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Related Concept Videos

State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
State Space to Transfer Function01:21

State Space to Transfer Function

The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
Basic Continuous Time Signals01:22

Basic Continuous Time Signals

Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
Transfer Function to State Space01:23

Transfer Function to State Space

State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...

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Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
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Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps

Published on: February 9, 2017

Deep Continuous-Time State-Space Models for Marked Event Sequences.

Yuxin Chang1, Alex Boyd2, Cao Xiao2

  • 1University of California, Irvine.

Advances in Neural Information Processing Systems
|May 20, 2026
PubMed
Summary
This summary is machine-generated.

We introduce the state-space point process (S2P2) model for analyzing event sequences. S2P2 overcomes limitations of existing models, achieving state-of-the-art results with improved predictive likelihoods.

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Area of Science:

  • Machine Learning
  • Time Series Analysis
  • Stochastic Processes

Background:

  • Marked temporal point processes (MTPPs) are crucial for modeling event sequences in various fields.
  • Existing MTPP models face limitations in capturing continuous-time dynamics and expressivity.
  • Deep state-space models (SSMs) offer advanced techniques for sequence modeling.

Purpose of the Study:

  • Propose a novel and performant MTPP model, the state-space point process (S2P2).
  • Address limitations of current MTPP models by leveraging deep SSM techniques.
  • Imbue inductive biases for continuous-time event sequences not captured by discrete models.

Main Methods:

  • Developed the S2P2 model, integrating stochastic jump differential equations with nonlinearities.
  • Built upon classical linear Hawkes processes for an intensity-based MTPP.
  • Utilized a parallel scan for efficient training and inference with linear complexity.

Main Results:

  • S2P2 achieves state-of-the-art predictive likelihoods across eight real-world datasets.
  • Demonstrated an average improvement of 33% over existing MTPP approaches.
  • Showcased efficient training and inference with sublinear scaling.

Conclusions:

  • The S2P2 model offers a highly expressive and performant solution for MTPPs.
  • S2P2 effectively models continuous-time event sequences with strong inductive biases.
  • This novel approach advances MTPP modeling in healthcare, finance, and social networks.