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  1. Article ; Online: Reservoir computing with noise.

    Nathe, Chad / Pappu, Chandra / Mecholsky, Nicholas A / Hart, Joe / Carroll, Thomas / Sorrentino, Francesco

    Chaos (Woodbury, N.Y.)

    2023  Volume 33, Issue 4

    Abstract: This paper investigates in detail the effects of measurement noise on the performance of reservoir computing. We focus on an application in which reservoir computers are used to learn the relationship between different state variables of a chaotic system. ...

    Abstract This paper investigates in detail the effects of measurement noise on the performance of reservoir computing. We focus on an application in which reservoir computers are used to learn the relationship between different state variables of a chaotic system. We recognize that noise can affect the training and testing phases differently. We find that the best performance of the reservoir is achieved when the strength of the noise that affects the input signal in the training phase equals the strength of the noise that affects the input signal in the testing phase. For all the cases we examined, we found that a good remedy to noise is to low-pass filter the input and the training/testing signals; this typically preserves the performance of the reservoir, while reducing the undesired effects of noise.
    Language English
    Publishing date 2023-04-26
    Publishing country United States
    Document type Journal Article
    ZDB-ID 1472677-4
    ISSN 1089-7682 ; 1054-1500
    ISSN (online) 1089-7682
    ISSN 1054-1500
    DOI 10.1063/5.0130278
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article: Dataset of Bessel function [formula omitted] maxima and minima to 600 orders and 10000 extrema

    Mecholsky, Nicholas A. / Akhbarifar, Sepideh / Lutze, Werner / Brandys, Marek / Pegg, Ian L.

    Data in Brief. 2021 Dec., v. 39

    2021  

    Abstract: Bessel functions of the first kind are ubiquitous in the sciences and engineering in solutions to cylindrical problems including electrostatics, heat flow, and the Schrödinger equation. The roots of the Bessel functions are often quoted and calculated, ... ...

    Abstract Bessel functions of the first kind are ubiquitous in the sciences and engineering in solutions to cylindrical problems including electrostatics, heat flow, and the Schrödinger equation. The roots of the Bessel functions are often quoted and calculated, but the maxima and minima for each Bessel function, used to match Neumann boundary conditions, have not had the same treatment. Here we compute 10000 extrema for the first 600 orders of the Bessel function J. To do this, we employ an adaptive root solver bounded by the roots of the Bessel function and solve to an accuracy of 10−19. We compare with the existing literature (to 30 orders and 5 maxima and minima) and the results match exactly. It is hoped that these data provide values needed for orthogonal function expansions and numerical expressions including the calculation of geometric correction factors in the measurement of resistivity of materials, as is done in the original paper using these data.
    Keywords data collection ; equations ; geometry ; heat flow
    Language English
    Dates of publication 2021-12
    Publishing place Elsevier Inc.
    Document type Article
    ZDB-ID 2786545-9
    ISSN 2352-3409
    ISSN 2352-3409
    DOI 10.1016/j.dib.2021.107508
    Database NAL-Catalogue (AGRICOLA)

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  3. Book ; Online: Reservoir Computing with Noise

    Nathe, Chad / Pappu, Chandra / Mecholsky, Nicholas A. / Hart, Joseph D. / Carroll, Thomas / Sorrentino, Francesco

    2023  

    Abstract: This paper investigates in detail the effects of noise on the performance of reservoir computing. We focus on an application in which reservoir computers are used to learn the relationship between different state variables of a chaotic system. We ... ...

    Abstract This paper investigates in detail the effects of noise on the performance of reservoir computing. We focus on an application in which reservoir computers are used to learn the relationship between different state variables of a chaotic system. We recognize that noise can affect differently the training and testing phases. We find that the best performance of the reservoir is achieved when the strength of the noise that affects the input signal in the training phase equals the strength of the noise that affects the input signal in the testing phase. For all the cases we examined, we found that a good remedy to noise is to low-pass filter the input and the training/testing signals; this typically preserves the performance of the reservoir, while reducing the undesired effects of noise.
    Keywords Computer Science - Neural and Evolutionary Computing
    Publishing date 2023-02-28
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Article ; Online: Dataset of Bessel function

    Mecholsky, Nicholas A / Akhbarifar, Sepideh / Lutze, Werner / Brandys, Marek / Pegg, Ian L

    Data in brief

    2021  Volume 39, Page(s) 107508

    Abstract: Bessel functions of the first kind are ubiquitous in the sciences and engineering in solutions to cylindrical problems including electrostatics, heat flow, and the Schrödinger equation. The roots of the Bessel functions are often quoted and calculated, ... ...

    Abstract Bessel functions of the first kind are ubiquitous in the sciences and engineering in solutions to cylindrical problems including electrostatics, heat flow, and the Schrödinger equation. The roots of the Bessel functions are often quoted and calculated, but the maxima and minima for each Bessel function, used to match Neumann boundary conditions, have not had the same treatment. Here we compute 10000 extrema for the first 600 orders of the Bessel function
    Language English
    Publishing date 2021-10-30
    Publishing country Netherlands
    Document type Journal Article
    ZDB-ID 2786545-9
    ISSN 2352-3409 ; 2352-3409
    ISSN (online) 2352-3409
    ISSN 2352-3409
    DOI 10.1016/j.dib.2021.107508
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  5. Article ; Online: Geometry and Geodesy on the Primary Visual Cortex as a Surface of Revolution

    Lorenzo G. Resca / Nicholas A. Mecholsky

    Mathematical and Computational Applications, Vol 25, Iss 4, p

    2020  Volume 64

    Abstract: Biological mapping of the visual field from the eye retina to the primary visual cortex, also known as occipital area ... V 1 ... , is central to vision and eye movement phenomena and research. That mapping is critically dependent on the ...

    Abstract Biological mapping of the visual field from the eye retina to the primary visual cortex, also known as occipital area <semantics> V 1 </semantics> , is central to vision and eye movement phenomena and research. That mapping is critically dependent on the existence of cortical magnification factors. Once unfolded, <semantics> V 1 </semantics> has a convex three-dimensional shape, which can be mathematically modeled as a surface of revolution embedded in three-dimensional Euclidean space. Thus, we solve the problem of differential geometry and geodesy for the mapping of the visual field to <semantics> V 1 </semantics> , involving both isotropic and non-isotropic cortical magnification factors of a most general form. We provide illustrations of our technique and results that apply to <semantics> V 1 </semantics> surfaces with curve profiles relevant to vision research in general and to visual phenomena such as ‘crowding’ effects and eye movement guidance in particular. From a mathematical perspective, we also find intriguing and unexpected differential geometry properties of <semantics> V 1 </semantics> surfaces, discovering that geodesic orbits have alternative prograde and retrograde characteristics, depending on the interplay between local curvature and global topology.
    Keywords geodesy ; vision ; primary visual cortex ; differential geometry ; Applied mathematics. Quantitative methods ; T57-57.97 ; Mathematics ; QA1-939 ; Electronic computers. Computer science ; QA75.5-76.95
    Subject code 511
    Language English
    Publishing date 2020-09-01T00:00:00Z
    Publisher MDPI AG
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  6. Article ; Online: Dataset of Bessel function Jn maxima and minima to 600 orders and 10000 extrema

    Nicholas A. Mecholsky / Sepideh Akhbarifar / Werner Lutze / Marek Brandys / Ian L. Pegg

    Data in Brief, Vol 39, Iss , Pp 107508- (2021)

    2021  

    Abstract: Bessel functions of the first kind are ubiquitous in the sciences and engineering in solutions to cylindrical problems including electrostatics, heat flow, and the Schrödinger equation. The roots of the Bessel functions are often quoted and calculated, ... ...

    Abstract Bessel functions of the first kind are ubiquitous in the sciences and engineering in solutions to cylindrical problems including electrostatics, heat flow, and the Schrödinger equation. The roots of the Bessel functions are often quoted and calculated, but the maxima and minima for each Bessel function, used to match Neumann boundary conditions, have not had the same treatment. Here we compute 10000 extrema for the first 600 orders of the Bessel function J. To do this, we employ an adaptive root solver bounded by the roots of the Bessel function and solve to an accuracy of 10−19. We compare with the existing literature (to 30 orders and 5 maxima and minima) and the results match exactly. It is hoped that these data provide values needed for orthogonal function expansions and numerical expressions including the calculation of geometric correction factors in the measurement of resistivity of materials, as is done in the original paper using these data.
    Keywords Bessel functions ; GCF ; Extrema ; Minimum ; Maximum ; Computer applications to medicine. Medical informatics ; R858-859.7 ; Science (General) ; Q1-390
    Subject code 510
    Language English
    Publishing date 2021-12-01T00:00:00Z
    Publisher Elsevier
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

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    Inter-library loan at ZB MED

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  7. Article ; Online: Density of States for Warped Energy Bands.

    Mecholsky, Nicholas A / Resca, Lorenzo / Pegg, Ian L / Fornari, Marco

    Scientific reports

    2016  Volume 6, Page(s) 22098

    Abstract: Warping of energy bands can affect the density of states (DOS) in ways that can be large or subtle. Despite their potential for significant practical impacts on materials properties, these effects have not been rigorously demonstrated previously. Here we ...

    Abstract Warping of energy bands can affect the density of states (DOS) in ways that can be large or subtle. Despite their potential for significant practical impacts on materials properties, these effects have not been rigorously demonstrated previously. Here we rectify this using an angular effective mass formalism that we have developed. To clarify the often confusing terminology in this field, "band warping" is precisely defined as pertaining to any multivariate energy function E(k) that does not admit a second-order differential at an isolated critical point in k-space, which we clearly distinguish from band non-parabolicity. We further describe band "corrugation" as a qualitative form of band warping that increasingly deviates from being twice differentiable at an isolated critical point. These features affect the density-of-states and other parameters ascribed to band warping in various ways. We demonstrate these effects, providing explicit calculations of DOS and their effective masses for warped energy dispersions originally derived by Kittel and others. Other physical and mathematical examples are provided to demonstrate fundamental distinctions that must be drawn between DOS contributions that originate from band warping and contributions that derive from band non-parabolicity. For some non-degenerate bands in thermoelectric materials, this may have profound consequences of practical interest.
    Language English
    Publishing date 2016-02-24
    Publishing country England
    Document type Journal Article ; Research Support, Non-U.S. Gov't ; Research Support, U.S. Gov't, Non-P.H.S.
    ZDB-ID 2615211-3
    ISSN 2045-2322 ; 2045-2322
    ISSN (online) 2045-2322
    ISSN 2045-2322
    DOI 10.1038/srep22098
    Database MEDical Literature Analysis and Retrieval System OnLINE

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