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2,370 papers
This paper explores a novel Bayesian hierarchical diffusion process within vector spaces, designed to facilitate the continuous and adaptive creation of complex mathematical functions. Traditional diffusion methods frequently rely on discrete steps, limiting the generation of intricate and nuanced mathematical expressi...
Groundwater pressure diffusion in fractured rock is fracture slow P-wave, but the diffusional mode is only valid for frequency lower than 0.1 Hz.
Non-Euclidean geometries, characterized by non-regular shapes and complex topology, present a unique challenge to traditional geometric modeling. This paper explores the development of a novel class of diffusion processes within these spaces, utilizing continuous, non-linear differential geometry as a foundational fram...
This is a self-contained, graduate-level exposition tracing the path fromelementary probability to modern option pricing. Every model is built from itsmathematical foundations, every formula is derived, and every assumption isstated and examined. Part I develops the complete theoretical framework for Black-Scholes pric...
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This paper presents a novel phase-field modeling approach for fluid dynamics, specifically designed to accommodate and accurately represent non-Newtonian viscosity. Traditional phase-field methods often struggle to capture the complex behavior of fluids exhibiting non-linear viscosity distributions. We introduce a modi...
This paper explores the extension of standard diffusion equations to incorporate a landscape parameter, introducing a feedback loop that drives the evolution of diffusion patterns. Traditional diffusion models, while widely used, often lack the capacity to generate complex and unpredictable behavior. We propose a novel...
This research investigates the emergence of complex patterns within stochastic diffusion processes, proposing a novel approach centered on identifying and quantifying 'emergent complexity' through the application of a "statistical resonance" algorithm. We explore how this algorithm maps information flow across a networ...
This paper proposes a novel computational paradigm, termed Algorithmic Morphogenesis, which posits that complex computation can emerge through the controlled diffusion of algorithmic elements within a system. The core idea is that a collection of interconnected agents, each governed by a simple algorithmic rule, can, w...
The full technical report on a latent-workspace language model built on a frozen Qwen3-0.6B decoder, and the ten preregistered prototype experiments that falsified it at this scale. Routing failed causal liveness on 10 of 10 seed-runs; ablating the read-out's 34 memory positions changed graded accuracy by 0.000 on one...
Quantum annealing offers a novel approach to simulating diffusion processes, promising accelerated optimization and enhanced pattern generation. This paper explores the potential of this technique to address a critical bottleneck in simulating diffusion, specifically focusing on the efficient exploration of the solutio...
This paper presents a novel theoretical framework for understanding and modeling temporal dynamics, focusing on the propagation of patterns and information across spatial and temporal scales. The core of the work centers on the development of a model incorporating non-linear interactions and diffusion processes, utiliz...
ADAPTIVE RESILIENCY THROUGH CONSTRAINED DIVERGENCE (ARCD) A Fluidic Topological Framework for Macroscopic and Quantum Phenomena (Version 12.0) This manuscript introduces the Adaptive Resiliency through Constrained Divergence (ARCD) framework, a deterministic, fluidic topological architecture designed to resolve the fun...
We’re on a journey to advance and democratize artificial intelligence through open source and open science.
A new computational approach reveals how cells communicate to assemble into tissues. This could accelerate stem cell engineering, improve disease models, and inform therapies.
We’re on a journey to advance and democratize artificial intelligence through open source and open science.
Learn how Google DeepMind and GovTech Singapore uses lightweight on-device Gemma models to intercept conversational scams in private chats with zero cloud data egress.
We’re giving developers, enterprises, scientists, and consumers access to Gemini 4 Argon, our latest frontier model.
StudentSim is a research system for evaluating and improving AI tutoring tools before they are tested with learners. It models how individuals may engage with tutors, giving feedback to improve tutor performance across subjects like chess, writing, and mathematics. The post Simulating student learning for better AI tutoring appeared first on Microsoft Research.
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