One examines the infinitely deep quantum cavity, also known as the quantum infinite square well, within the framework of the real Hilbert space. The solutions are considered in terms of complex wave functions, and also in terms of quaternionic wave functions. The complex results reproduce the usual achievements established in the complex Hilbert space, but also extend them to non-stationary solutions, as well as to distorted stationary solutions, different energy spectra, and dislocated observed position. The quaternionic cases further admit the incidence of self-interaction, something that cannot be observed in complex solutions. Therefore, both the complex and quaternionic solutions are more general than previous cases, thus opening the way to further one-dimensional solutions to be researched in the non-relativistic theory.

We propose a new approach to improve the accuracy of ground state estimates in Variational Quantum Eigensolver (VQE) algorithms by employing subspace representations with soft-coded orthogonality constraints. As in other subspace-based VQE methods, such as the Subspace-Search VQE (SSVQE) and Multistate Contracted VQE (MCVQE), once the parameters are optimized to maximize the subspace overlap with the low-energy sector of the Hamiltonian, one diagonalizes the Hamiltonian restricted to the subspace. Unlike these methods, where \emph{hard-coded} orthogonality constraints are enforced at the circuit level among the states spanning the subspace, we consider a subspace representation where orthogonality is \emph{soft-coded} via penalty terms in the cost function. We show that this representation allows for shallower quantum circuits while maintaining high fidelity when compared to single-state (standard VQE) and multi-state (SSVQE or MCVQE) representations, on two benchmark cases: a $3\times 3$ transverse-field Ising model and random realizations of the Edwards--Anderson spin-glass model on a $4\times 4$ lattice.

We demonstrate an alternative approach based on complex-valued inverse temperature and partition function to probe quantum phases of matter with nontrivial spectra and dynamics. It leverages thermofield dynamics (TFD) to quantitatively characterize quantum and thermal fluctuations, and exploit the correspondence between low-energy excitations and Fisher zeros. Using the quantum XY chain in an external field as a testbed, we show that the oscillatory gap behavior manifests as oscillations in the long-time dynamics of the TFD spectral form factor. We also identify giant bubbles, i.e. large-scale closed lines, of Fisher-zeros near the gapless XX limit. They provide a characteristic energy scale that seems to contradict the predictions of the low energy theory of a featureless Luttinger liquid. We identify this energy scale and relate the motion of these giant bubbles with varying external field to the transfer of spectral weight from high to low energies. The deep connection between Fisher zeros, dynamics, and excitations opens up promising avenues for understanding the unconventional gap behaviors in strongly correlated many-body systems.

Growing stress-free epitaxial films by van der Waals epitaxy (vdWE) is of interest for realizing flexible optoelectronics and energy devices from freestanding epilayers. However, vdWE of non-layered materials is often presumed or claimed on layered substrates such as mica with inadequate experimental evidence. Here, we demonstrate that the growth of single-domain rocksalt ScN(111) films by sputter deposition on fluorophlogopite mica(001) occurs by conventional epitaxy. X-ray diffraction and electron microscopy reveal the film/substrate epitaxial relationship to be [-101](111)ScN||[010](001)mica. Our results indicating strain buildup seen from the dependence of (111) interplanar spacings, and strain relaxation by dislocation generation, question prior claims of vdWE of non-layered metal nitrides on mica. Our findings show that conventional epitaxy should be the default assumption for non-layered materials unless conditions for vdWE are explicitly established.

Accurate 3D dose calculation for Pencil Beam Scanning Proton Therapy (PBSPT) is typically performed with Monte Carlo (MC) engines, but their runtimes limit adaptive workflows and repeated evaluations. Current deep-learning proton dose engines often require orthogonality between proton rays and the CT grid, forcing computationally expensive beamlet-wise 3D reinterpolation. We propose the Angle-dependent Dose Transformer Algorithm (ADoTA), which eliminates grid rotation by augmenting the model input with a fast analytical beamlet-shape projection that explicitly encodes beam direction. The model was trained on CT data from 108 patients to predict beamlet dose distributions for initial energies of $70$--$270\,\mathrm{MeV}$ over an $80\times110\,\mathrm{mm}^2$ field, and tested on an independent cohort of 50 patients. On the test set, gamma pass rates $(1\%,3\,\mathrm{mm})$ were $99.40\pm0.86\%$ (thorax) and $99.87\pm0.23\%$ (abdomen/pelvis). Single-beamlet inference took $1.72\pm0.8\,\mathrm{ms}$. By avoiding reinterpolation, end-to-end 3D dose computation was reduced by $\approx86\%$ relative to the fastest published reinterpolation-based methods. For full treatment plans, gamma pass rates $Γ(2\%,2\,\mathrm{mm})$ with a 10\% dose cut-off reached $98.4\%$ (lung) and $98.9\%$ (prostate). ADoTA provides an angle-aware deep-learning proton dose engine that preserves MC-level accuracy across heterogeneous anatomies while substantially reducing computational overhead.

Mid-circuit measurements (MCMs) are critical components of the quantum error correction protocols expected to enable utility-scale quantum computing. MCMs can be modeled by quantum instruments (a type of quantum operation or process), which can be characterized self-consistently using gate set tomography. However, experimentally estimated quantum instruments are often hard to interpret or relate to device physics. We address this challenge by adapting the error generator formalism -- previously used to interpret noisy quantum gates by decomposing their error processes into physically meaningful sums of "elementary errors" -- to MCMs. We deploy our new analysis on a transmon qubit device to tease out and quantify error mechanisms including amplitude damping, readout error, and imperfect collapse. We examine in detail how the magnitudes of these errors vary with the readout pulse amplitude, recover the key features of dispersive readout predicted by theory, and show that these features can be modeled parsimoniously using a reduced model with just a few parameters.

Superconductivity is usually understood as a phase in which charge-$2e$ Cooper pairs are condensed. Charge-$4e$ superconductivity has largely been discussed as a vestigial order at finite temperature emerging from charge-$2e$ states. Primary charge-$4e$ superconducting phases at zero temperature remain scarce in both experiments and microscopic models. Here we argue that a doped featureless Mott insulator with $SU(4)$ symmetry provides a natural platform for primary charge-$4e$ superconductivity, based on perturbative renormalization group arguments and group theoretic considerations. As a concrete realization, we construct a bilayer Hubbard model with tunable onsite $SU(4)$ and $Sp(4)$ symmetries that exhibits a featureless Mott insulating phase at half filling. Its low energy physics is captured by a generalized ESD model, featuring an effective Hamiltonian that is purely kinetic within the constrained Hilbert space. Using density matrix renormalization group (DMRG) simulations, we find a primary charge-$4e$ superconducting phase in the $SU(4)$ ESD model and a conventional primary charge-$2e$ phase in the $Sp(4)$ case. We further characterize the corresponding normal states and discuss the resulting finite temperature phase diagram.

We propose a novel method that performs adaptive clustering with DPMM using collapsed VI, while incorporating weakly-informative priors for DP concentration parameter alpha and base distribution G0. We illustrate the importance of G0 covariance structure and prior choice by considering different parameterisations of the data covariance matrix. On high-dimensional Gaussian simulations, our model demonstrates substantially faster convergence than a state-of-the-art MCMC splice sampler. We further evaluate performances on Negative Binomial simulations and conduct sensitivity analyses to assess robustness on realistic data conditions. Application to a publicly available leukemia transcriptomic data set comprising 72 samples and 2,194 gene expression successfully recovers every known sub-type, all while identifying additional gene expression-based sub-clusters with meaningful biological interpretation.

We have performed Zeno protective measurements of quantum polarization states by coupling the polarization to a temporal pointer (arrival time) in a birefringent optical fiber. It is necessary to actively stabilize the polarization, and we do this by using the signal photon counts themselves as the error signal in a feedback loop. We compare these measurements to a stabilization scheme using a classical reference beam as the error signal. The method using photon counts has higher signal levels and significantly reduced background. These improvements allow us to increase the number of Zeno stages in our measurements from 9 to 13, with a corresponding decrease in the measurement uncertainty.

We present a class of numerical schemes for two-dimensional systems of nonlocal conservation laws, which are based on utilizing well-known monotone numerical flux functions after suitably approximating the nonlocal terms. The considered systems are weakly coupled by the nonlocal terms and the underlying flux function is rather general to guarantee that our results are applicable to a wide range of common nonlocal models. We state sufficient conditions to ensure the convergence of the monotone-based numerical schemes to the unique weak entropy solution. Moreover, we provide an error estimate that yields the convergence rate of $\mathcal{O}(\sqrt{Δt})$ for the numerical approximations of the solution. Our results include an existence and uniqueness proof of the nonlocal system, too. Numerical results illustrate our theoretical findings.

Power domination is a graph-theoretic model for the observance of a power grid using phasor measurement units (PMUs). There are many costs associated with the installation of a PMU, but also costs associated with not observing the entire power grid. In this work, we propose and study a power domination cost function, which balances these two costs. Given a graph $G$, a set of sensor locations $S$, and a parameter $β$ (which is the ratio of the cost of a PMU to the cost of non-observance of any given vertex), we define the cost function \[ \mathrm{C}(G;S,β)=|S|+β\cdot (|V(G)|-|\mathrm{Obs}(G;S)|) \] where $|\mathrm{Obs}(G;S)|$ is the number of vertices observed by sensors placed at $S\subseteq V(G)$ in the power domination process. We explore the values of $k$ for which there is a set $S$ of size $k$ that minimizes this cost function, and explore which values of $β$ guarantee that it is optimal to observe the entire power grid to minimize cost. We also introduce notions of marginal cost and marginal observance, providing tools to analyze how many PMUs one should install on a given power grid.

This work evaluates the potential of High-Altitude Platform Stations (HAPS) and Low Earth Orbit (LEO) satellites as alternative or complementary systems to enhance Internet of Things (IoT) connectivity. We first analyze the transmission erasure probability under different connectivity configurations, including only HAPS or LEO satellites, as well as hybrid architectures that integrate both aerial/spatial and terrestrial infrastructures. To make the analysis more realistic, we considered movement of LEO satellites regarding a fixed region, elevation angle between gateway and devices, and different fading models for terrestrial and non-terrestrial communication. We also analyze LR-FHSS (Long-Range Frequency Hopping Spread Spectrum) random access uplink technology as a potential use case for IoT connectivity, showing the scalability impact of the scenarios. The simulation results demonstrate that HAPS can effectively complement sparse terrestrial networks and improve the performance of satellite-based systems in specific scenarios. Furthermore, considering the deployment and operational costs, respectively, CAPEX and OPEX, the economic analysis reveals that although HAPS exhibits higher costs, these remain within a comparable order of magnitude to LEO and terrestrial deployments. In addition, specific use cases, such as natural disasters, transform HAPS into a competitive technology for conventional infrastructures.

Following limb amputation and targeted muscle reinnervation (TMR), nerves that originally innervated agonist and antagonist muscles are rerouted into one or more residual target muscles. This rerouting profoundly alters the natural mechanical coupling and afferent signalling that normally link muscle groups in intact limbs. Despite this disruption, in this study we demonstrate, using high-density intramuscular microelectrode arrays implanted in reinnervated muscles of three TMR participants, that motor units (MUs) associated with agonist and antagonist tasks remain functionally coupled. Specifically, over 40% of motor units active during agonist tasks were also recruited during the corresponding antagonist tasks, even though no visual feedback on antagonist neural activity was provided. These motor units exhibited significantly different firing rates depending on their functional role. These results provide the first motor-unit-level evidence that the central nervous system preserves coordinated agonist-antagonist control after TMR and inform restorative surgical strategies and prosthetic systems capable of regulating both limb kinematics and dynamics based on agonist-antagonist commands interplay.

We study skein modules of 3-manifolds by embedding them into the Hilbert spaces of 4d ${\cal N}=4$ super-Yang-Mills theories. When the 3-manifold has reduced holonomy, we present an algorithm to determine the dimension and the list of generators of the skein module with a general gauge group. The analysis uses a deformation preserving ${\cal N}=1$ supersymmetry to express the dimension as a sum over nilpotent orbits in its Lie algebra. We find that the dimensions often differ between Langlands-dual pairs beyond the A-series, for which we provide a physical explanation involving chiral symmetry breaking and 't Hooft operators. We also relate our results to the structure of $\mathbb{C}^*$-fixed loci in the moduli space of Higgs bundles. This approach helps to clarify the relation between the gauge-theoretic framework of Kapustin and Witten with other versions of the geometric Langlands program, explains why the dimensions of skein modules do not exhibit a TQFT-like behavior, and provides a physical interpretation of the skein-valued curve counting of Ekholm and Shende.

We consider mixed four-point correlators of 1/2-BPS operators $\mathcal{O}_{k}$ in the maximally supersymmetric CFTs, i.e. the 3d $\mathcal{N}=8$, 4d $\mathcal{N}=4$, and 6d $\mathcal{N}=(2,0)$ theories. In arXiv:hep-th/0405180, Dolan, Gallot, and Sokatchev demonstrated that four-point correlators of identical $\mathcal{O}_{k}$ in these SCFTs can be expressed in terms of a number of unconstrained one- and two-variable ``reduced correlator" functions acted on by a $2(\varepsilon-1)$nd order differential operator $Δ_\varepsilon$, which is non-local in odd dimensions $d=2(\varepsilon+1)$. We generalize this construction to mixed correlators $\langle \mathcal{O}_{k_1}\mathcal{O}_{k_2}\mathcal{O}_{k_3}\mathcal{O}_{k_1+k_2+k_3-2\mathcal{E}}\rangle$ up to extremality $\mathcal{E}=2$. To construct superconformal blocks, we generalize the R-symmetry channel equations and use Jack polynomial expansions to recursively generate the full spectrum of conformal blocks in a superblock from a single channel. We observe that for each $\varepsilon$, this channel equation can be inverted to expand the reduced correlators in ``reduced superblocks" involving blocks with shifted external kinematics. These reduced blocks reproduce what is known in 4d, generalize the known $\langle \mathcal{O}_{2}\mathcal{O}_{2}\mathcal{O}_{k}\mathcal{O}_{k}\rangle$ case in 6d, and offer a novel result in 3d.

One of the key features of sixth-generation (6G) mobile communications will be integrated sensing and communication (ISAC). While the main goal of ISAC in standardization efforts is to detect objects, the byproducts of radar operations can be used to enable new services in 6G, such as weather sensing. Even though weather radars are the most prominent technology for weather detection and monitoring, they are expensive and usually neglect areas in close vicinity. To this end, we propose reusing the dense deployment of 6G base stations for weather sensing purposes by detecting and estimating weather conditions. We implement both a classifier and a regressor as a convolutional neural network trained across measurements with varying precipitation rates and wind speeds. We implement our approach in an ISAC proof-of-concept and conduct a multi-week experiment campaign. Experimental results show that we are able to jointly and accurately classify weather conditions with accuracies of 99.38% and 98.99% for precipitation rate and wind speed, respectively. For estimation, we obtain errors of 1.2 mm/h and 1.5 km/h, for precipitation rate and wind speed, respectively. These findings indicate that weather sensing services can be reliably deployed in 6G ISAC networks, broadening their service portfolio and boosting their market value.

In this paper, we suggest a sufficient condition on the properadic envelope of a quadratic dioperad to be Koszul in terms of twisted associative algebras. As a particular new example, we show that the properad of quadratic Poisson structures is Koszul.

Platforms matching spatially distributed supply to demand face a fundamental design choice: given a fixed total budget of service range, how should it be allocated across supply nodes ex ante, i.e. before supply and demand locations are realized, to maximize fulfilled demand? We model this problem using bipartite random geometric graphs where $n$ supply and $m$ demand nodes are uniformly distributed on $[0,1]^k$ ($k \ge 1$), and edges form when demand falls within a supply node's service region, the volume of which is determined by its service range. Since each supply node serves at most one demand, platform performance is determined by the expected size of a maximum matching. We establish a uniformity principle: whenever one service range allocation is more uniform than the other, the more uniform allocation yields a larger expected matching. This principle emerges from diminishing marginal returns to range expanding service range, and limited interference between supply nodes due to bounded ranges naturally fragmenting the graph. For $k=1$, we further characterize the expected matching size through a Markov chain embedding and derive closed-form expressions for special cases. Our results provide theoretical guidance for service-range allocation and incentive design in ride-hailing, on-demand labor markets, and drone delivery platforms, highlighting the benefits of reducing disparities in supply-side flexibility.

Mean-field Hartree theory is a central tool for reducing interacting many-body dynamics to an effective nonlinear one-particle evolution. This approximation has been employed also when the Hamiltonian that governs the many-body dynamics is not Hermitian. Indeed, non-Hermitian Hamiltonians model particle gain/loss or the evolution of open quantum systems between consecutive quantum jumps. Furthermore, the validity of the Hartree approximation for generic non-Hermitian Hamiltonians lies at the basis of a quantum algorithm for nonlinear differential equations. In this work, we show that this approximation can fail. We analytically solve a model of $N$ bosonic qubits with two-body interactions generated by a purely anti-Hermitian Hamiltonian, determine an analytic expression for the limit for $N\to\infty$ of the one-particle marginal state and show that such a limit does not agree with the solution of the non-Hermitian Hartree evolution equation. We further show that there exists an initial condition such that the exact one-particle marginal state undergoes a finite-time transition to a mixed state, a phenomenon that is completely absent in the case of Hermitian Hamiltonians. Our findings challenge the validity of the mean-field Hartree approximation for non-Hermitian Hamiltonians, and call for additional conditions for the validity of the mean-field regime to model the dynamics of particle gain and loss and the open-system dynamics in bosonic many-body systems.

Beyond active material intrinsic properties, the electrode manufacturing process is a crucial step to reach high energy density and long-life of Li-ion batteries. In particular, very high pressures are applied to the electrode during the calendering step, that directly influence the microstructure and the electrochemical performances. This article reports the first calendering simulation of a NMC cathode using a finite element method (FEM), including the post-fracturation behaviour of the secondary NMC particles. Calibrated with nano-indentation experiments, the mechanical model provides stress-strain predictions fully consistent with experimental data. On assemblies up to 100 particles, simulations reveal three calendering regimes along compression: particle rearrangement, moderatepressure fracturing, and complete crushing. The model shows the strong sensitivity of the electrode microstructure to the calendering pressure level, and can thus be used as a guidance in the multi-criteria optimization of the manufacturing process.

Neuronal systems often preserve their characteristic functions and signalling patterns, also referred to as regimes, despite parametric uncertainties and variations. For neural models having uncertain parameters with a known probability distribution, probabilistic robustness analysis (PRA) allows us to understand and quantify under which uncertainty conditions a regime is preserved in expectation. We introduce a new computational framework for the efficient and systematic PRA of dynamical systems in neuroscience and we show its efficacy in analysing well-known neural models that exhibit multiple dynamical regimes: the Hindmarsh-Rose model for single neurons and the Jansen-Rit model for cortical columns. Given a model subject to parametric uncertainty, we employ generalised polynomial chaos to derive mean neural activity signals, which are then used to assess the amount of parametric uncertainty that the system can withstand while preserving the current regime, thereby quantifying the regime's robustness to such uncertainty. To assess persistence of regimes, we propose new metrics, which we apply to recurrence plots obtained from the mean neural activity signals. The overall result is a novel, general computational methodology that combines recurrence plot analysis and systematic persistence analysis to assess how much the uncertain model parameters can vary, with respect to their nominal value, while preserving the nominal regimes in expectation. We summarise the PRA results through probabilistic regime preservation (PRP) plots, which capture the effect of parametric uncertainties on the robustness of dynamical regimes in the considered models.

Motivated by the question of defining a $p$-adic string worldsheet action in genus one, we define a Laplacian operator on the Tate curve, and study its Green's function. We show that the Green's function exists. We provide an explicit formula for the Green's function, which turns out to be a non-Archimedean counterpart of the Archimedean Green's function on a flat torus. In particular, it turns out that this Green's function recovers the Néron local height function for the Tate curve in the $p\to\infty$ limit, when the $j$-invariant has odd valuation. So this non-Archimedean height function now acquires a physics meaning in terms of the large $p$ limit of a non-Archimedean conformal field theory two point function on the Tate curve, as well as a direct analytic interpretation as a Green's function, on the same footing as in the Archimedean place.

In this paper, we discuss the construction of a map between weak (gauge) and strong (string) coupling degrees of freedom for the supersymmetric Wilson line-defect in the planar N=4 Super-Yang-Mills. By analysing the Partition Functions at zero and infinite coupling, we propose a map from degrees of freedom capturing single- and singlet two-particle states at zero coupling to infinite coupling. This map predicts that the dimension of states in these particular sectors doubles as it goes from zero to infinite coupling. We test this prediction against the non-perturbative spectrum of insertions on the Wilson line obtained using integrability. In addition to already available integrability-based results, we obtain the non-perturbative scaling dimensions of the simplest non-trivial operators with transverse spin about the Wilson line, thereby extending the Quantum Spectral Curve construction to such charged sectors.

Sodium iodide (NaI) is a widely used scintillator in direct dark matter searches. In particular, NaI-based cryogenic scintillating calorimeters have emerged as promising candidates, like in the COSINUS experiment, for testing the annually modulating signal reported by DAMA/LIBRA. In this study, we investigate defect formation within NaI crystals and its impact on the dark matter detection signal. Using molecular dynamics simulations and density functional theory techniques, we simulate a DM particle collision on an NaI crystal, focusing on the possible defects formation and their structural and electronic properties. Our analysis includes a detailed study of the electronic states associated with the interstitial atoms and vacancies, the energetic cost of defect formation, and the anisotropic threshold displacement energy. Finally, we highlight the potential to exploit dark matter-induced defects as a novel detection channel, enabled by the introduction of new states within the electronic band gap.

The room impulse response (RIR) characterizes sound propagation in a room from a loudspeaker to a microphone under the linear time-invariant assumption. Estimating RIRs from a limited number of measurement points is crucial for sound propagation analysis and visualization. Physics-informed neural networks (PINNs) have recently been introduced for accurate RIR estimation by embedding governing physical laws into deep learning models; however, the role of network depth has not been systematically investigated. In this study, we developed a deeper PINN architecture with residual connections and analyzed how network depth affects estimation performance. We further compared activation functions, including tanh and sinusoidal activations. Our results indicate that the residual PINN with sinusoidal activations achieves the highest accuracy for both interpolation and extrapolation of RIRs. Moreover, the proposed architecture enables stable training as the depth increases and yields notable improvements in estimating reflection components. These results provide practical guidelines for designing deep and stable PINNs for acoustic-inverse problems.

A powerful method for analyzing quantum error-correcting codes is to map them onto classical statistical mechanics models. Such mappings have thus far mostly focused on static codes, possibly subject to repeated syndrome measurements. Recent progress in quantum error correction, however, has prompted new paradigms where codes emerge from stabilizer circuits in spacetime -- a unifying perspective encompassing syndrome extraction circuits of static codes, dynamically generated codes, and logical operations. We show how to construct statistical mechanical models for stabilizer circuits subject to independent Pauli errors, by mapping logical equivalence class probabilities of errors to partition functions using the spacetime subsystem code formalism. We also introduce a modular language of spin diagrams for constructing the spin Hamiltonians, which we describe in detail focusing on independent circuit-level X-Z error channels. With the repetition and toric codes as examples, we use our approach to analytically rank logical error rates and thresholds between code implementations with standard and dynamic syndrome extraction circuits, describe the effect of transversal logical Clifford gates on logical error rates, and perform Monte Carlo simulations to estimate maximum likelihood thresholds. Our framework offers a universal prescription to analyze, simulate, and compare the decoding properties of any stabilizer circuit, while revealing the innate connections between dynamical quantum systems and noise-resilient phases of matter.

QED formulated in prescribed classical background electromagnetic fields is a standard framework for strong-field and laser\textendash matter interactions. It is usually treated as a theory modified by externally imposed fields, obscuring its precise relation to full QED and, in particular, the role of asymptotic boundary conditions for the gauge field. Starting from an operator-based formulation, we show that QED with background fields is not a distinct theory but arises as a well-defined boundary-condition limit of full QED, in which the classical background field emerges from coherent-state boundary conditions on the quantized electromagnetic field. In this limit, the conventional generating functional used in calculations with prescribed background fields is recovered naturally, while relaxing the boundary conditions allows depletion and backreaction effects to be incorporated within the same framework. The central new result is a rigorous operator-level proof of the equivalence between the fixed background-field approximation and coherent-state asymptotic boundary conditions\textemdash a formulation that, to our knowledge, has not been made explicit in previous approaches. We further demonstrate that the apparent time dependence of background fields does not originate from an explicitly time-dependent Hamiltonian, but instead reflects the choice of picture\textemdash Schrödinger versus Heisenberg\textemdash in the underlying quantum theory. Rather than introducing new properties of coherent states, our analysis provides a first-principles reinterpretation of the fixed background-field approximation as a controlled and picture-dependent limit of full QED.

With the rapid development of large language models in code generation, AI-powered editors such as GitHub Copilot and Cursor are revolutionizing software development practices. At the same time, studies have identified potential defects in the generated code. Previous research has predominantly examined how code context influences the generation of defective code, often overlooking the impact of defects within commented-out code (CO code). AI coding assistants' interpretation of CO code in prompts affects the code they generate. This study evaluates how AI coding assistants, GitHub Copilot and Cursor, are influenced by defective CO code. The experimental results show that defective CO code in the context causes AI coding assistants to generate more defective code, reaching up to 58.17 percent. Our findings further demonstrate that the tools do not simply copy the defective code from the context. Instead, they actively reason to complete incomplete defect patterns and continue to produce defective code despite distractions such as incorrect indentation or tags. Even with explicit instructions to ignore the defective CO code, the reduction in defects does not exceed 21.84 percent. These findings underscore the need for improved robustness and security measures in AI coding assistants.

Cognitive training for sustained attention and working memory is vital across domains relying on robust mental capacity such as education or rehabilitation. Adaptive systems are essential, dynamically matching difficulty to user ability to maintain engagement and accelerate learning. Current adaptive systems often rely on simple performance heuristics or predict visual complexity and affect instead of cognitive load. This study presents the first implementation of real-time adaptive cognitive load control in Virtual Reality cognitive training based on eye-tracking and physiological data. We developed a bidirectional LSTM model with a self-attention mechanism, trained on eye-tracking and physiological (PPG, GSR) data from 74 participants. We deployed it in real-time with 54 participants across single-task (sustained attention) and dual-task (sustained attention + mental arithmetic) paradigms. Difficulty was adjusted dynamically based on participant self-assessment or model's real-time cognitive load predictions. Participants showed a tendency to estimate the task as too difficult, even though they were objectively performing at their best. Over the course of a 10-minute session, both adaptation methods converged at equivalent difficulty in single-task scenarios, with no significant differences in subjective workload or game performance. However, in the dual-task conditions, the model successfully pushed users to higher difficulty levels without performance penalties or increased frustration, highlighting a user tendency to underestimate capacity under high cognitive load. Findings indicate that machine learning models may provide more objective cognitive capacity assessments than self-directed approaches, mitigating subjective performance biases and enabling more effective training by pushing users beyond subjective comfort zones toward physiologically-determined optimal challenge levels.

We study mechanism design when a designer repeatedly uses a fixed mechanism to interact with strategic agents who learn from observing their allocations. We introduce a static framework, calibrated mechanism design, requiring mechanisms to remain incentive compatible given the information they reveal about an underlying state through repeated use. In single-agent settings, we prove implementable outcomes correspond to two-stage mechanisms: the designer discloses information about the state, then commits to a state-independent allocation rule. This yields a tractable procedure to characterize calibrated mechanisms, combining information design and mechanism design. In private values environments, full transparency is optimal and correlation-based surplus extraction fails. We provide a microfoundation by showing calibrated mechanisms characterize exactly what is implementable when an infinitely patient agent repeatedly interacts with the same mechanism. Dynamic mechanisms that condition on histories expand implementable outcomes only by weakening incentive constraints, but not by enriching the designer's ability to obfuscate learning.