Papers

We establish a generalized quantum cluster algebra structure, defined by Bai–Chen–Ding–Xu, on the reduced Lê–Roger–Yang skein algebra of every quasi-triangulable punctured surface. We define Frobenius maps for generalized quantum cluster algebras at roots of unity and use these maps, together with the cluster algebra structure, to construct Frobenius maps for the (reduced) Lê–Roger–Yang skein algebras of all punctured surfaces. As applications of the Frobenius map, we determine the centers of both the Muller–Roger–Yang skein algebras and the reduced Lê–Roger–Yang skein algebras at roots of unity, and compute their ranks as modules over their centers.

Adaptive control is usually developed through Lyapunov stability, excitation, and parameter convergence, whereas neighboring fields describe learning using convexity, information geometry, variational principles, and stochastic thermodynamics. This paper develops a constrained common language for these viewpoints. For linearly parameterized models, the excitation Gramian is simultaneously the Hessian of accumulated prediction loss and, under Gaussian observations, Fisher information up to scaling. Persistent, finite, and partial excitation become uniform, finite-horizon, and restricted temporal curvature; memory methods retain previously acquired curvature. On a closed convex parameter set, deterministic adaptation is a projected gradient/Onsager flow, with tangent and normal cones recovering projection, while composite learning supplies data-dependent symmetric dissipation. Reflected Langevin dynamics, no-flux Fokker–Planck evolution, and constrained free-energy flow provide the stochastic counterpart. The framework distinguishes information supplied by data from confinement supplied by regularization or hard constraints and connects familiar adaptive-control structures to modern variational and information-theoretic language.

We report a demonstration of a self-shunted superconducting flux qubit (SSFQ) as an ultracompact, strongly anharmonic, and long-lifetime qubit by using the full epitaxially grown NbN/AlN/NbN Josephson junctions. The NbN-junction-based SSFQ achieved a high anharmonicity of 797 MHz as well as drastically reduced footprint of the qubit compared to capacitively shunted (C-shunt) flux qubits with a large shunt capacitor. The lifetime of the SSFQ reached 13 - 25 $\mu$s, which is comparable to or relatively higher than that of NbN-based C-shunt flux qubits and Al-based flux qubits with more than 10 times smaller junctions. This indicates that the large epitaxial NbN-based junction can be adopted for SSFQ as well as merged-element transmon with the relatively large junctions. The results presented in this work will offer a new choice of the scalable qubits as well as the material platform toward the realization of large-scale superconducting quantum computers.

Epitaxial NbN/AlN/NbN Josephson junctions are promising alternatives to conventional Al/AlO$_x$/Al junctions for superconducting qubits due to their crystalline tunnel barriers and the high transition temperature of NbN. However, their integration into quantum circuits typically requires complex fabrication processes involving amorphous interlayer dielectrics, which can degrade qubit coherence times. To address these issues, we developed sidewall spacer passivated epitaxial NbN/AlN/NbN junctions using a fabrication process that reduces both the volume of amorphous dielectric material and fabrication complexity. The fabricated junctions exhibited a large gap voltage of approximately 5.6 mV and low subgap leakage currents. By varying the thickness of the AlN tunnel barrier, high-quality junctions were fabricated over a wide range of critical current densities ${\it J}_c$, from 0.3 to 10$^4$ A/cm$^2$. In addition, the comparison of the current-voltage characteristics before and after buffered hydrofluoric acid treatment indicated that the wet etching process did not degrade the electrical characteristics of the junctions. These results establish a scalable fabrication process for epitaxial Josephson junctions and provide a promising platform for high-coherence nitride-based superconducting qubits.

Deaf inclusion across sub-Saharan society faces regional hurdles, with Nigeria as the core empirical focus. Existing recognition models demand heavy computational infrastructure. However, standard mobile phones used locally rarely exceed 1 GB to 4 GB of RAM. This study addresses constraints through a lightweight YOLO11n object-detection framework. The system provides real-time Nigerian Sign Language recognition for low-resource hardware. A benchmark dataset containing 11,208 raw gesture images was established. The data spans 33 static classes collected from five signers. Partitioning isolates signers S1 through S3 for training. Signer S4 provides validation data. Signer S5 is reserved for testing. Spatial augmentations are restricted strictly to the training set. This yields 23,509 training images. The validation and test sets each maintain 1,681 images across varied environments. The framework integrates a quantization-aware compression objective. Loss functions merge with squared Frobenius-norm penalties to govern weight distortion. A Spatial-Density Occlusion Index quantifies background complexity and self-occlusion. A latency-profiling equation relates floating-point operations and memory bandwidth to chipset clock speed. Performance testing on physical Android hardware utilizes unquantized FP32 weights. Mean inference latencies span 405.5 ms to 1,759.4 ms. Measured against test data, the algorithm attains a Precision of 0.9975. Recall reaches 0.9991. Mean Average Precision is 0.9942. Outcomes support offline functionality on constrained mobile devices. Practical deployment operates through a mobile utility using CameraX. The application captures gestures in real time. Recognized signs display as text instantly.

Positive cyclic quantum mutations at a third root of unity induce an explicit weight on polygon flip graphs. We study the resulting discrepancy between minimum flip count and minimum accumulated normalization loss. Every pentagon three-to-two replacement strictly decreases weight, and in connected types $A_1$, $A_2$, and $A_3$ every minimum-weight path is a flip geodesic. In type $A_4$, however, a six-flip path has smaller weight than the unique five-flip geodesic. A compatible positive projective gluing construction amplifies this example to an exponential success-probability separation in every connected type $A_n$, $n\ge4$. We also give a quantitative perturbation bound preserving the separation. The low-rank minimality statement has an exhaustive finite certificate; the pentagon inequality and the all-rank construction are analytic. In the associated sequential postselection model, differences of path weights determine success-probability ratios independently of the input state. The comparison holds for separately normalized exact mutation steps.

Generative-AI workflows are programs assembled from independently developed models and operators. Their correctness depends on relationships among model families, tensor geometry, control modalities, and quantization levels. In ComfyUI, these relationships can be violated even when every connection is accepted by its validator, causing expensive runtime crashes or silent failures. To measure how often such semantic composition failures occur, we classify all 8,766 issues and 1,368 discussion threads of ComfyUI's GitHub repository with an LLM, checked for cross-model agreement. They account for 8% of issue reports and 21% of issue-tracker runtime failures, and 32% of them are silent. Because execution cannot reliably reveal those failures, we present ComfyTy, a gradual refinement type system that checks component compatibility before execution as a compositional property of workflow graphs. Each node declares a reusable schema that states which model families, sizes, modalities, and quantizations it accepts and produces. Wiring nodes together combines their schemas into constraints, which ComfyTy solves to find and report incompatibilities. To evaluate ComfyTy, we first inject faults into official ComfyUI workflows and execute every resulting graph. ComfyTy detects 66.4% of the confirmed injected faults, all of which ComfyUI's own validator admits. On real workflows across more model families, it raises no false alarm on 765 known-good workflows and detects 67% of 108 failures rebuilt from user reports. Finally, in a user study with 10 participants, its diagnostics raise fault-localization accuracy on faulty workflows from 35.0% to 87.5% and repair accuracy from 30.0% to 62.5%.

LLM-based multimodal emotion reasoning systems perform well on standard benchmarks, but improving them through instruction tuning can be computationally expensive. Agentic pipelines built from frozen models avoid this cost, but introduce a different challenge: when a prediction is wrong, the system must identify which agent or stage caused the error. We address this problem with an agentic framework for traceable multimodal emotion reasoning and prompt-space adaptation. Modality-specific perception agents analyze visual, acoustic, and lexical inputs and post evidence-cited observations to a shared board. An integration agent combines these observations with retrieved multimodal examples to produce an emotion description, label set, and supporting citations, while an MLLM critic can request one revision before the output is finalized. For incorrect predictions, a separate evidence-grounded verification stage applies deterministic checks to verify that cited evidence and references are valid, and an entailment check to determine whether the final claims are supported by that evidence. Detected failures are then grouped by the responsible component and failure type, converted into targeted prompt patches, and accepted only after validation on a held-out set. This adapts the agent prompts without updating model weights. On the MER2025 dataset, targeted prompt adaptation outperforms the frozen static pipeline on all four MLLMs, ranging from 2B to 38B parameters, and matches or outperforms undifferentiated reflection baselines on each of them: VideoLLaMA3-2B, Phi-3.5-vision-instruct, Qwen2.5-VL-7B-Instruct, and InternVL2.5-38B. It improves F-score by 0.6–2.2 points depending on the backbone, including an increase from 52.3 to 54.5 on Qwen2.5-VL-7B.

Knowledge Graphs (KGs) have been popularized during the last few decades and are increasingly constructed and consumed by Large Language Models (LLMs). Various applications therefore rely on KGs to provide concise, complete, accurate, faithful, fresh, and traceable answers. However, what is the quality of those KGs? In which cases should a KG be used, and can it be trusted to ground an LLM? How might it be evaluated? We reviewed the literature on quality assessment (QA) of data, information, linked data, KGs, and the intersection of KGs and LLMs. We extended the current state-of-the-art frameworks to a catalog of 24 quality dimensions (QDs) and various quality metrics (QMs). Furthermore, we propose a general-purpose, customizable to a domain or task, and practical QA framework for assessing the quality of KGs.

Persona-conditioned language models are used as simulated patients and affective agents, but there is no validated way to ask whether a belief assigned to such a model organizes its behaviour or whether the model has merely adopted a mood. We present the Schema Coherence Inventory (SCI): 96 forced-choice items at eight levels of Beck's cognitive model, each offering six replies keyed to three negative self-schemas and their positive counterparts, scored by length-normalized log-likelihood so that nothing is generated or parsed. Affect alone can move a model onto a default belief, so the discriminant criterion is target specificity: a condition built for one belief must select that belief more often than conditions built for the other beliefs of its pole. Six validation studies over 107 conditions on five backbones (1.7B-14B parameters) support this reading. Nine clinically trained raters recover the keyed belief at 79.5% (chance 16.7%). Belief adapters are target-specific on every backbone (+17.7 points; 30/30 belief cells positive), and a condition's SCI profile identifies its own free generations in 24/30 cases against 5 expected by chance. A 48-item short form correlates r = 0.73 with the other 48 items. Applied to six published patient simulators, none carries its formulation's core belief better than a one-sentence statement of it. The validation route, which separates a construct from the affect that accompanies it and checks model judges against clinicians, offers a template for affective measurement in language models; we outline its extension across task types, raters, sites and languages. We release the items, scoring code and short form.

Many structural breaks are announced in advance, yet adaptive conformal methods learn of them only from their own errors. A reset at the announced date serves one of two audits, conformal reliability of the next interval or frequency calibration of a closed window, and the two can disagree. For independent scores, restarting the empirical quantile at the boundary attains the minimax reliability rate, of order one over the square root of the post-break count. Restarting an adaptive recursion attains a frequency gap of order one over that count on bounded scores when its floor adds a bounded total. That gap bounds nothing about the next interval. After a large synthetic break, the restarted quantile's coverage error at the 50th forecast is 0.035, against 0.052 for the best of five adaptive baselines. The restarted recursion has the smallest frequency gap over the first 50 forecasts after every synthetic break. Real breaks are mostly smaller. The restarted quantile beats two baselines after an electricity market reform and trails all five after monetary policy decisions. Of nine announced breaks screened, only one is large enough for a detectable gain, and there every method misses nominal coverage by more than 0.1.

We establish a conditional boundary-localization statement for the Hawking temperature. For a static, Euclideanizable black hole with a non-degenerate horizon, the temperature is determined entirely by the first non-vanishing near-horizon data. This result is obtained consistently through three approaches: removal of the Euclidean conical defect, the horizon boundary term in the two-dimensional Gauss-Bonnet theorem, and a complex residue calculation. In asymptotically anti-de Sitter spacetime, the Euclidean time periodicity selected at the horizon extends to the conformal boundary, so the boundary conformal field theory inherits the same thermal period up to time normalization. This provides only a weak, temperature-sector extension of the AdS/CFT framework and does not imply a full duality. For dynamical spherical spacetimes, the Hamilton-Jacobi analysis selects the trapping or apparent horizon as the local thermal boundary, whereas a separated event horizon is generally not associated with the relevant pole. Vaidya and charged-Vaidya examples support this boundary-selection picture and reduce to the standard stationary result when the horizons coincide. The construction is further checked using anti-de Sitter black holes, numerical contour calculations, limiting cases, and an extremal counterexample. The result concerns where the Hawking temperature is localized and does not replace the quantum-field-theoretic mechanism of Hawking radiation.

Let $n=2^d$. We prove that the worst-start total-variation mixing time of the full labelled Thorp shuffle satisfies, for every fixed $0<\varepsilon<1$, \[ t_{\mathrm{mix}}(\varepsilon) \le C_* d^{5/3}+O_\varepsilon\!\left(d^{4/3}\log(d+2)\right), \qquad C_*=5.1536951454\ldots . \] Time is measured in ordinary Thorp shuffles. This improves the previously published full-deck upper bound $O(d^3)$ of Morris. The geometric starting point is elementary: label the $n=2^d$ positions by binary strings. One physical Thorp shuffle is a random swap layer on one coordinate matching of the $d$-dimensional cube, followed by a deterministic cyclic rotation of the coordinates. In a rotating frame that deterministic rotation disappears, so $d$ successive physical shuffles become one sweep: one independent random swap layer in each coordinate direction. The proof then combines five ingredients. First, a collision-graph representation and negative dependence give pointwise smoothing for ordered marked cards. Second, an entropy argument is sharpened by moving an endpoint moment up to the critical exponent $\beta_c=\log_2(3/2)$, yielding an entropy-preparation clock $s^2/(2\log(3/2))+O(s\log s)$. Third, exact multiplicities in the ordered $h$-tuple permutation representation amplify marked-card bounds into Fourier operator and energy estimates on low representation levels. Fourth, entropy truncation produces a positive mixture whose regular component retains the marked-card budget. Finally, only two long blocks need this entropy regularization: a shorter third block is used solely for additional low-level smoothing. Optimizing the three block lengths gives the constant above.

Abel's classical theorem shows that a continuously differentiable one-dimensional associative law with a two-sided unit is locally equivalent to addition under a change of coordinate. We prove an $n$-valued analogue in the algebraic and formal settings. Over a field of characteristic zero, every associative algebraic $n$-valued monoid on $\mathbb P^1$ with a strong two-sided unit is commutative. Over a reduced commutative $\mathbb Q$-algebra, any one-dimensional formal $n$-valued group is commutative. We then classify $n$-valued formal groups over arbitrary $\mathbb Q$-algebras that are integral domains: for any $n$-valued formal group there is a unique divisor $m$ of $n$ such that the law is strongly isomorphic to the $n/m$-fold diagonal of the cyclic elementary $m$-valued law $\mathbb G_m$. This proves Kholodov's classification conjecture over integral domain $\mathbb Q$-algebras.

Frontier language models reliably refuse to explain how to cause physical harm. We ask whether this refusal survives when the same models control a robot. We introduce RoboHarm, a physical AI safety benchmark of harmful robot instructions, and test seven frontier models on it. We hold each model fixed and vary only the interface, from text to Code as Policies to vision agents that command end-effector poses or joint angles. In a MuJoCo simulation twin of a bimanual YAM arm robot, refusal falls from 73% of text requests to 18-25% once the model controls the robot, even when it is told what the objects are. On the physical robot, six models with end-effector control refused 18% of 612 trials against 19% in sim, and three with joint control refused 41% of 252 against 31%. GPT-5.6 Sol refused every text request and none of its trials on the real robot. Case studies of the robot transcripts show that models miss the hazard, name it without inferring its consequences, or act despite recognizing it, and their refusals often hinge on uncertainty about what an object is rather than on the harm of the action. Safety alignment learned in text thus fails to generalize to action, leaving current models with a poorly understood safety gap in the physical world.

Ono, Schneider and Wagner found a partition-theoretic analogue of Alladi's duality formula: for many sets $S\subseteq\N$, the series $-\sum\mu_{\mathcal P}(\lambda)q^{|\lambda|}$ over partitions into distinct parts with smallest part in $S$ tends to the density of $S$ as $q\to1$. We determine when this happens. Radially, the summation kernel is a Gumbel density, and Wiener's theorem shows that for bounded $f$ the associated series tends to $L$ if and only if $f$ has mean $L$ on every interval $(x,x+cx/\log x]$; natural density does not suffice. Multiplied by $\log(1/(1-q))$, the series tends to $\delta$ if and only if $S$ has $(c\delta+o(1))x/(\log x)^2$ elements in each such interval; this gives a partition analogue of Alladi's theorem for Chebotarev sets of primes. Off the real axis the largest weights grow like $e^{\Psi_\beta/t}$ with $\Psi_\beta>0$. Along $q=e^{-t(1+i\beta)}$, the formula for residue classes modulo $m\ge3$ holds exactly when $|\beta|<\beta_m$, an explicit Clausen-function threshold with $\beta_m\to0$, and it fails almost surely for random sets of bounded discrepancy. These results correct several published claims.

Dynamical wave-function collapse must not violate causality: a record selected "now" has no frame-independent meaning, and a nonlinear law can let distant observers signal. We ask whether this conflict is avoided when classical spacetime, with its causal structure, itself arises from localisation, as proposed in generalized trace dynamics (GTD), where the fluctuations that select a record come from unresolved pregeometric degrees of freedom ordered by Connes time, not by a spacetime coordinate. The hypersurface question is then not posed where selection happens; it returns as the requirement that emergent records do not signal. We apply the standard no-signalling theorem to an effective collapse law of CSL type. The norm-preserving, response-free law of a naive coarse-graining never selects. In history form, record weights are martingales only if the fluctuation history leans towards the leading record with gain twice its own diffusion and, for operators with three or more collinear eigenvalues, the linear law carries its counter-term, which a smooth coefficient drive gives with the wrong sign; any other gain signals. For an equilibrium sea the fluctuation-dissipation relation fixes the gain, so the Born gain is an Einstein relation between coupling, temperature and correlation time. A rate that reads the entanglement of the conditioned state signals; enhancement must sit in fixed collective operators. Positive states annihilate the Grassmann bilinear carrying the collapse coefficient, so the physical block is a reconstruction with positive kinetic form. The coefficient noise is evaluated for the Sutherland texture of GTD's relational master matrix: a block coupled to its local strain acquires an Ohmic spectral density with computed friction, continuum criterion and recurrence, while a kinetic cross-coupling yields none. What remains is the projection supplying counter-term and gain.

We formulate a two-state neutrino spin–flavor system coupled through a transition magnetic moment to a single quantized electromagnetic mode and establish its operator-level correspondence with the quantum Rabi model (QRM). For the sector $\{\lvert\nu_{iL}\rangle,\lvert\nu_{jR}\rangle\}$, the diagonal splitting is $\Delta_s=(m_i^2-m_j^2)/(2E)+V_{iL}-V_{jR}$, while quantization of a transverse electromagnetic mode gives a coupling $g_\nu=\mu_{ij}B_{\rm zpf}$. The effective Hamiltonian consequently has the QRM form $H_\nu=\Delta_s\sigma_z/2+\omega_c a^\dagger a+g_\nu\sigma_x(a+a^\dagger)$. We then formulate the correspondence at the level of the exact QRM spectrum, focusing on its exceptional (Juddian) states, and transfer the QRM constraint polynomials directly to neutrino variables. This yields explicit algebraic conditions on the neutrino mass splitting, energy, transition magnetic moment, zero-point magnetic field, and mode frequency. We also identify QRM phenomena that would become conditional predictions of the quantized-field neutrino model—including counter-rotating corrections, parity structure, spin–field entanglement, and occupation-dependent dynamics. The trapped-ion QRM experiments provide benchmarks for the operator family, while none of these QRM phenomena is presented as an already observed neutrino effect.

We show that for certain classes of matrices over octonions, a weak version of breakthrough numerical radius inequalities obtained by Kittaneh [\textit{{Stud. Math.}, 2005}] hold.

An emergent gravity model was shown to contain an associated emergent breaking of Lorentz invariance and violations of stress-energy conservation. Its simplest flat dust solution accelerates at late times without vacuum energy and has already been used as an analytic benchmark for observational tests. We study the wider homogeneous dynamics and solutions of this theory. For a single non-conserved dust fluid, the variables $\Omega_m=\rho/(3H^2)$ and $u=(HL_2)^{-1}$ form a two-dimensional autonomous system with an exact first integral. The complete expanding solution space separates into three classes: trajectories ending on an asymptotically de Sitter fixed line, a critical trajectory corresponding to the analytic solution of Isichei and Magueijo, and trajectories that turn around and recollapse. We then consider the phenomenologically cleaner model in which only cold dark matter violates energy conservation (while the baryons and photons behave as normal). The phase space becomes three-dimensional, with a line of matter repellers and a line of vacuum fixed points. Each normally attracting vacuum point with $0<u_0<3$ possesses a two-dimensional stable sheet. The limit in which the CDM abundance tends to zero is singular: finite-$u_0$ sheets meet the exactly baryonic plane on trajectories containing a cosmological-constant-like integration constant, whereas the zero-integration-constant baryonic solution remains at $\Omega_b=1$ and runs to $u\to\infty$. The critical endpoint $u_0=3$ separates these late-time behaviours and generalizes the special single-fluid solution.

Self-driving laboratories (SDLs) are transforming chemical and materials discovery through closed-loop automation, yet automated infrastructure for physical manipulation of soft, deformable matter remains beyond current robotic platforms. A critical instance is autonomous droplet transport on an open surface, where contact-angle hysteresis, capillary pinning, and surface heterogeneity produce partially observable dynamics that pose significant challenges for classical model-based controllers. We introduce the first robotic platform for closed-loop autonomous liquid droplet navigation on an open, unconfined surface using model-based reinforcement learning. A two-axis tilting board coated with a thin silicone oil film drives the droplet, while an overhead camera provides real-time feedback. A learned policy was trained on just 50 to 150 physical episodes depending on geometric complexity, without simulation or analytical models. Beyond performance alone, the platform demonstrates three capabilities of interest to the SDL community: it robustly transfers zero-shot to unseen geometries; it autonomously discovers an oscillatory depinning strategy to free the droplet when it sticks; and it completes its full training pipeline in under 90 minutes. These results extend reinforcement-learning manipulation from rigid microrobots to deformable soft-matter systems for next-generation SDLs.

Quantifying language distance among closely related languages remains a core challenge in quantitative linguistics. Our previous work [1] introduced QuanLing (Quantitative Linguistics via Pretrained Language Models), a quantitative framework combining language distance metrics (sentence embedding distance, tokenization fragmentation rate) with language property analysis (MLM prediction probability), validated on North Germanic (Danish, Norwegian Bokmål, Swedish). This paper extends QuanLing to Western Romance–French, Portuguese, Spanish, Italian–testing cross-branch applicability with the same metric family and aggregation protocol as our North Germanic study, adapted for four languages (English anchor, quadruplet construction). Using 150 four-language parallel sentences, we compute LaBSE sentence embedding distances, tokenization fragmentation rates from four monolingual BERT tokenizers, and mBERT masked language model mutual intelligibility. Results show that Portuguese–Spanish are closest (LaBSE distance 0.0229), French–Italian most distant (0.0338); LaBSE and mBERT rankings agree on 4 of 6 pairs, confirming cross-model robustness. Western Romance shows a wider absolute distance span than North Germanic (0.011 vs. 0.008) but comparable relative ratios (1.48 vs. 1.67), consistent with longer divergence time. French exhibits notably higher MLM predictability (36.12% top-1 accuracy vs. 29.28% for Italian), reflecting its orthography–phonology decoupling. This cross-branch validation provides further evidence for QuanLing's generalizability beyond a single language branch.

Musical-instrument recognition is a fundamental music information retrieval (MIR) task supporting transcription, source separation, and audio understanding. Despite significant algorithmic progress, there is still room for improvement in recognizing acoustically similar instruments, particularly in polyphonic mixtures. We examine the contribution of ultrasonic components, i.e., frequencies above the audible 0-20 kHz range. Although most of this content cannot be represented at conventional 44.1/48-kSPS sampling rates under the Nyquist criterion, it is available in high-quality 96-kSPS recordings. Using a 96-kSPS multitrack corpus covering 15 classes across performers, instruments, studios, and sessions, we compare full-band, low-pass, and ultrasonic-only inputs using classical machine-learning and deep-learning classifiers. Our results show that source-dependent ultrasonic extensions and broadband transients contain instrument-specific information that significantly improves isolated and polyphonic recognition and motivates wider-bandwidth studies of other MIR tasks.

Safety-critical Model Predictive Control (MPC) formulations based on Control Barrier Functions (CBFs) often require multiple tuning parameters and may become conservative or difficult to keep feasible, particularly for high-relative-degree constraints. To address these limitations, in this paper we draw inspiration from the recently introduced Taylor-Lagrange Control (TLC) method, and propose an MPC formulation based on a Taylor expansion with Lagrange remainder (MPC-TLR). To enable digital implementation, we develop a numerical approximation of the Lagrange remainder under zero-order-hold control. The resulting safety constraint includes a tunable margin to account for approximation errors and balance safety, feasibility, and conservativeness. Comparisons with MPC using high-order CBFs (MPC-HOCBF), discrete-time high-order CBFs (MPC-DHOCBF), and direct safety constraints (MPC-DC) on a unicycle obstacle-avoidance problem show that MPC-TLR yields safer trajectories than MPC-DHOCBF and MPC-DC, while requiring fewer tuning parameters and being less conservative than MPC-HOCBF. Its broader control-input coverage under the adopted discretization can improve feasibility and control performance for short prediction horizons.

We provide potential function proofs of the competitive ratios of DoubleCoverage for the hard $k$-taxi problem on HSTs and general weighted trees of bounded depth. Buchbinder, Coester, and Naor (2023) obtained these ratios using time-reverse dual fitting and noted that they did not know a pure potential proof beyond $k=2$. We observe that the minimum matching distance between the online and offline taxi configurations can be expressed as an integral over the rooted tree of the absolute difference between their taxi counts below each point. This representation lets us analyse DoubleCoverage over short movement intervals and apply the resulting estimates to potentials that remain unchanged when both serving taxis are relocated from pickup to destination.

Knowledge graph embedding (KGE) methods represent entities and predicates in continuous vector spaces to infer missing knowledge. Despite strong benchmark performance, their predictions often lack principled reliability guarantees, limiting their use in high-stakes applications. Moreover, uncertainty arises throughout the KGE pipeline, from incomplete or probabilistic input knowledge to stochastic training and prediction. This thesis systematically investigates three sources of uncertainty in KGE: knowledge uncertainty, arising from incomplete, noisy, or probabilistic input knowledge; algorithmic uncertainty, induced by randomness in model training; and predictive uncertainty, concerning the reliability of model outputs. To address algorithmic uncertainty, the thesis demonstrates that models trained under identical settings can produce substantially different predictions and introduces a voting-based aggregation framework to mitigate this instability. To quantify predictive uncertainty, it adapts conformal prediction to KGE, constructing answer sets with distribution-free coverage guarantees and extending them to provide predicate-conditional reliability guarantees. To support reasoning under knowledge uncertainty, it develops statistically valid prediction intervals for confidence-scored triples and an embedding-based approach to approximate probabilistic reasoning over statistical ontologies with formal soundness guarantees. Together, these complementary, model-agnostic methods provide a practical and theoretically grounded approach to uncertainty in KGE, advancing beyond predictive accuracy toward reliable and uncertainty-aware knowledge graph reasoning.

Melt-pool monitoring is central to qualifying metal additive manufacturing (AM), yet no public event-camera benchmark exists for this domain. Event cameras report per-pixel brightness changes with microsecond timing instead of reading full frames, giving the temporal resolution AM transients demand at a fraction of the data rate. We present SynAM-E (Synthetic AM Events), the first public multi-source simulated event-camera benchmark for metal-AM melt-pool monitoring: 85 physics-calibrated event shards from 15 sources across 8 institutions, with public baselines and fixed cross-machine evaluation splits. On a single-machine case study, event-spatial monitoring matches dense-frame accuracy (0.874 versus 0.863 macro-F1), and the absolute intensity that events discard adds only +0.006 under fusion. On the NIST Additive Manufacturing Metrology Testbed (AMMT) build, a near-sensor event-rate counter recovers a raw-frame-confirmed 528.7 Hz intensity oscillation at ~380 times less sensor readout than the frame stream requires. A compact 93 k-parameter spiking model runs at 15 times lower modeled inference energy for a 0.073 macro-F1 cost. Every cross-source task includes a built-in trust test against camera identity shortcuts: process-type classification passes while material classification remains confounded by camera band, a corpus-structural limitation the release documents and the trust test exposes.

Multimodal Large Language Models (MLLMs) have demonstrated impressive capabilities in visual understanding and multimodal reasoning, yet they remain fundamentally limited in Human Action Feedback Generation. Existing methods infer coaching feedback directly from visual observations, producing generic advice, limited interpretability, and physically implausible hallucinations. In contrast, expert human coaches diagnose performance through explicit biomechanical reasoning over joint kinematics, posture, and body dynamics. We introduce BoT-Feedback, a framework that grounds MLLM reasoning in structured biomechanical evidence. Our key contribution is Biomechanics of Thought (BoT), a four-stage reasoning framework that progressively identifies the action, localises the critical body regions, analyses quantitative biomechanical differences between expert and student performances, and synthesises interpretable coaching feedback. To support this reasoning process, we develop a plug-and-play Biomechanical Data Parser (BDP) that converts videos into structured biomechanical descriptors and an alignment strategy that temporally matches expert and student motions. We further introduce BiomAF, a benchmark containing paired teacher-student videos, 3D skeletons, biomechanical attributes, and expert-coaching annotations. Experiments across twelve open- and closed-source MLLMs demonstrate that grounding reasoning in biomechanical evidence consistently improves feedback quality, interpretability, and robustness while substantially reducing biomechanical hallucinations. BoT-Feedback improves the average expert evaluation score from 2.07 to 2.95 (+40%), enabling compact open-source MLLMs to approach the performance of substantially larger proprietary systems for explainable action feedback generation.

Traditional data pipelines are notoriously brittle, often failing due to upstream schema drift, API contract changes, or website DOM modifications. Present observability tools only raise alerts but for human engineers, resulting in a high Mean Time to Repair (MTTR) and operational fatigue. In this paper we propose AegisFlow (Agentic Engine for Intelligent Self-healing and Graph-driven Operations for Workload remediation), a novel agentic framework that closes the loop between detection and resolution. AegisFlow uses a Watchdog agent to collect runtime telemetry and has a Repair agent to automatically create, test and deploy code patches based on Large Language Models (LLMs). The framework presents the non-intrusive execution model called Parallel Shadow Patching, a non-intrusive execution model based on the Monitor, Analyze, Plan, Execute, Knowledge (MAPE-K) loop to generate and verify patches in digital twin environments. Through experimental testing, we have evaluated AegisFlow across five common failure scenarios, and see 98.1 percent improvement in MTTR (from an average of 170 minutes per patch to 3.2 minutes) and a patch success rate of 92 percent . In particular, the system is successful in dealing with changes in the JSON schema (96 percent ) and punctuation drift (98 percent ), and is least successful in Shadow DOM cases (85 percent ). AegisFlow frees up about 98 percent of data engineering on-call time from firefighting and reallocates it towards innovation. The framework is deployment agnostic consisting of a system that can be deployed in a plugin fashion into an existing pipeline orchestration system with minimal uplift to the existing system.

Egocentric bimanual hand pose estimation is important for virtual interaction, wearable control, and rehabilitation, but visual observations are often degraded by self-occlusion, hand-hand contact, and object manipulation. We propose EVFormer, a multimodal framework that combines the current RGB frame with the preceding 200 ms of bilateral wrist surface electromyography (sEMG) to estimate 44 finger and wrist joint angles. EVFormer separately encodes visual spatial features and sEMG temporal features, enables cross-modal information exchange through sequential bidirectional cross-attention, and integrates the two modalities using feature-wise gated fusion. We evaluate EVFormer in a single-participant feasibility study using one synchronized public EgoEMG recording with chronologically separated training, validation, and test splits. On 296 test samples, EVFormer achieves a mean absolute error of 11.482 degrees, compared with 13.228-13.610 degrees for vision-only, sEMG-only, late-fusion, and training-mean baselines. This corresponds to relative error reductions of 13.20% compared with the vision-only model and 14.23% compared with late fusion. EVFormer also achieves the lowest error in four of the five evaluated gesture classes. These results provide preliminary evidence that feature-level interaction between egocentric vision and sEMG can improve bimanual hand pose estimation. Further evaluation across participants, recording sessions, sensor placements, and real-world interaction conditions is required to establish the generalizability of the approach.