arXiv subjects

Carlos Rodriguez

Publications and source records attributed to Carlos Rodriguez.

18 recordsLinked to original sources

arXiv2026

Benchmarks in Leipzig

Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers. Most of the work was done during the 3-day workshop *Benchmarks in Leipzig* with 35 participants at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany. We present the resulting collection of 100 questions. We evaluated these questions in three stages: a single attempt by five state-of-the-art LLMs, followed by a 20-runs-per-model evaluation with three of these models, and finally a 3-run attempt with two heavy-thinking models. After Stage 1, 41 questions remained completely unsolved; after Stage 2, this count dropped to 16; and we concluded Stage 3 with only 2 unsolved questions. This demonstrates that the mathematical reasoning capabilities of LLMs are becoming impressive.

math.HO↗

arXiv2025

Border Bases in the Rational Weyl Algebra

Border bases are a generalization of Gr\"obner bases for zero-dimensional ideals in polynomial rings. In this article, we introduce border bases for a non-commutative ring of linear differential operators, namely the rational Weyl algebra. We elaborate on their properties and present algorithms to compute with them. We apply this theory to represent integrable connections as cyclic $D$-modules explicitly. As an application, we visit differential equations behind a string, a Feynman as well as a cosmological integral. We also address the classification of particular $D$-ideals of a fixed holonomic rank, namely the case of linear PDEs with constant coefficients as well as Frobenius ideals. Our approach rests on the theory of Hilbert schemes of points in affine space.

math.AG↗

arXiv2025

A double copy from twisted (co)homology at genus g

We study a family of generalized hypergeometric integrals defined on punctured Riemann surfaces of genus g. These integrals are closely related to g-loop string amplitudes in chiral splitting, where one leaves the loop-momenta, moduli and all but one puncture un-integrated. We study the twisted homology groups associated to these integrals, and determine their intersection numbers. We make use of these homology intersection numbers to write a double-copy formula for the "complex" version of these integrals -- their closed-string analogues. To verify our findings, we develop numerical tools for the evaluation of the integrals in this work. This includes the recently introduced Enriquez kernels -- integration kernels for higher-genus polylogarithms.

hep-th↗

arXiv2025

Deriving motivic coactions and single-valued maps at genus zero from zeta generators

Multiple polylogarithms are equipped with rich algebraic structures including the motivic coaction and the single-valued map which both found fruitful applications in high-energy physics. In recent work arXiv:2312.00697, the current authors presented a conjectural reformulation of the motivic coaction and the single-valued map via zeta generators, certain operations on non-commuting variables in suitable generating series of multiple polylogarithms. In this work, the conjectures of the reference will be proven for multiple polylogarithms that depend on any number of variables on the Riemann sphere.

hep-th↗

arXiv2023

A double copy from twisted (co)homology at genus one

We study the twisted (co)homology of a family of genus-one integrals -- the so called Riemann-Wirtinger integrals. These integrals are closely related to one-loop string amplitudes in chiral splitting where one leaves the loop-momentum, modulus and all but one puncture un-integrated. While not actual one-loop string integrals, they share many properties and are simple enough that the associated twisted (co)homologies have been completely characterized [Goto2022,arXiv:2206.03177]. Using intersection numbers -- an inner product on the vector space of allowed differential forms -- we derive the Gauss-Manin connection for two bases of the twisted cohomology providing an independent check of [Mano&Watanabe2012]. We also use the intersection index -- an inner product on the vector space of allowed contours -- to derive a double-copy formula for the closed-string analogues of Riemann-Wirtinger integrals (one-dimensional integrals over the torus). Similar to the celebrated KLT formula between open- and closed-string tree-level amplitudes, these intersection indices form a genus-one KLT-like kernel defining bilinears in meromorphic Riemann-Wirtinger integrals that are equal to their complex counterparts.

hep-th↗

arXiv2023

Motivic coaction and single-valued map of polylogarithms from zeta generators

We introduce a new Lie-algebraic approach to explicitly construct the motivic coaction and single-valued map of multiple polylogarithms in any number of variables. In both cases, the appearance of multiple zeta values is controlled by conjugating generating series of polylogarithms with Lie-algebra generators associated with odd zeta values. Our reformulation of earlier constructions of coactions and single-valued polylogarithms preserves choices of fibration bases, exposes the correlation between multiple zeta values of different depths and paves the way for generalizations beyond genus zero.

hep-th↗

arXiv2023

Basis decompositions of genus-one string integrals

One-loop scattering amplitudes in string theories involve configuration-space integrals over genus-one surfaces with coefficients of Kronecker-Eisenstein series in the integrand. A conjectural genus-one basis of integrands under Fay identities and integration by parts was recently constructed out of chains of Kronecker-Eisenstein series. In this work, we decompose a variety of more general genus-one integrands into the conjectural chain basis. The explicit form of the expansion coefficients is worked out for infinite families of cases where the Kronecker-Eisenstein series form cycles. Our results can be used to simplify multiparticle amplitudes in supersymmetric, heterotic and bosonic string theories and to investigate loop-level echoes of the field-theory double-copy structures of string tree-level amplitudes. The multitude of basis reductions in this work strongly validate the recently proposed chain basis and stimulate mathematical follow-up studies of more general configuration-space integrals with additional marked points or at higher genus.

hep-th↗

arXiv2022

Open-string integrals with multiple unintegrated punctures at genus one

We study integrals appearing in intermediate steps of one-loop open-string amplitudes, with multiple unintegrated punctures on the $A$-cycle of a torus. We construct a vector of such integrals which closes after taking a total differential with respect to the $N$ unintegrated punctures and the modular parameter $\tau$. These integrals are found to satisfy the elliptic Knizhnik-Zamolodchikov-Bernard (KZB) equations, and can be written as a power series in $\alpha$' -- the string length squared -- in terms of elliptic multiple polylogarithms (eMPLs). In the $N$-puncture case, the KZB equation reveals a representation of $B_{1,N}$, the braid group of $N$ strands on a torus, acting on its solutions. We write the simplest of these braid group elements -- the braiding one puncture around another -- and obtain generating functions of analytic continuations of eMPLs. The KZB equations in the so-called universal case is written in terms of the genus-one Drinfeld-Kohno algebra $\mathfrak{t}_{1,N} \rtimes \mathfrak{d}$, a graded algebra. Our construction determines matrix representations of various dimensions for several generators of this algebra which respect its grading up to commuting terms.

hep-th↗

arXiv2021

Coaction and double-copy properties of configuration-space integrals at genus zero

We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye (KLT) relations in string theory. For this purpose, explicit bases of twisted cycles and cocycles are worked out whose orthonormality simplifies the coaction. We present methods to efficiently perform and organize the expansions of configuration-space integrals in the inverse string tension $\alpha'$ or the dimensional-regularization parameter $\epsilon$ of Feynman integrals. Generating-function techniques open up a new perspective on the coaction of multiple polylogarithms in any number of variables and analytic continuations in the unintegrated punctures. We present a compact recursion for a generalized KLT kernel and discuss its origin from intersection numbers of Stasheff polytopes and its implications for correlation functions of two-dimensional conformal field theories. We find a non-trivial example of correlation functions in $(\mathfrak{p},2)$ minimal models, which can be normalized to become uniformly transcendental in the $\mathfrak{p} \to \infty$ limit.

hep-th↗

arXiv2020

Enhancing the predictive capabilities for high P/T fuel sprays; non-ideal thermodynamic modelling using PC-SAFT

The present work aims to investigate the complex phenomena occurring during high-pressure/high-temperature fuel injection of the Engine Combustion Network (ECN) Spray-A case. While commonly in the literature transcritical mixing cases are approached using traditional cubic equation-of-state models, such models can prove insufficient in the accurate prediction of liquid density and speed of sound. The purpose of the present investigation is to employ a general tabulated approach which can be applied to any type of thermodynamic closure. At the same time, a more advanced model based on the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) is employed to create the thermodynamic table, as it is proven superior to the traditional cubic models, while also having the capacity of predicting Vapor-Liquid-Equilibrium. The model has been used for a combination of dodecane and nitrogen mixing, corresponding to the well known Spray-A conditions. Vapor penetration and mixing both in terms of temperature and mass fraction are found in agreement to experiments, within the experimental errors. Also, the thermodynamic states correspond well with the adiabatic isobaric-mixing curve, demonstrating the energy-conservative nature of the approach.

physics.flu-dyn↗

arXiv2020

A Survey on Future Railway Radio Communications Services: Challenges and Opportunities

Radio communications is one of the most disruptive technologies in railways, enabling a huge set of value-added services that greatly improve many aspects of railways, making them more efficient, safer, and profitable. Lately, some major technologies like ERTMS for high-speed railways and CBTC for subways have made possible a reduction of headway and increased safety never before seen in this field. The railway industry is now looking at wireless communications with great interest, and this can be seen in many projects around the world. Thus, railway radio communications is again a flourishing field, with a lot of research and many things to be done. This survey article explains both opportunities and challenges to be addressed by the railway sector in order to obtain all the possible benefits of the latest radio technologies.

cs.NI↗

arXiv2020

PHELP: Pixel Heating Experiment Learning Platform for Education and Research on IAI-based Smart Control Engineering

Thermal processes are one of the most common systems in the industry, making its understanding a mandatory skill for control engineers. So, multiple efforts are focused on developing low-cost and portable experimental training rigs recreating the thermal process dynamics and controls, usually limited to SISO or low order 2x2 MIMO systems. This paper presents PHELP, a low-cost, portable, and high order MIMO educational platform for uniformity temperature control training. The platform is composed of an array of 16 Peltier modules as heating elements, with a lower heating and cooling times, resulting in a 16x16 high order MIMO system. A low-cost real-time infrared thermal camera is employed as a temperature feedback sensor instead of a standard thermal sensor, ideal for high order MIMO system sensing and temperature distribution tracking. The control algorithm is developed in Matlab/Simulink and employs an Arduino board in hardware in the loop configuration to apply the control action to each Peltier module in the array. A temperature control experiment is performed, showing that the platform is suitable for teaching and training experiences not only in the classroom but also for engineers in the industry. Furthermore, various abnormal conditions can be introduced so that smart control engineering features can be tested.

eess.SY↗

arXiv2019

Phase Diagram for a model of Spin-Crossover in Molecular Crystals

Spin-crossover has a wide range of applications from memory devices to sensors. This has to do mainly with the nature of the transition, which may be abrupt, gradual or incomplete and may also present hysteresis. This transition alters the properties of a given sample, such as magnetic moment, color and electric resistance to name some. Yet, a thorough understanding of the phenomenon is still lacking. In this work a simple model is provided to mimic some of the properties known to occur in spin-crossover. A detailed study of the model parameters is presented using a mean field approach and exhaustive Monte Carlo simulations. A good agreement is found between the analytical results and the simulations for certain regions in the parameter-space. This mean field approach breaks down in parameter regions where the correlations and cooperativity may no longer be averaged over.

cond-mat.str-el↗

arXiv2017

Programming Bots by Synthesizing Natural Language Expressions into API Invocations

At present, bots are still in their preliminary stages of development. Many are relatively simple, or developed ad-hoc for a very specific use-case. For this reason, they are typically programmed manually, or utilize machine-learning classifiers to interpret a fixed set of user utterances. In reality, real world conversations with humans require support for dynamically capturing users expressions. Moreover, bots will derive immeasurable value by programming them to invoke APIs for their results. Today, within the Web and Mobile development community, complex applications are being stringed together with a few lines of code -- all made possible by APIs. Yet, developers today are not as empowered to program bots in much the same way. To overcome this, we introduce BotBase, a bot programming platform that dynamically synthesizes natural language user expressions into API invocations. Our solution is two faceted: Firstly, we construct an API knowledge graph to encode and evolve APIs; secondly, leveraging the above we apply techniques in NLP, ML and Entity Recognition to perform the required synthesis from natural language user expressions into API calls.

cs.SE↗

arXiv2017

Algorithms and Architecture for Real-time Recommendations at News UK

Recommendation systems are recognised as being hugely important in industry, and the area is now well understood. At News UK, there is a requirement to be able to quickly generate recommendations for users on news items as they are published. However, little has been published about systems that can generate recommendations in response to changes in recommendable items and user behaviour in a very short space of time. In this paper we describe a new algorithm for updating collaborative filtering models incrementally, and demonstrate its effectiveness on clickstream data from The Times. We also describe the architecture that allows recommendations to be generated on the fly, and how we have made each component scalable. The system is currently being used in production at News UK.

cs.IR↗

arXiv2017

Ephemeral Context to Support Robust and Diverse Music Recommendations

While prior work on context-based music recommendation focused on fixed set of contexts (e.g. walking, driving, jogging), we propose to use multiple sensors and external data sources to describe momentary (ephemeral) context in a rich way with a very large number of possible states (e.g. jogging fast along in downtown of Sydney under a heavy rain at night being tired and angry). With our approach, we address the problems which current approaches face: 1) a limited ability to infer context from missing or faulty sensor data; 2) an inability to use contextual information to support novel content discovery.

cs.IR↗

arXiv2017

Higher-order corrections for the deflection of light around a massive object

From the Schwarzschild metric we obtain the higher-order terms (up to 20-th order) for the deflection of light around a massive object using the Lindstedt-Poincar\'e method to solve the equation of motion of a photon around the stellar object. Additionally, we obtain diagonal Pad\'e approximants from the perturbation expansion, and we show how these are a better fit for the numerical data. Furthermore, we use these approximants in ray-tracing algorithms to model the bending of light around the massive object.

gr-qc↗

arXiv2005

Metalinguistic Information Extraction for Terminology

This paper describes and evaluates the Metalinguistic Operation Processor (MOP) system for automatic compilation of metalinguistic information from technical and scientific documents. This system is designed to extract non-standard terminological resources that we have called Metalinguistic Information Databases (or MIDs), in order to help update changing glossaries, knowledge bases and ontologies, as well as to reflect the metastable dynamics of special-domain knowledge.

cs.CL↗