Performance predictability is critical for modern DBMSs because index maintenance can trigger rare but severe I/O spikes. In a B or B+-tree with height H, node split propagation means the cost of a single insert can vary from H + 1 to 3H + 1 I/Os when splits reach the root, nearly a three times degradation. We formalize performance fluctuation as the gap between best- and worst-case insert behavior and introduce the notions of safe and critical nodes to capture when splits become unavoidable. We introduce the FFBtree, a B+-tree insert algorithm that preemptively splits some critical nodes, and prove that when navigating from root to leaf the insert algorithm will encounter at most one critical node that must be split, ensuring no split propagation can occur and producing fluctuation-free performance. Our implementation maintains critical-node metadata efficiently and integrates with optimistic lock coupling for concurrency. Experiments with simulated indexes show the FFBtree caps I/O fluctuation by eliminating split propagation and consistently reduces insert spikes compared to conventional baselines, and real-index experiments confirm comparable improvements.

If massive primordial black holes (PBHs) exist and constitute a fraction of the dark matter, they can dramatically catalyze galaxy formation. By acting as pre-existing, high-density seeds, they can shorten the galaxy assembly time to as little as 100 Myr for up to 10^8 solar mass PBH seeds, allowing for the rapid formation of host halos. Furthermore, low surface brightness or diffuse galaxies may represent a natural outcome of this process, perhaps as the residue of halos seeded by smaller PBHs that failed to accrete a major baryonic component.

Python's Global Interpreter Lock prevents execution on more than one CPU core at the same time, even when multiple threads are used. However, starting with Python 3.13 an experimental build allows disabling the GIL. While prior work has examined speedup implications of this disabling, the effects on energy consumption and hardware utilization have received less attention. This study measures execution time, CPU utilization, memory usage, and energy consumption using four workload categories: NumPy-based, sequential kernels, threaded numerical workloads, and threaded object workloads, comparing GIL and free-threaded builds of Python 3.14.2. The results highlight a trade-off. For parallelizable workloads operating on independent data, the free-threaded build reduces execution time by up to 4 times, with a proportional reduction in energy consumption, and effective multi-core utilization, at the cost of an increase in memory usage. In contrast, sequential workloads do not benefit from removing the GIL and instead show a 13-43% increase in energy consumption. Similarly, workloads where threads frequently access and modify the same objects show reduced improvements or even degradation due to lock contention. Across all workloads, energy consumption is proportional to execution time, indicating that disabling the GIL does not significantly affect power consumption, even when CPU utilization increases. When it comes to memory, the no-GIL build shows a general increase, more visible in virtual memory than in physical memory. This increase is primarily attributed to per-object locking, additional thread-safety mechanisms in the runtime, and the adoption of a new memory allocator. These findings suggest that Python's no-GIL build is not a universal improvement. Developers should evaluate whether their workload can effectively benefit from parallel execution before adoption.

We investigate the interaction between relativistic jets and supernova (SN) ejecta as a potential origin of X-ray knots in radio galaxies, employing knot A in M 87 as a test case. By modeling the dynamical evolution of the interaction, we evaluate this scenario based on particle acceleration efficiency and spatial morphology. Our modeling indicates that the ejecta shock expands to only ~ 30 pc, which is inconsistent with the observed spatial scale of knot A (~ 60 pc). In contrast, the jet shock can successfully reproduce the observed scale after approximately 3000 yr, with the ejecta being accelerated to a bulk velocity of β~ 0.43. We fit the multi-wavelength spectral energy distribution (SED) using a one-zone leptonic framework, attributing the X-rays to synchrotron radiation from electrons accelerated up to~1 PeV at the jet shock. The derived magnetic field is approximately 70 uG in the SN ejecta rest frame, which is significantly below the equipartition value. Protons may be accelerated up to ~ EeV, supporting the hypothesis that the jets of radio galaxies (RGs) may be the potential site for ultra-high-energy cosmic-ray (UHECR) acceleration within the framework of the jet-ejecta interaction.

The low-altitude economy (LAE) is a rapidly emerging paradigm that builds a service-centric economic ecosystem through large-scale and sustainable uncrewed aerial vehicle (UAV)-enabled service provisioning, reflecting the transition of the 6G era from technological advancement toward commercial deployment. The significant market potential of LAE attracts an increasing number of service providers (SPs), resulting in intensified competition in service deployment. In this paper, we study a realistic LAE scenario in which multiple SPs dynamically deploy UAVs to deliver multiple services to user hotspots, aiming to jointly optimize communication and computation resource allocation. To resolve deployment competition among SPs, an authenticity-guaranteed auction mechanism is designed, and game-theoretic analysis is conducted to establish the solvability of the proposed resource allocation problem. Furthermore, a resilient federated reinforcement learning (FRL)-based solution is developed with strong fault tolerance, effectively countering transmission errors and malicious competition while facilitating potential cooperation among self-interested SPs. Simulation results demonstrate that the proposed approach significantly improves service performance and robustness compared with baseline methods, providing a practical and scalable solution for competitive LAE service deployment.

Structured light fields exploit spin and orbital angular momentum for precision manipulation, advanced imaging, and high-capacity communication. Orbital angular momentum coherent state beams interpolate between Hermite- and Laguerre-Gaussian beams, enabling continuous spatial control. We introduce a symmetry-based framework for joint control of polarization and spatial structure under the shared \$su(2)\$ Lie algebra of spin and orbital angular momentum. Within this structure, we construct total angular momentum fields as superpositions of circular polarization and Laguerre-Gaussian beams, and define their \$su(2)\$ coherent states within fixed-angular-momentum subspaces. A single complex parameter controls both polarization and spatial degrees of freedom, enabling continuous, symmetry-preserving tuning.

Near Field Communication (NFC) is a promising technology for ultra-low-power wearables, yet its short communication range limits its use to narrow-area, point-to-point interactions. We propose a body-scale NFC networking system that extends NFC coverage around the body, enabling surface-to-multipoint communication with distributed NFC sensor tags. This demonstration introduces two key technologies: Meander NFC and picoRing NFC. First, Meander NFC expands a clothing-based NFC networking area up to body scale while enabling a stable readout of small NFC tags occupying 1% of the coverage area. Meander NFC uses a meander coil which creates a spatially confined inductive field along the textile surface, ensuring robust coupling with small tags while preventing undesired electromagnetic body coupling. Second, picoRing NFC solves the weak inductive coupling caused by distance and size mismatches. By leveraging middle-range NFC and coil optimization, picoRing NFC extends the communication range to connect these disparate nodes between the ring and wristband.

In this paper we study the conjugacy relation on one-sided subshifts in the viewpoint of descriptive set theory. We show the conjugacy relation on one sided subshifts with the alphabet set $\{0,1\}$ is non-treeable and non-amenable.

This is the third of five papers comprising The Semantic Arrow of Time. Parts I and II identified computing's hidden semantic arrow of time, the FITO category mistake, and presented the constructive alternative: the OAE link state machine with its mandatory reflecting phase. This paper examines what happens when those principles are violated at industrial scale. Remote Direct Memory Access (RDMA) is the highest-performance data movement technology in production, deployed across Meta's 24,000-GPU clusters, Google's data centers, and Microsoft's Azure infrastructure. We argue that RDMA's completion semantics contain a category mistake: they guarantee placement (data written to a remote NIC buffer) but not commitment (data semantically integrated by the receiving application). We call this the completion fallacy. We document the fallacy through seven temporal stages of an RDMA Write operation, showing that the gap between completion signal and application semantic satisfaction can be arbitrarily large. We trace consequences through four case studies: Meta's RoCE fabric, Google's 1RMA redesign, Microsoft's DCQCN failures, and SDR-RDMA partial completions. A comparative analysis shows CXL 3.0, NVLink, and UALink each address parts of the completion fallacy but none eliminates it entirely. Only a protocol architecture with a mandatory reflecting phase can close the gap between delivery and commitment.

We propose a universal approach based on Hamiltonian inverse engineering to realize a set of parameterized two-qubit gates. This method possesses unique advantages to simultaneous control of transitions among four energy levels, providing a simpler and effective way to construct composite two-qubit gates with fewer operations than traditional methods. Applied to silicon double quantum dots (DQDs), one can realize a one-step fSim gate and a B gate with only one pulse switch. Of note, the method can be further integrated with various optimization theories to enhance gate performance. Based on quantum optimal control theory, we develop a high-fidelity fSim gate scheme with experimentally feasible pulse shapes, featuring an average gate time of 50 ns and a theoretical fidelity of 99.95% in the presence of decoherence and approximation error. By incorporating geometric quantum gate principles, we propose a combined geometric and dynamic fSim gate scheme. Numerical simulations demonstrate that this hybrid scheme exhibits stronger robustness against systematic errors compared to the purely dynamic approach. Our method is generalizable to arbitrary two-qubit physical systems, offering a feasible pathway for rapidly and robustly constructing composite two-qubit gates.

Relativistic Hartree-Fock theory is combined with the Green's function method in coordinate space to study both single-particle bound and resonant states within a unified framework. Within this approach, single-particle resonance energies and widths are unambiguously extracted from the density of states, and the influence of the Coulomb exchange effects on proton resonances in $N=82$ isotones are systematically examined. It is found that the exact treatment of Coulomb exchange terms reduces proton resonance energies of approximate $0.09\sim0.21$ MeV, a significantly smaller effect than that obtained from the phenomenological treatment. Moreover, except for rather narrow resonances, the proton resonance widths are visibly reduced by the Coulomb exchange terms, also being much less pronounced than the phenomenological approach. Notably, clear shell effects are observed in the isotonic evolutions of the resonance energy reductions for specific resonances. All these highlight the necessity of a microscopical and exact treatment of the Coulomb exchange terms.

A flat torus is the quotient of the Euclidean plane over a lattice generated by a basis, and an axis-aligned rectangular tiling of a flat torus is a partition into finitely many rectangles whose sides are axis-aligned. We provide the minimum sum of the perimeter of rectangles for an axis-aligned rectangular tiling, and prove that it is attainable by either exactly one rectangle or exactly two rectangles.

Channel prediction has emerged as an effective solution for acquiring accurate channel state information (CSI) in the presense of channel aging. Existing methods have inherent limitations, with conventional Kalman filter (KF)-based approach being vulnerable to model mismatch and deep learning (DL)-based approaches producing overconfident predictions. To address these issues, we propose a DL-based conformal Bayes filter (DCBF) that integrates DL-based prediction, conformal quantile regression (CQR), and Bayesian filtering. The proposed framework enables principled fusion of calibrated priors and observations, yielding reliable channel predictions with the calibrated uncertainty. Simulation results demonstrate that DCBF significantly improves DL-based prediction and outperforms the KF-based method.

There has been increasing interest in developing efficient quantum algorithms for hard classical problems. The Network Signal Coordination (NSC) problem is one such problem known to be NP complete. We implement Grover's search algorithm to solve the NSC problem to provide quadratic speedup. We further extend the algorithm to a Robust NSC formulation and analyse its complexity under both constant and polynomial-precision robustness parameters. The Robust NSC problem determines whether there exists a fraction (alpha) of solutions space that will lead to system delays less than a maximum threshold (K). The key contributions of this work are (1) development of a quantum algorithm for the NSC problem, and (2) a quantum algorithm for the Robust NSC problem whose iteration count is O(1/sqrt(alpha)), independent of the search space size, and (3) an extension to polynomial-precision robustness where alpha = alpha_o/p(N) decays polynomially with network size, retaining a quadratic quantum speedup. We demonstrate its implementation through simulation and on an actual quantum computer.

Visual design instructors often provide multi-modal feedback, mixing annotations with text. Prior theory emphasizes the importance of actionable feedback, where "actionability" lies on a spectrum--from surfacing relevant design concepts to suggesting concrete fixes. How might creativity tools implement annotations that support such feedback, and how does the actionability of feedback impact novices' process-related behaviors, perceptions of creativity, learning of design principles, and overall outcomes? We introduce VizCrit, a system for providing computational feedback that supports the actionability spectrum, realized through algorithmic issue detection and visual annotation generation. In a between-subjects study (N=36), novices revised a design under one of three conditions: textbook-based, awareness-centered, or solution-centered feedback. We found that solution-centered feedback led to fewer design issues and higher self-perceived creativity compared with textbook-based feedback, although expert ratings on creativity showed no significant differences. We discuss the implications for AI in Creativity Support Tools, including the potential of calibrating feedback actionability to help novices balance productivity with learning, growth, and developing design awareness.

A three-way coupled thermo-mechanical fracture model is presented to predict the damage of brittle ceramics, in particular α-SiC, over a wide range of temperatures (20-1400 C). Predicting damage over such a range of temperatures is crucial for thermal protection systems for many systems such as spacecraft. The model, which has been implemented in MOOSE, is divided into three modules: elasticity, damage phase field, and heat conduction. Analytical approaches for determining crack length scales are presented for both simple tension and simple shear. Validation tests are conducted for both flexural strength and fracture toughness over the specified range of temperatures. Flexural strength simulation results fall within the uncertainty region of the experimental data, and mode I fracture toughness simulation results are also in agreement with the experimental data. Mode II and mixed mode fracture toughness simulations results are presented with the modified G-criterion. Finally, the parallel computing capabilities of the model is considered in various scalability tests.

This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the diffusion process. To construct a robust estimator, we first approximate the transition density of the diffusion process to the Gaussian density by using Kessler's approach and then employ two types of minimum robust divergence estimation methods. In this paper, we provide the asymptotic properties of the robust estimator using $γ$-divergence. Furthermore, we derive the conditional influence functions of the estimation using divergences and discuss its boundness.

For $N\geq n$, let $P_{N,n}$ be a random polytope in ${\mathbb R}^n$ with vertices $\pm X_i$, $1\leq i\leq N$, where $X_1,\dots,X_N$ are i.i.d standard Gaussian vectors in ${\mathbb R}^n$. Random polytopes $P_{N,n}$, as well as their duals, are classical objects of interest in high-dimensional convex geometry and local Banach space theory. In this paper, we provide a {\it dimension-independent} bound on the cotype of the corresponding normed space $({\mathbb R}^n,\|\cdot\|_{P_{N,n}})$, generated by $P_{N,n}$. Let $K'\geq K>1$, and assume that $K'\geq \frac{N}{n}\geq K$. We show that with probability $1-o(1)$, for any $k\geq 1$, and any collection $y_1,\dots,y_k$ of vectors in ${\mathbb R}^n$, $$ {\mathbb E}_σ\,\Big\|\sum_{i=1}^k σ_i y_i\Big\|_{P_{N,n}}^q \geq \frac{1}{C_q^q}\sum_{i=1}^k \big\|y_i\big\|_{P_{N,n}}^q, $$ where $σ=(σ_1,\dots,σ_k)$ is a vector of random signs, and where $q\in [2,\infty)$ and $C_q\in[1,\infty)$ may only depend on $K,K'$. We discuss the result in context of infinite-dimensional Banach spaces.

Hippocampal neurons track positions of self, others, and gaze direction. However, it is unclear how their respective neural codes differ enough to avoid confusion while allowing for abstraction. We recorded from populations of hippocampal neurons while participants performed a joystick-controlled virtual prey pursuit task involving multiple moving agents. We found that neurons have mixed selective responses that map positions of self, prey, and predator, as well as gaze. Their codes occupied mostly orthogonal subspaces, but these subspaces geometric structure allowed them to be aligned by simple linear transformations. Moreover, their geometry supported generalization across spatial maps, such that a linear rule learned on one agent transfers to another. This scheme enables reliable individuation and abstraction across both agent identity and viewpoint. Together, these findings suggest that hippocampal spatial knowledge is structured as a family of geometrically related manifolds that can be flexibly aligned to different agents and gaze directions.

Continuous-variable-discrete-variable (CV-DV) quantum simulators offer a natural route to simulating bosonic dynamics relevant to many branches of physics and chemistry. However, programmable simulation of arbitrary dynamics is an outstanding challenge. In particular, simulating anharmonic dynamics, which is ubiquitous across the physical sciences, is challenging due to the highly harmonic nature of oscillators used in CV-DV simulators. Here, we experimentally demonstrate programmable CV-DV quantum simulation of anharmonic dynamics in a range of double-well potentials, implemented in a trapped-ion system. We synthesise the time-evolution operators using a bosonic-quantum-signal-processing subroutine, which allows the potential to be tuned between experiments by controlling classical experimental parameters. We observe coherent dynamics in various double-well potentials, where a wavepacket tunnels through the potential barrier, and we suppress this effect by programmatically introducing asymmetry.

Sparse matrix-vector multiplication (SpMV) is a fundamental operation in scientific computing, data analysis, and machine learning. When the data being processed are sensitive, preserving privacy becomes critical, and homomorphic encryption (HE) has emerged as a leading approach for addressing this challenge. Although HE enables privacy-preserving computation, its application to SpMV has remained largely unaddressed. To the best of our knowledge, this paper presents the first framework that efficiently integrates HE with SpMV, addressing the dual challenges of computational efficiency and data privacy. In particular, we introduce a novel compressed matrix format, named Compressed Sparse Sorted Column (CSSC), which is specifically designed to optimize encrypted sparse matrix computations. By preserving sparsity and enabling efficient ciphertext packing, CSSC significantly reduces storage and computational overhead. Our experimental results on real-world datasets demonstrate that the proposed method achieves significant gains in both processing time and memory usage. This study advances privacy-preserving SpMV and lays the groundwork for secure applications in federated learning, encrypted databases, scientific computing, and beyond.

The combination of strong spin-orbit coupling and Coulomb interactions makes the $5d$ iridates a unique platform for realizing novel correlated electronic states. Here, utilizing infrared spectroscopy, we demonstrate that a robust Mott insulating state persists in the $1/3$-hole self-doped system La$_3$Ir$_3$O$_{11}$, evidenced by the collapse of the Drude response and the emergence of sharp excitations across the Mott gap. Our theoretical calculations reveal that the insulating behavior arises from the cooperative interplay of structural distortions, spin-orbit coupling, and Coulomb interactions. Specifically, octahedral distortion and Ir-Ir dimerization split the $t_{2g}$ orbitals, driving the $J_{\mathrm{eff}} = 1/2$ bands toward half-filling while keeping the $J_{\mathrm{eff}} = 3/2$ bands away from it. Consequently, electron correlations induce an orbital-selective Mott transition in the $J_{\mathrm{eff}} = 1/2$ bands, whereas a band-insulating gap develops in the $J_{\mathrm{eff}} = 3/2$ bands, thereby stabilizing the unconventional insulating state in La$_3$Ir$_3$O$_{11}$. These findings provide new insights into the design and understanding of the insulating ground state of spin-orbit-coupled iridates.

The thermodynamics of randomly quenched disordered Ising metamagnet has been studied by Monte Carlo simulations. The disorder has been implemented either by inserting nonmagnetic impurity or by uniformly distributed quenched random magnetic field. The staggered magnetisation ($M_s$) (calculated from the sublattice magnetisation) and the corresponding staggered susceptibility ($χ$) are studied as functions of the temperature ($T$). The antiferromagnetic phase transition has been found while cooling the system from the high temperature paramagnetic phase. The transition temperature(or pseudocritical temperature ($T_c$)) has been found to decrease as the concentration ($p$) of nonmagnetic impurity increased. The nonmagnetic impurity dependent staggered magnetisation has been found to show the scaling behaviour $M_sp^b \sim (T-T_c)p^a$ (with $a \cong -0.95$, $b \cong 0.09$ and $T_c \cong 4.45$) obtained through the data collapse. The zero temperature staggered magnetisation ($M_s(0)$) has been found to decrease linearly. The critical temperature($T_c$) is showing a linear ($T_c=mp+c$) dependence with the concentration ($p$) of nonmagnetic impurity. The antiferromagnetic phase transition has been found to take place at lower temperature for the higher value of the width ($s$) of the uniformly distributed quenched random field. The critical temperature ($T_c$) has been found to show the nonlinear dependence ($T_c=a+bs+cs^2$) on the width ($s$) of the uniformly distributed random magnetic field. The extrapolation (both for $p \to 0$ and $s \to 0$) restores the Neel temperature of three dimensional pure Ising antiferromagnet.

This paper presents an evaluation of three LLMs, GPT-4, Claude 3, and Gemini, for automated Behaviour-Driven Development (BDD) scenarios generation. To support this evaluation, we constructed a dataset of 500 user stories, requirement descriptions, and their corresponding BDD scenarios, drawn from four proprietary software products. We assessed the quality of BDD scenarios generated by LLMs using a multidimensional evaluation framework encompassing text and semantic similarity metrics, LLM-based evaluation, and human expert assessment. Our findings reveal that although GPT-4 achieves higher scores in text and semantic similarity metrics, Claude 3 produces scenarios rated highest by both human experts and LLM-based evaluators. LLM-based evaluators, particularly DeepSeek, show a stronger correlation with human judgment than with text similarity and semantic similarity metrics. The effectiveness of prompting techniques is model-specific: GPT-4 performs best with zero-shot, Claude 3 benefits from chain-of-thought reasoning, and Gemini achieves optimal results with few-shot examples. Input quality determines the effectiveness of BDD scenario generation: detailed requirement descriptions alone yield high-quality scenarios, whereas user stories alone yield low-quality scenarios. Our experiments indicate that setting temperature to 0 and top_p to 1.0 produced the highest-quality BDD scenarios across all models.

Orbital angular momentum (OAM), a topological degree of freedom of light, is theoretically invariant under continuous deformations; yet, its physical observability degrades precipitously in complex media, creating a fundamental "topology-observability gap." Here, we propose a novel paradigm for topological measurement based on the non-separable coupling between polarization and topological features in vectorial vortex beam. By constructing a topological non-separability measure derived from global Stokes fields, and integrating it with a physics-guided machine learning calibration framework that combines Bayesian Gaussian process regression with XGBoost-driven adaptive model selection, we achieve high-fidelity identification of topological features up to 200. Crucially, this robustness persists even when beam intensity and phase structures are completely distorted by extreme complex media, including strong atmospheric turbulence, oceanic turbulence, and high-temperature jet exhausts. This approach overcomes the dual bottlenecks of limited accessible OAM modes and susceptibility to perturbations that constrain conventional methods. Our work not only bridges the fundamental divide between topological theory and physical observability, but also establishes a robust framework for the reliable deployment of high-dimensional OAM in real-world complex environments, promising exciting advancements for wireless optical communications, remote topological sensing, and classical analogs of quantum information protocols.

This MSc dissertation is based on the papers arXiv:2502.12694 and arXiv:2408.14813. The AdS/CFT correspondence provides a powerful framework for modeling strongly coupled gauge theories and, as a consequence, investigating non-perturbative phenomena in QCD. In this work, following an overview of the ideas that encapsulate the AdS/CFT correspondence, we present a self-consistent dynamical holographic QCD model within the Einstein-Maxwell-dilaton framework, derived from the coupled field equations, to study the mass spectra and melting behavior of heavy and exotic mesons at finite temperature and density. Finite temperature analyses reveal a confinement-deconfinement transition and sequential quarkonia melting. At finite density, an increase in chemical potential accelerates meson melting, with spectral functions evolving smoothly across the phase transition line. Finally, using a nonlinear Einstein-Born-Infeld-dilaton model, magnetic field effects demonstrate a shift from inverse magnetic catalysis to magnetic catalysis, highlighting the impact of spatial anisotropy on quarkonium stability.

Smartphones equipped with sensors such as accelerometers, gyroscopes, and magnetometers offer valuable opportunities for physics education, allowing students to measure motion using their own devices. However, commonly used applications provide acceleration only in the device-fixed coordinate system, which makes it difficult to analyze two- or three-dimensional motion when the device rotates. To address this limitation, we developed a web-based accelerometer application that can provide acceleration in a stationary global coordinate system. This is achieved by simultaneously recording acceleration in the device-fixed coordinate system and Euler angles, and converting them to rotation-compensated acceleration in real time. We also built a companion web application for numerical integration, noise reduction, and visualization of the measured data. Both applications are installation-free and can be accessed directly through a smartphone browser. We demonstrate the capabilities of the newly developed system through several representative types of motion, including sliding motion, projectile motion, and circular motion, by showing that rotation-compensated acceleration enables accurate reconstruction of velocity, displacement, and trajectories even when the smartphone changes its orientation. The applications were implemented in undergraduate mechanics classes, where students used them in group-based experiments. Classroom observations suggested that the use of these tools facilitated a deeper understanding of the relationships among acceleration, velocity, and position. These results suggest that rotation-compensated smartphone measurements provide a practical and effective tool for physics education.

We performed numerical simulations along with radiative transfer calculations to reproduce an intriguing asymmetric shoulder feature in the dust-continuum emission of the protostellar disk around one of the eDisk targets, the Class 0 protostar IRAS 16544-1604 in CB 68. This is our first attempt to bridge the theoretical works of protostellar disk evolution and the eDisk observations. We found that while our hydrodynamic simulations form spiral structures caused by gravitational instability, they become less discernible after the disk is inclined and convolved with the telescope beam. The widths of the spiral structure as obtained by our numerical simulations are ~0.1-0.8 times the eDisk beam size of 4.5 au. Our modeling effor implies that the apparent absence of spiral features in the eDisk observations does not necessarily indicate the real absence of internal substructures and gravitational instability. We also found that the asymmetric shoulder structure of the continuum profile along the major axis appears when the disk is massive enough with a Toomre parameter Q~1. This mechanism offers a potential explanation for the observed, asymmetric shoulder features in the disks surrounding IRAS 16544-1604 and the other eDisk sources.

Neural networks offer powerful tools to solve partial differential equations (PDEs). We present a Variational Physics-Informed Neural Network (VPINN) designed for parabolic problems. Our approach combines a classical time discretization with a composed loss function, which minimizes the residual's dual norm at every time step. We validate the framework by modeling the freezing of coffee extracts in an industrial cylinder. The simulation accounts for temperature-dependent properties and experimental data. It successfully captures the thermal dynamics of the process.

We study the $P_3$-convexity, the path convexity generated by all three-vertex paths, and focus on the problem of counting the $P_3$-convex vertex sets of a graph $G$, denoted by $\noc(G)$. First, we settle the associated extremal question: we characterize the $n$-vertex graphs maximizing $\noc(G)$ among all graphs and determine the connected extremal graphs. Next, we investigate computational complexity and show that counting $P_3$-convex sets is $\#\mathsf{P}$-complete already on split graphs, even under additional structural restrictions. On the positive side, we identify two tractable subclasses, namely trees and threshold graphs, and obtain linear-time algorithms for both. Finally, we design nontrivial exact exponential-time algorithms for general graphs, combining structural decomposition, propagation rules capturing forced consequences of $P_3$-convexity, and fast counting of independent sets in auxiliary graphs. The resulting strategy becomes particularly effective on graph classes where large independent sets are guaranteed and can be found efficiently.