Extracting actionable insights from structured databases in regulated industries, such as credit unions, is often hindered by complex schemas, legacy systems, and stringent data governance requirements. We present Tursio, a secure, on-premises, database search platform that enables business users to query enterprise databases using natural language. Tursio automatically infers a context graph -- a schema-level metadata structure that captures join paths, column semantics, and domain annotations -- and uses it to systematically generate accurate query plans through LLM-assisted compilation, grounding, and rewriting. Unlike existing AI/BI tools that require extensive manual context curation, Tursio automates this end-to-end and deploys entirely on-premises. We demonstrate Tursio through realistic scenarios in the credit union domain, and discuss its applicability to other regulated settings.

Collective motion in animals and cells often exhibits rapid reorientations and scale-free velocity correlations. This allows information to spread rapidly through the group, allowing an adequate collective response to environmental changes and threats such as predators. To explain this phenomenon, we introduce a simple, biologically plausible mechanism: a minority-triggered reorientation rule. When local order is high, agents sometimes follow a strongly deviating neighbor instead of the majority. This rule qualitatively changes the macroscopic system behavior compared to traditional flocking models, as it generates heavy-tailed cascades of reorientations over broad parameter ranges. Our mechanism preserves cohesion while markedly enhancing collective responsiveness because localized directional cues elicit amplified group-level reorientation. Our results provide a parsimonious, biologically interpretable route to critical-like fluctuations and high responsiveness during flocking.

For a fixed linear-model basis, we show that the $A$ criterion factors into an inverse-$D$ scale term and a dimensionless sphericity factor that depends only on eigenvalue dispersion. This factor isolates exactly the part of $A$ not controlled by the determinant, explaining why designs that are exact or near ties in $D$ can differ materially in coefficient-variance, aliasing, and prediction-variance behavior. We illustrate the factorization on a published $D$ tie and on screening settings with infinitely many $D$-optimal solutions, then use the same scale/shape viewpoint as a lightweight post-screen within a space-filling candidate pool. A final section connects the same idea to Kiefer's $Φ$-class and introduces sphericity profiles.

We present an ab initio study of the one-neutron halo nucleus $^{11}$Be using nuclear lattice effective field theory with high-fidelity chiral interactions at N3LO. By employing the wavefunction matching method to mitigate the sign problem and the pinhole algorithm to sample many-body correlations, we successfully reproduce the ground-state parity inversion and the extended matter radius characteristic of the halo structure. We analyze the intrinsic density distributions and geometric shapes of $^{11}$Be in comparison with the core nucleus $^{10}$Be. Our results reveal a prominent two-cluster structure in both nuclei and the occupation of the $σ$ molecular orbital by the valence neutron in $^{11}$Be. It enhances the prolate deformation as well as the diffuse neutron tail, distinct from the $π$-orbital occupation observed in the $^{10}$Be ground state.

We present a production-oriented semantic retrieval system for Uber Eats that unifies retrieval across stores, dishes, and grocery/retail items. Our approach fine-tunes a Qwen2 two-tower base model using hundreds of millions of query-document interactions that were aggregated and anonymized pretraining. We train the model with a combination of InfoNCE on in-batch negatives and triplet-NCE loss on hard negatives, and we leverage Matryoshka Representation Learning (MRL) to serve multiple embedding sizes from a single model. Our system achieves substantial recall gains over a strong baseline across six markets and three verticals. This paper presents the end to end work including data curation, model architecture, large-scale training, and evaluation. We also share key insights and practical lessons for building a unified, multilingual, and multi-vertical retrieval system for consumer search.

Haar measure is a fundamental structure in harmonic analysis on locally compact groups. Its existence reflects the compatibility between topology and the associative algebraic structure of groups. In this paper we propose a framework for Haar-type measures on topological quasigroups. Since associativity is absent, strict translation invariance is generally too strong to expect. We therefore introduce quasi-invariant measures whose defect is measured by a modular cocycle attached to translations. We then explain, in a detailed and cautious form, how Moufang-type identities may impose strong constraints on this cocycle. In particular, under additional quasi-invariance assumptions for right translations, the Moufang-type identity $(N1)$ leads naturally to a multiplicativity relation for the cocycle. This suggests a measure-theoretic interpretation of Kunen's theorem: the emergence of loop structure may be viewed as the collapse of a modular defect in the translation geometry of a quasigroup.

Using tools from network theory, we analyze the organization of a MYH9-oriented drug-like library in chemical space using a multi-descriptor framework. The dataset is drawn from ZINC, a publicly available database of commercially accessible compounds curated for virtual screening and drug discovery. Starting from 6004 molecules, preprocessing yields 5000 structurally valid and descriptor-complete compounds. Similarity is defined via Tanimoto distance on Morgan fingerprints and single-descriptor distances for xLogP, HBD, HBA, molecular weight, and rotatable bonds. For each representation, we construct k-nearest-neighbor networks and identify communities using the Louvain-Leiden algorithm. All networks exhibit highly significant modularity (Q=0.91-0.99) relative to degree-preserving null models, demonstrating pronounced nonrandom chemical organization across descriptors. Cross-descriptor robustness is quantified through a co-clustering matrix over 1.25 X 10^7 molecular pairs, measuring how consistently compound pairs co-occur within the same community across descriptor-specific networks. Although most pairs show limited agreement, a sparse high-consensus core emerges, highlighting the complementarity of the descriptors. Minimum spanning trees derived from structural and consensus similarities reveal distinct backbone topologies: a scaffold-driven, sparse structure versus a compact, hub-rich consensus network. Betweenness centrality on these backbones identifies compounds that are both structurally central and descriptor-balanced. These results provide a statistically validated network representation of chemical space and a principled strategy to extract consensus-stable compounds for downstream screening.

High-throughput computational screening of polymers offers a powerful way to address the imbalance between the vast number of polymers synthesised for diverse applications and the relatively small subset that can be studied using atomistic simulations. This work presents an automatic workflow designed to enable the rapid and efficient screening of an extensive polymer library. The workflow integrates an automated annealing protocol with adaptive control, allowing for reproducible simulations with minimal human intervention and minimisation of the computational cost. The availability of a homogenous large set of simulations enables the adoption of machine learning approaches for a variety of tasks. We exemplify this possibility by proposing rapid machine-learning-based method to predict the (computed) polymer density and (experimental) glass transition temperature.

Let $\mathscr{A}$ be an abelian category and let $\mathscr{C}$ and $\mathscr{D}$ be additive subcategories of $\mathscr{A}$. As a generalization of Gorenstein categories, we introduce one-sided $n$-$(\C,\D)$-Gorenstein categories with $n\geq 0$. Under certain conditions, we give some equivalent characterizations of one-sided $n$-$(\C,\D)$-Gorenstein categories in term of the finiteness of projective and injective dimensions relative to one-sided Gorenstein subcategories, which induce some new equivalent characterizations of Gorenstein categories. Then we apply these results to categories of interest. In particular, a necessary condition is obtained for the validity of the Wakamatsu tilting conjecture.

We examine the implications of the recently proposed Geometric Masking scenario for the Active Galactic Nuclei (AGN) Unification Scheme, the blazar sequence, and broader blazar phenomenology, and evaluate its consistency with recent observations. Phase-resolved analysis of PKS 2155$-$304 indicates that extreme GeV spectral hardening events are locked to the trough of its $\sim 1.7$ yr quasi-periodic oscillation, suggesting that high-flux states are dominated by a soft, geometrically amplified envelope that outshines an underlying hard core. Independent support comes from the detection of TeV emission in the FSRQs S5 1027+74 and 3C 273 when integrating over low-flux states, revealing hard spectra that are difficult to reconcile with a purely cooling-dominated interpretation. We suggest that Doppler boosting preferentially enhances the soft component when the jet is closely aligned, creating a visibility bias that extends the AGN Unification Scheme and introduces a geometric modulation layer within the blazar sequence. In this framework, low-flux states correspond to windows of geometric transparency rather than intrinsic quiescence, and misaligned systems act as largely unmasked laboratories of particle acceleration. The scenario indicates that the duty cycle of extreme acceleration in AGN jets may be higher than inferred from flux-selected observations.

Substation reconfiguration via busbar splitting can mitigate transmission grid congestion and reduce operational costs. However, existing approaches neglect the security of substation topology, particularly for substations without busbar splitting (i.e., closed couplers), which can lead to severe consequences. Additionally, the computational complexity of optimizing substation topology remains a challenge. This paper introduces a MILP formulation for security-constrained substation reconfiguration (SC-SR), considering N-1 line, coupler and busbar contingencies to ensure secure substation topology. To efficiently solve this problem, we propose a heuristic approach with multiple master problems (HMMP). A central master problem optimizes dispatch, while independent substation master problems determine individual substation topologies in parallel. Linear AC power flow equations ensure PF accuracy, while feasibility and optimality sub-problems evaluate contingency cases. The proposed HMMP significantly reduces computational complexity and enables scalability to large-scale power systems. Case studies on the IEEE 14-bus, 118-bus, and PEGASE 1354-bus system show the effectiveness of the approach in mitigating the impact of coupler and busbar tripping, balancing system security and cost, and computational efficiency.

Assume that $n \geq 2$ and $B = (b_1,...,b_n)$ has distince integer entries $\geq 3.$ For $x > 0$ let $d_B(x) := (d_{b_1}(x),...,d_{b_n}(x))$ where $d_{b_i}(x) \in \{1,...,b_i-1\}$ is the leftmost digit in the base-$b_i$ positional notation representation of $x.$ We prove that if $d_B$ is surjective, then $\ln b_i$ and $\ln b_j$ are rationally independent whenever $i \neq j.$ We prove the converse for $n = 2,$ and for $n \geq 3$ if $\{\ln p : p \mbox{ prime} \}$ is algebraically independent, a condition implied by Schanuel's conjecture about transcendental numbers.

The study of the evolution of X-ray spectra in tidal disruption events (TDEs) is an important approach for understanding the physical processes occurring near a supermassive black hole. Observations show that the X-ray spectra of TDEs are very soft at the peak after the outburst, followed by a spectral hardening on a timescale of years. Theoretically, TDEs are suggested to undergo super-Eddington accretion at the time around the outburst. In this paper, we constructed a new disc-corona model to explain the observed X-ray spectral hardening in TDEs. In our model, there is a transition radius $r_{\text{tr}}$. For $r< r_{\text{tr}}$, the accretion flow exists in the form of a slim disc, the emission of which is dominated by soft X-rays. While for $r>r_{\text{tr}}$, the accretion flow exists in the form of a traditionally sandwiched disc-corona, in which a harder X-ray spectrum is produced. Our calculations show that $r_{\text{tr}}$ decreases with decreasing mass accretion rate $\dot {M}$, which intrinsically can predict the hardening of the X-ray spectra since the relative contribution of the outer disc-corona to the inner slim disc to the X-ray spectrum increases with decreasing $\dot {M}$. Our model has been applied to explain the observed X-ray spectral hardening in TDE candidate AT 2019azh, in which $\dot {M}$ is assumed to decrease proportionally to $t^{-5/3}$. Potential applications of the model in explaining the X-ray spectral evolution in upcoming rich TDE observations are also expected.

In this paper, we study an intertemporal utility maximization problem in which an investor chooses consumption and portfolio strategies in the presence of a stochastic factor and a no-borrowing constraint. In the spirit of the Kim-Omberg model, the stochastic factor represents the expected excess return of the risky asset. It is perfectly negatively correlated with shocks to the risky asset, and follows an Ornstein-Uhlenbeck process, thereby capturing the mean reversion of expected excess returns-a feature well supported by empirical evidence in financial markets. The investor seeks to maximize expected utility from consumption, subject to the constraint that wealth remains nonnegative at all times. To address the dynamic no-borrowing constraint, we use Lagrange duality to transform the primal problem into a singular control problem in the dual space. We then characterize the solution to the dual singular control problem via an auxiliary two-dimensional optimal stopping problem featuring stochastic volatility, and subsequently retrieve the primal value function as well as the optimal portfolio and consumption plans. Finally, a numerical study is conducted to derive economic and financial implications.

For general control-affine nonlinear systems in the positive orthant, and with positive controls, we show how strict CLFs can be utilized for inverse optimal stabilization. Conventional ``LgV'' inverse optimal feedback laws, for systems with unconstrained states and controls, assume sign-unconstrained inputs and input penalties that are class-K in the input magnitude, hence symmetric about zero. Such techniques do not extend to positive-state-and-control systems. Major customizations are needed, and introduced in this paper, for positive systems where highly asymmetric (or unconventionally symmetric) costs not only on the state but also on control are necessary. With the predator-prey positive-state positive-input benchmark system as inspiration, using a strict CLF built in our previous paper, we prototype two general inverse optimal methodological frameworks that employ particular ``contractor and expander functions.'' One framework (A) employs a triple consisting of a CLF, a stabilizing feedback, and an expander, whereas the other framework (B) employs a pair of a CLF and a contractor function. Both frameworks yield inverse optimal stabilizer constructions, on positive orthants of arbitrary dimensions. A stronger construction results from a stronger CLF condition. Biological interpretation for the predator-prey model illuminates that such inverse optimal control constructions are bio-ecologically meaningful. In addition to general frameworks, we present two fully explicit designs: two Sontag-like universal formulae for stabilization of positive-orthant systems by positive feedback, one of them with inverse optimality.

Understanding the aging behavior of Josephson junctions and the effect of annealing on junction resistances is important in building large-scale superconducting quantum processors. Here we study the effects of aging of Josephson junctions under different storage conditions from immediately after fabrication up to 2 to 3 months. We find that the aging curve follows a logarithmic curve, with the aging amplitude mainly determined by fabrication conditions and the aging speed determined by storage conditions. Junctions stored at ambient laboratory conditions aged faster compared to junctions stored in a nitrogen atmosphere or vacuum, with the aging speed appreciably changes when the storage condition changed. We also compared the effect of thermal annealing under nitrogen environment with annealing under ambient conditions up to 250$^\circ$ C. We find that under nitrogen environment, the resistances decreased at all temperatures tested, while under ambient environment the resistances increased at 200$^\circ$ C and decreased at 250$^\circ$ C instead. We were unable to decrease the resistance below the initial-time resistance, suggesting a lower limit on the range of resistance tuning.

The next generation of particle physics experiments will face a new era of challenges in data acquisition, due to unprecedented data rates and volumes along with extreme environments and operational constraints. Harnessing this data for scientific discovery demands real-time inference and decision-making, intelligent data reduction, and efficient processing architectures beyond current capabilities. Crucial to the success of this experimental paradigm are several emerging technologies, such as artificial intelligence and machine learning (AI/ML), silicon microelectronics, and the advent of quantum algorithms and processing. Their intersection includes areas of research such as low-power and low-latency devices for edge computing, heterogeneous accelerator systems, reconfigurable hardware, novel codesign and synthesis strategies, readout for cryogenic or high-radiation environments, and analog computing. This white paper presents a community-driven vision to identify and prioritize research and development opportunities in hardware-based ML systems and corresponding physics applications, contributing towards a successful transition to the new data frontier of fundamental science.

In this article, we prove weak type $(1,1)$ bounds for the variation and jump operators corresponding to the family of truncations of singular integrals with rough kernels. This resolves an open question raised by Jones, Seeger and Wright (Trans. Amer. Math. Soc. (2008)). Moreover, as an immediate consequence of the variational estimate, we recover the weak type $(1,1)$ boundedness of the maximal truncation operator corresponding to singular integrals with rough kernels.

DRESS is a deterministic, parameter-free framework that iteratively refines the structural similarity of edges in a graph to produce a canonical fingerprint: a real-valued edge vector, obtained by converging a non-linear dynamical system to its unique fixed point. $Δ^k$-DRESS extends the framework by running DRESS on every $k$-vertex-deleted subgraph of $G$; it was introduced and empirically evaluated in the companion paper, where the CFI staircase showed that $Δ^k$-DRESS matches $(k{+}2)$-WL for $k = 0, 1, 2, 3$. This paper provides the theoretical justification. The main contributions are: (i) an unconditional proof that $Δ^k$-DRESS distinguishes every CFI$(K_{k+3})$ pair for all $k \geq 0$ (CFI Staircase Theorem), established via a new CFI Deck Separation theorem and the Virtual Pebble Lemma; and (ii) a conditional proof that $Δ^k$-DRESS $\geq$ $(k{+}2)$-WL for all graphs and all $k \geq 0$, assuming a single structural conjecture about the WL hierarchy (WL-Deck Separation).

In this paper, we will provide a complete derivation of the decoherence rate for a magnetic nanoparticle in quantum superposition in the presence of the fluctuating electromagnetic field in a thermal background by using the fluctuation-dissipation theorem in the long-wavelength limit. The long-wavelength limit assumes that the superposition size is much smaller than the wavelength of the electromagentic filed fluctuations. We will extend this computation to two diamagnetic nanoparticles kept in quantum superposition adjacent to each other. We will also show how the drag force on a single nanoparticle arises from external electromagnetic-field fluctuations, and compare our results with those for the nanoparticle's dielectric properties.

Resonant inelastic X-ray scattering (RIXS) is the workhorse experimental technique for probing the structural degradation of higher-capacity cathode materials. However, the interpretation of experimental spectra is challenging due to the lack of accurate simulations. In this work, we propose a quantum algorithm for simulating the RIXS spectrum of molecular clusters hypothesized to form in Li-excess cathodes. The algorithm uses quantum phase estimation to sample the spectrum from a state encoding the scattering transition amplitudes of the cluster valence excitations. We prepare this state in the quantum computer using a block-encoding of the dipole operator and quantum signal processing to implement the Green's function propagator over intermediate core-excited states. To showcase the algorithm, we use a model cluster proposed in recent experimental works consisting of an oxygen dimer bonded to a manganese atom. Using the PennyLane software platform, we report resource estimation for simulating RIXS spectra for chemically motivated active spaces of increasing sizes. For a classically challenging active space with 20 orbitals, the algorithm requires $2.0 \times 10^{10}$ Toffoli gates and $414$ logical qubits.

The basic power function $t_n(x)=x^n$ is in some sense a classical limit for large $x$, of the monictised Chebyshev polynomial of the first kind $T_n(x)/2^{n-1}$. A theorem of Ritt says they are the only two families of polynomials $p_n(x)$ over $\mathbb{C}$ which satisfies the commutativity relation $p_n(p_m(x))=p_m(p_n(x))$. The commutativity $t_n(t_m(x))=t_m(t_n(x))$ is the reason why the RSA scheme allow also digital signature but the Diffie-Hellman key exchange protocol depends only on the commutativity. The DH scheme and many results in elementary local (at a fixed prime) multiplicative number theory is about properties of the power function $t_n(x)$ and they have natural analogue extension to $T_n(x)$. Recently we discovered a Chebyshev version of Euler's primality criterion , which however depends on two quadratic characters $ε_p(a)=\left ( \frac{a^2-1}{p} \right)$ and $δ_p(a)=\left( \frac{2(a+1)}{p} \right)$. This gives rise to a local partition of $(\mathbb{Z}/p\mathbb{Z}) \setminus \{ \pm 1 \}$ into 4 disjoint sets $A_{εδ}$. This can be thought of as a real refinement of the residue/non-residue as it arise from viewing $T_n(x)$ is the "real" part of the $n$th power of the unit $ω_x=x+\sqrt{x^2-1}$, namely $ω_x^n=T_n(x)+U_{n-1}(x)\sqrt{x^2-1}$. There are obvious analogue of Chebyshev version of pseudoprimes, Wieferich primes, Lucas-Lehmer, AKS, Diffie-Hellman, cyclotomic expansions and probably others.

Reconfigurable Intelligent Surfaces (RIS) enable dynamic electromagnetic control for 6G networks, but existing control schemes lack responsiveness to fast-varying network conditions, limiting their applicability for ultra-reliable low latency communications. This work addresses uplink delay minimization in multi-RIS scenarios with heterogeneous per-user latency and reliability demands. We propose Delay-Aware RIS Orchestrator (DARIO), an O-RAN-compliant framework that dynamically assigns RIS devices to users within short time windows, adapting to traffic fluctuations to meet per-user delay and reliability targets. DARIO relies on a novel Stochastic Network Calculus (SNC) model to analytically estimate the delay bound for each possible user-RIS assignment under specific traffic and service dynamics. These estimations are used by DARIO to formulate a Nonlinear Integer Program (NIP), for which an online heuristic provides near-optimal performance with low computational overhead. Extensive evaluations with simulations and real traffic traces show consistent delay reductions up to 95.7% under high load or RIS availability.

Let $\mathcal{E}$ be the class of finite-dimensional algebras isomorphic to endomorphism algebras of silting complexes over hereditary abelian categories. It is proved that the class $\mathcal{E}$ is closed under taking idempotent quotients, idempotent subalgebras and $τ$-reduction. We also show that the proper class consisting of shod algebras is also closed under these operations. In addition, several classic classes of algebras -- including laura, glued, weakly shod algebras -- are proved to be closed under idempotent quotients, thereby generalizing a known result originally established for specific idempotents.

Quantum stochastic processes are widely used in describing open quantum systems and in the context of quantum foundations. Physically relevant quantum stochastic processes driven by multiplicative colored noise are generically non-Markovian and analytically intractable. Further, their Markovian limits are generically inequivalent when using either the Ito or Stratonovich conventions for the same quantum stochastic processes. We introduce a quantum noise homogenization scheme that temporally coarse-grains non-Markovian, colored-noise-driven quantum stochastic processes and connects them to their effective white-noise (Markovian) limits. Our approach uses a novel phase-space augmentation that maps the non-Markovian dynamics into a higher-dimensional Markovian system and then applies a controlled perturbative coarse-graining scheme in the characteristic time scales of the noise. This allows an explicit analytical algorithm to derive effective Markovian generators with renormalized coefficients and enables various physical constraints, such as causality, to be imposed on them. We thus resolve the Ito--Stratonovich ambiguity for multiplicative colored-noise-driven quantum stochastic processes, wherein we show that their consistent Markovian limit corresponds to the Stratonovich convention with renormalized coefficients as well as correction terms in Ito's convention. By assuming their Markovian limit unravels causal, completely positive and trace-preserving dynamics, we further characterize a physically relevant family of non-Markovian quantum stochastic processes driven by multiplicative colored~noise.

The results of photometric, polarimetric, and spectroscopic observations are presented for the young star IRAS 21204+4913, whose visible brightness has increased by $\approx 5^{\rm m}$ since October 2025. The star's absorption spectrum in the $0.36 - 0.75 μ$m range resembles those of A - F giants and supergiants, but it also exhibits molecular TiO bands. The brightening was accompanied by a significant increase in the degree of polarization of the stellar radiation (to $\approx 16 \%$ in the I-band), likely due to scattering by dust in an expanding circumstellar shell. The P Cygni profile of the H$α$ line implies a dusty wind velocity of $\approx 300$ km/s. We believe that the outburst of IRAS 21204+4913 is caused by an increase in the accretion rate of protoplanetary disk's matter onto the young star with a mass of $\lesssim 0.5$ M$_\odot$ to $\gtrsim 3\times 10^{-5}$ M$_\odot$ yr$^{-1}$. Furthermore, IRAS 21204+4913 displays several unusual features: the dependence of the width and radial velocity of absorption lines on the excitation potential, emission in the TiO molecular bands, and a comparably bright outburst that occured in 1948. Several T Tauri stars and a group of Herbig-Haro objects are found in the vicinity of the star.

Spin textures are ubiquitous in antiferromagnets, yet their consequences for altermagnets remain largely unexplored. We show that smooth spatial variations of the Néel order act on itinerant electrons as emergent gauge fields, producing strong, tunable in-plane anisotropies in dc transport and interband optical absorption, even without intrinsic spin-orbit coupling. As a concrete example, we analyze a coplanar spin helix and predict that the principal axes of the conductivity and linear dichroism are set by the helix wave vector. Moreover, the optical anisotropy exhibits two distinct frequency regimes separated by a crossover: at low frequencies the absorption axis is locked to crystal axes, while at high frequencies it tracks the helix. Our results identify polarization-resolved optics and anisotropic transport as direct probes of textured altermagnetic states and suggest a simple route to direction-selective electronic and optical functionality in altermagnets.

Let $\mathcal{F}\subseteq{[n]\choose k}$ be a $t$-intersecting family. Define the $t$-covering number $τ_t(\mathcal{F})$ of $\mathcal{F}$ as the minimum size of a subset $S$ of $[n]$ with $|S\cap F|\geqslant t$ for each $F\in\mathcal{F}$. In this paper, we characterize $\mathcal{F}$ for which $|\mathcal{F}|$ takes the maximum value under the condition that $τ_t(\mathcal{F})\geqslant t+2$ and $n$ is sufficiently large, thereby generalizing two results by Frankl.

A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly positive lower bound on the diffusion coefficients, extending previous results that were restricted to one-dimensional domains and relied on uniformly positive diffusion. The analysis is carried out under boundedness assumptions on the collision and breakage kernels. The proof is based on the construction of a suitable regularized system, combined with weak $L^2$ a priori estimates and compactness arguments in $L^1$, which allow the passage to the limit in the nonlinear fragmentation operator.

Large language models(LLMs) are now used to power complex multi-turn agentic workflows. Existing systems run agentic inference by loosely assembling isolated components: an LLM inference engine (e.g., vLLM) and a tool orchestrator (e.g., Kubernetes). Although agentic workflows involve multiple LLM and tool requests, these systems schedule and allocate resources separately on a per-request basis, without end-to-end knowledge of the workflow. This leads to sub-optimal management of KV cache and tool execution environments. To address the challenges, we propose ThunderAgent, a fast, simple, and program-aware agentic inference system. We first abstract agentic workflows as LLM Programs, enabling a unified view of heterogeneous resources, including KV caches, system states, and external tool assets such as disk memory and network ports. Built upon this abstraction, ThunderAgent introduces a program-aware scheduler and a tool resource manager designed to maximize KV cache hit rates, mitigate memory imbalances, and enable asynchronous environment preparation. Evaluations across coding, routing, and scientific discovery agents demonstrate that ThunderAgent achieves 1.5-3.6x throughput improvements in serving, 1.8-3.9x in RL rollout, and up to 4.2x disk memory savings compared to state-of-the-art inference systems. To facilitate reproducibility and support future development, we open-source the system implementations of the whole ThunderAgent at: https://github.com/Agentic-Kinetics/ThunderAgent.