Centre de Recerca Matemàtica

The shrinking core model (SCM) describes the reaction of a solid particle with a surrounding fluid. In this work, we revisit the SCM by deriving it from the underlying physical processes and performing a careful non-dimensionalisation, which highlights the limitations of the commonly used pseudo-steady-state approximation, particularly in liquid-solid systems where fluid and solid densities are comparable. To address these limitations, we derive approximate analytical solutions using a perturbation method that improves upon the pseudo-steady-state model. We also obtain a small-time solution capturing early transient behaviour. A semi-implicit finite difference scheme is implemented to solve the full model numerically and benchmark the analytical approximations. We demonstrate that the perturbation solution provides significantly improved accuracy over the pseudo-steady-state model, especially in diffusion-limited regimes. Finally, we propose a simple fitting procedure combining the perturbation with the early-time solutions to estimate physical parameters from experimental data at minimal computational cost.

Sharp Fourier restriction inequalities in euclidean spaces and the restriction phenomenon in finite fields have both been topics of interest in the last few decades. Very recently, the research at the intersection of these two topics began. In [8], it was established that, for the (3, 1)-cone Gamma(3)((3,1)) := {eta is an element of F-q(4) \ {0} : eta(2)(1) + eta(2)(2) + eta(2)(3) = eta(2)(4)}, the L-2 -> L(4 )Fourier extension inequality is saturated by constant functions when q = 3 (mod 4). In this manuscript, we advance this line of inquiry by establishing sharp forms of L-2 -> L(4 )Fourier extension inequalities for all the remaining cones Gamma(3) subset of F-q(4). These cones include the (2, 2)-cone Gamma(3)(2,2) := {eta is an element of F-q(4) \ {0} : eta(2)(1) + eta(2)(2) + eta(2)(3) = eta(2)(4)} for general q = p(n) and the (3, 1)-cone when q = 1 (mod 4). Moreover, we classify all the extremizers in both cases. We note that the corresponding problem for the (2, 2)-cone in the euclidean setting remains open. (c) 2026 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC license (http:// creativecommons.org/licenses/by-nc/4.0/).

We consider the problem of establishing limitations on the power of quantum query algorithms via the completely bounded polynomial method. In particular, we prove several optimal functional inequalities involving different notions of completely bounded polynomials. These inequalities lead to limiting theorems for the power of quantum query algorithms that improve on prior works. 1. An optimal root-influence bound for block-multilinear polynomials. Prior work showed that block-multilinear polynomials p of degree t satisfy a root-influence bound, p_cb≥∑_i √(Inf_i[p])/t^2, which is stronger than the bound appearing in the Aaronson-Ambainis conjecture. We find the optimal constant in that inequality: p_cb≥∑_i √(Inf_i[p])/t. Since the amplitudes of quantum algorithms that query disjoint blocks of inputs-such as t-fold forrelation- are block-multilinear polynomials with p_cb≤ 1, our inequality shows that they satisfy t≥∑_i√(Inf_i[p]). We prove that this inequality yields both a more efficient classical simulation than prior results based on the Aaronson-Ambainis argument, and a qualitative improvement: all classical queries are nonadaptive. 2. Optimal Fourier growth of the highest level of quantum query algorithms. We show that for every polynomial p defined on {-1,1}^n of degree 2t, the Fourier Growth at the level 2t, namely p_2t_ℓ_1, satisfies p_2t_ℓ_1≤ (en/(2t-1))^2t-1/2p_cb. This is optimal up to the factor e, as witnessed by 2t-fold forrelation. As quantum query algorithms that make t queries (to the whole input) satisfy p_cb≤ 1, this yields a Fourier growth bound for these algorithms, partially resolving a question by Girish (STOC, 2026).

In nonlinear approximation, it is common to consider classes of functions given by their expansion coefficients with respect to some basis Ψ=(ψ_𝐤) , i.e., f = ∑_𝐤∈ℤ^d a_𝐤ψ_𝐤 , with certain structural conditions imposed on the coefficients (a_𝐤) and certain conditions imposed on the basis (ψ_𝐤) . A classical example is given by absolutely convergent series ∑_𝐤∈ℤ^d|a_𝐤|<∞ with respect to an orthogonal or a Riesz basis (ψ_𝐤) , or even a redundant set of functions. Here, we study the classes of functions 𝐀_β^r,b(Ψ,𝒢) with the property ( ∑_𝐤∈ G_j∖ G_j-1|a_𝐤|^β)^ 1/β≤ 2^-rj j^b, j∈ℕ, where the index sets 𝒢=(G_j) satisfy G_j-1⊂ G_j and ⋃_j=1^∞ G_j = ℤ^d . It has been shown recently that universal sampling discretization and nonlinear sparse approximation are useful in the sampling recovery problem for this type of functions, namely, when (G_j) are dyadic cubes or dyadic hyperbolic crosses. In this paper, we generalize these particular results to the classes of functions defined by index sets (G_j) of a rather general structure.

Small flying target tracking in cluttered backgrounds is a critical capability for insects to search for and pursue mates or prey. Researchers have developed feedback neural network models to mimic this visual processing in insects. These models leverage the sophisticated visual systems of flying insects to detect and track small, dim targets effectively, even within complex, cluttered environments such as cityscapes. The neural networks use time-delayed feedback to discriminate small targets from background clutter, allowing for robust target tracking during rapid pursuits. In this paper, we propose an adaptive timedelayed feedback neural network designed to detect small flying targets, such as drones, birds, and planes, with varying velocities. In the proposed model, the strength of the feedback is controlled by estimating the average velocity between consecutive frames. This approach ensures effective detection of different aerial targets in the video sequence. Experimental results show that the adaptive feedback network outperforms the original time-delayed feedback models in detecting small moving targets across varying speeds. The proposed network provides an overall precision about 94% on the testing video data containing flying targets with different velocities.