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For two subspaces $U,V\subseteq\RR^n$, the circumcentered--reflection method (CRM) of Behling, Bello-Cruz, and Santos~\cite{BBS2018} computes the projection onto $U\cap V$ using only the reflections across $U$ and $V$, with known linear-convergence rate $c_F$, the cosine of the Friedrichs angle. We prove that, when CRM is initialized in $V$, it contracts at the strictly smaller rate $ρ_V=(\sin^2θ_p-\sin^2θ_F)/(\sin^2θ_p+\sin^2θ_F)$, where $θ_F\in(0,π/2]$ is the Friedrichs angle and $θ_p\in[θ_F,π/2]$ the largest principal angle between $U$ and $V$. The bound is sharp, attained on an explicit ray in $V$, and optimal among parameter-free single-step iterations. The constant itself is not new: Bauschke, Bello-Cruz, Nghia, Phan, and Wang~\cite{BBNPW2016} identified it as the optimal rate of the relaxed alternating-projection family and of their adaptive linesearch map $B_T$. Our contribution is that the parameter-free geometric circumcenter attains it as well, via Kantorovich's inequality applied to a single self-adjoint operator on $V$. Restricted to $V$, CRM coincides pointwise with the linesearch maps $A_T$ and $B_T$ from the Gubin--Polyak--Raik framework~\cite{GPR1967}. We further p

In this paper, we propose a notion of subdifferential defined via Busemann functions and use it to identify a condition under which the Fenchel-Young inequality of Bento, Cruz Neto and Melo (Appl. Math. Optim. 88:83, 2023) holds with equality. This equality condition is particularly significant, as it captures a fundamental duality principle in convex analysis, linking a primal convex function to its conjugate and clarifying the sharpness of the associated inequality on Riemannian manifolds. We also investigate the existence of non-trivial affine functions under Ricci curvature information. In particular, we extend the result of Bento, Cruz Neto and Melo, originally formulated for the case of negative Ricci curvature on an open set, to manifolds whose Ricci curvature may be non-zero. As a consequence, we prove new non-existence criteria for non-trivial affine functions and show that the assumption of non-zero Ricci curvature is, in general, necessary to ensure such a rigidity conclusion.

Analogously to the quantum case considered in Cruz-de-la-Rosa and Guerrero-Poblete (Open Syst. Inf. Dyn. 32, 2550005, 2025), this work proposes a graph-theoretic approach to studying non-equilibrium properties in Markov chains. We prove that the kernel of the incidence matrix associated with the interaction graph of the chain, which consists of cycles, is isomorphic to the space of anti-symmetric matrices with rows sum to zero. The main contribution of this work is the introduction of the called cycle matrices, which constitute a basis for the space of matrices that describe the non-equilibrium.

The centralized circumcentered-reflection method (\cCRM) of Behling, Bello-Cruz, Iusem, and Santos~\cite{Behling:2024} is known to converge superlinearly for the feasibility problem $\operatorname{find}\;z\in X\cap Y$ under a $\mathcal{C}^1$ smoothness assumption on the boundaries of $X$ and $Y$. We sharpen this to a quantitative rate: when the boundaries are $\mathcal{C}^2$ near the limit point $\bar z$, \cCRM\ converges Q-quadratically, with an asymptotic constant \( 2\max(κ_X,κ_Y)/ω\) governed by the boundary curvatures $κ_X,κ_Y$ at $\bar z$ and the local error-bound modulus $ω$. The estimate matches Newton-type second-order behavior even though \cCRM\ uses only projections and circumcenters, and numerical experiments on equality-constrained and spectral feasibility problems exhibit the predicted quadratic rate, with \cCRM\ reaching machine precision in a handful of steps where alternating projections and Douglas--Rachford take many. The argument is local and does not require $X\cap Y$ to have nonempty interior in $\re^n$: it suffices that the sets share an affine hull $L=\aff(X)=\aff(Y)$ and meet with nonempty relative interior, which is the natural setting for equality-constra

In the setting of multi-head finite-state dimensions, trailing heads lag behind a leading head, accessing past data to aid a finite-state gambler placing bets on successive bits read by the leading head. Cruz, Glashausser, Li, and Lutz (2026) proved that, for any fixed number of trailing heads, adaptive (data-dependent) movement rules can strictly outperform oblivious (data-independent) movement schedules. In this paper we strengthen that separation by proving that a single trailing head with adaptive movements can outperform, by a large and uniform margin, arbitrarily many trailing heads with oblivious movements. Formally, our main theorem states that there is a binary sequence whose adaptive two-head finite-state strong dimension is less than its oblivious multi-head finite-state dimension, and that the gap is greater than 0.3.

Behling, Bello-Cruz, Lara-Urdaneta, Oviedo, and Santos showed that the circumcentric direction $d$ of a finitely generated polyhedral cone $\KK\subset\RR^n$ admits an inscribed Euclidean ball of radius $ orm{d}^2$ inside the polar cone $\Kpolar$. We sharpen this result in several ways. The exact set of admissible perturbations is a polyhedron, strictly larger than the inscribed ball off the generators and unbounded along $\Kpolar$. From it we read off a closed form for $ orm{d}^2$ in terms of the inverse Gram matrix of the conic base, with two-sided spectral bounds, and an aperture identity $ orm{d}=\cosθ$ relating the generators to the axis $-d/ orm{d}$. The inscribed-ball estimate extends to closed convex pointed cones under one geometric condition: the normalized extremal section $E_\KK$ has affine hull avoiding the origin. The admissible set is then the intersection of half-spaces indexed by $E_\KK$, and the inscribed ball touches its boundary along $ orm{d}^2\,\closu E_\KK$. A Jordan-frame argument verifies the hypothesis for every simple symmetric cone and gives $ orm{d}^2=1/r$ for the Jordan rank $r$; the same value $1/n$ shows up for the doubly nonnegative cone, the direct-

We present ATLAS-RTC, a runtime control system for autoregressive language models that enforces structured output during decoding. ATLAS-RTC monitors generation at each step, detects drift from output contracts using lightweight signals, and applies targeted interventions such as biasing, masking, and rollback. Unlike post-hoc validation or static constrained decoding, it operates in a closed loop, enabling correction before errors materialize. Across structured generation and tool-calling tasks, ATLAS-RTC improves first-attempt success rates by 20 to 37.8 percentage points, with up to 88% latency reduction in failure-dominated settings. Results show that many failures arise from decoding artifacts rather than task misunderstanding, motivating runtime control as a distinct layer in LLM systems.

Basis pursuit is the problem of finding a vector with smallest $\ell_1$-norm among the solutions of a given linear system of equations. It is a well-known convex relaxation of the sparse affine feasibility problem, where sparse solutions to underdetermined systems are sought. Since basis pursuit admits a linear programming reformulation, standard LP solvers are directly applicable. We instead address the basis pursuit directly in its $\ell_1$-minimization form, without LP reformulation, via a scheme that uses alternating projections in its subproblems. These subproblems are designed to be inconsistent in the sense that they relate to two non-intersecting sets. Recently in [R. Behling, Y. Bello-Cruz and L.-R. Santos, SIAM J. Optim., 31 (2021), pp. 2863-2892], inconsistency coming from infeasibility has been shown to accelerate convergence of alternating projections. We deliberately enforce this inconsistency by constructing subproblems whose feasible sets are disjoint by design. We prove that the resulting $\ell_1$-radii converge linearly to the optimal value, and that when the solution is unique, all generated sequences converge linearly to it at a rate governed by a natural error

While defenses against single-turn jailbreak attacks on Large Language Models (LLMs) have improved significantly, multi-turn jailbreaks remain a persistent vulnerability, often achieving success rates exceeding 70% against models optimized for single-turn protection. This work presents an empirical analysis of automated multi-turn jailbreak attacks across state-of-the-art models including GPT-4, Claude, and Gemini variants, using the StrongREJECT benchmark. Our findings challenge the perceived sophistication of multi-turn attacks: when accounting for the attacker's ability to learn from how models refuse harmful requests, multi-turn jailbreaking approaches are approximately equivalent to simply resampling single-turn attacks multiple times. Moreover, attack success is correlated among similar models, making it easier to jailbreak newly released ones. Additionally, for reasoning models, we find surprisingly that higher reasoning effort often leads to higher attack success rates. Our results have important implications for AI safety evaluation and the design of jailbreak-resistant systems. We release the source code at https://github.com/diogo-cruz/multi_turn_simpler

We introduce AI Runtime Infrastructure, a distinct execution-time layer that operates above the model and below the application, actively observing, reasoning over, and intervening in agent behavior to optimize task success, latency, token efficiency, reliability, and safety while the agent is running. Unlike model-level optimizations or passive logging systems, runtime infrastructure treats execution itself as an optimization surface, enabling adaptive memory management, failure detection, recovery, and policy enforcement over long-horizon agent workflows.

We study the homological properties of Schur algebras $S(p, 2p)$ over a field $k$ of positive characteristic $p$, focusing on their interplay with the representation theory of quotients of group algebras of symmetric groups via Schur-Weyl duality. Schur-Weyl duality establishes that the centraliser algebra, $Λ(p, 2p)$, of the tensor space $(k^p)^{\otimes 2p}$ (as a module over $S(p, 2p)$) is a quotient of the group algebra of the symmetric group. In this paper, we prove that Schur-Weyl duality between $S(p, 2p)$ and $Λ(p, 2p)$ is an instance of an Auslander-type correspondence. We compute the global dimension of Schur algebras $S(p, 2p)$ and their relative dominant dimension with respect to the tensor space $(k^p)^{\otimes 2p}$. In particular, we show that the pair $(S(p, 2p), (k^p)^{\otimes 2p})$ forms a relative $4(p-1)$-Auslander pair in the sense of Cruz and Psaroudakis, thereby connecting Schur algebras with higher homological algebra. Moreover, we determine the Hemmer-Nakano dimension associated with the quasi-hereditary cover of $Λ(p, 2p)$ that arises from Schur-Weyl duality. As an application, we show that the direct sum of some Young modules over $Λ(p, 2p)$ is a full tilti

This paper presents the analysis, design, fabrication, and measurement of an integrated low-noise amplifier (LNA) implemented using a 130 nm CMOS technology, operating in the 2.4 GHz band. The LNA is a crucial component in the performance of receivers, particularly in integrated receivers. The proposed LNA was designed to meet the specifications of the IEEE 802.15.4 standard. Post-layout simulation results, including pads with electrostatic discharge (ESD) protection, are as follows: gain of 10.7 dB, noise figure of 2.7 dB, third-order input intercept point (IIP3) of 0.9 dBm, input and output impedance matching better than -20 dB with respect to 50~$Ω$ terminations, with a power consumption of 505 $μ$W powered from a 1.2 V supply. The obtained results fall within the range of those recently reported for the same topology and operating frequency. The measured scattering parameters (S-parameters) are consistent with the simulation results. This work contributes to the development of a new research line in Cuba on the design of radio-frequency (RF) integrated circuits.

We establish the existence of hypersurfaces with constant mean curvature and a prescribed boundary in Euclidean space, represented as radial graphs over domains of the unit sphere. Under the assumptions that the mean curvature of the domain's boundary is positive and that a subsolution exists for the associated Dirichlet problem, we extend Serrin's classical result to include the case of positive constant mean curvature.

In this work, we explore the effect at cosmological level of the extra contribution arising from the Geodetic Brane Gravity model within a thermodynamical perspective. As already known, the universe seen as an extended object embedded within a higher dimensional space time, modifies the dynamical background equations, which in turn results in correction contributions to the entropy and temperature of the apparent horizon. Additionally, we investigate the possibility that the apparent horizon and the bulk remain in thermal equilibrium across various matter contents, demonstrating that such properties are highly sensitive to the equation-of-state parameter.

This work addresses the open question of implementing fault-tolerant QRLCs with feasible computational overhead. We present a new decoder for quantum random linear codes (QRLCs) capable of dealing with imperfect decoding operations. A first approach, introduced by Cruz et al., only considered channel errors, and perfect gates at the decoder. Here, we analyze the fault-tolerant characteristics of QRLCs with a new noise-guessing decoding technique, when considering preparation, measurement, and gate errors in the syndrome extraction procedure, while also accounting for error degeneracy. Our findings indicate a threshold error rate ($\pth$) of approximately $\pnum$ in the asymptotic limit, while considering realistic noise levels in the mentioned physical procedures.