We pose several questions for the classical N-body problem inspired by connections between the virial equation and the Jacobi-Maupertuis formulationof mechanics. We answer some.

Large language models (LLMs) deployed behind APIs and retrieval-augmented generation (RAG) stacks are vulnerable to prompt injection attacks that may override system policies, subvert intended behavior, and induce unsafe outputs. Existing defenses often treat prompts as flat strings and rely on ad hoc filtering or static jailbreak detection. This paper proposes Prompt Control-Flow Integrity (PCFI), a priority-aware runtime defense that models each request as a structured composition of system, developer, user, and retrieved-document segments. PCFI applies a three-stage middleware pipeline, lexical heuristics, role-switch detection, and hierarchical policy enforcement, before forwarding requests to the backend LLM. We implement PCFI as a FastAPI-based gateway for deployed LLM APIs and evaluate it on a custom benchmark of synthetic and semi-realistic prompt-injection workloads. On the evaluated benchmark suite, PCFI intercepts all attack-labeled requests, maintains a 0% False Positive Rate, and introduces a median processing overhead of only 0.04 ms. These results suggest that provenance- and priority-aware prompt enforcement is a practical and lightweight defense for deployed LLM systems.

We investigate the long-time asymptotic behavior of a class of solutions to the defocusing Manakov system under nonzero boundary conditions. These solutions are characterized by a $3 \times 3$ matrix Riemann Hilbert problem. We find that they exhibit interesting asymptotic behavior within a narrow transition zone in the $x$-$t$ plane. We determine the leading-order asymptotic term and the error bound in this region, and we demonstrate that the leading term can be expressed in terms of the Hastings-McLeod solution of the Painlevé II equation. The proof is rigorously established by applying the Deift-Zhou nonlinear steepest descent method to the associated Riemann Hilbert problem.

Electric vehicles (EVs) in Vehicle-to-Grid (V2G) systems act as distributed energy resources that support grid stability. Centralized coordination such as the extended State Space Model (eSSM) enhances scalability and estimation efficiency but may introduce new cyber-attack surfaces. This paper presents a stealthy False Data Injection Attack (FDIA) targeting eSSM-based V2G coordination. Unlike prior studies that assume attackers can disrupt physical charging or discharging processes, we consider an adversary who compromises only a subset of EVs, and limiting their influence to the manipulation of reported State of Charge (SoC) and power measurements. By doing so, the attacker can deceive the operator's perception of fleet flexibility while remaining consistent with model-based expectations, thus evading anomaly detection. Numerical simulations show that the proposed stealthy FDIA can deteriorate grid frequency stability even without direct access to control infrastructure. These findings highlight the need for enhanced detection and mitigation mechanisms tailored to aggregated V2G frameworks

In 1983, Brockett developed a topological necessary condition for the existence of continuous, asymptotically stabilizing control laws. Building upon recent work on necessary conditions for set stabilization, we develop Brockett-like necessary conditions for the existence of control barrier functions (CBFs). By leveraging the unique geometry of CBF safe sets, we provide simple and self-contained derivations of necessary conditions for the existence of CBFs and their safe, continuous controllers. We demonstrate the application of these conditions to instructive examples and kinematic nonholonomic systems, and discuss their relationship to Brockett's necessary condition.

Weak gravitational lensing is a widely used probe in cosmological analysis. It allows astrophysists to understand the content and evolution of the Universe. We are entering an era where we are not limited by the data volume but by systematic uncertainties. It is in this context that we present here a simple python-based software package to help in the computation of E-/B-mode decomposition, which can be use for systematic checks or science analysis. As we demonstrate, our implementation has both the high precision and speed required to perform this kind of analysis while avoiding a scenario wherein either numerical precision or computational time is a significant limiting factor.

Negativities in quasiprobability distributions, a foundational concept originating in quantum optics, serve as a fundamental signature of quantum nonclassicality, with entanglement quasiprobabilities offering a necessary and sufficient criterion for entanglement. However, practical reconstruction of entanglement quasiprobabilities conventionally requires full quantum state tomography, severely limiting scalability. Here, we propose a deep-learning framework that reconstructs entanglement quasiprobabilities directly from incomplete local projective measurements, bypassing full state reconstruction. Using a residual neural network, partial measurement outcomes are mapped to high-fidelity entanglement quasiprobabilities. Numerical benchmarks up to three qubits show more than a $30\times$ reduction in reconstruction error compared with state-of-the-art tomographic methods. Experimental validation on photonic entangled states demonstrates reconstruction and entanglement detection with substantially reduced measurement resources. Our results establish machine-learning-assisted reconstruction of entanglement quasiprobabilities as a scalable and practical tool for entanglement characterization in quantum optical systems.

Despite being a simple and well-motivated thermal relic scenario, coannihilation dark matter (DM) has remained largely unexplored experimentally due to the difficulty of probing its nearly degenerate mass spectrum. Recent LHC searches, however, have significantly improved the sensitivity to such compressed spectra, motivating a reassessment of the viable parameter space. We revisit the bino-slepton coannihilation scenario in supersymmetric (SUSY) models, incorporating the latest experimental results. We first focus on the minimal scenario, in which only the bino-like neutralino and left- or right-handed sleptons are light ($O(100)$ GeV), with all other SUSY particles decoupled. We find that the dark matter mass is constrained to be in the range of about 170-420 GeV (130-430 GeV) for left-handed (right-handed) slepton coannihilation, with lower bounds set by recent LHC searches. We then investigate scenarios with light higgsino, where direct detection experiments impose strong constraints on the higgsino mass. We also discuss the implications of these constraints for the muon $g-2$ in the so-called BHR, BHL, and BLR scenarios with coannihilation DM, and find that the combined LHC and LZ limits constrain the SUSY contribution to $|Δa_μ^{\rm SUSY}|\lesssim 1.2\times10^{-9}$.

A fundamental problem in noncooperative dynamic game theory is the computation of Nash equilibria under different information structures, which specify the information available to each agent during decision-making. Prior work has extensively studied equilibrium solutions for two canonical information structures: feedback, where agents observe the current state at each time, and open-loop, where agents only observe the initial state. However, these paradigms are often too restrictive to capture realistic settings exhibiting interleaved information structures, in which each agent observes only a subset of other agents at every timestep. To date, there is no systematic framework for modeling and solving dynamic games under arbitrary interleaved information structures. To this end, we make two main contributions. First, we introduce a method to model deterministic dynamic games with arbitrary interleaved information structures as Mathematical Program Networks (MPNs), where the network structure encodes the informational dependencies between agents. Second, for linear-quadratic (LQ) dynamic games, we leverage the MPN formulation to develop a systematic procedure for deriving Riccati-like equations that characterize Nash equilibria. Finally, we illustrate our approach through an example involving three agents exhibiting a cyclic information structure.

We study the cosmological implications of the minimal non-linear realisation of scale invariance within the Standard Model (SM). This framework provides a technically natural explanation for the hierarchy between the Planck scale and the electroweak scale and introduces only a light, feebly coupled dilaton field beyond the SM particles. Although the model is almost indistinguishable from the minimal SM at low energies, its cosmological consequences differ dramatically. In particular, the electroweak Higgs field remains trapped in the symmetric phase until the Universe cools to very low temperatures, $T_c^{(χ)}\sim 28$ MeV, where the first-order QCD chiral symmetry-breaking phase transition triggers the electroweak phase transition. This scenario offers intriguing possibilities for the production of primordial black holes, low-frequency gravitational waves, and multi-quark and lepton nuggets, which we explore in some detail using simplified approximations.

In this study, the classical results on the joint numerical radius for $n$-tuples of Hilbert space operators are extended to the setting of the joint $(f,δ)$-numerical radius. New and diverse contributions to this area are provided, including novel estimates for the lower and upper bounds of the $(f,δ)$-numerical radius in the context of sectorial operators.

Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these methods to PDE discretizations with immersed geometries is challenging, as standard interpolating wavelet transforms lose consistency near non-grid-aligned boundary intersections. To address this, we propose a high-order interpolating wavelet transform adaptation strategy compatible with sharp immersed boundary and interface discretizations. The approach performs consistent high-order wavelet transforms on narrow intervals using a 1D polynomial extrapolation technique. To maintain high order, the technique incorporates boundary values and derivatives, which are evaluated from multivariate interpolating polynomials similar to those used in high order immersed finite difference discretizations. Consequently, the proposed approach maintains the wavelet order on any arbitrary smooth multidimensional domain, including near concave geometry sections. This approach enables grid adaptation in complex domains while robustly bounding the numerical error via a manually set refinement threshold. The algorithm's performance is validated on both static and dynamic problems, including the Navier-Stokes equations with moving boundaries and temporally adapting grid resolutions. The results demonstrate that the proposed method enables effective grid adaptation, establishing a robust, predictable relationship between a user-defined refinement threshold and the overall solution error, even for problems with complex, moving boundaries.

Open-world missions often rely on repeated formulas, yet designers lack systematic ways to examine pacing, variation, and experiential balance across large portfolios. We introduce the Mission Action Quality Vector (MAQV), a six-dimensional framework-covering combat, exploration, narrative, emotion, problem-solving, and uniqueness-paired with an action block grammar representing missions as gameplay sequences. Using about 2200 missions from 20 AAA titles, we apply LLM-assisted parsing to convert community walkthroughs into structured action sequences and score them with MAQV. An interactive dashboard enables designers to reveal underlying mission formulas. In a mixed-methods study with experienced players and designers, we validate the pipeline's fidelity and the tool's usability, and use thematic analysis to identify recurring design trade-offs, pacing grammars, and systematic differences by quest type and franchise evolution. Our work offers a reproducible analytical workflow, a data-driven visualization tool, and reflective insights to support more balanced, varied mission design at scale.

TOI-1232 is a G-dwarf star with a mass of $1.06_{-0.06}^{+0.07} M_\odot$, a radius of $1.07\pm 0.05 R_\odot$, and slightly higher metallicity than solar of Fe/H = $0.18 \pm 0.05$. The star hosts a transiting warm Jovian-mass planet, TOI-1232 b, with an orbital period of $P_{b} = 14.256_{-0.001}^{+0.001}$ days, identified with data from multiple sectors of the $\textit{TESS}$ space telescope. The $\textit{TESS}$ light curve of TOI-1232 is complex, as it is contaminated by a background eclipsing binary with a period of $1.37$ days. The TOI-1232 b was firmly confirmed by ground-based transit follow-up campaigns from Las Cumbres, Hazelwood, Brierfield, and ASTEP observatories.Additionally, the $\textit{TESS}$ transits of TOI-1232 b exhibit strong transit timing variations (TTVs) with a super-period of $235.5 \pm 0.7$ days and a semi-amplitude of 27 minutes. Radial velocity (RV) follow-up with the FEROS spectrograph confirms the planetary nature of the transiting candidate, while a self-consistent $N$-body analysis of RVs and TTVs pinpoints the presence of a second outer Saturn-mass companion, TOI-1232 c with a period of $P_{c} = 30.356_{-0.012}^{+0.010}$ days. The TOI-1232 warm-giant system is particularly important due to the evidence of two massive planets that reside near the 2:1 commensurability but are not locked in a mean motion resonance (MMR). Thanks to $\textit{TESS}$, we have revealed a handful of these rare systems. Hence, TOI-1232 is an important addition to understanding the formation and dynamical evolution of such compact, massive, warm giant planets.

Design decisions are at the core of software engineering and appear in Q\&A forums, mailing lists, pull requests, issue trackers, and commit messages. Design discussions spanning a project's history provide valuable information for informed decision-making, such as refactoring and software modernization. Machine learning techniques have been used to detect design decisions in natural language discussions; however, their effectiveness is limited by the scarcity of labeled data and the high cost of annotation. Prior work adopted cross-domain strategies with traditional classifiers, training on one domain and testing on another. Despite their success, transformer-based models, which often outperform traditional methods, remain largely unexplored in this setting. The goal of this work is to investigate the performance of transformer-based models (i.e., BERT, RoBERTa, XLNet, LaMini-Flan-T5-77M, and ChatGPT-4o-mini) for detecting design-related discussions. To this end, we conduct a conceptual replication of prior cross-domain studies while extending them with modern transformer architectures and addressing methodological issues in earlier work. The models were fine-tuned on Stack Overflow and evaluated on GitHub artifacts (i.e., pull requests, issues, and commits). BERT and RoBERTa show strong recall across domains, while XLNet achieves higher precision but lower recall. ChatGPT-4o-mini yields the highest recall and competitive overall performance, whereas LaMini-Flan-T5-77M provides a lightweight alternative with stronger precision but less balanced performance. We also evaluated similar-word injection for data augmentation, but unlike prior findings, it did not yield meaningful improvements. Overall, these results highlight both the opportunities and trade-offs of using modern language models for detecting design discussion.

We study Fox colorings of tangle diagrams by $R=\mathbb{Z}$ or $\mathbb{Z}/p\mathbb{Z}$, where $p\geq3$ is an odd integer. For an $R$-colored $m$-string tangle diagram, the colors at the $2m$ boundary points form a vector $v\in R^{2m}$. We show that for classical tangle diagrams, such vectors are completely characterized by the alternating sum condition $Δ(v)=0$. We then investigate how this restriction changes in the virtual setting. For $R=\mathbb{Z}$, the realizability of $v$ is determined by a divisibility condition on $Δ(v)$. For $R=\mathbb{Z}/p\mathbb{Z}$, every vector is realizable by a virtual tangle diagram.

In this paper, we present a unified approach to constructing continuous and discrete $\mathrm{PGL}(3)$-invariant integrable systems, formulated in terms of the common dependent variables $z_1,z_2$, from linear spectral problems and their factorisation. Starting from third-order spectral problems, we first provide explicit forms of the differential and difference invariants, generalising the Schwarzian derivative and cross-ratio to the rank-$3$ setting. The factorisation induces dualities among linear spectral problems, underlying the exact discretisation and multi-dimensional consistency of the associated Boussinesq systems. Then, we derive both continuous and discrete $\mathrm{PGL}(3)$-invariant Boussinesq systems, representing natural rank-$3$ generalisations of the Schwarzian KdV and cross-ratio equations. A geometric lifting-decoupling mechanism is developed to explain the reduction of these systems to the $\mathrm{PGL}(2)$-invariant Boussinesq equations. Finally, we derive a ${\mathrm{PGL}}(3)$-invariant system of generating PDEs together with its Lagrangian structure, in which the lattice parameters serve as independent variables, providing the generating PDE system for the Boussinesq hierarchy.

Consider a parabolic SPDE \[ \partial_t u = Δu + σ(u)η, \] on $(0\,,\infty)\times\mathbb{R}^d$, where $η$ is a centered, generalized Gaussian noise with $\text{Cov}[η(t\,,x)\,,η(s\,,y)]=δ_0(t-s)Λ(x-y)$ for a tempered Borel measure $Λ$ that is positive definite and satisfies a mild weak-noise. The existence of invariant measures of versions of these types of SPDEs has been studied at great length, particularly in the ``weak-noise regime''; see for example Assing and Manthey \cite{AssingManthey2003}, Chen and Eisenberg \cite{ChenEisenberg2024}, Chen, Ouyang, Tindel, and Xia \cite{ChenOuyangTindelXia2024}, Eckmann and Hairer \cite{EckmannHairer2001}, Misiats and Stanzhytskyi \cite{MSY2020}, Yu Gu and Jiawei Li \cite{GuLi2020}, and Tessitore and Zabczyk \cite{TessitoreZabczyk1998}. Here, we characterize all annealed, ergodic, invariant measures for the above SPDE in the weak-noise regime.

Datacenter operators and electrical utilities rely on power traces at different spatiotemporal scales. Operators use fine-grained traces for provisioning, facility management, and scheduling, while utilities use site-level load profiles for capacity and interconnection planning. Existing datacenter power models do not capture LLM inference workloads, in which GPUs shift rapidly among compute-intensive prefill, lower-power decode, and idle states, and facility demand depends on how these states evolve and synchronize across many devices. We show that LLM inference power can be represented compositionally through two components: workload-driven transitions among operating states and configuration-specific power distributions within those states. Building on this observation, we develop a trace-generation framework that learns from measured traces and synthesizes power profiles for new traffic conditions and serving configurations. These traces aggregate from GPU servers to rack-, row-, and facility-scale load profiles at the temporal granularity required by the study. Across multiple LLMs, tensor-parallel settings, and GPU generations, our framework achieves median absolute energy error below 5% for most configurations while preserving temporal autocorrelation structure. The resulting traces support downstream analyses including oversubscription, power modulation, and utility-facing load characterization, enabling infrastructure evaluations that flat nameplate assumptions and static trace replay cannot support.

Understanding how complex behaviors, opinions, and innovations spread in online social networks remains a central challenge in computational social science. Existing models of complex contagion typically rely on stylized threshold mechanisms based solely on the number of infected neighbors and do not account for the interaction between individual preferences, local social influence, and global sentiment. Moreover, the emergence of virality through phase transitions and tipping points remains poorly characterized. In this paper, we propose a unified propagation cascade model in which notions propagate as high-dimensional vectors in the same feature space as network nodes. Node activations are governed by a unified decision function that integrates propagation affinity, local influence, and global influence. The resulting dynamics induce a stochastic, Markovian cascade process that enables efficient MCMC sampling of propagation outcomes. Using preferential attachment networks, we systematically study spread distributions, incubation dynamics, parameter sensitivity, and phase transition behavior. Our results show that balanced interactions between local reinforcement and global activation are critical for successful cascades and that early-stage growth patterns provide reliable signals of impending phase transitions.

Biclustering is a powerful unsupervised learning technique for simultaneously identifying coherent subsets of rows and columns in a data matrix, thus revealing local patterns that may not be apparent in global analyses. However, most biclustering methods are developed for continuous data and are not applicable for binary datasets such as single-nucleotide polymorphism (SNP) or protein-protein interaction (PPI) data. Existing biclustering algorithms for binary data often struggle to recover biclustering patterns under noise, face scalability issues, and/or bias the final results towards biclusters of a particular size or characteristic. We propose a Bayesian method for biclustering binary datasets called Binary Spike-and-Slab Lasso Biclustering (BiSSLB). Our method is robust to noise and allows for overlapping biclusters of various sizes without prior knowledge of the noise level or bicluster characteristics. BiSSLB is based on a logistic matrix factorization model with spike-and-slab priors on the latent spaces. We further incorporate an Indian Buffet Process (IBP) prior to automatically determine the number of biclusters from the data. We develop a novel coordinate ascent algorithm with proximal steps which allows for scalable computation. The performance of our proposed approach is assessed through simulations and two real applications on HapMap SNP and Homo Sapiens PPI data, where BiSSLB is shown to outperform other state-of-the-art binary biclustering methods when the data is very noisy.

We present the weak gravitational lensing dataset from the Super-pressure Balloon-Borne Imaging Telescope (SuperBIT), which imaged 30 galaxy clusters during its 45 night flight in April to May 2023. SuperBIT is a first-of-its-kind balloon-borne imaging telescope that achieved near diffraction-limited observations in near-space conditions above 98% of the Earth's atmosphere. We use the metacalibration algorithm to obtain calibrated galaxy shapes for our target clusters and several calibration fields, enabling unbiased reconstruction of the weak-lensing signal. We employ several diagnostics throughout the pipeline, including assessments of point-spread function (PSF) modeling residuals and their impact on weak-lensing measurements, as well as tests for correlations between galaxy shapes and measured galaxy and PSF properties. To assess the multiplicative shear bias of the pipeline, we analyze a parallel set of simulated images that incorporate the real observing conditions from the flight, including measured SuperBIT PSFs, observed sky backgrounds, and detector noise, yielding a bias of $(1.1 \pm 7.8)$~per~cent.

Sparse Tensor Compilers (STCs) have emerged as critical infrastructure for optimizing high-dimensional data analytics and machine learning workloads. The STCs must synthesize complex, irregular control flow for various compressed storage formats directly from high-level declarative specifications, thereby making them highly susceptible to subtle correctness defects. Existing testing frameworks, which rely on mutating computation graphs restricted to a standard vocabulary of operators, fail to exercise the arbitrary loop synthesis capabilities of these compilers. Furthermore, generic grammar-based fuzzers struggle to generate valid inputs due to the strict rules governing how indices are reused across multiple tensors. In this paper, we present TENSURE, the first extensible black-box fuzzing framework specifically designed for the testing of STCs. TENSURE leverages Einstein Summation (Einsum) notation as a general input abstraction, enabling the generation of complex, unconventional tensor contractions that expose corner cases in the code-generation phases of STCs. We propose a novel constraint-based generation algorithm that guarantees 100% semantic validity of synthesized kernels, significantly outperforming the ~3.3% validity rate of baseline grammar fuzzers. To enable metamorphic testing without a trusted reference, we introduce a set of semantic-preserving mutation operators that exploit algebraic commutativity and heterogeneity in storage formats. Our evaluation on two state-of-the-art systems, TACO and Finch, reveals widespread fragility, particularly in TACO, where TENSURE exposed crashes or silent miscompilations in a majority of generated test cases. These findings underscore the critical need for specialized testing tools in the sparse compilation ecosystem.

A quantum mirror is a device whose optical response, that is, transmission and reflection, can be controlled by a single qubit. Here, we propose the use of quantum mirrors as nodes in quantum networks. Propagating coherent states mediate the interaction between the control qubits of each quantum mirror. This allows implementing quantum teleportation, quantum state transfer, and entanglement swapping with success probability and average fidelity exponentially approaching unity as the average photon number increases. Furthermore, we show that quantum teleportation exhibits robustness against known sources of error, such as optical path phase difference, photon loss, and reduced quantum mirror reflectivity, presenting a promising alternative towards long-distance quantum communication.

The Lax equivalence theorem guarantees convergence of stable and consistent discretizations for linear hyperbolic partial differential equations (PDEs). For nonlinear problems, however, stability and consistency alone do not generally guarantee convergence, even for smooth solutions, and existing convergence results typically rely either on projection-based error decompositions or on linearization arguments that do not directly extend to entropy-stable split-form discretizations. In particular, general convergence results for entropy-stable discretizations of hyperbolic PDEs are currently lacking, despite their widespread use. In this work, we prove convergence under smoothness assumptions on the exact solution and fluxes for entropy-stable split-form discretizations of scalar and symmetric hyperbolic systems with homogeneous flux functions within the continuous summation-by-parts (C-SBP) framework. The scalar inviscid Burgers equation is presented as a canonical example. The analysis is based on a stability-consistency argument that yields a nonlinear error evolution inequality whose solution provides an explicit upper bound on the numerical error. We show that, for sufficiently small mesh spacing, and for degree-$p$ C-SBP discretizations in $d$ spatial dimensions with $p>1+d/2$, this bound remains finite on any finite time interval and tends to zero as the mesh is refined, implying convergence despite the presence of local linear instabilities. The results help clarify the relationship between consistency, entropy stability, nonlinear error growth, and convergence for discretizations of nonlinear hyperbolic problems.

The decidability of a logical system refers to the existence of an algorithm that can determine whether any given formula in that system is a theorem. In this paper, Harrop's lemma is used to prove the decidability of quantum modal logic.

In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous switching is designed. The upper bound of observation period as well as the lower bound of the control width are all obtained. Firstly, the finiteness and boundedness of the $p$-th moment of the solution are established under a generalized Khasminskii-type condition. Then reasonable conditions of control function, drift and diffusion coefficients are presented. Then exponential stability as well as the convergence rate of controlled system are proved. Finally, an example is presented to interpret the conclusion, which also indicates that the proportion of control interval has positive relation to the convergence rate.

The recent breakthroughs in laser-driving 229Th nuclear transition have created an urgent demand for coherent vacuum-ultraviolet (VUV) sources delivering high spectral brightness at the critical 148.38 nm isomer energy. However, generating sufficient photon flux to overcome the low nuclear excitation probability remains a challenge for compact setups. While resonant dispersive wave emission in gas-filled hollow-core fibers offers a promising route, standard capillaries face a fundamental trade-off: maximizing input coupling requires large core diameters, whereas efficient nonlinear VUV conversion demands the high intensities using small cores. Here, we resolve this conflict using a gas-filled tapered capillary fiber. This architecture utilizes a longitudinally decreasing core diameter to combine a large input aperture with adiabatic field concentration, thereby continuously enhancing the nonlinear interaction. Experimentally, we demonstrate a widely tunable source (135-240 nm) that achieves a twofold efficiency enhancement specifically at the 148.38 nm wavelength compared to uniform geometries. By providing a scalable route to high-flux VUV generation, this work establishes a critical tabletop tool for advancing solid-state nuclear clocks and time-resolved spectroscopy.

Event-based image sensors provide microsecond temporal resolution but lack spectral discrimination, whereas diffractive spectral imagers encode wavelength information at conventional frame rates. We introduce a fluorescence microscopy architecture that fuses asynchronous event streams with diffraction-encoded CMOS measurements to decouple temporal and spectral sampling. The system achieves ~3.9 um spatial resolution over a 0.5 mm field of view, effective temporal resolution down to 100 us, and differentiates fluorophores whose emission peaks are separated by only 23 nm. By synchronizing and computationally merging both sensing modalities, we enable spectrally resolved tracking at 100,000 frames/s without scanning or filter switching.

In this paper, we develop a distributionally robust optimal control approach for differentially private dynamical systems, enabling a plant to securely outsource control computation to an untrusted remote server. We consider a plant that ensures differential privacy of its state trajectory by injecting calibrated noise into its output measurements. Unlike prior works, we assume that the server only has access to an ambiguity set consisting of admissible noise distributions, rather than the exact distribution. To account for this uncertainty, the server formulates a distributionally robust optimal control problem to minimize the worst-case expected cost over all admissible noise distributions. However, the formulated problem is computationally intractable due to the nonconvexity of the ambiguity set. To overcome this, we relax it into a convex Kullback--Leibler divergence ball, so that the reformulated problem admits a tractable closed-form solution.