Physics-Informed Neural Networks (PINNs) have emerged as a powerful, mesh-free paradigm for solving partial differential equations (PDEs). However, they notoriously struggle with stiff, multi-scale, and nonlinear systems due to the inherent spectral...
Feb 19, 2025 · In this episode, Kasra Ferdows, an operations management professor at Georgetown University, explains how open digital platforms facilitate innovation and problem solving by making …
Visier helps you truly move the needle on the HR challenges that matter most. Understand your business through the lens of people data, so you can take targeted action.
Feynman famously asserted that interference is the only real mystery in quantum mechanics (QM). It is concluded that the reason for this mystery, and thereby the related mysteries of complementarity, non-commutativity of observables, the uncertainty...
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To enable the computation of effective randomized patrol routes for single- or multi-robot teams, we present RoSSO, a Python package designed for solving Markov chain optimization problems. We exploit machine-learning techniques such as reverse-mode...
Feb 21, 2026 · Data structures organize and manage data efficiently, shaping how algorithms work and enabling effective problem‑solving in software development. Data structures form the backbone of …
In the theory of elasticity, the constraint of compatibility conditions on displacement field is not equivalent to the property of displacement field. The difference may broaden the possibility of solutions to elasticity problems, which means that th...
For solving strongly convex optimization problems, we propose and study the global convergence of variants of the A-HPE and large-step A-HPE algorithms of Monteiro and Svaiter. We prove linear and the superlinear $\mathcal{O}\left(k^{\,-k\left(\frac{...
This dissertation reports research about the phase space perspective for solving wave problems, with particular emphasis on the phenomenon of mode conversion in multicomponent wave systems, and the mathematics which underlie the phase space perspec...
In this work, we critique two papers, "A Polynomial-Time Solution to the Clique Problem" by Tamta, Pande, and Dhami, and "A Polynomial-Time Algorithm For Solving Clique Problems" by LaPlante. We summarize and analyze both papers, noting that the algo...
Mar 29, 2024 · Human intelligence can be defined as the culmination of cognitive processes that include perception, memory, reasoning, problem-solving, and learning. But is that the only way to define …
Oct 16, 2025 · Although contemporary definitions of intelligence vary considerably, experts generally agree that intelligence involves mental abilities such as logic, reasoning, problem-solving, and planning.
The unit circle helps visualise key concepts such as periodicity, symmetry, and angle relationships in both degree s and radians, forming a foundation for solving trigonometric equations and modelling …
Advection-diffusion-reaction mass transport FEniCS codes for solving various biochemicals/cells in blood flow and atherosclerosis (⭐ 4)
Mar 29, 2024 · Human intelligence can be defined as the culmination of cognitive processes that include perception, memory, reasoning, problem-solving, and learning. But is that the only way to define …
Oct 16, 2025 · Although contemporary definitions of intelligence vary considerably, experts generally agree that intelligence involves mental abilities such as logic, reasoning, problem-solving, and planning.
The Wei-Norman technique allows to express the solution of a system of linear non-autonomous differential equations in terms of product of exponentials. In particular it enables to find a time-ordered product of exponentials by solving a set of nonli...
Data Assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state. This is a large...
Complex engineering problems can be modelled as optimisation problems. For instance, optimising engines, materials, components, structure, aerodynamics, navigation, control, logistics, and planning is essential in aerospace. Metaheuristics are applie...
2D-to-3D reconstruction is an ill-posed problem, yet humans are good at solving this problem due to their prior knowledge of the 3D world developed over years. Driven by this observation, we propose NeRDi, a single-view NeRF synthesis framework with...
Christopher Carroll's Lecture Notes on Solving Microeconomic Dynamic Stochastic Optimization Problems and Indirect Inference (⭐ 21)
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Configuring databases for efficient querying is a complex task, often carried out by a database administrator. Solving the problem of building indexes that truly optimize database access requires a substantial amount of database and domain knowledge,...
We propose a primal-dual interior-point (PDIP) method for solving quadratic programming problems with linear inequality constraints that typically arise form MPC applications. We show that the solver converges (locally) quadratically to a suboptimal...
Discover how Google AI is committed to enriching knowledge, solving complex challenges and helping people grow by building useful AI tools and technologies.
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale simulations. Eme...
Oct 16, 2025 · Although contemporary definitions of intelligence vary considerably, experts generally agree that intelligence involves mental abilities such as logic, reasoning, problem-solving, and planning.
61 votes, 200 comments. My little brother was talking about some possible lore on cool math games? He was talking about solving a ton of Morse andâ¦
We discuss semiempirical approaches and parametric methods developed for modeling molecular vibronic spectra. These methods, together with databases of molecular fragments, have proved efficient and flexible for solving various problems ranging fro...
Non-linear sound propagation is investigated computationally by simulating compressible time-developing mixing layers using the Large Eddy Simulation (LES) approach and solving the viscous Burgers Equation. The mixing layers are of convective Mach nu...
We take attention to the singular behavior of the Laplace operator in spherical coordinates, which was established in our earlier work. This singularity has many non-trivial consequences. In this article we consider only the simplest ones, which are...
Large language models (LLMs) demonstrate strong language generation capabilities but often struggle with structured reasoning, leading to inconsistent or suboptimal problem-solving. To mitigate this limitation, Guilford's Structure of Intellect (SOI)...
Non-interactive challenges leverage what is called a JavaScript proof-of-work and ask a client to prove that it is running a JavaScript-compatible browser by solving what is essentially a JavaScript math …
61 votes, 200 comments. My little brother was talking about some possible lore on cool math games? He was talking about solving a ton of Morse andâ¦
Tic Tac Toe is amongst the most well-known games. It has already been shown that it is a biased game, giving more chances to win for the first player leaving only a draw or a loss as possibilities for the opponent, assuming both the players play opti...
Traditional Linear Genetic Programming (LGP) algorithms are based only on the selection mechanism to guide the search. Genetic operators combine or mutate random portions of the individuals, without knowing if the result will lead to a fitter individ...
The goal of this project is to develop the Genetic Algorithms (GA) for solving the Schaffer F6 function in fewer than 4000 function evaluations on a total of 30 runs. Four types of Genetic Algorithms (GA) are presented - Generational GA (GGA), Steady...
We propose a variation of the standard genetic algorithm that incorporates social interaction between the individuals in the population. Our goal is to understand the evolutionary role of social systems and its possible application as a non-genetic...
Generalizing from individual skill executions to solving long-horizon tasks remains a core challenge in building autonomous agents. A promising direction is learning high-level, symbolic abstractions of the low-level skills of the agents, enabling re...