The Traveling Salesman Problem (TSP) is a classical NP-hard problem in combinatorial optimization, where determining the shortest route among a set of cities becomes computationally prohibitive as the problem size increases. This work explores quantum computing as an alternative approach to address this complexity. Unlike existing methods that primarily rely on quantum annealing, we propose a quantum iterative framework integrating Quantum Phase Estimation (QPE) and Grover's search algorithm. Route costs are encoded as quantum phases, enabling QPE to efficiently evaluate them, while Amplitude Amplification, implemented via the Grover-Long algorithm, iteratively refines the solution space toward the optimal route. A proof-of-concept case study on a small-scale TSP instance demonstrates the feasibility of this approach and its potential for scaling to larger optimization problems. Furthermore, under an expectation-based analysis, the algorithm exhibits an expected computational complexity of $O(\frac{m^2\log_2(m)\log_2(1/ε)}{\sqrtε})$ which depends on the error tolerance parameter $ε$. This estimation omits the initialization term, which we expect future refinements to render subdominant to Phase Estimation.

We study Brauer groups of the smooth loci in linear systems on simply connected smooth projective varieties. Under a suitable ampleness condition, we prove that the Brauer group is at most $\mathbb Z/2 \mathbb Z$. This applies when the underlying variety is the projective plane, a very general K3 surface, or a general cubic fourfold. As an application, we compute the Tate--Shafarevich group parametrizing torsors over the relative Jacobians of universal smooth plane curves. Our approach is via a study of the $2$-nodal locus in the linear system.

Hyperspectral standoff detection systems such as Focal Plane Array (FPA) Fourier Transform Infrared (FTIR) spectrometers provide high spatial resolution in detecting airborne chemical contaminants that are invisible to the human eye but potentially hazardous. When two such systems are operated simultaneously with a suitable opening angle, they enable tomographic reconstruction of contaminant plumes with improved spatial and temporal accuracy. This work presents a mathematical model of these measurement capabilities and an algorithm to identify, localize, and quantify contaminant release sources. The objective is to develop a a tool that reconstructs release locations and predict the future plume evolution from standoff measurement data, thereby supporting early warning and situational awareness in hazardous material release scenarios. The transport of contaminants is modeled by an advection-diffusion equation, and the corresponding inverse problem for source identification is formulated accordingly. Owing to the severe ill-posedness and underdetermination of the problem, a sparsity-promoting regularization approach is employed together with a high-performance optimization algorithm. To incorporate the tomographic measurement data into the discrete formulation, a level-set description of a threshold concentration is used, allowing the measurements to be represented independently of the computational mesh and avoiding costly remeshing procedures.

European Rail Traffic Management System (ERTMS) is a widely adopted standard unifying train management in the EU. While the standard allows for use cases like fully autonomous driving, cybersecurity has been an afterthought. Risk analysis enables the systematic assessment and prioritization of threats and mitigations. To date, it remains unclear which threats are most significant in ERTMS. This study systematically models components of ERTMS and analyzes their security in light of threats identified in the underlying technologies. The results suggest a concerning state of ERTMS, despite its critical role in railway safety. The use of legacy standards like EuroBalises and GSM-Railway (GSM-R) introduces vulnerabilities that persist across minimal ERTMS implementations, deployments incorporating various optional safety measures, and prospective future evolutions of the system, e.g., adopting Future Railway Mobile Communication System (FRMCS). Fully transitioning to European Train Control System (ETCS) level 2 was identified as the most significant measure for advancing ERTMS cybersecurity. The results indicate that a shift of ERTMS toward security is required to ensure availability and safe operation. While the chosen methodology proved its feasibility and shows remaining weaknesses of ERTMS, future work is needed to develop railway-centric adaptations to improve the quantification and evaluation of the computed risks.

Traceability information between requirements and source code greatly benefits the maintenance of a software system. Since manually establishing trace links is cumbersome and error-prone, previous research explored automated traceability link recovery (TLR) approaches to support this task. However, quality defects in requirements impact subsequent activities such as TLR, yet evidence about this remains scarce. Our objective is to contribute empirical evidence on this impact. At the same time, we aim to understand how the performance of TLR approaches varies given these quality defects. To this end, we annotated 28 types of quality defect in 189 use case descriptions from two datasets. Then, we executed five distinct TLR approaches on the dataset and measured their performance in recovering trace links. Finally, we performed statistical tests to quantify the defects' effect strength on this performance. Our results show that some quality defects harm TLR performance, e.g., sentences that do not start with noun phrases, while others actually benefit performance, e.g., use cases that include implementation details. Moreover, different types of approaches respond differently to these defects. As a consequence, the performance-optimizing choice of a TLR approach depends on the quality of the dataset.

The temperature increase in the contact regions between solids in sliding contact can easily reach several hundred Kelvin and thereby dramatically affect friction and wear. Here I extend an earlier multiscale theory for the flash temperature (Ref. \cite{MP}) to the case of accelerated motion, and present numerical results illustrating the theory.

Due to high power consumption and hardware costs of fully digital arrays, hybrid beamformers are often considered as a more economic alternative. Furthermore, using high resolution analog to digital converters (ADCs) can also have prohibitive power consumption, which leads to lower resolution converters being considered for radio frequency (RF) front end design. The finite quantization resolution as well as the nonlinearities caused by the power amplifiers (PAs) and low noise amplifiers (LNAs) can have a substantial impact on system performance. While widely studied for communications, the impact of hardware impairments on sensing performance is considerably less explored. In this work, we study the interplay between hybrid beamforming architectures, hardware impairments, and sensing and communications performance. Additionally, we define the concept of double-isotropy for pilot-combiner pairs, formalizing the notion of a perfectly energy-fair beam sweep. The multiple start (MS) space alternating generalized expectation maximization algorithm (SAGE) is also introduced, aimed at addressing the optimization issues arising from parametric channel estimation (PCE) in hybrid beamformed systems. We then provide a set of numerical results assessing the impacts of beamformer architecture and ADC resolution on PCE, sensing, and communications performance. The results show that medium resolution ADCs lead to the most power efficient configurations, with the best tradeoff between power consumption and performance for the majority of beamforming architectures. Additionally, fully digital beamforming architectures with high resolution converters can often be substituted for a hybrid beamformer setup with medium resolution converters without significant performance loss at a lower power consumption and overall hardware cost.

Hybrid HE/2PC private CNN inference remains bottlenecked by prime-modulus homomorphic arithmetic in convolution and by a precision flow that runs ReLU at doubled bitwidth before invoking a separate truncation protocol. We present Jaguar, a system built on a single design choice--a power-of-two ciphertext ring--that addresses both. The choice enables SPA-Conv, a coefficient-domain convolution kernel that replaces NTT-centric polynomial multiplication with scalar-polynomial accumulation, and an exact ciphertext-side truncation by local right shifts that lets ReLU run directly at the target fixed-point precision and eliminates the post-ReLU truncation protocol. Where NTT remains genuinely useful--at the client, for the single polynomial multiplication during decryption--we recover it through an auxiliary NTT prime, preserving the power-of-two protocol substrate while keeping decryption O(N log N). On ImageNet-scale ResNet-18, ResNet-50, and MobileNetV2 with AVX disabled, Jaguar achieves 2.07-3.72x lower end-to-end latency than Cheetah and 2.16-3.36x lower than Rhombus, with 1.16-1.76x lower communication than Cheetah.

We prove a singularity theorem in which the classical focusing hypothesis of Hawking--Penrose theory is replaced by a condition on asymptotic volume growth. Under the strong energy condition, we introduce asymptotic volume-expansion invariants associated with a compact Cauchy hypersurface and show that a uniform positive lower bound on these invariants implies past timelike geodesic incompleteness. More precisely, we obtain an explicit upper bound on the time-separation from the hypersurface to its chronological past. The theorem extends to globally hyperbolic Lorentzian length spaces satisfying the synthetic strong energy condition $\mathsf{TCD}^e_p(0,N)$, yielding an inextendibility result valid without any smoothness or differentiability assumption. We also prove an area comparison theorem for equidistant hypersurfaces and a volume singularity theorem based on related asymptotic expansion invariants.

The rapid evolution of cloud computing has resulted in the adoption of hybrid deployments that blend Infrastructure-as-a-Service (IaaS) and Function-as-a-Service (FaaS) service models to optimize resource utilization, scalability, and operational efficiency. This paper presents a comprehensive study and practical implementation of a metrics-driven approach for migrating microservices from a traditional IaaS service model to a hybrid IaaS + FaaS model, using two microservice applications as case studies. The research develops an automated framework to analyze service-level performance metrics to identify microservices that are best suited for serverless execution. The findings of our research highlight the benefits and limitations of different cloud service models and provide a scalable and replicable automated methodology for optimized deployment of cloud-native applications.

Meta-structures that display axial-twist coupling can be achieved through the emerging kinematics in Kresling origami patterns. A central challenge in these structures is understanding their nonlinear mechanical behaviour, specifically their equilibrium branches and bifurcation diagrams. This involves identifying relationships between desired responses and the geometric variables that define the design space, including the Kresling polygon count, initial twist angle, height, radius, and crease lengths. As the number of constituent units increases in an n-layer chain, we track complex equilibrium branches extending into the post-critical regime under successive instabilities, including branch-point bifurcations and limit-point instabilities. This work begins by establishing the relationship between the geometric design variables and the response curves of the assembled chain by modelling the crease lines as axial-load-carrying elements. Subsequently, equilibrium branches and instabilities are systematically investigated via continuation and bifurcation analysis, beginning with the single-layer system and progressively extending to two- and three-layer configurations. Finally, a generalisation strategy is proposed to extend these findings to an n-layer Kresling chain. This strategy enables the predictive construction of equilibrium paths and the inverse design of multi-layer meta-structures, using prescribed critical points to control post-critical behaviour. It provides a foundation for the inverse design and optimisation of architected mechanical metamaterials with programmable responses.

We study statistics of atypical measurement outcomes in the steady states of driven open quantum systems. In equilibrium, the probability distribution over the phase space, as encoded in, e.g., the Wigner function, is analytic in the phase-space coordinates. We show that this property is generically lost in driven dissipative systems: their {\it large-deviation function} develops lines and surfaces across which its derivatives are discontinuous. As an illustrative example, we consider a parametrically driven Kerr oscillator coupled linearly and/or nonlinearly to a dissipative bath. Rare fluctuations in the amplitude and phase of the induced oscillations are governed by semiclassical instanton trajectories of the corresponding Keldysh-Lindblad action. We demonstrate that a given fluctuation can be realized through multiple distinct instanton trajectories. The competition between these trajectories leads to abrupt switching of the dominant instanton and, consequently, to non-analytic features in the large-deviation function.

Veloce EQuilibrium (VEQ) is a compact parametric framework for tokamak modeling workflows that repeatedly query continuous fixed-boundary equilibria at low latency. The VEQPy implementation evaluated here is an axisymmetric fixed-boundary Grad-Shafranov solver whose main solve enforces a variationally induced projected residual. Its active unknowns are MXH-type flux-surface harmonics and shifted-Chebyshev coefficients for radial profile and source closures. Six input routes accept pressure-gradient, toroidal-field-function, poloidal-flux-gradient, enclosed toroidal current, current-density and safety-factor information through route-specific closures, while all routes map to the same finite-dimensional residual operator. Controlled tests show route consistency for smooth, mutually compatible inputs generated from a common reference equilibrium. For Pareto-selected reduced configurations in three G-EQDSK cases, the most accurate selected rows correspond to a D-shaped case (9 active parameters, minor-radius-normalized shape error 1.4e-3, solve-only median 1.6 ms), an H-mode case (65, 1.1e-3, 19 ms), and an X-point case treated as a smoothed fixed-boundary representation of a diverted boundary (94, 1.9e-3, 15 ms). Sampled pointwise strong-form Grad-Shafranov diagnostics show that enriching the active representation mainly improves interior force balance, whereas the global RMS and maximum values for the H-mode and X-point cases remain dominated by near-boundary contributions. In an isolated one-dimensional transport-geometry coupling test against the target geometry read from G-EQDSK, the temperature-profile response remains below about one percent. These results support using VEQ for repeated equilibrium-geometry queries, provided that pointwise diagnostics are retained to screen cases requiring boundary refinement, local correction or higher-fidelity equilibrium solves.

We consider linear programming in the oracle model: $\max\{c^\top x \,:\, x\in P\}$, where the polyhedron $P=\{x\in\mathbb{R}^n\,:\, Ax\le b\}$ is given by a separation oracle. We present an algorithm that finds exact primal and dual solutions using $O(n^2\log(n/δ))$ oracle calls and $O(n^4\log(n/δ)+n^5\log\log(1/δ))$ arithmetic operations, where $δ$ is a geometric condition number associated with the system $(A,b)$. These bounds do not depend on the cost vector $c$ and do not require a priori knowledge of $δ$. For rational data, $\log(1/δ)$ is polynomially bounded in the encoding size of $(A,b)$, thus providing a polynomial-time algorithm. The algorithm works in a black box manner, requiring a subroutine for approximate primal and dual solutions; the above running times are achieved when using the cutting plane method of Jiang, Lee, Song, and Wong (STOC 2020) for this subroutine. Whereas approximate solvers may return primal solutions only, we develop a general framework for extracting dual certificates based on the work of Burrell and Todd (Math. Oper. Res. 1985). Our algorithm strengthens results by Grötschel, Lovász, and Schrijver (Prog. Comb. Opt. 1984), and by Frank and Tardos (Combinatorica 1987) that rely on bit-complexity arguments. Our algorithm avoids rounding-based arguments such as simultaneous Diophantine approximation and uses geometric arguments instead.

Deep Joint Source-Channel Coding (JSCC) has emerged as a promising paradigm for overcoming the ``cliff effect" in wireless communications. However, existing Deep JSCC frameworks operate directly on raw analog data such as image pixels rather than the discrete semantic tokens that foundation models require. Moreover, traditional systems employ fixed, hand-designed constellations that treat all tokens equally, leading to catastrophic random errors under channel noise. In this paper, the Semantic Token Codebook Communication (STCC) is proposed as a unified source-channel semantic token coding framework designed to transmit the discrete semantic tokens of foundation models over noisy channels. The core of STCC is the Semantic Token Codec (STC). It accepts discrete tokens as input, which maintains compatibility with foundation models while employing a residual multiple layer perceptron, i.e., MLP-based encoder that learns geometrically structured constellations optimized with a triple-loss objective. This learned mapping forces the channel topology to align with the semantic embedding space, ensuring that channel noise results in topological errors rather than random corruption. This phenomenon is theoretically and empirically characterized, identifying ``Semantic Drift" in symbolic modalities and ``Structural Distortion" in perceptual modalities, where errors shift predictions to semantically or structurally similar tokens. Extensive experiments demonstrate that STCC significantly outperforms traditional systems in low-SNR regimes, effectively converting channel noise into semantic variations without requiring receiver-side modification.

Scalable distributed systems form the backbone of modern computing infrastructure. However, as scale grows, system complexity may lead to scalability faults. Scalability faults are challenging to uncover and diagnose, as they are often latent and only manifest at large-scale deployment. In this paper, we present the first comprehensive study on scalability faults and propose an approach for their detection. First, we systematically investigate 444 scalability issue reports from 10 large-scale distributed systems to understand the common anti-patterns and root causes of scalability faults. We found that the majority of these faults are caused by the synergy between dimensional code fragments and anti-patterns associated with them. Second, based on our findings, we design and implement ScaleLens, a novel approach to detect scalability faults. ScaleLens combines dynamic and static analyses to pinpoint dimensional code fragments and match them with anti-patterns. Our evaluation shows that ScaleLens detects 4.2x more dimensional code fragments associated with known scalability faults compared to the baseline. On the latest stable versions of Cassandra, HDFS, and Ignite, ScaleLens detects 334 dimensional code fragments with confirmed problematic behavior.

We prove sub-Riemannian Selberg trace formulae for compact quotients of SL(2, R). Using the Fourier decomposition along the SO(2)-fibers, we reduce the heat trace computation to the Selberg trace formula for Maass Laplacians on the hyperbolic plane. The resulting formula has an identity contribution and a hyperbolic contribution, the latter involving a character-dependent theta factor over closed geodesics. We then use this trace formula to compute the zeta-regularized determinant of the sub-Laplacian. The determinant formula is remarkably compact and is expressed in terms of a determinant depending only on the base hyperbolic surface and an explicit relative Selberg product.

This paper investigates the well-posedness issue for a reduced two-dimensional model of micropolar fluids. This reduced model presents a coupling between an Euler-type equation for the velocity field of the fluid and a transport-diffusion equation for the microrotation field (which is a scalar field, in this setting). We establish the local existence and uniqueness of strong solutions in the scale of Besov space $B^s_{p,1}$ having regularity index $s\geq1+2/p$. Furthermore, in the subcritical case when $s>1+2/p$, we prove that these solutions exist globally in time. The global persistence of regularity in the critical setting $s=1+2/p$ remains open.

Frequency conversion of ultrafast lasers is fundamentally constrained by the trade-off between pulse energy and repetition rate, limiting access to regimes critical for fundamental science and industry. Here, we demonstrate a frequency-conversion mechanism in which molecular coherence accumulates across ultrafast pulse trains in gas-filled hollow-core fibers. Unlike conventional nonlinear interactions initiated by individual high-energy pulses, this mechanism relies on the collective buildup of coherent molecular oscillations driven by successive pulses. Using this mechanism, we achieve Raman frequency conversion at repetition rates up to 3 GHz with nanojoule pulse energies. The results establish a regime of nonlinear optical interaction governed by coherence accumulation of gas molecular oscillations with broad implications for ultrafast laser science and frequency conversion technologies.

We establish a rigorous mathematical bridge from quantum many-body path integrals to the cusp catastrophe model by Lyapunov-Schmidt reduction, which provides a theoretical foundation for analyzing superconducting phase transition using the catastrophe theory. First, it is proved that, near the critical point the infinite-dimensional effective action is diffeomorphic to a finite-dimensional catastrophe. Secondly, starting from Ginzburg-Landau free energy functional, the Euler-Lagrange partial differential equation can be reduced to the cusp catastrophe model. Thirdly, the fermionic imaginary-time path integral to the cusp catastrophe is derived through the Hubbard-Stratonovich transformation, Matsubara frequency expansion, and Grassmann algebra. Furthermore, we connect this framework with the adsorption potential theory we proposed, elucidating the catastrophic topological nature of the electron pairing mechanism in high-temperature superconductivity. The precise microscopic derivation of the adsorption potential from first-principles electronic structure calculations would strengthen the predictive power of the theory.

We introduce Fourier integrator molecular dynamics (FIMD), a method for propagating selected vibrational motion of Hamiltonian systems stably and reversibly in time while analyzing and controlling dynamics in the frequency domain. This makes band selection and vibrational analysis features of the integrator rather than post-processing steps. We demonstrate the method with classical force fields, a machine-learned force field trained on quantum data, and semi-empirical quantum chemistry for CO$_2$ and the capped Ace--Phe--Tyr--NMe peptide. The method reproduces spectra within the chosen band, suppresses out-of-band response, reveals mode coupling, and demonstrates force-field dependence of spectral features, especially for the thermodynamically important low frequencies. FIMD offers an efficient and transparent way to probe the vibrational physics underlying spectroscopic and calorimetric observables.

We investigate $J/ψ$ photoproduction off the proton, $γp \to J/ψp$, to elucidate the nonexistence of hidden-charm pentaquark signals reported by the GlueX and CLAS12 experiments. Within a coupled-channel rescattering mechanism, we employ the transition amplitudes from a previous coupled-channel analysis that dynamically generates the $P_{c\bar{c}}$ states. The kernel amplitudes for the transition to the $J/ψN$ channel include both $t$-channel heavy-meson exchange and $u$-channel heavy-baryon exchange. We find that the rescattering contributions from the $\bar{D}^{(*)}Σ_c$ channels -- indispensable for the formation of the $P_{c\bar{c}}$ resonances -- are about one order of magnitude smaller than those from $\bar{D}^{(*)}Λ_c$, since $g_{\bar{D}^{(*)}NΣ_c}$ is roughly five times smaller than $g_{\bar{D}^{(*)}NΛ_c}$. Since the $P_{c\bar{c}}$ resonances couple to the $J/ψN$ channel predominantly through the $\bar{D}^{(*)}Σ_c$ intermediate states, their suppression prevents the pentaquark signal from appearing in photoproduction. With only a single parameter controlling the overall normalization, the present work describes the GlueX and CLAS12 cross sections well. These results suggest that the null result from photoproduction need not be in conflict with the pentaquark signals observed by the LHCb Collaboration.

Nonreciprocal interactions in active solids violate action-reaction symmetry and produce a net response to strain. Assuming invariance under Euclidean symmetries, we derive a shape-space formulation for the elastohydrodynamics of nonreciprocal slender bodies that separates intrinsic deformation from rigid motion. The resulting nonlinear reaction-advection-diffusion system represents a geometric flow whose activity-driven instabilities generate steady, oscillatory, and chaotic patterns. These manifest as rigid, swimming, and chaotic motion, linking nonreciprocal elastohydrodynamics to geometric pattern formation and unifying recent observations in slender active structures.

The rapid growth of consumer IoT devices has introduced unprecedented challenges in trustworthy anomaly detection against AI-enabled cyber threats, requiring real-time, privacy-preserving, and scalable defense mechanisms. Traditional centralized strategies face critical limitations, including communication bottlenecks, single points of failure, and privacy vulnerabilities when processing distributed consumer data. We propose SwarmSense-DNN, a novel decentralized neural framework employing swarm intelligence for secure, cooperative anomaly detection across distributed IoT environments. The framework integrates autonomous agents with deep neural networks to form a self-organizing defense system that detects evolving anomalies without centralized coordination. It utilizes hierarchical federated learning with graph neural networks and attention mechanisms to capture local and global anomaly behaviors while ensuring data privacy. Extensive experiments demonstrate SwarmSense-DNN's superior performance: it achieves 95.44% average detection accuracy across five benchmark datasets while reducing communication overhead by 67%. The framework maintains robust resilience against adversarial threats through differential privacy safeguards and demonstrates strong fault tolerance under node failures and AI-enabled attacks.

We present a high-pressure single-crystal X-ray diffraction study of the atomically precise $\mathrm{Au}_{25}(\mathrm{PET})_{18}^{q}$ cluster ($q=-1,0$) up to 10 GPa under strictly hydrostatic conditions. Our crystallographic analysis provides direct evidence for the pressure-induced phase transitions previously suggested by spectroscopic studies. Structural refinements reveal that the cluster accommodates compression through the reorganization of the flexible ligand shell and secondary distortions of the staple motifs, while the $\mathrm{Au}_{13}$ icosahedral core remains intact. Notably, the internal Au-Au distances exhibit a monotonic contraction that quantitatively mirrors the compressibility of bulk gold. This invariant rigidity at the sub-nanometer scale demonstrates that the fundamental stiffness of the metallic bond is preserved regardless of size. Our findings reconcile previous contradictions in the elasticity of metal nanostructures by isolating the intrinsic mechanical response of the gold kernel from extrinsic structural and experimental artifacts.

We propose novel semi-decoupled and fully-decoupled iterative algorithms for efficiently solving the fully-coupled nonlinear four-field thermo-poroelastic model discretized in space by discontinuous Galerkin method on polytopal grids. We present the model problem, its four-field formulation, and the arbitrary-order weighted symmetric interior penalty scheme exploited for its spatial discretization. Such a scheme is robust with respect to strong heterogeneities in the model coefficients. Then, we present the two solution strategies and prove that under suitable conditions both schemes are convergent. A wide set of numerical simulations is presented to assess the convergence and robustness properties of the proposed method. Moreover, we test the scheme with literature and physically sound test cases for proof-of-concept applications in the geophysical context.

Convex optimization problems with linear equality constraints arise ubiquitously in scientific computing, machine learning, and control theory. Classical Krylov methods are effective but rely on problem-specific preconditioners and high memory. Conversely, gradient-based methods like the augmented Lagrangian method (ALM) avoid these issues yet suffer from slow outer iterations. Developing accelerated outer-iteration schemes, therefore, remains a critical research objective. In this study, we demonstrate that incorporating a proximal operation into the augmented Lagrangian framework yields the proximal ALM, where the outer iteration is equivalent to an implicit gradient descent-ascent (GDA) scheme. We further establish that this equivalence extends naturally to the setting of variable step sizes. Through Lyapunov analysis, we show that the underlying potential function must be shifted from the conventional objective gap to a variational inequality measure, signaling a shift in perspective from pure convex optimization to minimax optimization. Motivated by these observations, we first develop an implicit GDA scheme with variable step sizes based on a continuous-time ODE framework, which achieves an $o(1/k)$ last-iterate convergence rate for both the primal-dual objective gap and the gradient norm. Building upon a second-order ODE framework, we then propose a family of Nesterov-type implicit GDA schemes parameterized by $r \geq 0$, which achieves an $o(1/k^{r+1})$ last-iterate convergence rate for the primal-dual objective gap. Furthermore, specializing the second-order ODE formulation to the case $r=0$, we derive a corresponding explicit GDA scheme and prove an $o(1/k)$ last-iterate convergence rate for the primal-dual objective gap. Finally, we present several numerical experiments to validate these theoretical results and demonstrate the effectiveness of the proposed methods.

Sub-femtosecond electron beams are powerful probes of ultrafast electronic, atomic, and nuclear dynamics, and promising drivers for ultrashort radiation generation from the extreme-ultraviolet to gamma-ray regimes. However, producing such beams at hundred-MeV energies with pC-level charge remains challenging. Here we propose a two-dimensional beam-compression scheme based on transverse--longitudinal coupling, in which dispersive beam optics convert the small transverse emittance of modern electron beams into an ultrashort longitudinal duration. Linear analysis and particle tracking show that, after the dominant longitudinal and energy-spread contributions are cancelled, the compressed bunch length is governed primarily by transverse beam quality and collective-effect growth. We further derive and verify a scaling law showing that, in the relevant parameter range, collective-effect-induced bunch-length degradation increases approximately linearly with bunch charge and decreases with beam energy. Start-to-end simulations of a realistic injector-to-compressor beamline produce a 200 MeV, pC-level bunch with an rms duration of 0.45 fs and a peak current of about 3.5 kA. Jitter studies indicate that sub-femtosecond performance is maintained for most error seeds. These results suggest a feasible route toward compact, high-energy attosecond electron beam sources and may provide a basis for future sub-femtosecond radiation sources based on undulator emission or inverse Compton scattering.

Uncertainty in standalone microgrid operation usually originates from mismatches between power references and forecasts. These deviations are compensated by grid-forming controlled units, which distribute the required power contribution based on their droop gains. To introduce an additional degree of flexibility, it is possible to treat droop gains as decision variables to redistribute active-power contributions according to system-level objectives. However, directly applying updated droop gain references from a supervisory layer to the primary controllers can introduce power and frequency transients. This paper investigates transition mechanisms for applying scheduled active-power droop gain changes during operation. Hard switching, rate-limited transition, first-order IIR low-pass filtering, and cubic as well as quintic S-curve transitions are compared experimentally on two parallel 15 kW grid-forming inverter units. The results show that shaping the droop gain trajectory significantly reduces transient deviations compared to hard switching. In the considered case study, the S-curve transitions provide the strongest transient mitigation, reducing the active-power overshoot from 632.7 W to approximately 115 W and limiting the frequency overshoot to about 0.003 Hz.

A new Block Coordinate Gradient (BCG) method, dubbed bAdag, for smooth, nonconvex minimization problem is proposed; it falls in the class of Objective Function Free Optimization (OFFO) methods, and it is based on the AdaGrad algorithm. At each iteration, our method computes an adaptive step size based on the cumulative sum of block gradients, instead of full gradients as in AdaGrad-type methods. We prove ergodic, sublinear convergence rates for the bAdag algorithm when minimizing a smooth, possibly nonconvex objective under the (block) Lipschitz continuity assumption on the gradient. Our theory covers three widely popular block selection strategies: the Cyclic (C) rule, Uniform Random selection (UR), and the greedy Gauss-Southwell (GS) rule. We also extend our algorithm and its convergence theory to box-constrained smooth functions. We validate the proposed algorithms through synthetic and real-world experiments.