SOCR APS Apr 2023 ILT Shen - Revision history

Dinov: /* Paper & Slidedeck */

2023-04-27T12:28:20Z

‎Paper & Slidedeck

Dinov at 12:27, 27 April 2023

2023-04-27T12:27:55Z

Dinov: /* Abstract */

2023-04-26T13:36:31Z

‎Abstract

Dinov: /* Example: Time-series to Kime-surface Mapping */

2023-04-18T13:38:14Z

‎Example: Time-series to Kime-surface Mapping

Dinov at 13:36, 18 April 2023

2023-04-18T13:36:39Z

Dinov: Created page with "== SOCR News & Events: ''Numerical Methods and Analysis for Computing Forward and Inverse Laplace Transform For discrete and continuous signals'' == Image:..."

2023-04-09T14:16:45Z

Created page with "== SOCR News & Events: ''Numerical Methods and Analysis for Computing Forward and Inverse Laplace Transform For discrete and continuous signals'' == Image:..."

New page

== [[SOCR_News | SOCR News & Events]]: ''Numerical Methods and Analysis for Computing Forward and Inverse Laplace Transform For discrete and continuous signals'' ==

[[Image:Spacekime_TCIU_Trivial_PolarCylinder_WaveEqu_Phase.png|150px|thumbnail|right| [https://www.socr.umich.edu/TCIU/ Spacekime/TCIU Project] ]]

== Presenter==
: [https://www.socr.umich.edu/people/SOCR_Personnel_Yueyang.html Yueyang Shen] ([https://www.umich.edu University of Michigan], [https://www.socr.umich.edu SOCR], [https://bids-tp.umich.edu/ BIDS-TP]).

:: Yueyang Shen is a [https://medicine.umich.edu/dept/dcmb/yueyang-shen PhD candidate in the Department of Computational Medicine and Bioinformatics] and enrolled as [https://bids-tp.umich.edu/fellows-and-trainees Trainee in the Biomedical Informatics and Data Science Program] at the University of Michigan.

: [https://socr.umich.edu/people/Milen_Velev.html Milen V. Velev (BTU)]

: [https://socr.umich.edu/people/dinov Ivo D. Dinov (Michigan)]

==Session Logistics==

* [https://meetings.aps.org/Meeting/APR23/Session/WW03 Session: ''WW03: V: General Physics III''; APS April Meeting 2023, Minneapolis, Minnesota (Apr 15-18), Virtual (Apr 24-26); Time Zone: Central Time]
* Chair: Alexey Grinin, Northwestern University, Center for Fundamental Physics, Room: Virtual Room 3

== Abstract==
: Specialized data maps transforming (probabilistic) state representations mapping the original signal representation into a more manipulatable state space capitalizes on contemporary computational advances and relates to well-known application scenarios, such as kernel machines, MDP transition dynamics modeling and policy optimization, and generative modeling. In this work we focus on the classic example of Laplace transform, which maps the subspace of differential equations to the space of algebraic equations, where the differential equation solution can be obtained by inverting the algebraic equation solution. Effective integral transformations enable simplification of mathematical modeling and computational inference. The Laplace transform (LT) with its inverse (ILT) represents a family of integral transforms that have direct applications in contemporary data science, statistical inference, and probabilistic modeling. However, practical computational challenges inhibit their utilization on complex or implicit functions, noisy observations, and incomplete data.

: We propose a numerical LT-ILT computing framework, empirically robust, implemented in R, and facilitates numerical computations through appropriate parameter estimations and signal approximations. We illustrate an idealized analysis relaxing the data matrix construction assumptions to bound the smallest singular values to argue algorithmic stability according to theoretical results in random matrix theory.

'''Slidedeck''' (pending)

==Background==
* [[SOCR_News | SOCR News & Events]]
* [https://www.socr.umich.edu/html/SOCR_UserGoogleMap.html SOCR Global Users]
* [https://socr.umich.edu/html/Navigators.html SOCR Navigators]
* [[SOCR_Data | SOCR Datasets and Challenging Case-studies]]
* [[SOCR_Books|Electronic Textbooks]]:
** [[EBook| Probability and Statistics EBook]]
** [[SMHS | Scientific Methods for Health Sciences]]
** [https://dspa2.predictive.space Data Science and Predictive Analytics]

==References==
* Dinov, ID and Velev, MV (2021) [https://doi.org/10.1515/9783110697827 Data Science: Time Complexity, Inferential Uncertainty, and Spacekime Analytics], De Gruyter (STEM Series), Berlin/Boston, ISBN 9783110697803 / 3110697807, DOI 10.1515/9783110697827.
* Wang, Y, Shen Y, Deng, D, Dinov, ID. (2022) [https://doi.org/10.1016/j.padiff.2022.100280 Determinism, Well-posedness, and Applications of the Ultrahyperbolic Wave Equation in Spacekime], Journal of Partial Differential Equations in Applied Mathematics, DOI: 10.1016/j.padiff.2022.100280, in press.
* Zhang, R, Zhang, Y, Liu, Y, Guo, Y, Shen, Y, Deng, D, Qiu, Y, Dinov, ID. (2022) [https://doi.org/10.1007/s00521-021-06789-8 Kimesurface Representation and Tensor Linear Modeling of Longitudinal Data], Neural Computing and Applications Journal, DOI: 10.1007/s00521-021-06789-8.
* [https://www.socr.umich.edu/spacekime/ Spacekime website]
* [https://tciu.predictive.space/ Time-Complexity and Inferential Uncertainty (TCIU)]

<hr>
{{translate|pageName=https://wiki.socr.umich.edu/index.php?title=SOCR_APS_Apr_2023_ILT_Shen}}

@@ Line 25: / Line 25: @@
 ==Paper & Slidedeck==
-* Paper: [https://arxiv.org/abs/2304.13204 DOI:
+* Paper: [https://arxiv.org/abs/2304.13204 DOI: https://doi.org/10.48550/arXiv.2304.13204]
 * Slides
 : [https://wiki.socr.umich.edu/images/5/5a/Shen_Laplace_Transform_APS_April_2023.pdf Slidedeck Version 1]

@@ Line 24: / Line 24: @@
-===Slidedeck===
+==Paper & Slidedeck==
-* [https://wiki.socr.umich.edu/images/5/5a/Shen_Laplace_Transform_APS_April_2023.pdf Slidedeck Version 1]
+* Paper: [https://arxiv.org/abs/2304.13204 DOI:
-* [https://wiki.socr.umich.edu/images/7/76/Shen_Laplace_Transform_APS_April_2023_v2.pdf Slidedeck Version 2]
+https://doi.org/10.48550/arXiv.2304.13204]
 == Example: Time-series to Kime-surface Mapping==

← Older revision		Revision as of 13:36, 26 April 2023
Line 24:		Line 24:


−	~~'''~~Slidedeck~~''' (pending)~~	+	===Slidedeck===
		+	* [https://wiki.socr.umich.edu/images/5/5a/Shen_Laplace_Transform_APS_April_2023.pdf Slidedeck Version 1]
		+	* [https://wiki.socr.umich.edu/images/7/76/Shen_Laplace_Transform_APS_April_2023_v2.pdf Slidedeck Version 2]

	== Example: Time-series to Kime-surface Mapping==		== Example: Time-series to Kime-surface Mapping==

@@ Line 29: / Line 29: @@
 The first animation shows a spatially-extended time-series wave, whereas the second animation illustrates the corresponding kime-surface obtained via the Laplace transform (LT). [https://www.socr.umich.edu/TCIU/HTMLs/Chapter4_Laplace_Transform_Meijer_G_Functions.html More details are available on the TCIU/Spacekime analytics website].
-[[Image:ClassicalExpanded_TimeseriesSignal4KimesurfaceMapping.gif|right| [https://www.socr.umich.edu/TCIU/ Spacekime/TCIU Project] ]]
+: [[Image:ClassicalExpanded_TimeseriesSignal4KimesurfaceMapping.gif|right| [https://www.socr.umich.edu/TCIU/ Spacekime/TCIU Project] ]]
 ==Background==

← Older revision		Revision as of 13:36, 18 April 2023
Line 25:		Line 25:

	'''Slidedeck''' (pending)		'''Slidedeck''' (pending)
		+
		+	== Example: Time-series to Kime-surface Mapping==
		+	The first animation shows a spatially-extended time-series wave, whereas the second animation illustrates the corresponding kime-surface obtained via the Laplace transform (LT). [https://www.socr.umich.edu/TCIU/HTMLs/Chapter4_Laplace_Transform_Meijer_G_Functions.html More details are available on the TCIU/Spacekime analytics website].
		+
		+	[[Image:ClassicalExpanded_TimeseriesSignal4KimesurfaceMapping.gif\|right\| [https://www.socr.umich.edu/TCIU/ Spacekime/TCIU Project] ]]
		+	[[Image:KimesurfaceMapping_of_ClassicalExpanded_TimeseriesSignal.gif\|right\| [https://www.socr.umich.edu/TCIU/ Spacekime/TCIU Project] ]]
		+

	==Background==		==Background==