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This monograph presents a selection of the author's recent works on the control, stability, and stabilization of some classes of linear time-delay systems. After a detailed introduction to topics related to time-delay systems covered in the monograph, its main contents are presented in a series of mostly independent chapters.
We refine a bound of Cheng-Feyzbakhsh to prove an asymptotic $Γ$-Bayer-Macrì-Toda ($Γ$-BMT) inequality on every smooth polarized complex threefold. The proof relies on a reduction to small tilt stability parameters. Using this inequality we verify Feyzbakhsh-Thomas's condition $(wBG)$ whenever $K_{X}$ is numerically proportional to the polarization. For polarized Calabi-Yau threefolds, this yields a reduction of positive rank generalized Donaldson-Thomas (DT) invariants to those counting sheaves pure in codimension one. We further express these invariants in terms of rank one generalized DT invariants. Thus, the rank reductions of Feyzbakhsh-Thomas hold without assuming the BMT conjecture.
Core-level spectra in solution are governed by the interplay of core-hole relaxation, electron correlation, specific solute--solvent interactions, and environmental polarization. We report the first application of RASSCF--RASPT2 combined with the fluctuating-charges polarizable embedding to X-ray photoelectron (XPS) and X-ray absorption (XAS) spectroscopy in aqueous solution. The protocol couples a multireference treatment of core-ionized and core-excited states with molecular-dynamics sampling, and is assessed for the carbon and nitrogen K-edges of glycine in the gas phase and in water. The calculated spectra are compared with experiment and with fixed-charges electrostatic embedding. Gas-phase ionization and absorption features are accurately reproduced. In solution, configurational averaging captures inhomogeneous broadening, while XPS peak positions, relative intensities, and widths depend strongly on the solvent parametrization. The best-performing polarizable model improves the spectral profile, although aqueous ionization energies remain overestimated. For XAS, the carbon K-edge is reproduced close to the experimental energy scale, whereas the nitrogen K-edge line shape is recovered after rigid alignment. These results support multireference polarizable embedding as a promising framework for core-level spectroscopy in solution.
Continual learning requires a model to keep acquiring new skills and knowledge without compromising its existing capabilities. Parametric methods suffer from catastrophic forgetting and loss of plasticity. Non-parametric methods, such as prompts, skills, and harnesses, leverage in-context learning but are limited by context length and lossy plain-text compression. To effectively combine their complementary strengths, we propose HERD (Harness-Evolving Recursive Distillation), a hybrid continual learning framework that learns efficiently in the harness and internalizes experience into cumulative capabilities via distillation. On the harness side, HERD continually refines its skills to capture reusable patterns, while retaining high-residual examples that the skills fail to capture in a bounded memory. On the parameter side, HERD performs drift-constrained distillation with dual anchors, substantially reducing forgetting over long recursive runs. On the 25-stage task stream of TRACE+17, under fixed memory and compute budgets, HERD matches the strongest parametric baseline in new-task acquisition while exhibiting the least forgetting and the strongest retention of general capabilities.
Let k be a number field. We prove that for every quadratic extension F/k, every real zero beta of L(s, chi_{F/k}) satisfies (1 - beta) log d_F >= c(k) with an effective constant c(k) > 0, and we deduce (through a reduction of Stark) that the Brauer-Siegel theorem holds effectively and uniformly over all Galois extensions K of k, in the form h_K R_K >= c(k) d_K^{1/2} / ((2 pi)^{[K:Q]} log d_K). Stark's effective cases of the Brauer-Siegel theorem were the fields without quadratic subfields, since the quadratic subfields carried the ineffectivity of Siegel's theorem; over a base field k, the first result removes it. Both rely on a uniform bound for Chebotarev sums. Let K/k be a Galois extension with group G, and suppose S is a subset of G containing the identity. For any prime p of k, let delta_p be the proportion of the primes of K above p whose Frobenius lies in S. Then the sum over Np <= X of delta_p log Np / Np is at most (|S|/|G| + epsilon) log X + O(1), uniformly in K, as soon as X >= d_K^C with C depending only on epsilon and the degree [K:Q]. The proof is Kerr's form of the OpenAI argument, simple vanishing at the points (iota theta)_{iota in S}, with theta in a box in O_K, and Masser's zero estimate. The field enters only through Masser's invariant of the lattice of points, which we compute to be [K:Q]/|S| by averaging over the Galois group of the normal closure. Over Q, the determinant method of Green, Barreto, and Kominers gives sharper Chebotarev bounds, and we explain the comparison.
One considers the NP-hard problem of minimizing real cubic and quartic forms on the Euclidean unit sphere. One first extends the Hessian spectral characterization of local minima by the author. In particular one provides a gap-depth characterization of negative global and spurious minima, and proves that the minimum value of an odd degree-d form is recovered (up to the factor d(d -1)) by minimizing the smallest eigenvalue of its ambient Hessian over the sphere (and equivalently the unit ball). Next, one exhibits several classes of benign families of cubic and quartic forms (i.e. with no spurious local minima on the sphere) and prove that some are robust to small coefficient perturbation (i.e. the resulting form remains benign even if it leaves the initial family). Therefore the class of benign cubic and quartic forms is full-dimensional (in the ambient space of coefficients), for n $\ge$ 2. Also for every odd degree d, the class of benign degree-d forms increases with the dimension (however it does not imply that such forms become more frequent when the dimension increases).
Computer-use agents increasingly handle private information and act on users' behalf across desktop and web applications, including email. Phishing therefore poses privacy and security risks that depend not only on whether agents recognize malicious messages, but also on how they respond. Existing phishing datasets were developed primarily for conventional detection, leaving agent susceptibility to persuasive malicious requests insufficiently characterized. To expose vulnerabilities that pre-existing datasets may miss, we introduce AgentPhishing, a benchmark for evaluating whether persuasive phishing attacks can evade detection and induce LLM email agents to comply with malicious requests. We develop PhishOpt, which optimizes reusable email-generation skills against individual agents under fixed benchmark constraints and a realism constraint. We analyze the generated emails using Cialdini's persuasion principles to identify strategies associated with agent failures and use these findings to construct a universal generation skill. Our evaluation shows that agents can handle pre-existing phishing emails safely yet remain susceptible to attacks adapted to agent behavior, while in an AgentPhishing evaluation of nine agents, four exhibit phishing-detection rates below $10\%$ and malicious-request compliance rates above $45\%$. These results highlight the limits of inferring agent safety from conventional phishing evaluations and the need to assess how agents respond to persuasive malicious requests.
Let $u$ be the torsion function of a bounded domain $Ω$ in $\mathbb{R}^n$ for the Ornstein--Uhlenbeck operator, that is, the solution of $-Δu + x\cdot\nabla u = 1$ in $Ω$ with $u=0$ on the boundary. We prove that for every $n\ge2$ there are bounded, centrally symmetric domains whose torsion function is not concave. These domains have boundary with a flat piece and can be smoothed so that the boundary is $C^\infty$, strictly convex with principal curvatures bounded below by a positive constant, while keeping the torsion function not concave. In contrast, the torsion function for every ellipse centered at the origin is concave, and for every ball centered at the origin we prove the sharp bound $D^2u\leq-\frac{1}{n}I$. The ellipse result follows by deformation from the disk, using a boundary flux estimate and third-order boundary identities to exclude a first zero eigenvalue of the Hessian.
We construct a quantum theory of light in nonlinearly responding materials with dispersion and absorption and, in particular, show the emergence of non-Gaussian noise associated with nonlinear absorption processes. Our theory is based on a path-integral formulation of the microscopic Huttner-Barnett model including cubic matter self-interaction required for $χ^{(2)}$ nonlinear processes. We show that the noise polarization emerges naturally from a decoupling of the stochastic weights of the bath response which, in case of cubic self-interactions, leads to a decoupling via Airy functions. As the theory is, by construction, consistent with the nonlinear fluctuation-dissipation theorem, it constitutes a viable quantum theory of light in nonlinear media.
Multilingual language models can give different identity judgments when the same people's names are written in different scripts. We study this effect using 601 audited identity pairs with attested Devanagari and Latin forms, holding the question and relation fixed. Qwen2.5-7B's same-person accuracy falls from 35.1% in Latin to 8.5% in Devanagari under Marathi prompts, while different-person accuracy remains above 98%. Evaluation across five models reveals distinct response biases, and reduced tokenization fragmentation does not reliably close the gap. Replicating the design on 374 audited Malayalam pairs built from the same entities reproduces the effect in a second script and language family: same-person accuracy falls to 5.3%, about half the matched Devanagari rate, while the margin still ranks matching above non-matching names at 0.925 AUROC. Latin-trained probes recover label information from Devanagari states, exceeding a string-feature baseline under similarity-matched negatives. Scalar calibration recovers 87% of the raw model-probe balanced-accuracy gap, identifying decision criterion placement as a major contributor. Activation patching localises causal sensitivity to the second entity in Qwen's middle layers; one shared sensitivity direction transfers about half the full-state margin correction. A fact-independent intervention at this site raises held-out Marathi same-person accuracy from 6.5% to 33.5%, with 98.5% different-person accuracy. Together, these results distinguish script-dependent discrimination from criterion placement and identify a causal site for improving identity judgments.
We formulate anisotropic relativistic spin hydrodynamics in a parity-even magnetized medium using an Israel--Stewart entropy-current construction. Treating the magnetic field at leading order in the gradient expansion reduces the rotational symmetry to $SO(2)$ and separates spin susceptibilities and dissipative transport into longitudinal, transverse, and mixed channels. A restricted quadratic entropy current yields transient equations for the retained dissipative stresses and spin fluxes. We analyze a minimal linear closure around an unpolarized homogeneous equilibrium, retaining dynamical magnetic-flux perturbations but no explicit spin-magnetization coupling; spin and magnetic fluctuations mix through the fluid variables. Infrared coefficient equations and ultraviolet characteristic expansions organize the magnetosonic and Alfvén-like spectra together with spectator spin-flux poles. The first-order truncation exhibits unstable boost-sector poles and superlinear large-wave-number branches, interpreted as diagnostics of the truncated equations rather than microscopic dispersion predictions. For the baseline parameters, finite relaxation times yield asymptotically linear propagation branches and finite relaxation poles, with no growing modes found on the sampled grid. The characteristic speeds depend nonmonotonically on spin transport and provide necessary light-cone diagnostics, without establishing general stability or strong hyperbolicity.
Unaccounted-for observation-error correlations have long been known to be detrimental to the quality of atmospheric and ocean analyses produced by data assimilation (DA) systems. While progress has been made over the past decade on modelling inter-channel error correlations, modelling spatial error correlations remains a challenge for large datasets. Common strategies for mitigating the harmful effects of spatial error correlations, such as variance inflation or data thinning, prevent the extraction of valuable small-scale information from the observations. With the emergence of new sources of high-resolution observations, such as those from the Surface Water and Ocean Topography (SWOT) wide-swath altimeter, the need to address this limitation of DA systems has become increasingly pressing. To do so, we consider a diffusion-based observation-error correlation operator, extending previous work on modelling correlated errors in conventional nadir altimeter data. When observation-error correlation length scales are large, the original method can suffer from an excessive sensitivity of the inverse correlation operator to small-scale perturbations. Since actual estimates of observation-error correlations from SWOT suggest the presence of large length scales, a more robust formulation of the method is required. We present a regularised formulation of the diffusion-based correlation operator that eliminates this excessive sensitivity while preserving computational efficiency. We describe the implementation of the operator for a mesh constructed from SWOT observation locations and demonstrate its application in a global ocean DA system. To validate the new formulation, we perform DA experiments with simulated SWOT observations. These experiments confirm that the regularised correlation operator provides an effective, robust and practical approach for representing wide-swath altimeter observation-error correlations in operational ocean DA systems.
In a previous paper, we constructed a closed skew monoidal structure on the category of Gray-categories and Gray-functors whose internal hom Psd(A, B) captures pseudomaps and pseudo-transformations. In the present paper we give a symmetric description of the Gray-category Psd(A,B) and use this to prove that the skew monoidal structure is symmetric skew monoidal.
We prove that the deformation functor associated to an algebra over a sufficiently nice Koszul operad can be lifted to an operadic formal moduli problem over the Koszul dual operad. We further show that this operadic formal moduli problem corresponds to the derived center of the algebra under the operadic Lurie-Pridham correspondence. As an application, we prove that the classical Gerstenhaber algebra structure on polyvector fields of a commutative algebra agrees with the derived center of the algebra as an abelian Poisson algebra.
Vector quantization (VQ), in particular lattice-based methods, offer strong rate-distortion trade-offs for low-bit large language models (LLMs), yet their behavior under quantization-aware training (VQ-QAT) remains poorly understood. We scale lattice VQ-QAT to billion-parameter LLMs and multi-billion-token training regimes, and introduce SQuAT, a shape-gain VQ-QAT approach trained with a separate straight-through estimator (STE) for the shape and gain. SQuAT decomposes weights into direction and magnitude: normalized directions are quantized using an $E_8$-derived spherical codebook, while gains are quantized independently with low-bit scalar quantizers. We show that, unlike a standard STE applied to the full quantizer, which ignores the shape-gain structure, these separate STEs induce tangent-space updates for directions, yielding an implicit form of spherical (Riemannian) optimization. To enable scalability, we develop a distributed exact nearest-neighbor assignment scheme, in which workers quantize disjoint weight blocks and communicate only discrete indices, reducing VQ-QAT training time by 12.8$\times$ and allowing us to scale it to 10B tokens. Across instruction-tuned LLaMA-3.2-1B/3B, Qwen3-4B, and base Qwen3-1.7B, SQuAT consistently outperforms standard VQ-QAT STE under identical quantizers and initialization, and achieves SOTA VQ-QAT accuracy.
We introduce a new approach to high-energy spectra in AdS$_3$/CFT$_2$, addressing the open challenge of incorporating spectral statistics into the modular bootstrap. Using the analytic theory of $L$-functions attached to two-dimensional CFTs, we leverage modular constraints among high-energy states to derive a sum rule relating the spectral edge to bulk spectral fluctuations. As an application, we establish a refined modular bootstrap bound: letting $Δ_1$ be the conformal dimension of the lightest excited Virasoro primary of a unitary CFT of central charge $c$, we show that $Δ_1 - {c-1\over 12} \leq o(c)$, with at most one exceptional value of the scalar gap at each sufficiently large $c$; moreover, along any sequence in $c$ for which such exceptional gaps are realized, the remaining gaps obey the stronger bound $Δ_1 - {c-1\over 12} \leq O(1)$. The result applies to theories with logarithmic rigidity of spectral counting fluctuations, as in random matrix theory.
With the growth of scientific output, the peer review system is approaching a breaking point: reviewers are increasingly hard to secure, and turnaround times lengthen accordingly. LLM-assisted or LLM-generated peer review has been proposed as a remedy, but how such models would treat manuscripts already published in top-tier journals, the closest thing the current system has to a gold standard of scientific validity, is not known. Here we assembled a corpus of 200 articles, each released under a CC BY 4.0 license and published in 2026, from 20 general-science, life-science, and clinical-medicine journals including Nature, Science, and Cell, and asked four current LLMs (two proprietary, two open-weight) to produce independent peer-review reports of each one under a blinded protocol. Their decisions were overwhelmingly harsh and starkly inconsistent with each other: 605 of 800 reviews (75.6%) recommended major revision or rejection, but the rate at which any single model did so ranged from 17.5% to 100% (p < 0.001), disagreement on manuscripts that had, by construction, already survived real editorial review at the journals in question. When the same manuscripts were doctored with one deliberately planted, field-specific methodological or statistical flaw, detection rates varied from 17.0% to 60.5% across models (p < 0.001). Recommending revision for papers that had already passed editorial review (low specificity) while missing flaws deliberately placed in front of them (low sensitivity), these models produce output that should be read for what it is: an uneven, framing- and model-dependent signal.
Code-switched (CS) automatic speech recognition (ASR) remains difficult because real CS speech is scarce and synthetic speech does not fully match it. We investigate whether synthetic CS speech is more useful for learning an adaptation-friendly initialization than for ordinary continual fine-tuning. We propose SyRA-CS, a pair-specific synthetic-to-real adaptation framework based on Reptile meta-learning. For each language pair and pretrained model, we meta-train on the corresponding synthetic CS-FLEURS subset and then adapt using one hour of labeled real target speech. We evaluate four architectural settings: Encoder-CTC, FastConformer-RNN-T, Attention Encoder-Decoder (AED) and Speech-LLM. Experiments cover on Arabic-, French-, German-, and Hindi-English, against synthetic-only transfer, real-only fine-tuning, and continual fine-tuning. SyRA-CS improves over continual fine-tuning on WER in all 16 model-pair comparisons and on CER in 15 of 16, with relative macro WER reductions of 17.7% for XLS-R and 5.3-5.8% for the other three models. The gains hold across the tested models but vary in size across architectures, language pairs and metrics.