METHODS OF USING GENERALIZED ORDER DIFFERENTIATION AND INTEGRATION OF INPUT VARIABLES TO FORECAST TRENDS

• US 20130054662A1
• Filed: 04/12/2011
• Published: 02/28/2013
• Est. Priority Date: 04/13/2010
• Status: Abandoned Application

• Current Assignee: Regents of the University of California (University of California)
• Original Assignee: Regents of the University of California (University of California)
• Inventors: Coimbra, Carlos F. M.
• Application Number:
  US13/641,083
• Publication Number:
  US 20130054662A1
• Time in Patent Office: Days
• US Class Current: 708/230
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06Q 10/04 Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem" market predictions or forecasting for commercial activities G06Q30/0202
• CPC Class Codes: G06Q 30/02 Marketing; Price estimation or determination; Fundraising
• CPC Class Codes: G16H 50/20 for computer-aided diagnosis, e.g. based on medical expert systems
• CPC Class Codes: G16H 50/50 for simulation or modelling of medical disorders

Abstract

Disclosed are methods and apparatuses to generate a forecast based on generalized differentiation or integration, including but not limited to non-integer or variable order differentiation or integration.

Claims

1. A method for generating a forecast in a custom computing apparatus comprising at least one processor and a memory, the method comprising:

receiving, in the memory, a plurality of data points of a measurement;

accessing, by the at least one processor the plurality of data points;

calculating, by the at least one processor, a forecast for the measurement with a mathematical method using one or more differentiation or integration of the plurality of data points as inputs, wherein at least one of the one or more differentiation or integration is a non-integer or variable order differentiation or integration.

2. The method of claim 1, further comprising displaying the forecast in a suitable format on a screen or on a printing device.

4. The method of claim 1, wherein the mathematical method comprises a probability model.

5. The method of claim 1, wherein the mathematical method comprises a stochastic model.

6. The method of claim 1, wherein the mathematical method is one or more of an artificial neural network, a Turing machine, a genetic algorithm, an artificial immune system, or a hidden Markov model.

7. The method of claim 1, wherein the forecast is a time-dependent forecast and the plurality of data points comprise historic data points.

8. The method of claim 1, wherein the forecast is a prediction of unmeasured data points and the plurality of data points comprise measured data points.

9. The method of claim 1, wherein the forecast is selected from the group consisting of weather forecast, gaming forecast, stock market forecast, solar or wind power prediction, biological behavior prediction, social behavior prediction, earthquake prediction, epidemiological prediction and medical diagnosis or prognosis.

10. The method of claim 1, wherein at least one of the one or more differentiation or integration is an n-order differentiation or integration, wherein n is a non-integer.

11. The method or the computing apparatus of claim 10, wherein n is less than 1.

12. The method or the computing apparatus of claim 10, wherein n is greater than 1.

13. The method of claim 1, wherein at least one of the one or more differentiation or integration is a variable order differentiation or integration.

14. The method or the computing apparatus of claim 13, wherein the variable order differentiation or integration is a restricted form of variable order differentiation or integration.

15. The method or the computing apparatus of claim 14, wherein the restricted variable order differentiation or integration is determined by Equation I:

16. The method or the computing apparatus of claim 13, wherein the variable order differentiation or integration is a generalized variable order differentiation or integration.

17. The method or the computing apparatus of claim 16, wherein the generalized variable order differentiation or integration is determined by Equation II:

18. The method of claim 1, wherein the plurality of data points comprise data points from at least one type of measurement.

19. The method or the computing apparatus of claim 18, wherein the plurality of data points comprise data points from at least two types of measurements.

3. A custom computing apparatus comprising:

at least one processor;

a memory coupled to the at least one processor;

a storage medium in communication with the memory and the at least one processor, the storage medium containing a set of processor executable instructions that, when executed by the processor configure the custom computing apparatus to generate a forecast, comprising a configuration to;

receive, in the memory, a plurality of data points of a measurement;

access, by the at least one processor the plurality of data points; and

calculate, by the at least one processor, a forecast for the measurement with a mathematical method using one or more differentiation or integration of the plurality of data points as inputs, wherein at least one of the one or more differentiation or integration is a non-integer or variable order differentiation or integration.