Related papers: Generating functionals for guided self-organizatio…
Living systems exhibit a range of fundamental characteristics: they are active, self-referential, self-modifying systems. This paper explores how these characteristics create challenges for conventional scientific approaches and why they…
This is a compendium of generating functions involving single, double sums and definite integrals. These generating functions also involve special functions in both the summand function and closed form solution.
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
Deep generative models produce data according to a learned representation, e.g. diffusion models, through a process of approximation computing possible samples. Approximation can be understood as reconstruction and the large datasets used…
This paper examines two related problems that are central to developing an autonomous decision-making agent, such as a robot. Both problems require generating structured representafions from a database of unstructured declarative knowledge…
By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…
Generative art is a rules-driven approach to creating artistic outputs in various mediums. For example, a fluid simulation can govern the flow of colored pixels across a digital display or a rectangle placement algorithm can yield a…
We introduce a novel method for obtaining a wide variety of moments of any random variable with a well-defined moment-generating function (MGF). We derive new expressions for fractional moments and fractional absolute moments, both central…
Compared with traditional design methods, generative design significantly attracts engineers in various disciplines. In thiswork, howto achieve the real-time generative design of optimized structures with various diversities and…
The recently developed theory of extended generating functions of symplectic maps are combined with methods to prove invertibility via high-order Taylor model methods to obtain rigorous lower bounds for the domains of definition of…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to…
Time evolution is formulated and discussed in the framework of Schroeder's functional equation. The proposed method yields smooth, continuous dynamics without the prior need for local propagation equations.
This work's purpose is to understand the dynamics of some social systems whose properties can be captured by certain iterated function systems. To achieve this intension, we start from the theory of iterated function systems, and then we…
Keyframes are a standard representation for kinematic motion specification. Recent learned motion-inbetweening methods use keyframes as a way to control generative motion models, and are trained to generate life-like motion that matches the…
In this work, we introduce an efficient generation procedure to produce synthetic multi-modal datasets of fluid simulations. The procedure can reproduce the dynamics of fluid flows and allows for exploring and learning various properties of…
We investigate meandric systems with a large number of loops using tools inspired by free probability. For any fixed integer $r$, we express the generating function of meandric systems on $2n$ points with $n-r$ loops in terms of a finite…
This paper contains analysis of main modern approaches to dynamic code generation, in particular generation of new classes of objects during program execution. The main attention was paid to universal exploiters of homogeneous classes of…
Automatically reasoning about future human behaviors is a difficult problem but has significant practical applications to assistive systems. Part of this difficulty stems from learning systems' inability to represent all kinds of behaviors.…
Digital learning platforms enable students to learn on a flexible and individual schedule as well as providing instant feedback mechanisms. The field of STEM education requires students to solve numerous training exercises to grasp…