refs.bib

@book{astm1970tcmanual,
  title = {Manual on the use of thermocouples in temperature measurement},
  author = {{ASTM Committee E-20 on Temperature Measurement} and
    {ASTM Committee E-20 on Temperature Measurement. Subcommittee
  E20.04 on Thermocouples}},
  year = {1970},
  publisher = {American Society for Testing and Materials},
  address = {Philadelphia}
}

@techreport{wu2023,
  author = {Wu, Joseph},
  title = {A Basic Guide to Thermocouple Measurements},
  institution = {Texas Instruments Incorporated},
  number = {SBAA274A},
  year = {2023},
  month = {3},
  type = {Application Note},
  url = {https://www.ti.com/lit/an/sbaa274a/sbaa274a.pdf},
  urldate = {2025-10-28}
}

@article{wilson1981,
  author = {I.O. Wilson },
  title = {Magnesium oxide as a high-temperature insulant},
  journal = {IEE Proceedings A (Physical Science, Measurement and
  Instrumentation, Management and Education, Reviews)},
  volume = {128},
  issue = {3},
  pages = {159-164},
  year = {1981},
  doi = {10.1049/ip-a-1.1981.0026},
  URL = {https://digital-library.theiet.org/doi/abs/10.1049/ip-a-1.1981.0026},
  eprint =
  {https://digital-library.theiet.org/doi/pdf/10.1049/ip-a-1.1981.0026},
  abstract = { Magnesium oxide is widely used as a high-temperature insulant in
    the form of compacted powder. The reasons for its selection, and the nature
    of electrical conduction in refractory oxides at high temperatures, are
    discussed. The literature dealing with conduction in single crystals is
    reviewed, and results of resistivity measurements on compressed powders are
    reported. These show the effects on powder resistivity of impurities,
    specific surface, and of adsorbed or bound water. At 1000°C the resistivity
    of commercially available fused magnesia powders approaches that of
  high-purity single crystals.}
}

@article{zhang2025,
  title = {Electrical aging life assessment of magnesium oxide insulation in
  heating cables},
  journal = {Electric Power Systems Research},
  volume = {247},
  pages = {111791},
  year = {2025},
  issn = {0378-7796},
  doi = {10.1016/j.epsr.2025.111791},
  url = {https://www.sciencedirect.com/science/article/pii/S0378779625003748},
  author = {Wanpeng Zhang and Jingang Zhang and Chao Zhou and Bin Zhang and
    Hongbing Song and Hang Xie and Panlei Shi and Yijun Zhang and Hai Jin and
  Kaixin Wu},
  keywords = {Magnesium oxide, Lifespan prediction, Electrical aging, The
  inverse power law, Heating cables},
  abstract = {This study investigates the electrical aging mechanisms of
    magnesium oxide (MgO) insulation in heating cables, focusing on enhancing
    long-term reliability through material and process optimization.
    Accelerated aging tests under constant and stepwise voltage conditions were
    conducted at 350 °C on two types of magnesium oxide (KF99 and DG99),
    combined with finite element modeling (COMSOL) to analyze defect-induced
    electric field distortions. Results demonstrate that KF99, with 15\% higher
    density and 30\% lower porosity compared to DG99, exhibits a 40\% longer
    lifespan, attributed to its superior resistance to partial discharge. The
    inverse power law model revealed a life index n = 11.17 for KF99, 3.2\%
    higher than DG99, validating the critical role of porosity reduction in
    extending insulation durability. Furthermore, multiphysics simulations
    identified air gaps as key contributors to localized field enhancement,
    accelerating aging by 22\%. These findings provide actionable
    strategies—such as particle size optimization and compaction pressure
    control—to improve MgO insulation design for high-reliability industrial
    applications, particularly in downhole heating systems for petroleum
  extraction.}
}

@article{zeraoulia2025,
  doi = {10.20944/preprints202509.1804.v1},
  url = {https://doi.org/10.20944/preprints202509.1804.v1},
  year = 2025,
  month = {September},
  publisher = {Preprints},
  author = {Rafik Zeraoulia},
  title = {Entropy—Sieve Methods and Energy Functionals in the Erdős Problem
  [Er79] on Quadratic Prime Representations},
  journal = {Preprints}
}

@inproceedings{he2016deep,
  author={He, Kaiming and Zhang, Xiangyu and Ren, Shaoqing and Sun, Jian},
  booktitle={2016 IEEE Conference on Computer Vision and Pattern
  Recognition (CVPR)},
  title={Deep Residual Learning for Image Recognition},
  year=2016,
  pages={770-778},
  keywords={Training;Degradation;Complexity theory;Image
  recognition;Neural networks;Visualization;Image segmentation},
  doi={10.1109/CVPR.2016.90},
  url={https://www.cv-foundation.org/openaccess/content_cvpr_2016/papers/He_Deep_Residual_Learning_CVPR_2016_paper.pdf}
}

@inproceedings{deng2009imagenet,
  author={Deng, Jia and Dong, Wei and Socher, Richard and Li,
  Li-Jia and Kai Li and Li Fei-Fei},
  booktitle={2009 IEEE Conference on Computer Vision and Pattern
  Recognition},
  title={ImageNet: A large-scale hierarchical image database},
  year=2009,
  pages={248-255},
  doi={10.1109/CVPR.2009.5206848},
  url={https://www.image-net.org/static_files/papers/imagenet_cvpr09.pdf}
}

@article{kingma2014adam,
  title={Adam: A Method for Stochastic Optimization},
  author={Kingma, Diederik P and Ba, Jimmy},
  journal={arXiv preprint arXiv:1412.6980},
  year=2014,
  doi={10.48550/arXiv.1412.6980},
  url={https://arxiv.org/abs/1412.6980}
}

@inbook{paszke2019pytorch,
  author = {Paszke, Adam and Gross, Sam and Massa, Francisco and
    Lerer, Adam and Bradbury, James and Chanan, Gregory and Killeen,
    Trevor and Lin, Zeming and Gimelshein, Natalia and Antiga, Luca
    and Desmaison, Alban and K\"{o}pf, Andreas and Yang, Edward and
    DeVito, Zach and Raison, Martin and Tejani, Alykhan and
    Chilamkurthy, Sasank and Steiner, Benoit and Fang, Lu and Bai,
  Junjie and Chintala, Soumith},
  title = {PyTorch: an imperative style, high-performance deep
  learning library},
  year = 2019,
  publisher = {Curran Associates Inc.},
  address = {Red Hook, NY, USA},
  abstract = {Deep learning frameworks have often focused on either
    usability or speed, but not both. PyTorch is a machine learning
    library that shows that these two goals are in fact compatible:
    it provides an imperative and Pythonic programming style that
    supports code as a model, makes debugging easy and is consistent
    with other popular scientific computing libraries, while
    remaining efficient and supporting hardware accelerators such as
    GPUs.In this paper, we detail the principles that drove the
    implementation of PyTorch and how they are reflected in its
    architecture. We emphasize that every aspect of PyTorch is a
    regular Python program under the full control of its user. We
    also explain how the careful and pragmatic implementation of the
    key components of its runtime enables them to work together to
    achieve compelling performance. We demonstrate the efficiency of
    individual subsystems, as well as the overall speed of PyTorch on
  several common benchmarks.},
  booktitle = {Proceedings of the 33rd International Conference on
  Neural Information Processing Systems},
  articleno = {721},
  numpages = {12},
  doi = {10.48550/arXiv.1912.01703},
  url =
  {https://proceedings.neurips.cc/paper_files/paper/2019/file/bdbca288fee7f92f2bfa9f7012727740-Paper.pdf}
}

@book{szeliski2022computer,
  title={Computer Vision: Algorithms and Applications},
  author={Szeliski, Richard},
  year=2022,
  publisher={Springer Nature},
  edition={2nd},
  doi={10.1007/978-3-030-34372-9},
  url={szeliski.org/Book/}
}

@software{splitfolders,
  author = {Juergen Filter},
  title = {split-folders: A Python library for splitting image datasets},
  year = 2022,
  url = {https://github.com/jfilter/split-folders},
  version = {0.5.1},
  note = {Github Repository}
}

@misc{oeis_web,
  Author = {{OEIS Foundation Inc.}},
  Note = {Published electronically at \url{http://oeis.org}},
  Title = {The {O}n-{L}ine {E}ncyclopedia of {I}integer {S}equences},
  Year = 2026
}

@misc{toml,
  author = {Preston-Werner, Tom and Gedam, Pradyun},
  title = {{TOML}: Tom's Obvious Minimal Language},
  year = {2025},
  month = {Dec},
  howpublished = {\url{https://toml.io/en/v1.1.0}},
  note = {Accessed: 2026-03-30}
}

@article{skilling2004,
  author = {Skilling, John},
  title = {Programming the Hilbert curve},
  journal = {AIP Conference Proceedings},
  volume = {707},
  number = {1},
  pages = {381-387},
  year = {2004},
  month = {04},
  abstract = {The Hilbert curve has previously been constructed
    recursively, using p levels of recursion of n‐bit Gray codes to
    attain a precision of p bits in n dimensions. Implementations have
    reflected the awkwardness of aligning the recursive steps to
    preserve geometrical adjacency. We point out that a single global
    Gray code can instead be applied to all np bits of a Hilbert
    length. Although this “over‐transforms” the length, the excess work
    can be undone in a single pass over the bits, leading to compact
  and efficient computer code.},
  issn = {0094-243X},
  doi = {10.1063/1.1751381},
  url = {https://doi.org/10.1063/1.1751381},
  eprint =
  {https://pubs.aip.org/aip/acp/article-pdf/707/1/381/11557416/381_1_online.pdf},
}

@techreport{dam1998,
  author      = {Erik B. Dam and Martin Koch and Martin Lillholm},
  title       = {Quaternions, Interpolation and Animation},
  institution = {Department of Computer Science, University of Copenhagen},
  year        = {1998},
  type        = {Technical Report},
  number      = {DIKU-TR-98/5},
  address     = {Copenhagen, Denmark},
  url         = {https://web.mit.edu/2.998/www/QuaternionReport1.pdf},
  month       = {July}
}

@misc{eberly2002,
  author       = {David Eberly},
  title        = {Quaternion Algebra and Calculus},
  howpublished = {Magic Software, Inc.},
  year         = {2002},
  month        = {September},
  note         = {Created March 2, 1999},
  url          = {https://www.sci.utah.edu/~jmk/papers/Quaternions.pdf}
}


@techreport{naif2003,
  title        = {Quaternions White Paper},
  author       = {{Navigation and Ancillary Information Facility (NAIF)}},
  institution  = {Jet Propulsion Laboratory, California Institute of
  Technology},
  year         = {2003},
  month        = {November},
  url          =
  {https://naif.jpl.nasa.gov/pub/naif/misc/Quaternion_White_Paper/Quaternions_White_Paper.pdf}
}

@incollection{shoemake1992,
  title = {III.6 - UNIFORM RANDOM ROTATIONS},
  editor = {DAVID KIRK},
  booktitle = {Graphics Gems III (IBM Version)},
  publisher = {Morgan Kaufmann},
  address = {San Francisco},
  pages = {124-132},
  year = {1992},
  isbn = {978-0-12-409673-8},
  doi = {https://doi.org/10.1016/B978-0-08-050755-2.50036-1},
  url =
  {https://www.sciencedirect.com/science/article/pii/B9780080507552500361},
  author = {Ken Shoemake},
  abstract = {Publisher Summary
    A planar rotation can be represented in several ways—for example,
    as an angle between 0 and 2π or as a unit complex number x + iy =
    cos θ + i sin θ. Planar rotations combine by summing their angles
    modulo 2π ; so one way to generate a uniform planar rotation is to
    generate a uniform angle. This chapter describes a uniformly
    distributed spatial rotation as one not having a uniformly
    distributed angle. For a unit quaternion, the ω component is the
    cosine of half the angle of rotation. When the angle is uniformly
    distributed between 0 and 2π, the average magnitude of ω will be
    2/π 0.6366, which exceeds the correct value for a uniform rotation
    by a factor of 3/2. It is easy to generate random unit quaternions
    and, hence, rotations with the correct distribution. Pairs of
    independent variables with Gaussian distribution can easily be
    generated using the polar or Box–Muller method, which transforms a
    point uniformly distributed within the unit disk. The Gaussian
    generation can be folded into the unit quaternion generation to
  give an efficient algorithm.}
}

@article{pervin2018,
  author = "Edward  Pervin and Jon A. Webb",
  title = "{Quaternions in computer vision and robotics}",
  year = "2018",
  month = "6",
  url =
  "https://kilthub.cmu.edu/articles/journal_contribution/Quaternions_in_computer_vision_and_robotics/6608771",
  doi = "10.1184/R1/6608771.v1"
}


@misc{sarkka2007,
  author = {Simo Särkkä},
  title  = {Notes on Quaternions},
  year   = {2007},
  month  = {June},
  url    = {https://users.aalto.fi/~ssarkka/pub/quat.pdf},
  note   = {Accessed: 2026-04-14}
}

@article{shoemake1985,
  author = {Shoemake, Ken},
  title = {Animating rotation with quaternion curves},
  year = {1985},
  isbn = {0897911660},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  url = {https://doi.org/10.1145/325334.325242},
  doi = {10.1145/325334.325242},
  abstract = {Solid bodies roll and tumble through space. In computer
    animation, so do cameras. The rotations of these objects are best
    described using a four coordinate system, quaternions, as is shown
    in this paper. Of all quaternions, those on the unit sphere are
    most suitable for animation, but the question of how to construct
    curves on spheres has not been much explored. This paper gives one
    answer by presenting a new kind of spline curve, created on a
    sphere, suitable for smoothly in-betweening (i.e. interpolating)
    sequences of arbitrary rotations. Both theory and experiment show
    that the motion generated is smooth and natural, without quirks
  found in earlier methods.},
  booktitle = {Proceedings of the 12th Annual Conference on Computer
  Graphics and Interactive Techniques},
  pages = {245–254},
  numpages = {10},
  keywords = {spline, spherical geometry, rotation, quaternion,
    interpolation, in-betweening, approximation, animation, B-spline,
  B\'{e}zier curve},
  series = {SIGGRAPH '85}
}

@misc{motekew2014,
  author      = {Kurt A. Motekew},
  title       = {Quaternion to DCM and Back Again},
  month       = {April},
  year        = {2014},
  url         = {https://motoq.github.io/doc/tnotes/dcmq.pdf}
}

@techreport{crassidis2024,
  author      = {John L. Crassidis},
  title       = {Quaternion Identities},
  institution = {NASA Engineering and Safety Center (NESC) Academy},
  year        = {2024},
  url         =
  {https://nescacademy.nasa.gov/review/downloadfile.php?file=quat_ident.pdf&id=120&distr=Public},
  note        = {Accessed: April 15, 2026}
}


@techreport{dantam2014,
  author      = {Dantam, Neil},
  title       = {Quaternion Computation},
  institution = {Georgia Institute of Technology, Institute for
  Robotics and Intelligent Machines},
  address     = {Atlanta, GA, USA},
  year        = {2014},
  month       = {October},
  note        = {Work in Progress -- Updated 2014-10-01},
  url         = {http://www.neil.dantam.name/note/dantam-quaternion.pdf}
}

@article{markley2008,
  author = {Markley, F. Landis},
  title = {Unit Quaternion from Rotation Matrix},
  journal = {Journal of Guidance, Control, and Dynamics},
  volume = {31},
  number = {2},
  pages = {440-442},
  year = {2008},
  doi = {10.2514/1.31730},
  URL = {https://doi.org/10.2514/1.31730},
  eprint = {https://doi.org/10.2514/1.31730}
}

@article{baritzhack2000,
  author = {Bar-Itzhack, Itzhack Y.},
  title = {New Method for Extracting the Quaternion from a Rotation Matrix},
  journal = {Journal of Guidance, Control, and Dynamics},
  volume = {23},
  number = {6},
  pages = {1085-1087},
  year = {2000},
  doi = {10.2514/2.4654},
  URL = {https://doi.org/10.2514/2.4654},
  eprint = {https://doi.org/10.2514/2.4654}
}

@InProceedings{sarabandi2019,
  author="Sarabandi, Soheil
  and Thomas, Federico",
  editor="Lenarcic, Jadran
  and Parenti-Castelli, Vincenzo",
  title="Accurate Computation of Quaternions from Rotation Matrices",
  booktitle="Advances in Robot Kinematics 2018",
  year="2019",
  publisher="Springer International Publishing",
  address="Cham",
  pages="39--46",
  url={https://digital.csic.es/bitstream/10261/179990/1/Accurate\%20Computation_Sarabandi.pdf},
  doi = {
    10.1007/978-3-319-93188-3_5
  },
  abstract={The main non-singular alternative to 3x3 proper
    orthogonal matrices, for
    representing rotations in R3, is quaternions. Thus, it is important to have
    reliable methods to pass from one representation to the other.
    While passing from a quaternion to the corresponding rotation
    matrix is given by Euler-Rodrigues formula, the other way round can
    be performed in many different ways. Although all of them are
    algebraically equivalent, their numerical behavior can be quite
    different. In 1978, Shepherd proposed a method for computing the
    quaternion corresponding to a rotation matrix which is considered
    the most reliable method to date. Shepperd's method, thanks to a
    voting scheme between four possible solutions, always works far
    from formulation singularities. In this paper, we propose a new
    method which outperforms Shepperd's method without increasing the
  computational cost.},
  isbn={978-3-319-93188-3}
}

@article{shepherd1978,
  author = {Shepherd, Stanley W.},
  title = {Quaternion from Rotation Matrix},
  journal = {Journal of Guidance and Control},
  volume = {1},
  number = {3},
  pages = {223-224},
  year = {1978},
  doi = {10.2514/3.55767b},
  URL = {https://doi.org/10.2514/3.55767b},
  eprint = {https://doi.org/10.2514/3.55767b}
}

@article{wu2019,
  author = {Wu, Jin},
  title = {Optimal Continuous Unit Quaternions from Rotation Matrices},
  journal = {Journal of Guidance, Control, and Dynamics},
  volume = {42},
  number = {4},
  pages = {919-922},
  year = {2019},
  doi = {10.2514/1.G004043},
  URL = {https://doi.org/10.2514/1.G004043},
  eprint = {https://doi.org/10.2514/1.G004043}
}

@book{bate1971,
  added-at = {2014-01-24T09:34:44.000+0100},
  address = {New York},
  author = {Bate, Roger R. and Mueller, Donald D. and White, Jerry E.},
  biburl =
  {https://www.bibsonomy.org/bibtex/2aeb09e7fa80cf97d766b68d612cb9b35/cut},
  interhash = {f831bf7de969fb677709f7e477d87f02},
  intrahash = {aeb09e7fa80cf97d766b68d612cb9b35},
  keywords = {astrodynamics bathesis-luri},
  publisher = {Dover Publications},
  timestamp = {2015-09-25T21:50:07.000+0200},
  title = {{Fundamentals} of {Astrodynamics}},
  year = 1971
}

@article{witten1987,
  author = {Witten, Ian H. and Neal, Radford M. and Clearly, John G.},
  title = {Arithmetic coding for data compression},
  year = {1987},
  issue_date = {June 1987},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  volume = {30},
  number = {6},
  issn = {0001-0782},
  url = {https://doi.org/10.1145/214762.214771},
  doi = {10.1145/214762.214771},
  abstract = {The state of the art in data compression is arithmetic
    coding, not the better-known Huffman method. Arithmetic coding
    gives greater compression, is faster for adaptive models, and
  clearly separates the model from the channel encoding.},
  journal = {Commun. ACM},
  month = jun,
  pages = {520–540},
  numpages = {21}
}

@book{mclyman2004,
  title={Transformer and Inductor Design Handbook},
  author={McLyman, Colonel Wm. T.},
  edition={3rd},
  year={2004},
  publisher={Marcel Dekker Inc.},
  address={New York, NY},
  isbn={9780824753931}
}