Modern agentic frameworks (e.g., CrewAI and AutoGen) have evolved into complex, autonomous multi-agent systems, introducing unique reliability challenges beyond earlier pipeline-based LLM libraries. However, existing empirical studies focus on earlier LLM libraries or task-level bugs, leaving the unique complexities of these agentic frameworks unexplored. We bridge the gap by conducting a comprehensive study of 409 fixed bugs from five representative agentic frameworks. We propose a five-layer abstraction to capture structural complexities in agentic frameworks, spanning from orchestration to infrastructure. Our study uncovers specialized symptoms, such as unexpected execution sequences and user configurations ignored, which are unique to autonomous orchestration. We further identify agent-specific root causes, including modelrelated faults, cognitive context mismanagement, and orchestration faults. Statistical analysis reveals cross-framework consistency and significant associations among these bug dimensions. Finally, our automated pattern mining identifies frequent bug-triggering patterns (e.g., model backend-ID combinations), and we show their transferability across different framework designs. Our findings facilitate cross-platform testing and improve the reliability of agentic systems.

We investigate the well-posedness of scalar conservation laws whose flux depends on the solution both pointwise and nonlocally through integral averages. Our analysis is based on a fixed-point formulation, in which the nonlocal dependence is incorporated as a space- and time-dependent component of the flux, together with classical stability estimates for entropy solutions. This framework unifies and extends several models previously considered in the literature and applies, in particular, to conservation laws with memory effects (nonlocality in time) or delay. We prove the existence and uniqueness of weak entropy solutions on a sufficiently short time horizon and show that under additional assumptions, existence and uniqueness can be obtained on any finite time horizon. In addition, we present numerical simulations to illustrate the qualitative effects of memory on the solution dynamics.

While the high oxidation states in heavy alkali fluorides (Cs, Ba, Ra) have been attributed to a pressure-driven upshift of energy level of inner p states, this route is largely ineffective for Rb because its smaller ionic radius suppresses the required level rise even under strong compression. Here, we predict a high-pressure layered ternary phase, RbBF5, in which 12-fold truncated-cube-like F coordination around Rb breaks local symmetry and activates the Rb 4p inner shell. The resulting orbital splitting selectively elevates the in-plane Rb 4px,y levels toward the F 2p manifold, enabling inner-shell participation and stabilizing Rb-F bonding under compression. More broadly, this symmetry-lowering coordination motif may provide a general mechanism for activating inner-shell p states in other alkali metals (e.g., K and Cs inner p states). These findings extend inner-shell chemistry to lighter main-group elements and establish a design principle for accessing unconventional bonding and oxidation states at high pressure.

A color Lie algebra is a generalization of a Lie (super)algebra by an Abelian group $Γ$. The underlying vector space and defining relations of the algebra are graded by $Γ$, and the color Lie algebra admits graded Casimir elements. Furthermore, its loop algebra admits graded central extensions. We present a general method for constructing 2nd order graded Casimir elements and graded central extensions for a given color Lie algebra and its loop algebra, respectively. We also show that there exists a large class of color Lie algebras admitting such graded Casimir elements or central extensions by providing three examples, namely, $\mathfrak{sl}(2)$ for $Γ= \mathbb{Z}_3^2$, and $\mathfrak{q}(n)$ and $\mathfrak{osp}(m|2n)$ for $Γ= \mathbb{Z}_2^2$.

In recent years, remarkable progress has been made for Distribution dependent stochastic equations (DDSDEs) with singular interactions, existing results include wellposedness, propagation of chaos, entropy cost inequality and ergodicity. As a continuation to the existing study, in this paper we establish Bismut type formulas for the intrinsic derivative of DDSDEs with singular interactions, which extends the existing formula established for the case with Lion's differentiable drifts.

As AI agents become increasingly capable of complex knowledge tasks, the lack of context limits their capability to proactively reason about a user's latent needs throughout a long evolving project. In scientific research, many researchers still manually query a deep research system and compress their rich project contexts into short, targeted queries. Further, a deep research system produces exhaustive reports, making it difficult to identify concrete actions. To explore the opportunities of research assistants that are proactive throughout a research project, we conducted several studies (N=42) with a technology probe and an iterative prototype. The latest iteration of our system, Omakase, is a research assistant that monitors a user's project documents to infer timely queries to a deep research system. Omakase then distills long reports into suggestions contextualized to their evolving projects. Our evaluations showed that participants found the generated queries to be useful and timely, and rated Omakase's suggestions as significantly more actionable than the original reports.

Fast and reliable inference of gravitational-wave source parameters is crucial for analyzing large catalogs that are reaching the size of hundreds of detections, and for identifying short-lived electromagnetic counterparts. Neural posterior estimation has emerged as a powerful inference method, where the model is trained on simulated gravitational-wave data at considerable computational cost, but thereafter enables extremely fast and inexpensive inference at test time. Here, we extend this approach by incorporating domain-specific physical insights and methods in the model architecture. These include compressing the data by heterodyning against a reference waveform chosen via approximate likelihood maximization, removing parameter degeneracies through tailored coordinate systems, and eliminating known multimodalities by folding the parameter space. As a result, the network is approximately equivariant to changes in the source parameters, and achieves a reduced training cost and improved model interpretability. Our implementation, called labrador, can be trained end-to-end on a 1-day timescale on $\sim 10^2$ CPU cores and a V100 GPU, achieving a median importance-sampling efficiency of 1% on quadrupolar, aligned-spin signals in a broad mass range (chirp mass $\mathcal M \in 1\text{-}50\,\mathrm{M}_\odot$, mass ratio $q > 0.1$). labrador is the first neural inference code to achieve extensive coverage of long-duration signals with secondary masses $m_2 < 10\,\mathrm{M}_\odot$, rendered possible by its equivariance property. Among our novel contributions is a numerically stable procedure that enables neural posterior estimation when the simulation and inference priors differ.

We present a theoretical model for the power spectrum and bispectrum of galaxy clustering that exploits the complementarity between small-scale power spectrum information and large-scale bispectrum measurements. We extend the FOLPS code by combining its one-loop EFT galaxy power spectrum with a tree-level galaxy bispectrum projected onto the tripolar spherical harmonics (Sugiyama) basis. To access additional small-scale information, we also consider a line-of-sight damping factor in both statistics, mirroring approaches commonly used in studies of redshift-space distortions. We test the model using DESI DR2 galaxy mocks. Even without damping, the joint analysis of the EFT power spectrum and bispectrum significantly improves constraints and reduces parameter degeneracies relative to power spectrum analyses alone. For LRG-like samples, including the damping further extends the range beyond $k\sim 0.3 \,h \text{Mpc}^{-1}$ in the power spectrum and $k \sim 0.24 \,h \text{Mpc}^{-1}$ in the bispectrum without introducing statistically significant parameter biases. This leads to up to $\sim 30\%$ tighter constraints on $A_s$ and $ω_{cdm}$. For low signal-to-noise tracers such as QSOs, however, the damping parameters are weakly constrained and can absorb noise fluctuations, leading to shifts in inferred parameters. Similar limitations may arise in models where cosmological information is encoded in power-spectrum shape features degenerate with the damping, such as scenarios with massive neutrinos. In contrast, for $w_0w_a$CDM we obtain $15\%$ and $21\%$ tighter constraints on $w_0$ and $w_a$, respectively, yielding a deviation from constant dark energy at slightly more than the $1σ$ level using full-shape information alone. The code is publicly available at https://github.com/cosmodesi/FolpsD

For a spectrally negative Lévy process with Laplace transform $ψ$, the $q$-scale function is characterized as the function whose Laplace transform is $(ψ(\cdot)-q)^{-1}$. It has applications in fluctuation theory, for example, exit problems and first hitting probabilities. It is also used in areas like ruin theory, risk theory, continuous state branching processes and optimal control. In this paper, we extend the scale function representation of Ivanovs (2021) from spectrally negative Lévy processes with phase-type jumps to the general case of matrix-exponential jumps. The extension is non-trivial because the probabilistic arguments employed by Ivanovs rely on an embedding to a Markov-modulated Brownian motion, a framework that does not accommodate the algebraic generality of matrix-exponential distributions. We overcome this limitation by embedding the Lévy process into a stochastic fluid process modulated by a rational arrival process (RAP), a class of continuous-valued Markov processes driven by orbit processes. This approach yields iterative schemes related to those of Ivanovs (2021) to provide a simple and explicit formula for the scale function. Our method gives the same fixed point when restricted to the phase-type case, and demonstrates the utility of orbit representations in analytical problems beyond the phase-type setting.

AI development is embracing open-source paradigm, but the fundamental distinction between AI models and traditional software artifacts may lead to a divergent open-source development paradigm with different collaborative practices, which remains unexplored. We therefore bridge the knowledge gap by quantifying and characterizing the differences in the collaborative development paradigms of traditional open source software (OSS) and open source AI models (OSM), and investigating the underlying factors that may drive these distinctions. We collect 1,428,792 OSS repositories from GitHub and 1,440,527 OSM repositories from HF Hub, and conduct comprehensive statistical, social network and content analyses to measure and understand the differences in collaboration intensity, collaboration openness, and user innovation across the two development paradigms, complementing these quantitative results with semi-structured interviews. In consequence, we find that compared to OSS development paradigm, the OSM development paradigm exhibits significantly lower collaboration intensity; lower collaboration openness regarding direct contribution while persisting relatively open knowledge exchange; and a divergence toward adaptive utilization user-innovation rather than collaborative improvement. Through semi-structured interviews, we further elucidate the socio-technical factors underlying these differences. These findings reveal the paradigmatic divergence in open source development between traditional OSS and OSM across three critical dimensions of open source collaboration and potential underlying factors, shedding light on how to improve collaborative work techniques and practices within the context of AI development.

Inspired by the work of Atar and Miyazawa [1] (2026) as well as applications to energy-saving problems, we are interested in the heavy-traffic limit of the stationary queue length distribution, which is not addressed in [1]. In this paper, we consider this heavy-traffic limit for the single server queue which has the most general possible state-dependence. Namely, arrival and service speeds may take any values depending on the queue length. Here, the terminology, heavy-traffic limit, stands for a diffusion-scaled limit in heavy-traffic for processes, distributions and modeling primitives. This general model is referred to as a state-dependent queue. There are two motivations for this generalization. One is interest in the state-dependent queue itself because it allows finer control of service speed in application. Another is making it clear how the heavy-traffic limit is obtained under what conditions for the state-dependent queue. Thus, we start to study basic properties of this state-dependent queue, including its stability. We then take the sequence of the stationary distributions of its diffusion scaled queue-length processes. We have three main results for this sequence. We first show that it is tight if the heavy-traffic limit of their drifts exists and is negative as the queue length goes to infinity, where a drift is the arrival speed minus the service speed. We next assume the condition that the limit of every vaguely convergent subsequence has a density, which is referred to as a density condition, and show that the heavy-traffic limit of the stationary distributions is obtained in a closed form if and only if that negative drift condition holds. We then show that the density condition is always satisfied for the multi-level queue, so the problem is nicely solved for the multi-level queue.

Toxic interactions in open-source software development harm community collaboration. To combat this, we propose ToxiShield, a realtime browser extension that identifies and detoxifies toxic code reviews. The framework comprises three modules: toxicity identification, reasoned multiclass classification, and code review detoxification. Our fine-tuned BERT-based binary classifier achieved a 97% F1-score on 38,761 code review texts. For multiclass classification, Claude 3.5 Sonnet with prompt engineering achieved a 39% MCC and 42% F1 on 1,200 samples. Finally, our fine-tuned Llama 3.2 detoxification model reached 95.27% style transfer accuracy, 97.03% fluency, 67.07% content preservation, and an 84% J-score. Validation with 10 software developers suggests ToxiShield effectively fosters a more inclusive open-source environment.

In three dimensional toroidal domains without symmetry, the standard magnetohydrodynamic (MHD) equilibrium model used for magnetic confinement fusion does not generally support smooth solutions. Instead, solutions have singular plasma currents on resonant magnetic surfaces that violate the MHD assumption of length-scale separation, further leading to the non- or slow convergence of numerical approximations under refinement. In this work, we present an improved equilibrium principle derived from a statistical model for plasma fluctuations. Instead of being static, we assume that the plasma magnetic field is ergodically and rapidly fluctuating relative to the MHD time scale. By averaging the resulting force, we derive a variational equilibrium problem for the statistical mean magnetic field which depends on fluctuation variance. Then, through asymptotics, numerical simulations, and a Grad-Shafranov type argument, we show that the variational principle supports smooth solutions for specific fluctuation statistics chosen to minimally modify the standard equilibrium modeling paradigm. Physically, this model smooths singular current sheets with a length scale determined by the magnetic field fluctuations.

Laser cooling of alkali atoms typically requires time-varying magnetic fields, introducing unwanted coupling between atom preparation and coherent operations. Here we demonstrate sub-Doppler laser cooling and optical transport of alkali atoms in a fully static magnetic-field configuration. Using a blue-detuned Type-II magneto-optical trap (MOT) operating on the closed $F=3 \rightarrow F'=2$ transition of the D2 line in cesium, we achieve temperatures of 17(1) $μ$K without changing the magnetic-field gradient between cooling stages. This enables direct loading into a shallow optical lattice and transport over 17 cm within the same static-field environment. In contrast to conventional alkali cooling schemes with dynamic fields, our approach establishes a continuous cooling and transport protocol compatible with static-field platforms. These results validate Type-II cooling as a practical technique for alkali atoms and provide a new route toward continuous-operation architectures in sensing and quantum computing.

Understanding the structures and energetics of nanovoid-solute complexes is essential for elucidating the coupled evolution of defects in metals. Yet their vast and complex configurational space poses a major challenge to conventional approaches. Using W-Re as a representative system, we demonstrate that solute segregation at nanovoid surfaces can be decomposed into direct nanovoid-solute interactions and nanovoid-mediated solute-solute interactions. Both are governed by local coordination motifs, with identical motifs giving nearly identical energetics. Based on first-principles data, we trained machine-learning models to map diverse local motifs to their energetics, enabling the energetics of any nanovoid-solute complex to be reconstructed from a finite set of constituent local motifs. We further developed a size-dependent configurational-search framework to efficiently identify thermodynamically stable structures, using exhaustive enumeration, simulated annealing, and greedy addition for small, medium-sized, and large complexes, respectively. This framework enabled the construction of a large database, revealed the staircase-like segregation behavior of Re, and derived a simple criterion based on Re surface coverage for rapid energy prediction across a wide size range. It also links Re segregation to vacancy-mediated nanovoid evolution and provides benchmarks for existing models and empirical potentials. Extensions to Os and Ta support the generality of the local-motif concept, and the predicted segregation behavior of solutes at nanovoids agrees with a range of experimental observations. This work establishes a physically transparent, accurate, and transferable framework for studying nanovoid-solute co-evolution in metals and provides reliable energetic inputs for multiscale simulations.

In this paper we study a path-following problem on $R^3$ with a non-holonomic constraint. The geometric structure associated to the velocity constraint is explored, and general principles for constructing guiding vector fields are obtained, fulfilling the path-following requirements on a neighborhood of the desired path while allowing the design of vector fields to be conducted in global coordinates.

Quantum-mechanical incompatibility, which precludes the simultaneous precise measurement of non-commuting observables, imposes fundamental limits on the rate at which classical information can be extracted. While the potential to surpass these limits using entangling collective measurements has been explored for two parameters, the regime of three or more parameters remains largely unexplored despite its fundamental and technological importance. Here, we investigate the three-parameter trade-off relations for estimating the Bloch vector components of a qubit, comparing conventional individual measurements with entangling collective measurements. We theoretically derive and experimentally implement optimal collective measurements on two identically prepared qubits using a programmable photonic circuit. Our experimental results demonstrate a clear violation of the entanglement-free trade-off relation -- by an average of 16 standard deviations -- achieving a tomography precision beyond the reach of any individual measurement scheme. This work directly confirms that optimal collective measurements can surpass the fundamental quantum limits of individual schemes in a three-parameter setting -- thereby deepening our understanding of quantum uncertainty relations beyond the two-parameter regime and providing a clear strategy to overcome the precision trade-offs imposed by quantum incompatibility.

This paper establishes an approximation theorem for randomized neural networks (RaNNs) whose hidden-layer parameters are uniformly sampled from a prescribed bounded domain. Our analysis shows that, for RaNNs of the form $\mathop{\sum}_i W_i σ(A_i, b_i)$, the size of the sampling domain required to achieve optimal approximation is intrinsically linked to the smoothness of the target function and the number of neurons. Motivated by this theoretical insight, we integrate a partition of unity (PoU) with RaNNs to develop an adaptive physics-informed randomized neural network (PIRaNN) method for solving partial differential equations with limited local regularity. The proposed adaptive strategy refines the PoU based on a posteriori error indicators, enabling the network to efficiently capture localized solution features. Numerical experiments validate the theoretical results and demonstrate the strong approximation capabilities of RaNNs, confirming the effectiveness of the adaptive PIRaNN method on a range of benchmark problems.

Spatial self-similarity is a hallmark of critical phenomena. We study the dynamic process of percolation, in which bonds are incrementally added to an initially empty lattice until the system becomes fully occupied. By tracking the gap -- the size increment of clusters upon bond addition -- and the corresponding merged cluster, we identify scale-invariant temporal patterns in both quantities throughout a large portion of the process. This reveals a form of temporal self-similarity that has not been reported before. We further establish quantitative relations between the dynamic scaling exponents and the conventional static critical exponents, which enable the determination of critical behavior without prior knowledge of the critical point. The same self-similar dynamics is observed in both bond and site percolation on lattices and networks, and extends to other systems such as explosive and rigidity percolation. Moreover, similar temporal scaling is found in the initial nonequilibrium evolution of the Bak-Tang-Wiesenfeld sandpile model, suggesting a dynamic critical behavior distinct from its equilibrium state. These results provide a unified framework for understanding critical dynamics and may find applications in a broad range of complex systems.

Stringology-Based Cryptanalysis (SBC) offers a suitable and a structurally aligned approach for uncovering structural patterns in stream ciphers that traditional statistical tests may often fail to detect. Despite \texttt{EChaCha20}'s design enhancements, no systematic investigation has been performed to determine whether its expanded 6$\times$6 state matrix and modified Quarter-Round Function (\texttt{QR-F}) introduce subtle keystream patterns, rotational biases, or partial collisions that could serve as statistical distinguishers. As such, addressing this gap is critical to ensure that the cipher's modifications do not unintentionally reduce its security margin. Therefore, this paper leverages Knuth-Morris-Pratt (\texttt{KMP}) and Boyer-Moore (\texttt{BM}) algorithms to analyze \texttt{EChaCha20}, which is a variant of ChaCha20 that features an expanded 6$\times$6 state matrix and an enhanced \texttt{QR-F}. The author has developed and optimized adaptations of the \texttt{KMP} and \texttt{BM} algorithms for 32-bit word level pattern analysis and employed them to investigate $m$-bit pattern frequency distributions to assess the \texttt{EChaCha20}'s resistance of rotational-differential attacks. Our experimental results on large-scale one million keystream datasets have confirmed that \texttt{EChaCha20} is able to maintain strong pseudorandomness at 16-bit and 32-bit levels with minor irregularities observed in the 8-bit domain. In addition to these, the differential tests have indicated a rapid diffusion, exhibiting an avalanche effect after two \texttt{QR-F} rounds and no statistically significant rotational collisions were observed within the evaluated bounds, consistent with expected ARX diffusion behavior beyond 3 rounds. This work puts forward SBC as a complementary tool for ARX cipher evaluation and provide new thoughts on the security properties of \texttt{EChaCha20}.

The design of coupler-based superconducting two-qubit gates simplifies circuit layout and alleviate frequency crowding, thereby enhancing the scalability and flexibility of quantum chips. However, in such architectures, a trade-off often exists between suppressing crosstalk and reducing gate duration, and how to achieve synergistic optimization of both remains an open challenge. To address this, this paper proposes a coupler-assisted superconducting two-qubit geometric gate scheme oriented towards crosstalk robustness. By introducing additional parametric degrees of freedom, the scheme steers the system evolution along desired trajectories, thereby flexibly avoiding crosstalk-sensitive operational regions. Numerical simulations demonstrate that the proposed scheme can effectively suppress crosstalk errors while enabling fast gate operations, and exhibits strong robustness against typical experimental imperfections such as qubit frequency drift. Moreover, even when accounting for unavoidable high-frequency oscillation terms and qubit decoherence in realistic physical systems, our crosstalk-robust two-qubit geometric gates still achieve high fidelity. This work provides a feasible pathway toward robust and efficient two-qubit gate implementation in superconducting quantum computation.

This paper investigates the optimal privacy-aware networked control problem, in which the dynamical system affected by a private input process sends its measurement to a remote controller after stochastic quantization. An adversary seeks to infer private system inputs from quantization results and control outputs. The optimal privacy-aware quantizer and controller are obtained by solving a stochastic control problem with mutual information regularization, where the mutual information measures the privacy leakage through the quantizer and controller. We first derive the coupled Bellman equations for the optimal quantizer and controller using the dynamic programming decomposition method. We then analyze the structural properties of the solution, showing that the optimal controller is deterministic, while the optimal quantizer regulates the adversary's belief in a closed-loop manner to enhance privacy. To enable numerical optimization, the quantizer and controller are jointly parameterized and then updated via policy gradient methods, and a binary classification approach is used to approximate privacy leakage. Finally, we validate the effectiveness of the proposed approach through numerical experiments on a building control system.

We introduce a class of paired binary matrices called admixed arrays, which arise in analyses of large-scale genetic data and can be viewed as weighted edge colorings of complete bipartite graphs. This combinatorial structure gives rise to two natural families of marginal constraints: a row-sum constraint and a paired column-sum constraint, the latter inducing an inequality among entries of the matrix pair. We study the enumeration of admixed arrays under these constraints in dense regimes. First, we obtain exact formulas for the sizes of the families defined by each constraint in isolation and derive a finite-size criterion characterizing when one constraint is more restrictive than the other. In the large-dimension limit, this comparison simplifies to an entropy inequality, yielding an information-theoretic interpretation and a quantifiable error bound in the semi-regular case. We then analyze the asymptotic enumeration of the doubly constrained family in a semi-regular setting. Using saddle-point approximation and probabilistic techniques, we derive a detailed asymptotic expansion for the logarithm of the count, isolating an explicit fourth-moment contribution and establishing quantitative control of the higher-order remainder. A consequence of this analysis is a phenomenon absent from classical binary and integer matrix models: in the regime $N=Θ(P)$ with uniform margins and density bounded away from zero, the two constraint families obey the independence heuristic with a correction factor $1/\sqrt[4]{e}$ rather than the familiar $e^{\pm1/2}$. Numerical experiments corroborate the analytical approximations, and we implement and extend an algorithm of Miller and Harrison (2013) as open-source software to enumerate constrained admixed arrays.

We derive and analyze a relativistic quantum hydrodynamic (RQHD) system on the Heisenberg group. Starting from the Klein--Gordon--Poisson system, we apply the Madelung transformation to obtain a fluid-type model in which the relativistic and quantum parameters are explicitly separated. The Heisenberg-group structure gives rise to an additional geometric term in the momentum equation, reflecting the underlying noncommutative structure. A central analytical difficulty is the possible appearance of vacuum, where the phase function and the quantum potential become singular. To address this issue, we reformulate the RQHD system as an extended hyperbolic--elliptic system with auxiliary variables. For this extended system, we establish uniform higher-order energy estimates on $\mathbb H^1$ by combining the Banach algebra property of sub-elliptic Sobolev spaces with noncommutative Fourier analysis. We then prove that the extended system is equivalent to the original RQHD system at the level of classical solutions. As a consequence, we obtain the local-in-time existence and uniqueness of non-vacuum classical solutions to the RQHD system on $\mathbb H^1$. The result also provides a framework for the study of related singular limits, including the semiclassical and non-relativistic limits on nilpotent Lie groups.

cTreeBalls (cBalls for short) is a Python/C package useful to measure (2,3)-point clustering statistics. cBalls can efficiently calculate 3-point correlations of more than 200 million HEALPix pixels ( a full sky simulation with Nside = 4096) in less than 10 minutes on a single high-performance computing node, enabling a feasible analysis for the upcoming LSST data. It builds upon octree (Barnes & Hut, 1986) and kd-tree algorithms (Bentley, 1975), and supplies a user-friendly interface with flexible input/output (I/O) of catalogue data and measurement results, with the built program configurable through external parameter files and tracked through enhanced logging and warning/exception handling. For completeness and complementarity, methods for measuring two-point clustering statistics for periodic boxes are also included in the package. cTreeBalls was developed for its use in the Dark Energy Science Collaboration (DESC) of the Rubin Observatory Legacy Survey of Space and Time (LSST).

Rapid growth in AI-driven data center loads is creating significant challenges for transmission grid interconnection. This paper proposes robust and risk-aware frameworks to quantify transmission capacity as firm and flexible capacities. We efficiently solve the robust optimization problem to determine firm capacity when minimizing unserved data center demand. Building upon this, we introduce a risk-aware allocation for flexible capacity, showing that tolerating a minimal probability of service interruption and blackout can unlock substantial flexible capacity of transmission networks and accelerate data center interconnection. To efficiently allocate scarce transmission capacities among competing data centers, we adopt the simultaneous ascending auction, characterizing products by capacity, risk level, and location. Under additive or symmetric concave valuation functions, the auction converges to a competitive equilibrium and achieves efficient allocation.

Randomized experiments have long been the gold standard for scientists seeking to learn about cause and effect. When randomized experiments are infeasible, scientists often resort to observational studies, which are widely available and often large but rely on untestable assumptions that, when violated, may result in biased estimates. Uncertainty about bias leads to a phenomenon known as the illusion of learning from observational research (Gerber, Green and Kaplan, 2004a): absent prior information about bias, observational results cannot meaningfully contribute to the estimation of a causal parameter. To shatter the illusion, we take an empirical Bayes perspective. We show that the distribution of observational biases can be learned from calibration studies-experiments that target a causal effect that is known a priori to be zero. Calibration identifies the distribution of observational bias and allows observational studies to inform the estimation of causal parameters via empirical Bayes shrinkage. We formalize the illusion phenomenon in an empirical Bayes setting and show that, with an increasing number of calibration and observation studies, both the bias distribution and the causal effect can be consistently recovered. We illustrate our method through a simulation study and a semi-synthetic application based on Ferraro and Miranda (2013)'s water-usage experiment.

The goal of this chapter is to investigate the effects of relaxation and dephasing on the quantum Rabi model in the ultrastrong coupling regime, and to provide explicit formulas to implement and numerically solve the resulting nonunitary dynamics from first principles. The quantum Rabi model constitutes the most fundamental description of light-matter interaction, describing a single two-level system coupled to a single mode of a quantized cavity field. The ultrastrong coupling regime is typically defined by $g \gtrsim 0.1ω$, where $ω$ denotes the cavity-mode frequency. In this regime, the standard master equation of quantum optics -- commonly referred to as the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation -- becomes inaccurate. The reason is that strong light-matter interaction hybridizes the bare atom and field states, so that dissipation cannot be consistently described in the uncoupled basis. A consistent treatment must therefore incorporate this hybridization directly into the dissipative terms. One such approach is the dressed-picture Markovian master equation derived by Beaudoin, Gambetta, and Blais, in which the qubit-field interaction is explicitly included in the construction of the system-bath coupling operators. In this chapter, we numerically solve both the GKSL master equation and the dressed master equation (DME) for various initial field states, including coherent, odd Schrödinger cat, squeezed vacuum, squeezed coherent, and thermal states. We also examine photon generation from the vacuum induced by external time-dependent modulation of the qubit parameters, as well as multiphoton Rabi oscillations for an initially excited qubit. Two reservoir spectral densities are considered: white and Ohmic noise. The differences between the two approaches are illustrated through numerical results for several physical observables.

We propose a universal scaling law linking the Nusselt number (Nu) and the Bejan number (Be) in natural convection. Using entropy generation analysis and boundary-layer scaling, we demonstrate that Be^-1 - 1 = a Nu^b emerges independently of geometry and boundary conditions when transport is governed by a single control parameter. The relation is validated using a canonical square cavity. This result establishes a direct connection between heat transfer and thermodynamic irreversibility, revealing a fundamental constraint in convective transport.

The bilayer skyrmion composed of upper and lower tightly coupled skyrmions on two layers with completely compensated topological charges (called as anti-topology here), has become one feasible improvement of conventional skyrmion to realize straight motion without skyrmion Hall effect, which has aroused great interest in practical applications. The present work investigates a general model (without external magnetic field) for the frustration-induced anti-topological bilayer magnetic textures with rich morphologies, and discusses the modulations of key parameters on the energy barrier and the current-driven dynamics. It is revealed that the interlayer coupling plays a key role in preventing distortion, and thus helps to reach a faster velocity. This model can be realized in various frustrated magnetic materials with antiferromagnetically coupled bilayer, providing a helpful guidance for the material design and application of topological magnetic textures.