Hasil untuk "Applied mathematics. Quantitative methods"

Kassem Danach, Samir Haddad, Wissam Khalil et al.

IntroductionThe rapid growth of e-commerce has increased pressure on postal logistics networks, especially in remote regions.MethodsThis study proposes a fuzzy hyperheuristic genetic algorithm for optimizing a facilitated hub-and-spoke network with drone integration under uncertainty.ResultsThe proposed approach improves service robustness by 25–35% and expands drone coverage to 93.4% of remote demand, with only a modest cost increase (8–12%).DiscussionResults highlight the effectiveness of fuzzy optimization and adaptive hyperheuristics in designing resilient and cost-efficient postal logistics systems.

Marwan Alquran

This study investigates the perturbed Korteweg–de Vries equation modified by incorporating time-dependent perturbation coefficient to model random fluctuations within the wave dynamics. This enhanced equation captures the probabilistic aspects of wave behavior in uncertain environments, accounting for the effects of inherent noise. The Hirota bilinear method, tanh-expansion approach, and the sine(cosine)-function method are employed to derive perturbed soliton solutions. By assigning various functional forms such as periodic, polynomial, and decaying exponential, to the proposed time-dependent coefficient, novel solitary wave patterns of types like-breather, regular(singular)-bell shaped, and periodic solutions are emerged with fluctuations. These findings are relevant for systems where environmental variability or intrinsic noise significantly affects dynamics, such as diffusion processes in physics and uncertainty behavior of water waves.

Iman Tavassoly, Adel Mehrpooya, Parsa Mirlohi et al.

Multisite protein phosphorylation plays a pivotal role in regulating cellular signaling and decision-making processes. In this study, we focus on the mathematical underpinnings and informational aspects of sequential, distributive phosphorylation systems. We first provide rigorous steady-state solutions derived using geometric series arguments and formal mathematical induction, demonstrating that the distribution of phosphorylation states follows a geometric progression determined by the kinase-to-phosphatase activity ratio. We then extend the analysis with entropy-based insights, quantifying uncertainty in phosphorylation states and examining the mutual information between kinase activity and phosphorylation levels through a truncated Poisson model. These results highlight how phosphorylation dynamics introduce both structured patterns and inherent signal variability. By combining exact mathematical proofs with entropy analysis, this work clarifies key quantitative features of multisite phosphorylation from a systems-level perspective.

Francesco Caravelli

These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be readily applied across disciplines. Beginning with a compendium of matrix identities and inversion techniques, the text develops the connections between spectra, dynamics, and structure in finite-dimensional systems. Applications range from dynamical stability and random walks on networks to input-output economics, PageRank, epidemic spreading, memristive circuits, synchronization phenomena, and financial stability. Throughout, the guiding principle is that eigenvalues, eigenvectors, and resolvent operators provide a common language linking problems in physics, mathematics, computer science, and beyond. The presentation is informal, accessible to advanced undergraduates, yet broad enough to serve as a reference for researchers interested in spectral approaches to complex systems.

Hermenegildo Borges de Oliveira

In this work, we study a one-equation turbulence \(k\)-epsilon model that governs fluid flows through permeable media. The model problem under consideration here is derived from the incompressible Navier-Stokes equations by the application of a time-averaging operator used in the \(k\)-epsilon modeling and a volume-averaging operator that is characteristic of modeling unsteady porous media flows. For the associated initial- and boundary-value problem, we prove the existence of suitable weak solutions (average velocity field and turbulent kinetic energy) in the space dimensions of physics interest.

Luis Cárdenas Florido, Leonardo Trujillo, Daniel E. Hernandez et al.

Machine learning and artificial intelligence are growing in popularity thanks to their ability to produce models that exhibit unprecedented performance in domains that include computer vision, natural language processing and code generation. However, such models tend to be very large and complex and impossible to understand using traditional analysis or human scrutiny. Conversely, Symbolic Regression methods attempt to produce models that are relatively small and (potentially) human-readable. In this domain, Genetic Programming (GP) has proven to be a powerful search strategy that achieves state-of-the-art performance. This paper presents a new GP-based feature transformation method called M5GP, which is hybridized with multiple linear regression to produce linear models, implemented to exploit parallel processing on graphical processing units for efficient computation. M5GP is the most recent variant from a family of feature transformation methods (M2GP, M3GP and M4GP) that have proven to be powerful tools for both classification and regression tasks applied to tabular data. The proposed method was evaluated on SRBench v2.0, the current standard benchmarking suite for Symbolic Regression. Results show that M5GP achieves performance that is competitive with the state-of-the-art, achieving a top-three rank on the most difficult subset of black-box problems. Moreover, it achieves the lowest computation time when compared to other GP-based methods that have similar accuracy scores.

J.A. García-Rodríguez, Guy Yaoyotzin Cortés S․, Roberto Carlos Diaz-Velazco et al.

Diabetes Mellitus (DM) is emerging as a global concern, affecting people from early ages to adulthood and positioning itself as one of the leading causes of mortality worldwide. The post-COVID-19 era has been characterized by notable progress in the domains of medicine, science, and engineering, creating a favorable atmosphere for the investigation of innovative solutions. The present manuscript aims to investigate the problem of glucose regulation in adults diagnosed with Type 1 Diabetes mellitus (T1D) using a two-degree-of-freedom robust controller technique. A physiological mathematical model involving individuals with T1D serves as the foundation for the proposed closed-loop technique. The control algorithm approach successfully maintains safe glycemic levels in a virtual population of 10 adults using a sophisticated, well-known physiological T1D simulator. We evaluated this with continuous 24-hour simulations. Simulation results support the practicality of the presented approach, and we further validate it using a statistical analysis that incorporates a probability density function and control variability grid analysis (CVGA). Despite being a theoretical and simulation-based methodology, the results of this study demonstrate promise, offering promising opportunities for developments in the field of artificial pancreas technology using Mexican technology.

Walter Dean, Alberto Naibo

This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity theory show that proof discovery is an inherently difficult problem. We then illustrate how several recent applications of artificial intelligence-inspired methods -- respectively involving automated theorem proving, SAT-solvers, and large language models -- do indeed raise novel questions about the nature of mathematical proof. We also argue that the results obtained by such techniques do not tell against our basic argument. This is so because they are embodiments of brute force search and are thus capable of deciding only statements of low logical complexity.

Noah Kravitz, Borys Kuca, James Leng

Using PET and quantitative concatenation techniques, we establish box-norm control with the "expected" directions for counting operators for general multidimensional polynomial progressions, with at most polynomial losses in the parameters. Such results are often useful first steps towards obtaining explicit upper bounds on sets lacking instances of given such progressions. In the companion paper arXiv:2407.08637, we complete this program for sets in $[N]^2$ lacking nondegenerate progressions of the form $(x, y), (x + P(z), y), (x, y + P(z))$, where $P \in \mathbb{Z}[z]$ is any fixed polynomial with an integer root of multiplicity $1$.

Gabriel R. Barrenechea, Tristan Pryer, Alex Trenam

In this work, we introduce and analyse discontinuous Galerkin (dG) methods for the drift-diffusion model. We explore two dG formulations: a classical interior penalty approach and a nodally bound-preserving method. Whilst the interior penalty method demonstrates well-posedness and convergence, it fails to guarantee non-negativity of the solution. To address this deficit, which is often important to ensure in applications, we employ a positivity-preserving method based on a convex subset formulation, ensuring the non-negativity of the solution at the Lagrange nodes. We validate our findings by summarising extensive numerical experiments, highlighting the novelty and effectiveness of our approach in handling the complexities of charge carrier transport.

Yuqi Jin, Hui Cao, Xiaxia Xu

This paper discusses a mathematical model describing the formation of tuberculosis(TB) granulomas. The main purpose is to analyze the change trend of Mtb and immune cells in different stages after Mtb invaded the host. The theoretical analysis indicates that the existence and global stability of bacteria-free equilibrium and bacteria-present equilibrium under different conditions. In addition, the sensitivity analysis is performed on the parameters, which determines the parameters that have the greatest impact on Mtb invading the host. The stage of no infection, the latent TB infection(LTBIs) and active TB corresponding to the clearance, survival or growth and reproduction of Mtb are displayed by the numerical simulations. The results suggest that whether the individuals infected with Mtb will be progressed to the active TB depends on the immune system of individuals.

Shiv G. Yücel, Rafael H. M. Pereira, Pedro S. Peixoto et al.

Abstract The COVID-19 pandemic has shed light on how the spread of infectious diseases worldwide are importantly shaped by both human mobility networks and socio-economic factors. However, few studies look at how both socio-economic conditions and the complex network properties of human mobility patterns interact, and how they influence outbreaks together. We introduce a novel methodology, called the Infection Delay Model, to calculate how the arrival time of an infection varies geographically, considering both effective distance-based metrics and differences in regions’ capacity to isolate—a feature associated with socio-economic inequalities. To illustrate an application of the Infection Delay Model, this paper integrates household travel survey data with cell phone mobility data from the São Paulo metropolitan region to assess the effectiveness of lockdowns to slow the spread of COVID-19. Rather than operating under the assumption that the next pandemic will begin in the same region as the last, the model estimates infection delays under every possible outbreak scenario, allowing for generalizable insights into the effectiveness of interventions to delay a region’s first case. The model sheds light on how the effectiveness of lockdowns to slow the spread of disease is influenced by the interaction of mobility networks and socio-economic levels. We find that a negative relationship emerges between network centrality and the infection delay after a lockdown, irrespective of income. Furthermore, for regions across all income and centrality levels, outbreaks starting in less central locations were more effectively slowed by a lockdown. Using the Infection Delay Model, this paper identifies and quantifies a new dimension of disease risk faced by those most central in a mobility network.

Yuhao Chen, Chloe Wong, Hanwen Yang et al.

This study critically evaluates the efficacy of prompting methods in enhancing the mathematical reasoning capability of large language models (LLMs). The investigation uses three prescriptive prompting methods - simple, persona, and conversational prompting - known for their effectiveness in enhancing the linguistic tasks of LLMs. We conduct this analysis on OpenAI's LLM chatbot, ChatGPT-3.5, on extensive problem sets from the MATH, GSM8K, and MMLU datasets, encompassing a broad spectrum of mathematical challenges. A grading script adapted to each dataset is used to determine the effectiveness of these prompting interventions in enhancing the model's mathematical analysis power. Contrary to expectations, our empirical analysis reveals that none of the investigated methods consistently improves over ChatGPT-3.5's baseline performance, with some causing significant degradation. Our findings suggest that prompting strategies do not necessarily generalize to new domains, in this study failing to enhance mathematical performance.

Rand Askar, Luís Bragança, Helena Gervásio

A growing interest has been expressed in the issue of building adaptability over the past decade, perceiving it as an intrinsic criterion for sustainability. In light of the circular economy (CE) and its application in the construction sector, more attention has been paid to buildings’ design for adaptability (DfA) towards the realization of circular buildings. DfA is considered a key enabler for other circular design strategies such as design for disassembly (DfD), multi-functionality, spatial transformability, and design reversibility. However, implementation and assessment frameworks, and design-support tools for the circular building, are still in development as the characterization of circular buildings continues with endeavors to draw a defined shape by identifying the prerequisites for circularity where the design takes an important place. For the sake of objectifying the role of DfA in circularity frameworks in buildings, this paper carries out an analytical review and discussion on two types of assessment and design-support frameworks; the first addresses adaptability criteria and considerations in assessment frameworks that handle the concept individually while the second classifies existing circularity assessment endeavors into four main categories under which multiple tools are reviewed. A reflection on the scope and objectives for both types is later performed, illustrating the state of adaptability evaluation and criteria as well as its role in circularity frameworks. Results show that the concept of building adaptability lacks quantitative methods that quantify a building’s capacity to adapt as well as empirical data that prioritize the most valuable criteria facilitating adaptations. Moreover, many circularity assessment frameworks fail to consider adaptability criteria at all hierarchal levels of a building composition. To address this shortcoming, a series of conceptual considerations and requirements is proposed towards a potential establishment of an inclusive framework of a circularity design-support tool in buildings. The study is concluded by identifying gaps and recommendations for further developments in the field.

Vladik Kreinovich

Experts usually express their degrees of belief in‎ ‎their statements by the words of a natural language (like ``maybe''‎, ‎``perhaps''‎, ‎etc.) If an expert system contains the degrees of‎ ‎beliefs $t(A)$ and $t(B)$ that correspond to the statements $A$‎ ‎and $B$‎, ‎and a user asks this expert system whether ``$A\,\&\,B$'' is‎ ‎true‎, ‎then it‎ ‎is necessary to come up with a reasonable estimate for the‎ ‎degree of belief of $A\,\&\,B$‎. ‎The operation that processes $t(A)$‎ ‎and $t(B)$ into such an estimate $t(A\,\&\,B)$ is called an $\&$-operation‎. ‎Many‎ ‎different $\&$-operations have been proposed‎. ‎Which of them to‎ ‎choose? This can be (in principle) done by interviewing experts and‎ ‎eliciting a $\&$-operation from them‎, ‎but such a process is very‎ ‎time-consuming and therefore‎, ‎not always possible‎. ‎So‎, ‎usually‎, ‎to choose a $\&$-operation‎, ‎we extend the finite‎ ‎set of actually possible degrees of belief to an infinite set‎ ‎(e.g.‎, ‎to an interval [0,1])‎, ‎define an operation there‎, ‎and‎ ‎then restrict this operation to the finite set‎. ‎In this paper‎, ‎we consider only this original finite set‎. ‎We show that a‎ ‎reasonable assumption that an $\&$-operation is continuous (i.e.‎, ‎that gradual change in $t(A)$ and $t(B)$ must lead to a gradual‎ ‎change in $t(A\,\&\,B)$)‎, ‎uniquely determines $\min$ as an‎ ‎$\&$-operation‎. ‎Likewise‎, ‎$\max$ is the only continuous‎ ‎$\vee$-operation‎. ‎These results are in good accordance with the‎ ‎experimental analysis of ``and'' and ``or'' in human beliefs‎.

Mario Di Nardo, Teresa Murino, Gianluca Osteria et al.

The Failure Mode and Effect Analysis (FMEA) is often used to improve a system’s reliability. This paper proposes a new approach that aims to overcome the most critical defects of the traditional FMEA. This new methodology combines the Entropy and Best Worst Method (BWM) methodology with the EDAS and System Dynamics, FMECA: The EN-B-ED Dynamic FMECA. The main innovation point of the proposed work is the presence of an unknown factor (Cost) that allows to obtain an objective weighted factor, a risk index when a machine failure occurs. The criticality analysis has been carried out using software (Vensim PLE x64) to simulate System Dynamics models to identify corrective actions and evaluate the possible implementation of these actions. The methodology proposed is applied to a case study in a relevant Italian company in the agri-food sector.

Jun Lu, Minhui Wu

In this note, we introduce how to use Volatility Index (VIX) for postprocessing quantitative strategies so as to increase the Sharpe ratio and reduce trading risks. The signal from this procedure is an indicator of trading or not on a daily basis. Finally, we analyze this procedure on SH510300 and SH510050 assets. The strategies are evaluated by measurements of Sharpe ratio, max drawdown, and Calmar ratio. However, there is always a risk of loss in trading. The results from the tests are just examples of how the method works; no claim is made on the suggestion of real market positions.

Amélie Loher

We derive quantitatively the Harnack inequalities for kinetic integro-differential equations. This implies Hölder continuity. Our method is based on trajectories and exploits a term arising due to the non-locality in the energy estimate. This permits to quantitatively prove the intermediate value lemma for the full range of non-locality parameter $s \in (0, 1)$. Our results recover the results from Imbert and Silvestre [22] for the inhomogeneous Boltzmann equation in the non-cutoff case. The paper is self-contained.

Ahmet Bahadır Şimşek

This study addresses the curricular practical training rotation problem, which is a type of staff assignment problem. Many educational institutions require theoretical knowledge to be complemented by practical training. Although the details of the implementation differ from institution to institution, it is necessary to prepare a rotation plan that determines how long the trainees will practice in which unit in which training period. Because of the complexity of the problem and humanistic reasons, the manual rotation plan can not reach the optimal level that satisfies all stakeholders and takes time. This study defines a general Curricular Practical Training Rotation Planning Problem specific to the curriculum-based trainee assignment process carried out in a university department and proposes an integer mathematical model for its solution. It is one of the important contributions of this study. It also provides a methodological approach to identify the most appropriate rotation strategy that will satisfy stakeholders. The methodological approach followed is a structure that can be adapted to different perspectives. The study has the potential to guide practitioners and researchers in the field and to lead a rich literature that will be formed with different side constraints and purposes to the problem.

Raimundo N.D. Costa Filho, V. Leonardo Paucar

A multi-objective optimization model for robust tuning of wide-area power system stabilizers (WAPSSs) aiming the improvement and control of angular stability of electric power system (EPS) is presented in this paper. In this work the WAPSSs are referred to power system stabilizers (PSSs) of fixed-structure with insertion of remote signals, from phasor measurement units (PMUs), in the control loops, that are used in a wide-area control system (WACS). The proposed model is composed of objective functions to maximize both the small-disturbance angular stability (SDAS) through the damping ratio and the large-disturbance angular stability (LDAS) using an index derived from transient energy function (TEF). Moreover, three objectives functions that contribute to the previous ones are taken into account: maximization of power system robustness for several operating conditions, minimization of eigenvalues sensitivity to small disturbances, and minimization of eigenvalues sensitivity with respect to time delay variations of remote signals. Swarm intelligence-based techniques are used to solve the multi-objective optimization model. Simulation results, with the benchmark interconnected system New England test system – New York power system (NETS-NYPS) of 16-generator and 68-bus, corroborate the applicability of the proposal.