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Many classical theorems in combinatorics establish the emergence of substructures within sufficiently large collections of objects. Well-known examples are Ramsey's theorem on monochromatic subgraphs and the Erdős-Rado sunflower lemma.
We study the planted clique problem in which a clique of size k is planted in an Erdos-Renyi graph G(n,1/2) and one is interested in recovering this planted clique. It is widely believed that it exhibits a statistical-computational gap when computational efficiency is equated with the existence of polynomial time algo...
The problem of deciding if a Traveling Salesman Problem (TSP) tour is minimal was proved to be coNP-complete by Papadimitriou and Steiglitz. We give an alternative proof based on a polynomial time reduction from 3SAT.
Sweep coverage is to realize the periodic coverage of targets by planning the periodic sweeping paths of mobile sensors. It is difficult for sensors to reduce energy consumption by reducing the moving distances.
We study the following model of disease spread in a social network. At first, all individuals are either infected or healthy.
We show that the problem of counting the number of Eulerian circuits in an undirected graph is complete for the class #P.
Let $\{f_i:\mathbb{F}_p^i \to \{0,1\}\}$ be a sequence of functions, where $p$ is a fixed prime and $\mathbb{F}_p$ is the finite field of order $p$. The limit of the sequence can be syntactically defined using the notion of ultralimit.
The question whether P equals NP revolves around the discrepancy between active production and mere verification by Turing machines. In this paper, we examine the analogous problem for finite transducers and automata.
We comment on a recent paper by D'Abramo [Chaos, Solitons & Fractals, 25 (2005) 29], focusing on the author's statement that an algorithm can produce a list of strings containing at least one string whose algorithmic complexity is greater than that of the entire list. We show that this statement, although ...
We consider the computational complexity of a problem modeling bribery in the context of voting systems. In the scenario of Swap Bribery, each voter assigns a certain price for swapping the positions of two consecutive candidates in his preference ranking.
We study the Sherali-Adams linear programming hierarchy in the context of promise constraint satisfaction problems (PCSPs). We characterise when a level of the hierarchy accepts an instance in terms of a homomorphism problem for an appropriate multilinear structure obtained through a tensor power of the constraint lan...
Finding a low-weight multiple (LWPM) of a given polynomial is very useful in the cryptanalysis of stream ciphers and arithmetic in finite fields. There is no known deterministic polynomial time complexity algorithm for solving this problem, and the most efficient algorithms are based on a time/memory trade-off.
We study pseudodeterministic constructions, i.e., randomized algorithms which output the same solution on most computation paths. We establish unconditionally that there is an infinite sequence $\{p_n\}_{n \in \mathbb{N}}$ of increasing primes and a randomized algorithm $A$ running in expected sub-exponential time suc...
Succinct representations of a graph have been objects of central study in computer science for decades. In this paper, we study the operation called \emph{Distance Preserving Graph Contractions}, which was introduced by Bernstein et al. (ITCS, 2018).
We design an algorithmic framework using matrix exponentials for time-domain simulation of power delivery network (PDN). Our framework can reuse factorized matrices to simulate the large-scale linear PDN system with variable stepsizes.
Protein structure prediction based on Hydrophobic-Polar energy model essentially becomes searching for a conformation having a compact hydrophobic core at the center. The hydrophobic core minimizes the interaction energy between the amino acids of the given protein.
To create heterogeneous, multiscale structures with unprecedented functionalities, recent topology optimization approaches design either fully aperiodic systems or functionally graded structures, which compete in terms of design freedom and efficiency. We propose to inherit the advantages of both through a data-driven...
This report aims to present my research updates on distance function wavelets (DFW) based on the fundamental solutions and the general solutions of the Helmholtz, modified Helmholtz, and convection-diffusion equations, which include the isotropic Helmholtz-Fourier (HF) transform and series, the Helmholtz-Laplace (HL) t...
In recent years, with the development of microarray technique, discovery of useful knowledge from microarray data has become very important. Biclustering is a very useful data mining technique for discovering genes which have similar behavior.
Reliability assessment of engineering systems is often hindered by the need to evaluate limit-state functions through computationally expensive simulations, rendering standard sampling impractical. An effective solution is to approximate the limit-state function with a surrogate model iteratively refined through activ...
It is well known that thermal insulation is a leading strategy for reducing energy consumption associated to heating or cooling processes in buildings. Nevertheless, building insulation can generate high expenditures so that the selection of an optimum insulation thickness requires a detailed energy simulation as well...
The iterative nature of topology optimization, especially in combination with nonlinear state problems, often requires the solution of thousands of linear equation systems. Furthermore, due to the pixelated design representation, the use of a fine mesh is essential to obtain geometrically well-defined structures and t...
Several works related to spatial crowdsourcing have been proposed in the direction where the task executers are to perform the tasks within the stipulated deadlines. Though the deadlines are set, it may be a practical scenario that majority of the task executers submit the tasks as late as possible.
The Cell Broad Engine (BE) Processor has unique memory access architecture besides its powerful computing engines. Many computing-intensive applications have been ported to Cell/BE successfully.
Compression molding of Sheet Molding Compounds (SMC) is a manufacturing process in which a stack of discontinuous fiber-reinforced thermoset sheets is formed in a hot mold. The reorientation of fibers during this molding process can be either described by macroscale models based on Jeffery's equation or by direct ...
Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to solution functions in contrast to classical neural networks that need re-training for e...
Deriving governing equations from observational data, known as Symbolic Regression (SR), is a cornerstone of scientific discovery. Large Language Models, (LLMs) have shown promise in this task by leveraging their vast cross-disciplinary scientific knowledge.
This paper presents an online reinforcement learning based application which increases the revenue of one particular electric vehicles (EV) station, connected to a renewable source of energy. Moreover, the proposed application adapts to changes in the trends of the station's average number of customers and their t...
In this work we define, analyze, and compare different numerical schemes that can be used to study the ground state properties of Bose-Fermi systems, such as mixtures of different atomic species under external forces or self-bound quantum droplets. The bosonic atoms are assumed to be condensed and are described by the...
We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element methods and custom loss functions from neural networks are merged to form the al...
Considering lateral influence from adjacent lane, an improved car-following model is developed in this paper. Then linear and non-linear stability analyses are carried out.
Most peridynamics models adopt regular point distribution and unified horizon, limiting their flexibility and engineering applications. In this work, a micropolar peridynamics approach with non-unified horizon (NHPD) is proposed.
This paper introduces capital flow to the single item stochastic lot sizing problem. A retailer can leverage business overdraft to deal with unexpected capital shortage, but needs to pay interest if its available balance goes below zero.
Distributed Generation (DG) units are increasingly installed in the power systems. Distribution Companies (DisCo) can opt to purchase the electricity from DG in an energy purchase contract to supply the customer demand and reduce energy loss.
Tumors constitute a wide family of diseases kinetically characterized by the co-presence of multiple spatio-temporal scales. So, tumor cells ecologically interplay with other kind of cells, e.g. endothelial cells or immune system effectors, producing and exchanging various chemical signals.
Trading and investing in stocks for some is their full-time career, while for others, it's simply a supplementary income stream. Universal among all investors is the desire to turn a profit.
X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy are two powerful tools to determine the protein 3D structure. However, not all proteins can be successfully crystallized, particularly for membrane proteins.
Electric load profiles of tropical islands in developed countries are characterised by morning, midday and evening peaks arising from all year round high power demand in the commercial and residential sectors, due mostly to air conditioning appliances and bad thermal conception of the building. The work presented in t...
We present a machine learning framework to train and validate neural networks to predict the anisotropic elastic response of the monoclinic organic molecular crystal $\beta$-HMX in the geometrical nonlinear regime. A filtered molecular dynamic (MD) simulations database is used to train the neural networks with a Sobol...
An integrated Equation of State (EOS) and strength/pore-crush/damage model framework is provided for modeling near to source (near-field) ground-shock response, where large deformations and pressures necessitate coupling EOS with pressure-dependent plastic yield and damage. Nonlinear pressure-dependence of strength up...
This paper presents an optimization technique for the multi-pass face milling process. Genetic algorithm (GA) is used to obtain the optimum cutting parameters by minimizing the unit production cost for a given amount of material removal.
Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's response. The solver with lower fidelity (coarse) is responsible for simul...
We present a novel combination of numerical techniques to improve the efficiency, accuracy, and robustness of multi-component compressible flow simulations. At the core of our approach is an Entropy-Stable formulation that preserves kinetic energy and integrates a Double-Flux scheme tailored for multi-component flows ...
Smoothed Particle Hydrodynamics (SPH) is plagued by the phenomenon of tensile instability, which is the occurrence of short wavelength zero energy modes resulting in unphysical clustering of particles. The root cause of the instability is the shape of derivative of the compactly supported kernel function which may yie...
The paper presents an assumed strain formulation over polygonal meshes to accurately evaluate the strain fields in nonlocal damage models. An assume strained technique based on the Hu-Washizu variational principle is employed to generate a new strain approximation instead of direct derivation from the basis functions ...
Natural disasters can have catastrophic impacts on the functionality of infrastructure systems and cause severe physical and socio-economic losses. Given budget constraints, it is crucial to optimize decisions regarding mitigation, preparedness, response, and recovery practices for these systems.
In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model.
This document presents a research agenda for financial services as a deliverable of UKFin+, a Network Plus grant funded by the Engineering and Physical Sciences Research Council. UKFin+ fosters research collaborations between academic and non-academic partners directed at tackling complex long-term challenges relevant...
Thermal multi-phase flow simulations are indispensable to understanding the multi-scale and multi-physics phenomena in metal additive manufacturing (AM) processes, yet accurate and robust predictions remain challenging. This book chapter summarizes the recent method development at UIUC for simulating thermal multiphas...
Optimizing fluid-dynamic performance is an important engineering task. Traditionally, experts design shapes based on empirical estimations and verify them through expensive experiments.
Adjoints are used in optimization to speed-up computations, simplify optimality conditions or compute sensitivities. Because time is reversed in adjoint equations with first order time derivatives, boundary conditions and transmission conditions through shocks can be difficult to understand.
A new numerical algorithm for solving the symmetric eigenvalue problem is presented. The technique deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques, and takes its inspiration from the contour integration and dens...
Offshore wind power is a renewable energy of growing relevance in current electric energy systems, presenting favorable wind conditions in comparison with the sites on land. However, the higher energy yield has to compensate the increment in installation and maintenance costs, thus the importance of optimizing resourc...
It is well known that modeling and forecasting realized covariance matrices of asset returns play a crucial role in the field of finance. The availability of high frequency intraday data enables the modeling of the realized covariance matrices directly.
The noval method for mutational disease prediction using bioinformatics tools and datasets for diagnosis the malignant mutations with powerful Artificial Neural Network (Backpropagation Network) for classifying these malignant mutations are related to gene(s) (like BRCA1 and BRCA2) cause a disease (breast cancer). Thi...
Iceberg calving at glacier termini results in mass loss from ice sheets, but the associated fracture mechanics is often poorly represented using simplistic (empirical or elementary mechanics-based) failure criteria. Here, we propose an advanced Mohr-Coulomb failure criterion that drives cracking based on the visco-ela...
Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors.
This work presents a framework to inversely quantify uncertainty in the model parameters of the friction model using earthquake data via the Bayesian inference. The forward model is the popular rate- and state- friction (RSF) model along with the spring slider damper idealization.
Artificial intelligence (AI) technologies have fundamentally transformed numerical-based high-performance computing (HPC) applications with data-driven approaches and endeavored to address existing challenges, e.g. high computational intensity, in various scientific domains. In this study, we explore the scenarios of ...
We describe three independent implementations of a new agent-based model (ABM) that simulates a contemporary sports-betting exchange, such as those offered commercially by companies including Betfair, Smarkets, and Betdaq. The motivation for constructing this ABM, which is known as the Bristol Betting Exchange (BBE), ...
Neural networks with sufficiently smooth activation functions can approximate values and derivatives of any smooth function, and they are differentiable themselves. We improve the approximation capability of neural networks by utilizing the differentiability of neural networks; the gradient and Hessian of neural netwo...
Financial sectors are rapidly adopting language model technologies, yet evaluating specialized RAG systems in this domain remains challenging. This paper introduces SMARTFinRAG, addressing three critical gaps in financial RAG assessment: (1) a fully modular architecture where components can be dynamically interchanged...
The ability to accomplish tasks via natural language instructions is one of the most efficient forms of interaction between humans and technology. This efficiency has been translated into practical applications with generative AI tools now allowing users to get things done through natural language queries.
The problem for selection of appropriate assets investing composition projects such as assets rationalization plays an important role in promotion of business systems. We consider the assets investing composition plan problems subject to grey multiobjective programming with the grey inequality constraints.
We develop new optimization methodology for planning installation of Flexible Alternating Current Transmission System (FACTS) devices of the parallel and shunt types into large power transmission systems, which allows to delay or avoid installations of generally much more expensive power lines. Methodology takes as an...
We evaluate the informational content of news-based sentiment indicators for forecasting Gross Domestic Product (GDP) and other macroeconomic variables of the five major European economies. Our data set includes over 27 million articles for 26 major newspapers in 5 different languages.
Electro-quasistatic field problems involving nonlinear materials are commonly discretized in space using finite elements. In this paper, it is proposed to solve the resulting system of ordinary differential equations by an explicit Runge-Kutta-Chebyshev time-integration scheme.
A model for corrosion-induced cracking of reinforced concrete subjected to non-uniform chloride-induced corrosion is presented. The gradual corrosion initiation of the steel surface is investigated by simulating chloride transport considering binding.
Point-feature label placement (PFLP) is a major area of interest within the filed of automated cartography, geographic information systems (GIS), and computer graphics. The objective of a label placement problem is to assign a label to each point feature so as to avoid conflicts, considering the cartographic conventio...
We present a general framework to predict precursors to extreme events in turbulent dynamical systems. The approach combines phase-space reconstruction techniques with recurrence matrices and convolutional neural networks to identify precursors to extreme events.
This paper aims to develop new mathematical and computational tools for modeling the distribution of portfolio returns across portfolios. We establish relevant mathematical formulas and propose efficient algorithms, drawing upon powerful techniques in computational geometry and the literature on splines, to compute th...
Stock prices, as an economic indicator, reflect changes in economic development and market conditions. Traditional stock price prediction models often only consider time-series data and are limited by the mechanisms of the models themselves.
Motivation: The Stochastic Simulation Algorithm (SSA) has largely diffused in the field of systems biology. This approach needs many realizations for establishing statistical results on the system under study.
Incorporating advanced information and communication technologies into smart grids (SGs) offers substantial operational benefits while increasing vulnerability to cyber threats like false data injection (FDI) attacks. Current SG attack analysis tools predominantly employ formal methods or adversarial machine learning ...
Proteomics is the large-scale analysis of the proteins. The common method for identifying proteins and characterising their amino acid sequences is to digest the proteins into peptides, analyse the peptides using mass spectrometry and assign the resulting tandem mass spectra (MS/MS) to peptides using database search t...
The optimization of industrial processes remains a critical challenge, particularly when no mathematical formulation of objective functions or constraints is available. This study addresses this issue by proposing a surrogate-based, data-driven methodology for optimizing complex real-world manufacturing systems using ...
This paper presents three distributed techniques to find a sparse solution of the underdetermined linear problem $\textbf{g}=\textbf{Hu}$ with a norm-1 regularization, based on the Alternating Direction Method of Multipliers (ADMM). These techniques divide the matrix $\textbf{H}$ in submatrices by rows, columns, or bo...
The expanding applications, utilized by more users, enhance hardware performance and further develop cloud systems for big data processing. This leads to numerous unexplored deep learning applications, especially in advanced computer vision for object recognition.
Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner kernel, a multi-dimensional function describing the effects of the potential over...
In this paper we solve the Boltzmann transport equation using AI libraries. The reason why this is attractive is because it enables one to use the highly optimised software within AI libraries, enabling one to run on different computer architectures and enables one to tap into the vast quantity of community based soft...
The ability to accurately quantify the performance an additively manufactured (AM) product is important for a widespread industry adoption of AM as the design is required to: (1) satisfy geometrical constraints, (2) satisfy structural constraints dictated by its intended function, and (3) be cost effective compared to ...
During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A levelset description of the boundary, when combined with an enriched finite element formulation, offers ...
High-quality computational and data-intensive (CDI) applications are critical for advancing research frontiers in almost all disciplines. Despite their importance, there is a significant gap due to the lack of comprehensive best practices for developing such applications.
Multigrid methods despite being known to be asymptotically optimal algorithms, depend on the careful selection of their individual components for efficiency. Also, they are mostly restricted to standard cycle types like V-, F-, and W-cycles.
Adverse drug reactions (ADR) are widely concerning for public health issue. In this study we propose an original approach to detect ADRs using a feature matrix and feature selection.
The influence of dynamic eccentricity on the harmonic spectrum of the torque of a permanent magnet synchronous machine is studied. The spectrum is calculated by an energy balance method.
A topology optimization approach for designing large deformation contact-aided shape morphing compliant mechanisms is presented. Such mechanisms can be used in varying operating conditions.
Sand production is an important issue for many hydrocarbon recovery applications in unconsolidated reservoirs. The model using the Computational Fluid Dynamics coupled with Discrete Element Method (CFD-DEM) can capture micro-scale features of sand transport problems.
Physics--informed neural networks (PINN) have shown their potential in solving both direct and inverse problems of partial differential equations. In this paper, we introduce a PINN-based deep learning approach to reconstruct one-dimensional rough surfaces from field data illuminated by an electromagnetic incident wav...
Although many problems in science and engineering are modelled by well-established PDEs, they often involve unknown or incomplete relationships, such as material constitutive laws or thermal response, that limit accuracy and generality. Existing surrogate-modelling approaches directly approximate PDE solutions but rem...
Model order reduction methods are a powerful tool to drastically reduce the computational effort of problems which need to be evaluated repeatedly, i.e., when computing the same system for various parameter values. When applying a reduced basis approximation algorithm to the Maxwell eigenvalue problem, we encounter sp...
The original research question here is given by marketers in general, i.e., how to explain the changes in the desired timescale of the market. Tangled String, a sequence visualization tool based on the metaphor where contexts in a sequence are compared to tangled pills in a string, is here extended and diverted to det...
We present an efficient computational framework to quantify the impact of individual observations in four dimensional variational data assimilation. The proposed methodology uses first and second order adjoint sensitivity analysis, together with matrix-free algorithms to obtain low-rank approximations of ob- servation...
XRP Ledger is one of the oldest, well-established blockchains. Despite the popularity of the XRP Ledger, little is known about its underlying peer-to-peer network.
Accurately learning solution operators for time-dependent partial differential equations (PDEs) from sparse and irregular data remains a challenging task. Recurrent DeepONet extensions inherit the discrete-time limitations of sequence-to-sequence (seq2seq) RNN architectures, while neural-ODE surrogates cannot incorpor...
We study the binomial, trinomial, and Black-Scholes-Merton models of option pricing. We present fast parallel discrete-time finite-difference algorithms for American call option pricing under the binomial and trinomial models and American put option pricing under the Black-Scholes-Merton model.
Powder bed fusion additive manufacturing (PBFAM) of metals has the potential to enable new paradigms of product design, manufacturing and supply chains while accelerating the realization of new technologies in the medical, aerospace, and other industries. Currently, wider adoption of PBFAM is held back by difficulty i...
In this paper, five different approaches for reduced-order modeling of brittle fracture in geomaterials, specifically concrete, are presented and compared. Four of the five methods rely on machine learning (ML) algorithms to approximate important aspects of the brittle fracture problem.
The design and optimisation of aircraft wings are critical tasks in aerospace engineering, requiring a balance between structural integrity, aerostructural performance, and manufacturability. This multifaceted challenge involves the interplay of various disciplines, each with distinct parameters and constraints.
Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to solve the nonlinearity in the convection term.

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