hours of adaptation material is required to match the performance of a mono-lingual model trained with 100 hours of data. This indicates that task-specific model adaptation may be an effective approach in low-resource speech emotion recognition problems.

Larger sample budgets benefit from higher sampling temperatures in LLMs, but what temperature tuning optimizes and why it works remain poorly understood. We seek to answer these questions: we pose decoding as pass@$k$ maximization subject to two constraints that encode critical decoding failure modes: an entropy floor preventing diversity collapse, and a cross-entropy ceiling preventing implausibility. We prove that this maximization takes the form of a single closed-form conditional sampling rule, the tilted temperature $q^\star \propto \bigl(p e^{\eta V}\bigr)^{1/T}$. Here, the tilt comes from a verifier potential $V$ that quantifies how likely a partial generation is to eventually pass. Ordinary temperature sampling, verifier-greedy decoding, and reward-tilted policies represent special cases. We further show that, under a natural rule for scaling the diversity budget with sample size $k$, the resulting optimal temperature increases with $k$, turning empirical choice into a theorem. The optimum still needs the unknown verifier potential, which we estimate using two design approaches. In the online setting, our J-EOS algorithm jointly tracks the two constraint multipliers and learns the verifier potential from binary pass/ fail feedback alone. In the offline setting, we show that when the model is calibrated, its log-probability tracks correctness up to an affine map. Under this condition, the tilt collapses into the exponent and the optimum reduces to ordinary temperature sampling. Calibrated Temperature Decoding (CTD) then fits one scalar offline and samples with zero additional inference-time overhead relative to temperature sampling. Building on these decision rules, we design a practical decoding algorithm for code generation and evaluate it alongside CTD on benchmarks including HumanEval and MBPP, showing improvements over standard and adaptive decoding baselines.

The polynomial threshold degree (or threshold degree) of a Boolean function is the least degree of a real polynomial whose sign represents it. We prove that almost every Boolean function has polynomial threshold degree among the central one or two integers. More precisely, a uniformly chosen Boolean function on $n$ variables has threshold degree either $\lfloor n/2\rfloor$ or $\lceil n/2\rceil$, except with probability at most $\exp(-c2^{n/2}/n)$, for an absolute constant $c>0$ and all sufficiently large $n$. The paper proves a 1991 conjecture of Aspnes, Beigel, Furst and Rudich. It also proves a 1991 conjecture of Wang and Williams for even $n$ and its main concentration assertion for odd $n$. A parity example gives a lower bound on the exceptional probability whose exponent differs from ours by a factor of order $n$. The proof relates polynomial sign representation to recovery of Reed–Muller codes from random erasures, and combines sharp-threshold estimates with bounds on generalized Hamming weights and minimum distance.

Large language models can post-edit ASR by using linguistic context to compare N-best hypotheses and rewrite the transcript when needed, often improving WER without retraining the recognizer. However, prompt-only correction is brittle: it may over-edit when top-1 is correct and hallucinate when the reference is absent, and often needs very large models. We propose oracle-guided fine-tuning that turns N-best lists into supervision via three curated pools: corrections (reference in the list but not top-1) to teach selection, regularizers (top-1 correct) to discourage unnecessary rewrites, and hard negatives (reference absent) to suppress hallucination. Fine-tuning on this data provides more effective supervision than random subset fine-tuning for learning a hybrid select-or-rewrite policy, with the clearest gains from around 3B parameters on the proprietary dataset but less conclusive results on CommonVoice, a divergence suggesting that public read-speech text may overlap with LLM pretraining and mask genuine post-editing gains.

Self-evolving agents are usually scored by endpoint Gain: held-out success after an update minus success before. That difference can credit a frozen rescore as evolution. We introduce Trace Evolution Bench (TEB), a protocol that separates that rescore from a context or weight update, together with three frozen 80/20/40 packs. An update is accepted only when validation does not fall, held-out identifiers never enter the update, and a text update is not ranked with a weight update. The primary scoreboard is coding, graded by hidden unit tests in a closed workspace. On that pack (40 held-out tasks, one family), DeepSeek v4 Pro under no_evolve never changes its policy yet moves 7.5, 5.0, and 12.5 percentage points across three seeds. Of nine text-update cells inspired by GEPA, ACE, and ExpeL, seven have positive excess above that seed's own band, and one gepa_llm seed moves down by the width of its band (-12.5, regression 0.48). GLM and MiniMax do not reproduce that seven-of-nine pattern. No method stays above its own band on every seed of all three models: GLM has two paired cells above their own bands, and MiniMax expel_llm seed 44 is a third (regression 0.30). The methods were fixed on a validation screen before held-out was read. Office, graded by rule-bounded delivery, and manufacturing table QA are separate packs: office DeepSeek does not exceed its own bands (widest 17.5 points), and manufacturing has no paired positive excess beyond its seed band.

Learning agents, whether humans or algorithms, adapt to one another rather than to a fixed environment. Selfish learning need not produce a good outcome for the group, especially when learners face a social dilemma. The iterated prisoner's dilemma (IPD) is the classical example, but it is usually studied in populations of agents who imitate successful strategies. Here, we instead study selfish gradient ascent learners on the two-dimensional space of reactive strategies. A reactive strategy is described by two continuous traits: reciprocity, the chance of cooperating after the co-player cooperates, and forgiveness, the chance of cooperating after the co-player defects. Each learner updates its strategy in the direction that most rapidly improves its payoff against all other learners, by an amount governed by its learning rate. We show that heterogeneity in learning rates can qualitatively change the long-term outcome: a population with uniform learning rates converges to always-defect (ALLD), whereas a population with variable learning rates approaches generous-tit-for-tat (GTFT), which produces nearly optimal collective payoffs. In simulations, every population passes through a transient state of minimal forgiveness, in which the distribution of reciprocity determines the outcome. Variable learning rates promote cooperation because slow learners preserve high reciprocity until the population reaches this state. We prove sufficient conditions on the distribution of reciprocity for convergence to ALLD or to tit-for-tat (TFT). Variable learning rates also allow cooperation to recover from perturbation, which is provably impossible under uniform learning. These results suggest that purely selfish and myopic learning can produce persistent cooperation provided the population has intrinsic variability in learning rates.

Dark matter environments can modify binary black hole mergers and imprint their gravitational-wave signals. We perform numerical-relativity simulations of nonspinning binary black holes immersed in complex scalar-field clouds, considering mass ratios $q=1,2,3,$ and $4$ and varying both the dimensionless scalar-field mass $\hat m_{\Phi}=m_{\Phi}M_0$ and initial amplitude $\Pi_0$, which controls the density. Our initial data keep the scalar energy-density profile and binary geometry unchanged when varying $\hat m_{\Phi}$ at fixed $\Pi_0$, allowing the dynamical effect of the field mass to be isolated. We find that the scalar environment generally accelerates the merger and significantly modifies the gravitational-wave signal. For unequal-mass binaries, differential scalar-field accretion changes the horizon-mass ratio during inspiral, weakly at low density but substantially at high density, thereby increasing the binary asymmetry before merger. Dense scalar environments suppress the energy and angular momentum carried by gravitational waves. Lighter scalar fields propagate more efficiently to large radii, whereas heavier fields remain more localized and show stronger inward energy transport. Scalar angular-momentum transport is more complex, showing nonmonotonic behavior and even direction reversal near the binary. For unequal-mass systems, gravitational and scalar radiation both carry net linear momentum, and their relative orientation determines whether the recoil is enhanced or suppressed. The largest kick is $2063.6~{\rm km,s^{-1}}$ for $q=2$, $\hat m_{\Phi}=0$, and $\Pi_0=0.0100$, compared with $137.8~{\rm km,s^{-1}}$ in vacuum. These results show that the scalar-field mass and density jointly control the binary asymmetry, dynamics, radiative channels, and momentum balance.

The paper addresses the synthesis of a cost-optimal hardware architecture of the automated process control system (APCS) for continuous processes. The problem is formalized as the search for a minimum-cost rooted tree of devices subject to constraints on the number of I/O channels, the types and number of communication interfaces, the information capacity of processors, the regulation time and the reliability. The signals are grouped by control rooms. The problem is NP-hard, and a hybrid method is proposed that combines a deterministic hierarchy construction with a modified ant colony optimization (ACO) for device-type selection, enhanced by an adaptive heuristic. On ten instances the method is compared with a genetic algorithm (GA), particle swarm optimization (PSO), simulated annealing (SA) and CP-SAT over 30 runs each. By the best found cost the hybrid ACO outperforms GA, PSO and SA on all instances with more than 100 IOs (by 14-38 %) and runs 9-14 times faster. By the median cost, however, the deterministic-greedy baselines are more reliable (GA attains the best Friedman rank) because the cost of the ACO runs is highly variable. All differences are confirmed by the Friedman and Wilcoxon tests. The method targets the early-design search for the cheapest feasible architecture and synthesizes one within minutes at industrial scale (A up to 1086).

In many complex systems, such as river networks and financial markets, extreme events propagate from causes to their effects, and the largest observations carry the most information about the underlying causal structure. Existing methods for causal discovery in extremes, however, are tailored to specific mechanisms, such as linear or max-linear models. This work develops causal discovery for heavy-tailed homogeneous structural causal models, a flexible class that contains linear, max-linear and norm-type mechanisms, which may differ from node to node. In these models, the causal structure is encoded by ancestral impulse responses, which measure how a shock at one node is transmitted to its descendants. We propose the extremal minimum ratio estimator of these responses, which uses only observations in which the potential cause is extreme. The estimator is consistent under regular variation alone, and we derive its exact rates of convergence and limiting distributions, which depend on both the causal relation and the type of mechanism. Building on these rates, we construct consistent estimators of the causal order and of the full set of ancestral relations, using a threshold that adapts to the data and requires no knowledge of the tail index. The method is illustrated on simulated data and on river discharges in the upper Danube basin.

In this paper, we prove two conjectures concerning parametric $q$- supercongruences related to Van Hamme's $\mathrm{(G.2)}$ supercongruence. First, we confirm Tang\rq s conjecture \cite[Conjecture $4.1$]{Tang G2} by establishing the corresponding congruences modulo $[m]\Phi_m(q)^2$. Second, we prove a conjecture of Wang and Xu \cite[Conjecture $2$]{WangXu24}, extending their $q$-supercongruence modulo $\Phi_m(q)^5$ to modulo $[m]\Phi_m(q)^4$ when $m\equiv1\pmod4$.

This study evaluates and compares five convolutional neural network (CNN) architectures, AlexNet, Inception, LeNet, VGG16, and MobileNet, for diagnosing branch dieback (seca-dos-ponteiros) in pequi trees (Caryocar brasiliense). This phytopathology represents a severe threat to tree development and fruit yield, causing substantial economic and ecological losses across the Brazilian Cerrado. The methodology implements computer vision techniques using deep learning frameworks to process and evaluate a field dataset expanded to 6,272 multi-scale images, captured via UAV and handheld sensors under uncontrolled illumination. The models were trained to detect pathological visual patterns across leaves, branches, and canopies. The experimental initial results reveal that architectural complexity did not guarantee diagnostic reliability, heavily parameterized networks experienced optimization failures (VGG16 collapsed into majority-class prediction), whereas compact architectures achieved greater stability. MobileNet delivered the most competitive overall performance, obtaining the highest Precision (0.71) and ROC-AUC (0.63), closely followed by LeNet (AUC = 0.62). These findings indicate the viability of lightweight CNNs as foundational tools for automated phytosanitary surveillance of native flora in resource-constrained field environments.

We investigate finite-amplitude waves in a liquid film containing a soluble surfactant as it flows down an inclined compliant substrate. The coupled motion of the liquid and a spring-backed plate is described by a conservative weighted-residual model, which also accounts for surfactant transport in the bulk and at the free surface. The reduction retains viscous terms arising from wall motion, and its pressure closure recovers fluid added mass under uniform translation. Comparison with the coupled Orr-Sommerfeld problem gives a difference of approximately $1\%$ in the peak growth rate of the film mode at $Re=25$. Nonlinear computations are then used to examine travelling states and their dependence on substrate properties and surfactant coupling. Along the prescribed stiffness-damping path, substrate displacement decreases by more than four orders of magnitude, while wave speed changes by less than $1\%$. The extrema of free-surface elevation and liquid thickness vary differently, so surface height alone does not reliably indicate film thinning over a deformable support. In the cases studied, Marangoni coupling reduces surfactant localisation and weakens the wave and substrate response. Moving-frame reconstruction reveals recirculation near the wave crest and distinguishes propagation of the deformation pattern from transverse substrate motion. The load-work budget identifies capillary pressure as the principal net source of substrate work for the two compliant supports considered. A control calculation in which stiffness is varied at fixed damping shows a substantial change in damping loss but a comparatively small change in deformation.

Variational regularization techniques are dominant in the field of mathematical imaging. The expressiveness of these methods heavily depends on the adopted regularization formulation which usually involves a number of parameters which have to be fine-tuned by the user. To circumvent the heavy computational costs associated with this parameter tuning, data-driven learning strategies have turned out to be a useful strategy. Selecting parameters by learning from data gives rise to a hierarchical (bilevel) optimization problem, which is in general computationally hard to solve. Our aim in this paper is to develop a data-efficient solution strategy for the bilevel learning problem. To that end, we propose a multilevel Monte Carlo derivative-free optimization method that couples Gaussian smoothing of the upper-level objective (parameter selection) with a hierarchy of lower-level (variational regularization) solution accuracies. Being agnostic towards the specific way the lower-level problem is solved, we derive explicit oracle complexity and computational cost statements for approximately solving the entire bilevel learning problem. Our statements are parameterized by the employed lower-level solution method, thus allowing for a direct cost accounting from the variational reconstruction method to the parameter selection problem. This enables us to give a universal end-to-end complexity analysis of bilevel learning, valid for the most important optimization routines in inverse problems, rather than for a specific choice of methods.

Beliefs in a Partially Observable Markov Decision Process (POMDP) are posterior distributions over the hidden state given the agent's history of actions and observations. They summarize everything the history says about the state, so planning in a POMDP is planning in a Markov decision process (MDP) over beliefs. Belief MDPs have continuous state spaces even for finite POMDPs, and exact planning in them is intractable in general. Planners must therefore approximate beliefs and estimate values. Monte Carlo planners do both inside a search tree, with an approximate belief at every node and a value estimate at every leaf. Approximations usually consist of sets of sampled states, with leaf values coming from rollouts, hand-designed bounds, or learned networks. Policies and values computed from these approximations are limited by their quality, and prior methods with learned networks rely on hand-chosen summaries of the sampled states. A belief representation should be computable from the parent node's representation through the POMDP's dynamics, let the search sample from it, and be learned so that it provides the information that policies and value functions need. We present Belief Embedding Tree Search (BETS), a Monte Carlo planner that meets these requirements by representing each node's belief with a generative distribution embedding (GDE) while updating it through the POMDP dynamics. BETS trains its belief model alongside its policy and value networks through experience, with the realized hidden state of the POMDP as the belief model's training target. We evaluate BETS on six configurations of RockSample, LightDark, and PocMan against BetaZero and three planners without learned components. BETS is competitive or leading on all six, while every baseline falls far behind on at least one. Where beliefs are highest-dimensional, it outperforms them by a large margin, even without search.

We study the recovery of a spatial coefficient in the principal memory flux of a three-dimensional wave equation with the prescribed exponential relaxation kernel $\beta e^{-\beta t}$, where $\beta>0$ is known. From a single finite-time lateral Cauchy measurement generated by one fixed, coefficient-independent initial displacement that is affine near the unknown region, with zero initial velocity, we establish global uniqueness and conditional $L^2$-Hölder stability. Two difficulties arise in this setting. The affine initial displacement makes the initial acceleration vanish in the unknown region, while the coefficient-difference equation contains a divergence-form source whose direct $L^2$ estimate loses a spatial derivative. We establish an acoustic Carleman estimate that controls the vector source and its time derivative without spatially differentiating the source. The affine condition identifies the relevant initial trace with a directional derivative of the coefficient difference, and the quadratic temporal vanishing of the source permits absorption in the weighted estimate. A transport estimate then yields stability uniformly over a bounded, uniformly coercive $W^{5,\infty}$ coefficient class, without an ordering condition or a smallness assumption near a reference coefficient.