We study two-dimensional translation-invariant CSS stabilizer codes over prime-dimensional qudits on the square lattice under twisted boundary conditions, generalizing the Kitaev $\mathbb{Z}_p$ toric code by augmenting each stabilizer with two additional qudits. Using the Laurent-polynomial formalism, we adapt the Gröbner basis to compute the logical dimension $k$ efficiently, without explicitly constructing large parity-check matrices. We then perform a systematic search over various stabilizer realizations and lattice geometries for $p\in\{3,5,7,11\}$, identifying qudit low-density parity-check codes with the optimal finite-size performance. Representative examples include $[[242,10,22]]_3$ and $[[120,6,20]]_{11}$, both achieving $k d^{2}/n=20$. Across the searched regime, the best observed $k d^{2}$ at fixed $n$ increases with $p$, with an empirical relation $k d^{2} = 0.0541 \, n^{2}\ln p + 3.84 \, n$, compatible with a Bravyi--Poulin--Terhal-type tradeoff when the interaction range grows with system size.

Conformal risk control is an extension of conformal prediction for controlling risk functions beyond miscoverage. The original algorithm controls the expected value of a loss that is monotonic in a one-dimensional parameter. Here, we present risk control guarantees for generic algorithms applied to possibly non-monotonic losses with multidimensional parameters. The guarantees depend on the stability of the algorithm -- unstable algorithms have looser guarantees. We give applications of this technique to selective image classification, FDR and IOU control of tumor segmentations, and multigroup debiasing of recidivism predictions across overlapping race and sex groups using empirical risk minimization.

We consider bosonization of supersymmetry in the context of Wess-Zumino quantum mechanics. Our motivation for this investigation is the flexibility the bosonic fock space affords as any classical probability distribution can be realized on it making it a versatile framework to work with for quantum processes. We proceed by constructing a minimal bosonization of a system with one bosonic and two fermionic degrees of freedom. We iterate this process to construct a tower of SUSY systems that is akin to unfolded Adinkras. We then identify an osp(2|2) symmetry of the system constructed. To build an irreducible representation of the system we induce representations across the sectors, a first to our knowledge, as the previous work have focused on induction only within the bosonic sector. First, we start with a fermionic representation using Clifford algebras and then induce a representation to gl(2|2) and restrict it to osp(2|2). In the second method, we induce a representation from that of the bosonic sector. In both cases, our representations are in terms of qubit operators that provide a way to solve SUSY problems using quantum information based approaches. Depending upon the direction of induction the representations are suitable for implementation on a hybrid qubit and fermionic or bosonic quantum computers.

We give a short exposition of Ren and Willis's analysis-free proof of the existence of exotic compact, orientable 4-manifolds. There are two distinguishing features of our exposition. First, we avoid skein lasagna modules; we use Beliakova and Wehrli's generalization of Rasmussen's s-invariant to links in $S^{3}$ directly. Second, we reduce the complexity of the computations by choosing clever induction hypotheses in Stošić's induction scheme; this in particular allows us to avoid Ren and Willis's Comparison Lemma.

We provide an explicit algorithm to solve the idempotent analogue of the discrete Monge-Kantorovich optimal mass transportation problem with the usual real number field replaced by the tropical (max-plus) semiring, in which addition is defined as the maximum and product is defined as usual addition, with minus infinity and zero playing the roles of additive and multiplicative identities. Such a problem may be naturally called tropical or "max-plus" optimal transportation problem. We show that the solutions to the latter, called the optimal tropical plans, may not correspond to perfect matchings even if the data (max-plus probability measures) have all weights equal to zero, in contrast with the classical discrete optimal transportation analogue, where perfect matching optimal plans in similar situations always exist. Nevertheless, in some randomized situation the existence of perfect matching optimal tropical plans may occur rather frequently. At last, we prove that the uniqueness of solutions of the optimal tropical transportation problem is quite rare.

We study the global-in-time dynamics of vortex rings for the three-dimensional incompressible Euler equations, under the assumption of axisymmetric flows without swirl. For a broad class of initial data sharing only the macroscopic invariants with a thin vortex ring, we prove that the vorticity remains sharply concentrated and propagates along the symmetry axis with leading-order speed given by the Kelvin--Hicks formula, providing the first global-in-time validation of the vortex filament conjecture for a single vortex ring arising from generic initial data. We further identify a universal filamentation mechanism driven by the competition between rapid core translation and slower local induction. This mechanism gives linear-in-time stretching of the vortex support under very general assumptions on the data, yielding dynamical instability of any thin vortex ring configurations in the $W^{2,\infty}$ norm.

Enormous fluid antenna systems (E-FAS) have recently emerged as a new wireless architecture in which intelligent metasurfaces act as guided electromagnetic interfaces, enabling surface-wave (SW) propagation with much lower attenuation and more control than conventional space-wave transmission. While prior work has reported substantial power gains under perfect channel state information (CSI), the impact of practical channel acquisition on E-FAS performance remains largely unexplored. This paper presents the first comprehensive analysis of E-FAS-assisted downlink transmission under pilot-based channel estimation. We develop an estimation framework for the equivalent end-to-end channel and derive closed-form expressions for the statistics of the minimum mean-square-error (MMSE) channel estimate and its estimation error. Building on these results, we analyze both single-user and multiuser operation while explicitly accounting for the training overhead. For the single-user case, we characterize the outage probability and achievable rate with imperfect CSI, and reveal an inherent signal-to-noise ratio (SNR) saturation phenomenon caused by residual self-interference. For the multiuser case, we study zero-forcing (ZF) precoding based on imperfect channel estimates and show that the system becomes interference-limited in the high SNR regime because of residual inter-user interference. Furthermore, we quantify the trade-off between spatial multiplexing gains and pilot overhead when the number of users increases. Analytical findings are validated via Monte Carlo simulations and benchmarked against least-squares (LS) estimation and conventional non-E-FAS transmission. The results reveal that despite CSI imperfections and training costs, E-FAS retains substantial performance advantages and provides robustness enabled by its amplified large-scale channel gain.

Diffusion language models (DLMs) have recently emerged as a promising alternative to autoregressive (AR) approaches, enabling parallel token generation beyond a rigid left-to-right order. Despite growing empirical success, the theoretical understanding of how unmasking schedules -- which specify the order and size of unmasked tokens during sampling -- affect generation quality remains limited. In this work, we introduce a distribution-agnostic unmasking schedule for DLMs that adapts to the (unknown) dependence structure of the target data distribution, without requiring any prior knowledge or hyperparameter tuning. In contrast to prior deterministic procedures that fix unmasking sizes, our method randomizes the number of tokens revealed at each iteration. We show that, for two specific parameter choices, the sampling convergence guarantees -- measured by Kullback-Leibler (KL) divergence -- scale as $\widetilde O(\mathsf{TC}/K)$ and $\widetilde O(\mathsf{DTC}/K)$ respectively. Here, $K$ is the number of iterations, and $\mathsf{TC}$ and $\mathsf{DTC}$ are the total correlation and dual total correlation of the target distribution, capturing the intrinsic dependence structure underlying the data. Importantly, our guarantees hold in the practically relevant parallel-sampling regime $K<L$ where $L$ is the token sequence length. These results significantly improve upon prior convergence theories and yield substantial sampling acceleration for low-complexity distributions. Overall, our findings unveil the adaptivity of DLMs to intrinsic data structures and shed light on the benefit of randomized unmasking sizes in inference schedule design.

For every $p,q\geq 1$, we construct minimal embeddings of $\mathbb{S}^p \times \mathbb{S}^q \times \mathbb{S}^1$ in $\mathbb{S}^{p + q + 2}$ by doubling the links of free-boundary minimal cones in $\mathbb{R}^{p+q+3}$ with bi-orthogonal symmetry. This solves problems posed by Hsiang-Lawson and Hsiang-Hsiang. The equivariance reduces the minimal surface equation to an ODE, and we prove the existence of capillary minimal cones for every contact angle. We obtain free-boundary solutions as limits of capillary surfaces via a singular shooting problem with infinite initial slope. As the contact angle degenerates to $0$, rescalings of the capillary cones converge to a homogeneous solution of the one-phase Bernoulli problem, further illustrating the connection between one-phase free boundaries and minimal surfaces through the capillary functional.

We study the Gaussian sequence compound decision problem and analyze a Bayesian nonparametric estimator from an empirical Bayes, regret-based perspective. Motivated by sharp results for the classical nonparametric maximum likelihood estimator (NPMLE), we ask whether an analogous guarantee can be obtained using a standard Bayesian nonparametric prior. We show that a Dirichlet-process-based Bayesian procedure achieves near-optimal regret bounds. Our main results are stated in the compound decision framework, where the mean vector is treated as fixed, while we also provide parallel guarantees under a hierarchical model in which the means are drawn from a true unknown prior distribution. The posterior mean Bayes rule is, a fortiori, admissible, whereas we show that the NPMLE plug-in rule is inadmissible.

For every prime $p \geq 5$, we compute the $p$-th power of the Ramanujan vector field that arises from the differential relations discovered by Ramanujan for the Eisenstein series $E_2,E_4$ and $E_6$. Our method results in explicit equations for the $p$-th power and uses classical results of Serre and Swinnerton-Dyer about modular forms modulo $p$. From this, we verify that a general conjecture by Sheperd-Barron and Ekedahl is valid for the Ramanujan vector field. Furthermore, we consider the affine realization of a certain moduli space of elliptic curves where the Ramanujan vector field is defined, and describe - in characteristic $p$ - the locus given by supersingular elliptic curves in two ways: a classical one - using equations for the supersingular polynomial - and a new one as the singular set of some vector fields. Additionally, we prove that the Ramanujan vector field is transversal to this locus.

Let $F$ denote a number field and let $\mathfrak{q}\subset O_F$ traverse a sequence of prime ideals with norm $N(\mathfrak{q}) \to \infty$ and for each $\mathfrak{q}$, let $χ\in \widehat{F^{\times}\setminus \mathbb{A}^\times}$ be a finite order character of conductor $\mathfrak{q}$. For a fixed unitary cuspidal automorphic representation $π$ of $\operatorname{GL}_3/F$ we show that \begin{equation*} L(π\otimes χ,\tfrac{1}{2})\ll \ N(\mathfrak{q})^{3/4-κ}.\end{equation*} holds for all $κ< \frac{1}{36}$.

We prove that every entire solution with quadratic growth, lying in a suitable cone, to the 2-Monge-Ampère equation on $\mathbb{R}^3$ is a quadratic polynomial. The proof proceeds by first establishing a concavity inequality, and then deriving a Pogorelov-type interior $C^2$ estimate.

Biological tissues have been observed to display emergent fluid-like properties, owing to physical interactions between cells. However, it remains unclear in general how these fluid-like properties affect tissue structure and function. Here, we are motivated by recent experiments in which cell aggregates were observed to behave as active droplets during collective migration along chemical gradients, or chemotaxis. To understand this process, we develop a minimal model of a growing thin active droplet driven by a self-generated chemical gradient. In broad agreement with the experiments, dynamic simulations reveal that chemotacting droplets exhibit proliferation-driven morphological transitions. To fully characterise these transitions, we perform a multiple scales analysis to show that the droplet dynamics follow a sequence of travelling wave solutions defined by a nonlinear eigenvalue problem parametrised by the slowly increasing droplet volume. Our analysis reveals that morphological transitions can occur continuously or through a discontinuous bifurcation. Further asymptotic analysis of the travelling wave problem reveals that these morphological transitions arise from exponentially small ("beyond-all-orders") asymptotic terms that originate from the rear and front contact lines. Moreover, we show that the nature of the transitions is fully determined by two key dimensionless parameters, which quantify the internal stress balance within the droplet and the strength of the coupling between the droplet migration dynamics and the external chemical field. Overall, our results provide a complete characterisation of the morphodynamics of a class of migrating active thin droplets, with implications in a range of biological systems where cell aggregates exhibit fluid-like behaviour.

We investigate scalar-field cosmologies in the Bianchi V spacetime using a dynamical-systems framework. Motivated by representative $α$-attractor potentials - the E-model and T-model - we apply averaging theorems and amplitude--phase reductions to monomial potentials $\sim ϕ^{2n}$ of the scalar field, which approximate the attractor models near their minima, in the presence of matter with barotropic index $γ$. The reduced averaged system admits five generic isolated equilibria: Kasner vacua $\mathcal{K}_0^\pm$, the matter FLRW point $\mathcal{F}$, the scalar FLRW point $\mathcal{S}$, and the curvature Milne-type point $\mathcal{K}$, together with special families for tuned $(n,γ)$. We find that $\mathcal{K}_0^\pm$ are always sources, $\mathcal{F}$ is generically a saddle but can act as a sink for $γ<\min\{\tfrac{2n}{n+1},\tfrac{2}{3}\}$, $\mathcal{S}$ is a sink if $0<n<\tfrac{1}{2}$ and $\tfrac{2n}{n+1}<γ\leq 2$, while $\mathcal{K}$ becomes a sink whenever $γ>\tfrac{2}{3}$ and $n>\tfrac{1}{2}$. These results demonstrate that isotropic FLRW $α$-attractor models extend naturally to anisotropic Bianchi~V cosmologies: inflationary attractors remain robust, while the Milne-type curvature solution emerges as the late-time state.

To measure the degree of agreement between two observers that independently classify $n$ subjects within $K$ categories, it is common to use different kappa type coefficients, the most common of which is the $κ_C$ coefficient (Cohen's kappa). As $κ_C$ has some weaknesses -such as its poor performance with highly unbalanced marginal distributions-, the $Δ$ coefficient is sometimes used, based on the $delta$ response model. This model allows us to obtain other parameters like: (a) the $α_i$ contribution of each $i$ category to the value of the global agreement $Δ=\sum α_i$; and (b) the consistency $\mathcal{S}_i$ in the category $i$ (degree of agreement in the category $i$), a more appropriate parameter than the kappa value obtained by collapsing the data into the category $i$. It has recently been shown that the classic estimator $\hatκ_C$ underestimates $κ_C$, having obtained a new estimator $\hatκ_{CU}$ which is less biased. This article demonstrates that something similar happens to the known estimators $\hatΔ$, $\hatα_i$, and $\hat{\mathcal{S}}_i$ of $Δ$, $α_i$ and $\mathcal{S}_i$ (respectively), proposes new and less biased estimators $\hatΔ_U$, $\hatα_{iU}$, and $\hat{\mathcal{S}}_{iU}$, determines their variances, analyses the behaviour of all estimators, and concludes that the new estimators should be used when $n$ or $K$ are small (at least when $n\leq 50$ or $K\leq 3$). Additionally, the case where one of the raters is a gold standard is contemplated, in which situation two new parameters arise: the $conformity$ (the rater's capability to recognize a subject in the category $i$) and the $predictivity$ (the reliability of a response $i$ by the rater).

For all $k\geq 2$, we provide almost-sharp quantitative results for the $k$-dimensional Duffin-Schaeffer conjecture, analogous to recent developments in the 1-D case of Koukoulopoulos-Maynard-Yang. In particular, for $ψ:\mathbb{N}\to[0,1/2]$ such that $\sum_{q\in \mathbb{N}}(ψ(q)φ(q)/q)^k$ diverges, $Q\geq 1$ and $α\in\mathbb{R}$, we denote by $S_k(α, Q)$ the number of pairs $(a,q)\in\mathbb{Z}^k\times \mathbb{N}$ with $q\leq Q$, $\gcd(a_i,q)=1$ for each $i\in\{1,\dots,k\}$, satisfying $\|qα-a\|_{\infty}<ψ(q)$. Defining $Ψ_k(Q)=\sum_{q\leq Q}(2ψ(q)φ(q)/q)^k$, we show that for all $\varepsilon>0$ and almost all $α$ one has $S_k(α,Q)=Ψ_k(Q)+O_{\varepsilon,k}(Ψ(Q)^{1/2+\varepsilon})$.

Integrated sensing and communication (ISAC) enables the efficient sharing of wireless resources to support emerging applications, but it also gives rise to new sensing-based security vulnerabilities. Here, potential communication security threats whereby confidential messages intended for legitimate users are intercepted, but also unauthorized receivers (Eves) can passively exploit target echoes to infer sensing parameters without users being aware. Despite these risks, the joint protection of sensing and communication security in ISAC systems remains unexplored. To address this challenge, this paper proposes a two-layer dual-secure ISAC framework that simultaneously protects sensing and communication against passive sensing Eves and communication Eves, without requiring their channel state information (CSI). Specifically, transmit beamformers are jointly designed to inject artificial noise (AN) to introduce interference to communication Eves, while deliberately distorting the reference signal available to sensing Eves to impair their sensing capability. Furthermore, the proposed design generates artificial ghosts (AGs) with fake angle-range-velocity profiles observable by all receivers. Legitimate receivers can suppress these AGs, whereas sensing Eves cannot, thereby significantly reducing their probability of correctly detecting the true targets. Numerical results demonstrate that the proposed framework effectively enhances both communication and sensing security, while preserving the performance of communication users and legitimate sensing receivers.

We explore the expressive power of HOL, a system of higher-order logic, and its relationship to the simply-typed lambda calculus and Church's simple theory of types, arguing for the potential of HOL as a unifying logical framework, capable of encoding a broad range of logical systems, including modal and non-classical logics. Along the way, we emphasize the essential role of discernment, the ability to tell things apart, as a language primitive; highlighting how it endows HOL with practical expressivity superpowers while elegantly enriching its theoretical properties.

We discuss no-dimensional (approximate) versions of Carathéodory's and Helly's theorems. Our goal is to draw attention to open problems and potential applications related to these results. We survey recent progress and pose several questions. We also point out a simple way to ``bring the dimension back into the picture'': by combining no-dimensional statements with dimension-dependent norm comparisons, one can transfer problems in $\ell_1^d$, $\ell_\infty^d$, and Schatten classes $S_1, S_\infty$ to nearby $\ell_p^d$ or $S_p$ spaces with better geometry. As elementary applications, we obtain a weak additive analogue of the Johnson--Lindenstrauss flattening lemma, local-to-global estimates for Chebyshev regression over the $\ell_1$ ball, and a local-to-global guarantee for quantum feasibility from locally consistent linear measurements.

Recently, Andrews and Ghosh Dastidar (Ramanujan J. \textbf{69}, Art. No. 26, 2026) studied two interesting functions $SOME(n)$ and $DSOME(n)$, where $SOME(n)$ is the sum of all the odd parts in the partitions of $n$ minus the sum of all even parts and $DSOME(n)$ is the sum of all the odd parts in the partitions of $n$ into distinct parts minus sum of all the even parts. They expressed the generating functions of $SOME(n)$ and $DSOME(n)$ in terms of $q$-series and found several interesting congruences modulo 4 and 5. In this paper, we express the generating function of $DSOME(n)$ in a closed form, which allows us to find some new congruences and internal congruences modulo 4 and 8 for $DSOME(n)$.

We study a three-dimensional fluid-structure interaction problem describing the motion of an incompressible, viscous fluid coupled with a deformable elastic shell of Koiter type that forms part of the fluid boundary. The fluid motion is governed by the incompressible Navier--Stokes equations posed on a time-dependent domain, while the shell evolution is described by a nonlinear elastic model. At the fluid-structure interface, we impose Navier slip boundary conditions, allowing for tangential slip penalized by friction. Our main result establishes the global-in-time existence of weak solutions up to the first possible self-intersection of the shell, for arbitrarily large initial data with finite energy. The analysis is carried out in a fully three-dimensional setting and addresses the major mathematical challenges arising from the moving domain, the geometric nonlinearity of the shell, and the reduced regularization induced by the slip boundary condition. The proof relies on a careful construction of suitable approximation schemes, novel compactness arguments adapted to the slip framework, and a new extension operator for divergence-free test functions compatible with the fluid-shell coupling. As a further contribution, we provide a direct approach to the strong convergence of second-order spatial derivatives of the shell displacement, which allows us to treat nonlinear Koiter shell models within the same framework.

We prove that the net of localised von Neumann algebras associated with a real scalar field propagating on Minkowski spacetime, in the KMS representation, satisfies a generalised version of Haag duality. Our proof combines ideas from existing arguments for the ground-state representation with purification techniques.

We study the global and local properties of positive solutions to the quasi-linear elliptic equation: \d u+|\nabla u|^q u^p=0,\quad x\in Ø\subset \mathbb{R}^n,\nonumber where $q\ge 0$ and $p\in\mathbb{R}$. Our contributions are twofold: 1. Based on an optimal and new identity for the modulus squared of the logarithmic gradient, we establish optimal and improved Liouville theorems for global positive solutions, and generalize these findings to the framework of Riemannian manifolds. 2. Based on a newly discovered mutual control relationship of two nonlinear iterms, for all index pairs \( (p, q) \) where the Liouville theorem holds, we derive several optimal gradient estimates for local positive solutions. As a direct corollary, we obtain the corresponding Harnack inequality. These results strengthen the related conclusions in Bidaut-Véron--García-Huidobro--Véron \cite {BGV} from both global and local perspectives.

GAP measures (also known as Scrooge measures) are a natural class of probability distributions on the unit sphere of a Hilbert space that come up in quantum statistical mechanics; for each density matrix $ρ$ there is a unique measure GAP$_ρ$. We describe and prove a property of these measures that was not recognized so far: If a wave function $Ψ$ is GAP$_ρ$ distributed and a collapse occurs, then the collapsed wave function $Ψ'$ is again GAP distributed (relative to the appropriate $ρ'$). This fact applies to collapses due to a quantum measurement carried out by an observer, as well as to spontaneous collapse theories such as CSL or GRW. More precisely, it is the conditional distribution of $Ψ'$, given the measurement outcome (respectively, the noise in CSL or the collapse history in GRW), that is GAP$_{ρ'}$.

A famous conjecture of Graham asserts that every set $A \subseteq \mathbb{Z}_p \setminus \{0\}$ can be ordered so that all partial sums are distinct. Although this conjecture was recently proved for sufficiently large primes by Pham and Sauermann in [16], it remains open for general abelian groups, even in the cyclic case $\mathbb{Z}_k$. For cyclic groups, the best known result is due to Bedert and Kravitz in [4], who proved - using a rectification and a two-step probabilistic approach - that the conjecture holds for any subset $A \subseteq \mathbb{Z}_k \setminus \{0\}$ such that $$ |A| \le \exp\!\big(c(\log p)^{1/4}\big), $$ for some constant $c>0$, where $p$ denotes the least prime divisor of $k$. In this paper, we improve their bound using a rectification argument again, followed by a one-shot probabilistic approach, showing that the conjecture holds whenever $$|A| \le \exp\!\big(c(\log p)^{1/3}\big), $$ thus improving the exponent $1/4$ from [4]. Moreover, the same one-shot approach adapts to the $t$-weak setting: by imposing all local constraints at once and applying the Lovász Local Lemma, we obtain the existence of a $t$-weak sequencing whenever $$ t \le \exp\!\big(c(\log p)^{1/4}\big). $$

Vision Transformers have achieved state-of-the-art performance in a wide range of computer vision tasks, but their practical deployment is limited by high computational and memory costs. In this paper, we introduce a novel tensor-based framework for Vision Transformers built upon the Tensor Cosine Product (Cproduct). By exploiting multilinear structures inherent in image data and the orthogonality of cosine transforms, the proposed approach enables efficient attention mechanisms and structured feature representations. We develop the theoretical foundations of the tensor cosine product, analyze its algebraic properties, and integrate it into a new Cproduct-based Vision Transformer architecture (TCP-ViT). Numerical experiments on standard classification and segmentation benchmarks demonstrate that the proposed method achieves a uniform 1/C parameter reduction (where C is the number of channels) while maintaining competitive accuracy.

We construct a scattering matrix with operator valued entries describing solutions to the 1+1 wave equation where permittivities has memory and depends on time and space. It is the analogue of the scattering matrix for spatially localised perturbations where the entries are functions of frequency and appear as Fourier multipliers in solutions of the wave equation. This provides a mathematical explanation of the numerical construction in the recent paper by Horsley et al. The appendix by Zhen Huang and Maciej Zworski presents a numerical scheme for solving the wave equation considered in this article.

We study ideals generated by $n+1$ powers of general linear forms in $R= k[x_1,\dots,x_n]$. By generalizing the ideas in a recent paper of Diethorn et al., we determine the Betti numbers of such ideals when at least one generator is a square. It follows that all such ideals are level. As a consequence, we show that a generic ideal in $R$ generated by $n+1$ forms, with at least one quadric generator, is level. We also determine the Betti numbers of the Artinian Gorenstein algebras linked to these almost complete intersections. By describing the dual generators of these algebras, we obtain a family of forms, including the elementary symmetric polynomials, whose annihilator ideals have the strong Lefschetz property. Finally, we give explicit generators for the annihilator ideal of any elementary symmetric polynomial.

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem with regularization. Such a problem depends on a variety of parameters, that is, the number of measurements, the regularization parameter and the discretization parameter, namely the size of the mesh on which we discretize the unknown coefficients of the Helmholtz type equation modelling our physical system. We show, through a convergence analysis, that one can carefully choose these parameters in such a way that the solution to this discrete regularized minimum problem is a good approximation of the looked-for solution to the inverse problem.