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Introduction to Limits01:30

Introduction to Limits

A limit describes the value a function approaches as its input moves closer to a particular point. Even when a function is undefined at a specific value, limits allow us to analyze its behavior near that point. This concept is fundamental in calculus and essential for understanding continuity, derivatives, and integrals.Mathematically, a function f(x) has a limit L at x = a if its values L approach x as x gets arbitrarily close to a. This is written as:This notation expresses that the function...
Migration00:53

Migration

Migration is long-range, seasonal movement from one region or habitat to another. This common strategy, carried out by many different organisms around the world, is an adaptive response that typically corresponds to changes in an organism’s environment, like resource availability or climate. Migrations can involve huge groups of thousands of animals as well as single individuals traveling alone and can range from thousands of kilometers to just a few hundred meters.
Random Error01:04

Random Error

Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
Limits of Multivariable Functions01:25

Limits of Multivariable Functions

Limits of multivariable functions describe how a function behaves as its input approaches a particular point in the plane. In single-variable calculus, a limit examines the behavior of a function as the input approaches a number from two directions along a line. For functions of two variables, the situation is more complex because the input can approach a point from infinitely many paths in the xy-plane. A limit exists only when the function approaches the same value along every possible...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Evaluating Limits by Direct Substitution01:29

Evaluating Limits by Direct Substitution

In the analysis of functions that represent continuous physical phenomena, it is often necessary to determine the output value as the input approaches a specific point. When a combination of algebraic terms defines the function and exhibits no discontinuities or abrupt changes near the point of interest, the limit of the function can be evaluated directly. This process, known as direct substitution, involves replacing the variable in the expression with the value it approaches.Direct...

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Updated: Jun 16, 2026

Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

人間の移動における予測可能性の限界

Chaoming Song1, Zehui Qu, Nicholas Blumm

  • 1Center for Complex Network Research, Department of Physics, Northeastern University, Boston, MA 02115, USA.

Science (New York, N.Y.)
|February 20, 2010
PubMed
まとめ
この要約は機械生成です。

人間の移動は高度に予測可能であり,個々の動きを予測する潜在的精度は93%です. この予測可能性は,さまざまな移動パターンと距離において一貫しており,人間の動態に関する洞察を提供します.

さらに関連する動画

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

関連する実験動画

Last Updated: Jun 16, 2026

Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

科学分野:

  • コンピューティング社会科学
  • ネットワーク科学 ネットワーク科学
  • 人間移動性の分析

背景:

  • 個人の居場所と移動を予測することは,流行病学,都市計画,電気通信などの様々な用途において極めて重要です.
  • 人間の行動の予測可能性を理解することは,社会科学における根本的な問題である.

研究 の 目的:

  • 人間のダイナミクスの予測可能性の限界を探求すること.
  • 匿名化された携帯電話データを用いて,個々の移動パターンの予測可能性を定量化します.

主な方法:

  • 匿名化された携帯電話ユーザー経路の分析.
  • 予測可能性を定量化するために軌道のエントロピーの測定.
  • 異なるユーザー移動パターンと距離における予測可能性の評価.

主要な成果:

  • ユーザベース全体において,ユーザのモビリティの93%の予測可能性が観察されました.
  • 予測可能性は,ユーザが走った距離から大きく独立して,顕著な変動の欠如を示した.
  • 個々の移動パターンの有意な差異は,全体的な移動の予測可能性に実質的な影響を及ぼさなかった.

結論:

  • 人間のモビリティは,高度な予測可能性を示しています.
  • この発見は,資源管理,都市計画,複雑な人間動態の理解などに意味を持ちます.
  • 個人の移動の予測可能性は,多様な行動パターンの間で一貫している堅固な特徴です.