Instituto de Investigación en Matemáticas (IMUVA)

Duals of multiplicity codes

2026-04-08T19:16:12Z

Multivariate multiplicity codes have been recently explored because of their importance for list decoding and local decoding. Given a multivariate multiplicity code, in this paper, we compute its dimension using Gröbner basis tools, its dual in terms of indicator functions, and explicitly describe a parity-check matrix. In contrast with Reed–Muller, Reed–Solomon, univariate multiplicity, and other evaluation codes, the dual of a multivariate multiplicity code is not equivalent or isometric to a multiplicity code (i.e., this code family is not closed under duality). We use our explicit description to provide a lower bound on the minimum distance for the dual of a multiplicity code.

The Impacts of Environmental Policy on Industrial Allocation: A Transboundary Pollution Dynamic Game

2026-03-19T20:01:36Z

We examine the impact of environmental policy on industrial location between two trading regions dealing with transboundary pollution. Firstly, we study how the distribution of firms and trade costs affect the governments’ environmental policies, particularly, the issuance of emission permits. Secondly, we study how the resulting environmental policies alter the allocation of the industry. The microeconomic behavior of the agents is framed within the Economic Geography literature, through a linear Footloose Capital (FC) model. The macroeconomic model that arises is a transboundary pollution dynamic game. When regions have different industrial shares, we find that if pollution damage is low, the more industrialized region adopts environmentally irresponsible behavior by increasing the offer of emission permits, which reduces their price. Firms benefit from lower production costs, ultimately attracting more firms (agglomeration force). However, due to transport costs, as the share of firms in a region increases, the benefits decrease (dispersion force). The final spatial distribution of the industry between the regions depends on the balance between agglomeration and dispersion forces. This agglomerative force and the governments’ strategic behavior, absent in the FC model, could lead to industrial activity fully concentrating in a core region. As pollution damage increases, agglomerative power loses strength.

The Schur product of evaluation codes and its application to CSS-T quantum codes and private information retrieval

2026-03-10T20:03:32Z

In this work, we study the Schur (componentwise) product of monomial-Cartesian codes by exploiting its correspondence with the Minkowski sum of their defining exponent sets. We show that J-affine variety codes are well suited for such products, generalizing earlier results for cyclic, Reed–Muller, hyperbolic, and toric codes. Using this correspondence, we construct CSS-T quantum codes from weighted Reed–Muller codes and from binary subfield-subcodes of J-affine variety codes, leading to codes with better parameters than previously known. Finally, we present Private Information Retrieval (PIR) constructions for multiple colluding servers based on hyperbolic codes and subfield-subcodes of J-affine variety codes, and show that they outperform existing PIR schemes.

A note on the averaging principle for ordinary differential equations depending on the slow time

2026-03-09T20:08:26Z

he work presents a ‘‘doubly’’ nonautonomous version of the averaging principle, applicable to equations that depend on a small parameter 𝜀 and on (fast) time 𝜏, but also on slow time 𝑡 = 𝜀𝜏. The objectives are to establish optimal conditions on the dependence of the coefficients of the equations on 𝑡 under which the averaging principle can be extended and to provide good estimates of the distance between the solutions of the initial equation and those of the averaged equation, always with 𝜏 varying in intervals of length proportional to 1∕𝜀. The applicability of these results is based on the fact that the estimates obtained are uniform with respect to the initial time at which the solutions of both equations coincide.

A mathematical model to simulate the biological action of Infliximab on TNF-α in patients with Inflammatory Bowel Disease: the critical role of drug clearance

2026-02-13T20:00:50Z

Inflammatory bowel disease (IBD), including Crohn s disease (CD) and ulcerative colitis (UC), is characterized by chronic intestinal inflammation driven by elevated tumor necrosis factor-alpha (TNF-α). Infliximab, an anti-TNF-α monoclonal antibody, is widely used in the treatment of inflammatory bowel disease but shows variable effectiveness due to interindividual pharmacokinetic diversity. We develop a low-dimensional mathematical model of ordinary differential equations to describe TNF-α dynamics, its interactions with receptors and infliximab, and the influence of drug clearance on treatment outcomes in CD and UC. This model is combined with a pharmacokinetic framework that enables the estimation of the infliximab clearance coefficient, which can then be used to guide dosage adjustments in the treatment. The model balances biological realism with analytical tractability, enabling rigorous mathematical analysis and numerical simulations. The parameters are adapted for CD and UC. The study investigates how drug clearance influences treatment efficacy, initially using constant clearance values and later incorporating values that vary with the level of inflammation. Simulations are performed across a range of clearance rates and dosing regimens, providing detailed insights into infliximab and TNF-α dynamics, as well as therapeutic drug monitoring parameters. Our results highlight the critical role of clearance and therapeutic drug monitoring in optimizing infliximab therapy. This approach offers valuable insights to support personalized treatment strategies in IBD.

On the image of a curve in a normal surface by a plane projection

2026-02-05T20:00:26Z

We consider a finite analytic morphism φ = (f, g) defined from a complex analytic normal surface (Z, z) to C2. We describe the topology of the image by φ of a reduced curve on (Z, z) by means of iterated pencils defined recursively for each branch of the curve from the initial one . This result generalizes the one obtained in a previous paper for the case in which (Z, z) is smooth and the curve irreducible. The methods we use also permit us to describe the topological type of the discriminant curve of φ, in particular, the topological type of each branch of the discriminant can be obtained from the map without previous knowledge of the critical locus.

HMC: Reducing the number of rejections by not using leapfrog and some results on the acceptance rate

2026-01-19T20:13:48Z

The leapfrog integrator is routinely used within the Hamiltonian Monte Carlo method and its variants. We give strong numerical evidence that alternative, easy to implement algo-rithms yield fewer rejections with a given computational effort. When the dimensionality of the target distribution is high, the number of accepted proposals may be multiplied by a factor of three or more. This increase in the number of accepted proposals is not achieved by impairing any positive features of the sampling. We also establish new non-asymptotic and asymptotic results on the monotonic relationship between the expected acceptance rate and the expected energy error. These results further validate the derivation of one of the integrators we consider and are of independent interest.

Nonautonomous modelling in energy balance models of climate. Limitations of averaging and climate sensitivity

2025-12-15T09:35:55Z

Starting from a classical Budyko-Sellers-Ghil energy balance model for the average surface temperature of the Earth, a nonautonomous version is designed by allowing the solar irradiance and the cloud cover coefficients to vary with time on a fast timescale, and to exhibit chaos in a precise sense. The dynamics of this model is described in terms of three existing nonautonomous equilibria, the upper one being attracting and representing the present temperature profile. The theory of averaging is used to compare the nonautonomous model and its time-averaged version. We analyse the influence of the qualitative properties of the time-dependent coefficients and obtain reasonable approximations close to the upper hyperbolic solution. Furthermore, previous concepts of two-point response and sensitivity functions are adapted to the nonautonomous context and used to value the increase in temperature when a forcing caused by CO_2 and other emissions intervenes.

Characterizing competition ranks within a comprehensive family of position operators

2025-11-07T20:00:45Z

There is only one way to assign positions to objects arranged in linear orders: following the sequence of natural numbers (1, 2, 3, 4, …). However, in weak orders, where ties arise, there are different possibilities to assign positions to tied objects. In this paper, we focus mainly on three relevant cases: the standard, modified, and fractional ranks. They are differentiated by the spaces that appear after, before, or on either side of the position values corresponding to the objects that are in a tie. For instance, if two objects are tied and are located immedi- ately below the top object, these ranks assign the positions (1, 2, 2, 4, …), (1, 3, 3, 4, …), and (1, 2.5, 2.5, 4, …), respectively. Collectively, and because of the common properties shown here, we call them “competition ranks”. In this paper, we characterize a parameterized family of position operators which includes the competition ranks. We also provide specific axiomatizations of each of them, taking into account the spaces in the sequence of as- signed position numbers. It is shown why the dense rank (1, 2, 2, 3, …), another position operator where gaps do not appear, is an essentially different approach. Furthermore, interesting duality relationships are revealed between the competition ranks and between the properties introduced to characterize them, which allow us to understand their internal logic and connections. Different examples, mainly from sports, bibliometrics, etc., illustrate the introduced concepts

Linear codes in the folded Hamming distance and the quasi MDS property

2025-12-16T20:07:40Z

In this work, we study linear codes with the folded Hamming distance, or equivalently, codes with the classical Hamming distance that are linear over a subfield. This includes additive codes. We study MDS codes in this setting and define quasi MDS (QMDS) codes and dually QMDS codes, which attain a more relaxed variant of the classical Singleton bound. We provide several general results concerning these codes, including restriction, shortening, weight distributions, existence, density, geometric description and bounds on their lengths relative to their field or alphabet sizes. We provide explicit examples and a binary construction with optimal lengths relative to their field or alphabet sizes, which beats any MDS code (in terms of length compared to the field or alphabet size).

Distributed matrix multiplication with straggler tolerance over very small fields

2025-12-16T10:24:43Z

The problem of distributed matrix multiplication with straggler tolerance over finite fields is considered, focusing on field sizes for which previous solutions were not applicable (for instance, the field of two elements). We employ Reed-Muller-type codes for explicitly constructing the desired algorithms and study their parameters by translating the problem into a combinatorial problem involving sums of discrete convex sets. We generalize polynomial codes and matdot codes, discussing the impossibility of the latter being applicable for very small field sizes, while providing optimal solutions for some regimes of parameters in both cases.

Social profiles and response patterns during the 2025 Iberian Peninsula power outage. The case of Spain

2025-10-20T19:00:58Z

On April 28, 2025, a large-scale power outage disrupted essential services across Spain, Portugal, Andorra, and parts of southern France, leaving more than 50 million people without electricity. The event affected critical infrastructures such as transportation, telecommunications, and healthcare, raising concerns about the population’s resilience in the face of unexpected crises. This study focuses on the case of Spain, using data from a representative flash survey conducted after the power outage, and analyzes the population’s response with statistical techniques for categorical data, specifically multiple correspondence analysis (MCA). The analysis focuses on three main aspects: emotional impact (fear), material preparedness (emergency kit), and access to information. The results reveal marked differences among social groups. Young adults, women, and the unemployed reported greater emotional vulnerability, while older and inactive in- dividuals were less emotionally affected. Preparedness was also unevenly distributed, with in- dividuals with higher education more likely to be prepared. Regarding access to information, the data show a stronger association between middle-aged individuals, lower emotional impact, and the perception of having received sufficient information during the power outage. By identifying distinct response patterns, the study contributes to a better understanding of the social di- mensions of crisis management and complements the existing literature on disasters and unex- pected situations.

Optimal sustainable inventory policy for items with price-and-time-dependent demand rate

2025-10-20T19:01:34Z

This paper studies a sustainable inventory model for items whose demand rate is the product of a time- dependent function and a price-dependent function. The inventory system allows shortages during the product management period. Carbon emissions from transportation and storage are included in the model. The consideration of a demand rate that combines the effects of a price-algebraic function and a time-power function, with full backlogging and environmental constraints, is a novel and more realistic hypothesis and it should be studied. To determine the optimal inventory policy for this system can help to improve the efficiency and sustainability practices in inventory control. The objective is to determine a sustainable inventory policy that maximizes the average profit per unit time. We include the following significant components in the objective function: the average revenue, the ordering cost, the purchasing cost, the shipping cost, the holding cost, the shortage cost, and the carbon emissions costs in transportation and storage. To find the solution to this sustainable inventory problem, four scenarios are analyzed and, for each scenario, the optimal inventory policy is obtained. This policy determines the lot size, the optimal selling price, the maximum shortage, and the maximum profit per unit time. Some numerical examples are presented to illustrate the proposed methodology for determining the optimal policy of this sustainable inventory problem. We examine the effects on the best inventory policy when some parameters of the system are changed. Useful managerial insights derived from these results are proposed.

Two-Variable Domination Structures and Applications in Vector Optimization

2025-12-09T07:35:48Z

In this paper, we introduce and study domination structures in real topological Hausdorff linear spaces that take into account the two involved points at each comparison. These binary relations are then applied to define notions of minimizer of a set and optimality concepts for vector optimization problems in the usual way, and their basic properties are obtained. Results on nonlinear scalarization to characterize them are also stated, which can be applied to vector optimization problems with variable ordering structures where the known ones do not work. Comparisons with results of the literature and illustrative examples are given as well.

Multilayer crisscross error and erasure correction

2025-10-20T12:52:41Z

In this work, multilayer crisscross errors and erasures are considered, which affect entire rows and columns in the matrices of a list of matrices. To measure such errors and erasures, the multi-cover metric is introduced. Several bounds are derived, including a Singleton bound, and maximum multi-cover distance (MMCD) codes are defined as those attaining it. Duality, puncturing and shortening of linear MMCD codes are studied. It is shown that the dual of a linear MMCD code is not necessarily MMCD, and those satisfying this duality condition are defined as dually MMCD codes. Finally, some constructions of codes in the multi-cover metric are given, including dually MMCD codes, together with efficient decoding algorithms for them.

Stroboscopic averaging methods to study autoresonance and other problems with slowly varying forcing frequencies

2025-06-18T19:05:02Z

Autoresonance is a phenomenon of physical interest that may take place when a nonlinear oscillator is forced at a frequency that varies slowly. The stroboscopic averaging method (SAM), which provides an efficient numerical technique for the integration of highly oscillatory systems, cannot be used directly to study autoresonance due to the slow changes of the forcing frequency. We study how to modify SAM to cater for such slow variations. Numerical experiments show the computational advantages of using SA