In this article, we present a new mixed-type dual problem for the challenging class of the interval-valued optimization problem with vanishing constraints. The introduced dual problem does not directly include the index set, but it still requires calculations related to index sets, which makes it challenging to address these models from an algorithm perspective. The relationship between the original interval-valued programming problem with vanishing constraints and its mixed-type dual are discussed by weak, strong and strict converse duality theorems using the assumption of generalized convexity. We also present a non-trivial example to illustrate the theoretical aspects. Our proposed interval-valued mixed-type dual technique unifies the dual techniques discussed in Hu et al. (2020).
Quantitative investment (quant) is an emerging, technology-driven approach in asset management, increasingy shaped by advancements in artificial intelligence. Recent advances in deep learning and large language models (LLMs) for quant finance have improved predictive modeling and enabled agent-based automation, suggesting a potential paradigm shift in this field. In this survey, taking alpha strategy as a representative example, we explore how AI contributes to the quantitative investment pipeline. We first examine the early stage of quant research, centered on human-crafted features and traditional statistical models with an established alpha pipeline. We then discuss the rise of deep learning, which enabled scalable modeling across the entire pipeline from data processing to order execution. Building on this, we highlight the emerging role of LLMs in extending AI beyond prediction, empowering autonomous agents to process unstructured data, generate alphas, and support self-iterative workflows.
In this paper, we study, in a nonlinear setting, the asymptotic behaviour of a generalized viscosity approximation method associated with a countable family of nonexpansive mappings satisfying resolvent-like conditions. We apply proof mining methods to obtain quantitative results on asymptotic regularity in W-hyperbolic spaces and rates of metastability in CAT(0) spaces.
Guilherme Giovanini, Cyro von Zuben de Valega Negrão, Ammar Alsinai
et al.
Cell phenotype dynamic homeostasis contrasts with the inherent randomness of intracellular reactions. Although feedback control of master regulatory genes (MRG) is a key strategy for maintaining gene network expression ranges limited, understanding the quantitative constraints and corresponding mechanisms enabling such a dynamic stability under noise remains elusive. Here we model MRG expression as a stochastic process and downstream genes as sensors which response conditionally induce MRG activity. We show that at homeostatic regime: i. the trajectories of the MRG expression levels can be adjusted towards specific ranges using both the exact solutions of the stochastic model and the exact stochastic simulation algorithm (SSA); ii. there exists a sampling rate which optimizes the feedback control of the MRG activity, and non-optimal controls resulting in alternative homeostatic dynamics; iii. the feedback control of MRG activity leads to updates which intensities and time intervals are non-linearly related; iv. the ON state probability of an MRG promoter has dynamics confined within a narrow domain. Our results help to understand the quantitative constraints underpinning dynamic homeostasis despite randomness, the mechanisms underlying alternative, non-optimal, homeostatic regimes, and may be useful for theoretically prototyping therapies aiming at gene networks modulation.
G. Yokeswari, I. Paulraj Jayasimman, L. Rajendran
et al.
A theoretical study of the new autocatalytic mechanisms (EC″) for irreversible homogeneous reaction on diffusion layer for steady-state conditions is provided. Emerging uses for this reaction system include energy recovery from surplus hydrogen and chloride reaction in hydrogen-halogen direct and regenerative fuel cells. The modelling of these mechanisms consists of solving the nonlinear diffusion equations. This paper uses a simple and new analytical procedure, the hyperbolic method, to solve the nonlinear reaction-diffusion equations. The concentration of redox components and the current response are expressed in closed-form as function reaction parameters, as well as the ratio of diffusion layer and reaction layer thickness. Analytical outcomes are compared with numerically simulated results to validate the model. Predictions of theoretical concentrations and Matlab-based numerical results show satisfactory agreement. These analytical findings enhance the comprehension of system behaviour. The system's parameters are optimised using the results of the analysis.
Farzaneh MansooriMooseloo, Maghsoud Amiri, Mohammad Taghi Taghavi Fard
et al.
Purpose: Most research in the field of designing and planning bioethanol supply chains has been based on deterministic models, which do not consider dynamic environmental conditions and thus do not provide reliable outputs. Classic robust models did not have this weakness, but due to their excessive conservatism, they increased supply chain costs, making them unattractive to investors. Therefore, the aim of this study is to design and optimize the biomass-to-bioethanol supply chain network using data-driven robust optimization methods and disjunctive uncertainty sets.Methodology: The methodology of this study is a multi-methodology approach based on mathematical modeling and machine learning algorithms. Initially, uncertainty sets for the non-deterministic model parameter were created using K-means and SVC methods. Then, a data-driven optimization model was designed to optimize the biomass-to-bioethanol supply chain network, addressing the issues of previous classic approaches.Findings: The findings of this study are presented in two categories: strategic and operational decisions. The strategic section focuses on determining the optimal locations for biomass cultivation, preprocessing centers, and refineries. In the operational section, the optimal amounts of biomass sent to preprocessing centers and refineries were determined.Originality/Value: This study, by producing robust solutions without the conservatism of traditional robust optimization approaches, can significantly attract public and private sector investors. Additionally, using a three-objective model based on a sustainable development approach that simultaneously considers economic, social, and environmental components, enhances the comprehensiveness of this research, providing more realistic and detailed results.
This paper is devoted to the study of a class of time periodic Lotka-Volterra competition system with nonlocal dispersal and shifting habitats. By using some known results of the periodic KPP model and employing the iterative techniques, we prove that there exist two positive numbers $c_{0}(d_{1})$ and $c_{0}(d_{2})$ such that the system admits a forced wave provided that the forcing speed $c\in(-c_{0}(d_{2}),c_{0}(d_{1}))$. In addition, based on the theoretical results, we show that the gap formations exist for $c>c_{0}(d_{1})$ and $c<-c_{0}(d_{2})$.
Abdullah Hasan Hassan, Dipo Aldila, Muhamad Hifzhudin Noor Aziz
This study presents a comprehensive analysis of the transmission dynamics of monkeypox, considering contaminated surfaces using a deterministic mathematical model. The study begins by calculating the basic reproduction number and the stability properties of equilibrium states, specifically focusing on the disease-free equilibrium and the endemic equilibrium. Our analytical investigation reveals the occurrence of a forward bifurcation when the basic reproduction number equals unity, indicating a critical threshold for disease spread. The non-existence of backward bifurcation indicates that the basic reproduction number is the single endemic indicator in our model. To further understand the dynamics and control strategies, sensitivity analysis is conducted to identify influential parameters. Based on these findings, the model is reconstructed as an optimal control problem, allowing for the formulation of effective control strategies. Numerical simulations are then performed to assess the impact of these control measures on the spread of monkeypox. The study contributes to the field by providing insights into the optimal control and stability analysis of monkeypox transmission dynamics. The results emphasize the significance of contaminated surfaces in disease transmission and highlight the importance of implementing targeted control measures to contain and prevent outbreaks. The findings of this research can aid in the development of evidence-based strategies for mitigating the impact of monkeypox and other similar infectious diseases.
Tomasz Kalwarczyk, Grzegorz Bubak, Jarosław Michalski
et al.
Advanced microscopy techniques are essential in biomedical research for visualising and tracking biomolecules within living cells and their compartments. Conventional fluorescence microscopy methods, however, often struggle with accurately measuring the absolute concentrations of fluorescent probes in living cells. To overcome these limitations, we introduce an open-source analysis tool, smICA (Single-Molecule Image to Concentration Analyser). The smICA method offers quantitative mapping of absolute fluorophore concentrations, lifetime-resolved filtering methods of the signal, intensity-based cell segmentation, and requires only a few photons per pixel. Our approach also reduces the time required for the determination of the mean concentration per cell, compared to the standard FCS measurement performed in multiple posts. To highlight the robustness of the method, we validated it against standard fluorescence correlation spectroscopy (FCS) measurements by performing in vitro (aqueous solutions of polymers) and in vivo (polymers and EGFP in living cells) experiments. The presented methodology, along with the software, is a promising tool for quantitative single-cell studies, including, but not limited to, protein expression, degradation of biomolecules (such as proteins and mRNA), and monitoring of enzymatic reactions.
The distribution of the sum of negative binomial random variables has a special role in insurance mathematics, actuarial sciences, and ecology. Two methods to estimate this distribution have been published: a finite-sum exact expression and a series expression by convolution. We compare both methods, as well as a new normalized saddlepoint approximation, and normal and single distribution negative binomial approximations. We show that the exact series expression used lots of memory when the number of random variables was high (>7). The normalized saddlepoint approximation gives an output with a high relative error (around 3–5%), which can be a problem in some situations. The convolution method is a good compromise for applied practitioners, considering the amount of memory used, the computing time, and the precision of the estimates. However, a simplistic implementation of the algorithm could produce incorrect results due to the non-monotony of the convergence rate. The tolerance limit must be chosen depending on the expected magnitude order of the estimate, for which we used the answer generated by the saddlepoint approximation. Finally, the normal and negative binomial approximations should not be used, as they produced outputs with a very low accuracy.
Komi Agbalenyo, Vincent Cailliez, Jonathan Cailliez
Many problems in applied mathematics require root finding algorithms. Unfortunately, root finding methods have limitations. Firstly, regarding the convergence, there is a trade-off between the size of it's domain and it's rate. Secondly the numerous evaluations of the function and its derivatives penalize the efficiency of high order methods. In this article, we present a family of high order methods, that require few functional evaluations ( One for each step plus one for each considered derivative at the start of the method), thus increasing the efficiency of the methods.
Abstract Shale gas reservoirs demonstrate low matrix porosity and permeability, and show obvious heterogeneity due to the existence of natural fractures. During the production process, fracturing fluid can easily invade the reservoir and result in a low fracturing flowback rate. The existing numerical methods are troublesome and have poor convergence. Therefore, it is necessary to develop a new approach to study the gas-water two-phase flow in shale gas reservoirs. In this paper, fractal theory is used to quantitatively characterize the heterogeneous fractures. A Mathematical model considering fractal induced-fracture distribution and gas-water two-phase flow in shale reservoirs is established. The meshless weighted least squares (MWLS) method is applied, for the first time, to the numerical simulation of gas-water two-phase flow in multi-fractured horizontal wells of shale gas reservoirs. Based on the moving least squares approximation, the variation principle is derived in detail. A numerical model of gas-water two-phase flow in the shale gas reservoir fracturing horizontal well based on the meshless method is obtained. The gas and water production of fractured horizontal shale gas wells are predicted by the model. The model simulation results are found to be in good consistent with the mathematical calculation results obtained through finite difference method. but the proposed new approach shows significant higher calculation efficiency. In addition, by applying this new approach, The influences of fracture distribution, initial water saturation, and reservoir reconstruction degree on the utilization range and production were also systematically compared and analyzed. The results showed that the smaller the fracture fractal index a in the reservoir reform area, the lower the pressure, the higher the daily gas production and the daily water production, indicating that the fracture network is densely distributed and the production effect is better. The larger the initial water saturation resulted in the greater flow resistance of the gas phase and the decrease of daily gas production. When the fracture spacing decreases in reservoir reconstruction, the daily gas production increases, but the increase range is gradually reduced and it has little effect on the daily water production.
The adoption of formal methods (FMs) as a software development methodology remains low. Advocates of FMs point to the advantages to be gained by producing highly dependable systems, while critics refer to the steep learning curve required to master the underlying mathematics and logic. The situation was similar for artificial intelligence (AI), but the advent of 4IR–5IR technologies has recently made AI a feasible technology for computing. We believe that the same could hold for FMs. In this article, we considered both the advantages and disadvantages of the use of FMs and unpacked them by problematizing the aspects that need to be considered in the 4IR–5IR worlds to facilitate the use of FMs as a viable software development methodology. We made the case that the 5IR embedding of harmonious collaboration between humans and machines could assist with difficult FM interfaces, similar to how human–computer interaction (HCI) has influenced technical and inflexible systems in the past. Since we view FMs as a technology, we further considered the role to be played by technology adoption, exemplified by the various technology adoption models, e.g., the TOE framework. This article culminates in the formulation of a problematization framework for the adoption of FMs in 4IR–5IR.
Alan Miguel Forero Sanabria, Martha Patricia Bohorquez Castañeda, Rafael Ricardo Rentería Ramos
et al.
Abstract This paper provides new tools for analyzing spatio-temporal event networks. We build time series of directed event networks for a set of spatial distances, and based on scan-statistics, the spatial distance that generates the strongest change of event network connections is chosen. In addition, we propose an empirical random network event generator to detect significant motifs throughout time. This generator preserves the spatial configuration but randomizes the order of the occurrence of events. To prevent the large number of links from masking the count of motifs, we propose using standardized counts of motifs at each time slot. Our methodology is able to detect interaction radius in space, build time series of networks, and describe changes in its topology over time, by means of identification of different types of motifs that allows for the understanding of the spatio-temporal dynamics of the phenomena. We illustrate our methodology by analyzing thefts occurred in Medellín (Colombia) between the years 2003 and 2015.
Fabrizia Guglielmetti, Philipp Arras, Michele Delli Veneri
et al.
The Atacama Large Millimeter/submillimeter Array with the planned electronic upgrades will deliver an unprecedented amount of deep and high resolution observations. Wider fields of view are possible with the consequential cost of image reconstruction. Alternatives to commonly used applications in image processing have to be sought and tested. Advanced image reconstruction methods are critical to meet the data requirements needed for operational purposes. Astrostatistics and astroinformatics techniques are employed. Evidence is given that these interdisciplinary fields of study applied to synthesis imaging meet the Big Data challenges and have the potentials to enable new scientific discoveries in radio astronomy and astrophysics.
Recent advances in brain organoid technology are exciting new ways, which have the potential to change the way how doctors and researchers understand and treat cerebral diseases. Despite the remarkable use of brain organoids derived from human stem cells in new drug testing, disease modeling, and scientific research, it is still heavily time-consuming work to observe and analyze the internal structure, cells, and neural inside the organoid by humans, specifically no standard quantitative analysis method combined growing AI technology for brain organoid. In this paper, an automated computer-assisted analysis method is proposed for brain organoid slice channels tagged with different fluorescent. We applied the method on two channels of two group microscopy images and the experiment result shows an obvious difference between Wild Type and Mutant Type cerebral organoids.
This is the second installment in a series of papers applying descriptive set theoretic techniques to both analyze and enrich classical functors from homological algebra and algebraic topology. In it, we show that the Čech cohomology functors $\check{\mathrm{H}}^n$ on the category of locally compact separable metric spaces each factor into (i) what we term their definable version, a functor $\check{\mathrm{H}}^n_{\mathrm{def}}$ taking values in the category $\mathsf{GPC}$ of groups with a Polish cover (a category first introduced in this work's predecessor), followed by (ii) a forgetful functor from $\mathsf{GPC}$ to the category of groups. These definable cohomology functors powerfully refine their classical counterparts: we show that they are complete invariants, for example, of the homotopy types of mapping telescopes of $d$-spheres or $d$-tori for any $d\geq 1$, and, in contrast, that there exist uncountable families of pairwise homotopy inequivalent mapping telescopes of either sort on which the classical cohomology functors are constant. We then apply the functors $\check{\mathrm{H}}^n_{\mathrm{def}}$ to show that a seminal problem in the development of algebraic topology, namely Borsuk and Eilenberg's 1936 problem of classifying, up to homotopy, the maps from a solenoid complement $S^3\backslashΣ$ to the $2$-sphere, is essentially hyperfinite but not smooth. In the course of this work, we record Borel definable versions of a number of classical results bearing on both the combinatorial and homotopical formulations of Čech cohomology; in aggregate, this work may be regarded as laying foundations for the descriptive set theoretic study of the homotopy relation on the space of maps from a locally compact Polish space to a polyhedron, a relation which embodies a substantial variety of classification problems arising throughout mathematics.
Abstract Enhancing the recovery of ultrafine magnetic particles in high gradient magnetic separation (HGMS) is a tough issue in industrial practice. Mathematic modeling has been adopted to describe particle capture in HGMS and many analytical models for regular shape (only circular and elliptic) matrices under ideal conditions (ideal potential flow) have been derived. Irregular shape matrices have better magnetic characteristics and can enhance particle recovery in HGMS. However, analytical models cannot be derived for irregular shape matrices and generally qualitative analyses were conducted, which can hardly be rigorous and convincing. It is essential to develop methods to conduct quantitative analyses for irregular shape matrices. In this paper, 3D numerical simulation was adopted to study particle capture by irregular matrices in axial HGMS. A simulation model consisting of a particle group and magnetic matrices (circular, elliptic, square and diamond cross-section) for axial HGMS was established. Evolution of particle group in the HGMS system employing the four kinds of matrices were detailly demonstrated. Particle motion trajectories were depicted and particle capture cross section area were calculated and compared quantitatively. Elliptic and diamond matrices present better particle capture performance than circular and square matrices under moderate induction range and can be applied to enhance recovery of ultrafine particles. The numerical simulation results are consistent with our previous theoretical studies using analytical models and experimental results on the matrices. The present study also indicates that there should exist optimal aspect ratio for diamond matrices and optimal tooth angle for grooved plates used in HGMS.