arXiv subjects

Alexander Demin

Publications and source records attributed to Alexander Demin.

At least 19 recordsLinked to original sources

arXiv2026

Observable functions of rational ODE models and how to find them

Consider a parametric ODE control model. A function of the states and parameters is called observable if its value can in principle be reconstructed from input-output data. The observable functions form a field, called the observation field, represented naturally by a set of generators. Even when the model is not fully observable, this field captures the information still accessible from input-output data. We present an algorithm for computing a concise generating set for the observation field of a model with rational dynamics. The algorithm relies on two new results: one allows observable functions to be extracted from the coefficients of repeated Lie derivatives of the outputs, while the other reduces the required orders of differentiation by exploiting identifiable parameter combinations. We implement the resulting algorithm in StructuralIdentifiability$.$jl (https://github.com/SciML/StructuralIdentifiability.jl). For computational efficiency, we employ recent techniques for differential elimination and rational function field simplification. Using models from epidemiology, chemical kinetics, and cancer modeling, we show that the algorithm produces generators with domain-specific interpretations that can inform model analysis and development.

math.DS↗

arXiv2026

Redactable blockchains and polynomial equations

We develop new tools for constructing redactable authenticated data structures with post-quantum security. In our construction, inverting the proposed one-way function means solving a polynomial equation (or a system of polynomial equations) in more than one variable. This is presently considered quantum-safe, i.e., there is no known quantum algorithm that could solve this problem efficiently if parameters are chosen wisely.

cs.CR↗

arXiv2026

Groebner.jl: Fast Gr\"obner Tracing in Julia

A standard way to control expression swell in computer algebra is to use multi-modular or evaluation-interpolation methods. In computations involving Gr\"obner bases, these techniques typically require repeatedly computing Gr\"obner bases of specializations of the same ideal. These repeated computations can be accelerated through precomputation, notably using Traverso's tracing. We present Groebner$.$jl (https://github.com/sumiya11/Groebner.jl), a Julia implementation of the F4 algorithm that exposes Traverso's tracing through a reusable public interface. The implementation supports SIMD-friendly coefficient types, such as tuples of machine integers, which Julia compiles to efficient code with little manual intervention. This lets other Julia software leverage tracing to obtain speedups in applications such as structural identifiability of ordinary differential equation models and polynomial system solving.

cs.SC↗

arXiv2026

Fast Rational Univariate Representation via Gaussian Elimination

In this note, we present RationalUnivariateRepresentation$.$jl (https://newrur.gitlabpages.inria.fr/RationalUnivariateRepresentation.jl/), a Julia package for computing rational univariate representations of zero-dimensional polynomial systems. The package uses dense linear algebra and Gaussian elimination for the FGLM-like stage. The purpose of this contribution is to advocate for this choice and explain the implementation details that turn the algorithm into practical software. In particular, we show that our implementation can compute guaranteedly correct parametrizations of ideals with thousands of solutions within seconds.

cs.SC↗

arXiv2026

Practical MCTS-based Query Optimization: A Reproducibility Study and new MCTS algorithm for complex queries

Monte Carlo Tree Search (MCTS) has been proposed as a transformative approach to join-order optimization in database query processing, with recent frameworks such as AlphaJoin and HyperQO claiming to outperform traditional methods. However, the fact that these frameworks rely on learned cost models raises concerns related to generalizability and deployment readiness. This paper presents a comprehensive reproducibility study of these methods, revealing that they often fail to support the claimed performance gains when subjected to diverse workloads. Through an ablation study, we diagnose the root cause of this instability: while the MCTS search strategy is effective, the accompanying learned cost models suffer from severe out-of-distribution generalization errors. Addressing this, we propose a novel MCTS framework. Unlike prior methods that rely on unstable learned components, our approach utilizes the database standard internal cost model, augmented by a new Extreme UCT (Upper Confidence Bound applied to Trees) selection policy to navigate the search space more robustly. We benchmark our method against the original AlphaJoin and HyperQO, as well as industry-standard baselines including Dynamic Programming (DP) and Genetic Query Optimization (GEQO), using the well-known Join Order Benchmark (JOB) and the new JOB-Complex benchmark. The results demonstrate that our approach outperforms learned MCTS methods and achieves superiority over a SOTA query optimizer in complex join scenarios on real-world data. We release the full implementation and experimental artifacts to support further research.

cs.DB↗

arXiv2026

Simple generators of rational function fields

Consider a subfield of the field of rational functions in several indeterminates. We present an algorithm that, given a set of generators of such a subfield, finds a simple generating set. We provide an implementation of the algorithm and show that it improves upon the state of the art both in efficiency and the quality of the results. Furthermore, we demonstrate the utility of simplified generators through several case studies from different application domains, such as structural parameter identifiability. The main algorithmic novelties include performing only partial Gr\"obner basis computation via sparse interpolation and efficient search for polynomials of a fixed degree in a subfield of the rational function field.

cs.SC↗

arXiv2025

Training-Free Query Optimization via LLM-Based Plan Similarity

Large language model (LLM) embeddings offer a promising new avenue for database query optimization. In this paper, we explore how pre-trained execution plan embeddings can guide SQL query execution without the need for additional model training. We introduce LLM-PM (LLM-based Plan Mapping), a framework that embeds the default execution plan of a query, finds its k nearest neighbors among previously executed plans, and recommends database hintsets based on neighborhood voting. A lightweight consistency check validates the selected hint, while a fallback mechanism searches the full hint space when needed. Evaluated on the JOB-CEB benchmark using OpenGauss, LLM-PM achieves an average speed-up of 21% query latency reduction. This work highlights the potential of LLM-powered embeddings to deliver practical improvements in query performance and opens new directions for training-free, embedding-based optimizer guidance systems.

cs.DB↗

arXiv2025

Some Computational Tools for Solving a Selection of Problems in Control Theory

This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among others) discriminant varieties and Rational Univariate Representation, while also supporting multi-precision interval computations. We showcase its applications to key control theory problems, including identification, stability analysis, and optimization, for both parameter-dependent and parameter-free systems.

cs.SC↗

arXiv2025

Parameter Estimation in ODE Models with Certified Polynomial System Solving

We consider dynamical models given by rational ODE systems. Parameter estimation is an important and challenging task of recovering parameter values from observed data. Recently, a method based on differential algebra and rational interpolation was proposed to express parameter estimation in terms of polynomial system solving. Typically, polynomial system solving is a bottleneck, hence the choice of the polynomial solver is crucial. In this contribution, we compare two polynomial system solvers applied to parameter estimation: homotopy continuation solver from HomotopyContinuation.jl and our new implementation of a certified solver based on rational univariate representation (RUR) and real root isolation. We show how the new RUR solver can tackle examples that are out of reach for the homotopy methods and vice versa.

cs.SC↗

arXiv2024

Learning-Augmented Online Caching: New Upper Bounds

We address the problem of learning-augmented online caching in the scenario when each request is accompanied by a prediction of the next occurrence of the requested page. We improve currently known bounds on the competitive ratio of the BlindOracle algorithm, which evicts a page predicted to be requested last. We also prove a lower bound on the competitive ratio of any randomized algorithm and show that a combination of the BlindOracle with the Marker algorithm achieves a competitive ratio that is optimal up to some constant.

cs.DB↗

arXiv2024

Adaptive Cost Model for Query Optimization

The principal component of conventional database query optimizers is a cost model that is used to estimate expected performance of query plans. The accuracy of the cost model has direct impact on the optimality of execution plans selected by the optimizer and thus, on the resulting query latency. Several common parameters of cost models in modern DBMS are related to the performance of CPU and I/O and are typically set by a database administrator upon system tuning. However these performance characteristics are not stable and therefore, a single point estimation may not suffice for all DB load regimes. In this paper, we propose an Adaptive Cost Model (ACM) which dynamically optimizes CPU- and I/O-related plan cost parameters at DB runtime. By continuously monitoring query execution statistics and the state of DB buffer cache ACM adjusts cost parameters without the need for manual intervention from a database administrator. This allows for responding to changes in the workload and system performance ensuring more optimal query execution plans. We describe the main ideas in the implementation of ACM and report on a preliminary experimental evaluation showing 20\% end-to-end latency improvement on TPC-H benchmark.

cs.DB↗

arXiv2024

EEvA: Fast Expert-Based Algorithms for Buffer Page Replacement

Optimal page replacement is an important problem in efficient buffer management. The range of replacement strategies known in the literature varies from simple but efficient FIFO-based algorithms to more accurate but potentially costly methods tailored to specific data access patterns. The principal issue in adopting a pattern-specific replacement logic in a DB buffer manager is to guarantee non-degradation in general high-load regimes. In this paper, we propose a new family of page replacement algorithms for DB buffer manager which demonstrate a superior performance wrt competitors on custom data access patterns and imply a low computational overhead on TPC-C. We provide theoretical foundations and an extensive experimental study on the proposed algorithms which covers synthetic benchmarks and an implementation in an open-source DB kernel evaluated on TPC-C.

cs.DB↗

arXiv2024

Reading Rational Univariate Representations on lexicographic Groebner bases

In this contribution, we consider a zero-dimensional polynomial system in $n$ variables defined over a field $\mathbb{K}$. In the context of computing a Rational Univariate Representation (RUR) of its solutions, we address the problem of certifying a separating linear form and, once certified, calculating the RUR that comes from it, without any condition on the ideal else than being zero-dimensional. Our key result is that the RUR can be read (closed formula) from lexicographic Groebner bases of bivariate elimination ideals, even in the case where the original ideal that is not in shape position, so that one can use the same core as the well known FGLM method to propose a simple algorithm. Our first experiments, either with a very short code (300 lines) written in Maple or with a Julia code using straightforward implementations performing only classical Gaussian reductions in addition to Groebner bases for the degree reverse lexicographic ordering, show that this new method is already competitive with sophisticated state of the art implementations which do not certify the parameterizations.

cs.SC↗

arXiv2023

Factoring sparse polynomials fast

Consider a sparse polynomial in several variables given explicitly as a sum of non-zero terms with coefficients in an effective field. In this paper, we present several algorithms for factoring such polynomials and related tasks (such as gcd computation, square-free factorization, content-free factorization, and root extraction). Our methods are all based on sparse interpolation, but follow two main lines of attack: iteration on the number of variables and more direct reductions to the univariate or bivariate case. We present detailed probabilistic complexity bounds in terms of the complexity of sparse interpolation and evaluation.

cs.SC↗

arXiv2023

Progress in End-to-End Optimization of Detectors for Fundamental Physics with Differentiable Programming

In this article we examine recent developments in the research area concerning the creation of end-to-end models for the complete optimization of measuring instruments. The models we consider rely on differentiable programming methods and on the specification of a software pipeline including all factors impacting performance -- from the data-generating processes to their reconstruction and the extraction of inference on the parameters of interest of a measuring instrument -- along with the careful specification of a utility function well aligned with the end goals of the experiment. Building on previous studies originated within the MODE Collaboration, we focus specifically on applications involving instruments for particle physics experimentation, as well as industrial and medical applications that share the detection of radiation as their data-generating mechanism.

physics.ins-det↗

arXiv2023

Groebner.jl: A package for Gr\"obner bases computations in Julia

We present Groebner.jl, a Julia package for computing Groebner bases with the F4 algorithm. Groebner.jl is an efficient, portable, and open-source software. Groebner.jl works over integers modulo a prime and over the rationals, supports basic multi-threading, and specializes in computation in the degree reverse lexicographical monomial ordering. The implementation incorporates various symbolic computation techniques and leverages the Julia type system and tooling, which allows Groebner.jl to compete with the existing state of the art, in many instances outperform it, and exceed them in extensibility. Groebner.jl is freely available at https://github.com/sumiya11/Groebner.jl.

cs.MS↗

arXiv2023

Exact hierarchical reductions of dynamical models via linear transformations

Dynamical models described by ordinary differential equations (ODEs) are a fundamental tool in the sciences and engineering. Exact reduction aims at producing a lower-dimensional model in which each macro-variable can be directly related to the original variables, and it is thus a natural step towards the model's formal analysis and mechanistic understanding. We present an algorithm which, given a polynomial ODE model, computes a longest possible chain of exact linear reductions of the model such that each reduction refines the previous one, thus giving a user control of the level of detail preserved by the reduction. This significantly generalizes over the existing approaches which compute only the reduction of the lowest dimension subject to an approach-specific constraint. The algorithm reduces finding exact linear reductions to a question about representations of finite-dimensional algebras. We provide an implementation of the algorithm, demonstrate its performance on a set of benchmarks, and illustrate the applicability via case studies. Our implementation is freely available at https://github.com/x3042/ExactODEReduction.jl

eess.SY↗

arXiv2022

Machine Learning with Probabilistic Law Discovery: A Concise Introduction

Probabilistic Law Discovery (PLD) is a logic based Machine Learning method, which implements a variant of probabilistic rule learning. In several aspects, PLD is close to Decision Tree/Random Forest methods, but it differs significantly in how relevant rules are defined. The learning procedure of PLD solves the optimization problem related to the search for rules (called probabilistic laws), which have a minimal length and relatively high probability. At inference, ensembles of these rules are used for prediction. Probabilistic laws are human-readable and PLD based models are transparent and inherently interpretable. Applications of PLD include classification/clusterization/regression tasks, as well as time series analysis/anomaly detection and adaptive (robotic) control. In this paper, we outline the main principles of PLD, highlight its benefits and limitations and provide some application guidelines.

cs.AI↗