How to Marry the Kernel and the Image Truc, Jean-Paul
The College mathematics journal,
09/2023, Volume:
ahead-of-print, Issue:
ahead-of-print
Journal Article
Peer reviewed
This note gives a general sufficient and necessary condition to obtain the direct sum
, where E is a finite dimensional space over the field
(
or
) and f is a linear transformation of E.
Accurate capacity estimation is crucial for the reliable and safe operation of lithium-ion batteries. In particular, exploiting the relaxation voltage curve features could enable battery capacity ...estimation without additional cycling information. Here, we report the study of three datasets comprising 130 commercial lithium-ion cells cycled under various conditions to evaluate the capacity estimation approach. One dataset is collected for model building from batteries with LiNi
Co
Al
O
-based positive electrodes. The other two datasets, used for validation, are obtained from batteries with LiNi
Co
Mn
O
-based positive electrodes and batteries with the blend of Li(NiCoMn)O
- Li(NiCoAl)O
positive electrodes. Base models that use machine learning methods are employed to estimate the battery capacity using features derived from the relaxation voltage profiles. The best model achieves a root-mean-square error of 1.1% for the dataset used for the model building. A transfer learning model is then developed by adding a featured linear transformation to the base model. This extended model achieves a root-mean-square error of less than 1.7% on the datasets used for the model validation, indicating the successful applicability of the capacity estimation approach utilizing cell voltage relaxation.
Abstract
The set with assosiative binary operations is semigroup. Of all set partial linear transformations with a composition function is semigroup which is called a partial linear transformation ...semigroup that is denoted by (PT (X), o). If Y is a subspace of X, with all images of PT (X) a subset of Y, so the semigroup which is formed is a semigroup of partial linear transformation with restricted range that is denoted by (PT(X,Y),o). A natural partial order is a relation which defined by a ≤ b if only if a = xb = by, xa = a for some x,y ∈PT(X,Y) in a semigroup partial linear transformation with restricted range. In this article using the literature study method, it discusses the characterization of natural partial order on partial linear transformations semigroups with restricted range resulting neccesary and sufficient condition for a natural partial order in semigroup partial linear transformation with restricted range.
•Proposed a method based on improved watershed for the identification and segmentation of tea sprout.•Based on adaptive threshold, the minimum error method is used to automatically obtain the ...threshold.•The “black dead zone” was treated with super threshold zero to improve the segmentation integrity of the highlight area of tea sprout.•Piecewise linear transformation was used to enhance the differentiation degree of old and tea sprout and segmentation accuracy.
In the automatic intelligent picking of famous tea sprouts, the images obtained by the robot vision system have the following problems: the highlighted surface of a tea sprout leads to identification omissions, and the color distinction rate between the sprout and old leaves is low, resulting in an incomplete tea sprout segmentation and high segmentation error rate for old tea leaves. A tea sprout recognition segmentation method based on an improved watershed algorithm is proposed in this study. First, images of naturally grown tea leaves in a tea garden are collected. After an experimental analysis and comparison, the collected tea samples are smoothed by Gaussian filtering to remove noise, split the channels, obtain R, G, and B components, and analyze their characteristics. Second, the optimal adaptation threshold T′ is determined using the minimum error method. For all pixels of the B component, the pixel values are set to be greater than the threshold of zero. Third, image operations are performed on the G and B′ components to obtain G-B′ components, and the minimum error method is used to obtain the best adaptation thresholds T1 and T2 and enhance them via piecewise linear transformation to improve the distinction between the young leaves and the background in the image. Lastly, binarization is performed, and the Canny operator is utilized for edge detection. The foreground and background areas are determined, the unknown area is calculated and marked, and the watershed function is used to complete the segmentation. A comparative experiment is conducted by comparing the 100 samples collected using the threshold segmentation algorithm, watershed segmentation algorithm, and the proposed segmentation algorithm. One group is randomly selected among tea samples numbered 1–10, and another nine groups of tea samples are selected with a number interval of 10 for a total of 10 groups. Their experimental data are analyzed. Results show that the improved algorithm has an average segmentation accuracy rate of 95.79%, and it improves the accuracy and integrity of the segmentation of tea leaves.
In higher algebra, Direct sum decomposition theorem for finite dimension of linear space is a classical result of linear transformation. This theorem has been widely used in many fields, such as ...algebra and mechanics and so on. In this paper, the proof is given by means of Hamilton Cayley theorem.
This paper explores the knowledge of linguistic structure learned by large artificial neural networks, trained via self-supervision, whereby the model simply tries to predict a masked word in a given ...context. Human language communication is via sequences of words, but language understanding requires constructing rich hierarchical structures that are never observed explicitly. The mechanisms for this have been a prime mystery of human language acquisition, while engineering work has mainly proceeded by supervised learning on treebanks of sentences hand labeled for this latent structure. However, we demonstrate that modern deep contextual language models learn major aspects of this structure, without any explicit supervision. We develop methods for identifying linguistic hierarchical structure emergent in artificial neural networks and demonstrate that components in these models focus on syntactic grammatical relationships and anaphoric coreference. Indeed, we show that a linear transformation of learned embeddings in these models captures parse tree distances to a surprising degree, allowing approximate reconstruction of the sentence tree structures normally assumed by linguists. These results help explain why these models have brought such large improvements across many language-understanding tasks.
Abstract Recently there has been growing interest in using photonics to perform the linear algebra operations of neuromorphic and quantum computing applications, aiming at harnessing silicon ...photonics’ (SiPho) high-speed and energy-efficiency credentials. Accurately mapping, however, a matrix into optics remains challenging, since state-of-the-art optical architectures are sensitive to fabrication imperfections. This leads to reduced fidelity that degrades as the insertion losses of the optical matrix nodes or the matrix dimensions increase. In this work, we present the experimental deployment of a 4 × 4 coherent crossbar (Xbar) as a silicon chip and validate experimentally its theoretically predicted fidelity restoration credentials. We demonstrate the experimental implementation of 10,000 arbitrary linear transformations achieving a record-high fidelity of 99.997% ± 0.002, limited mainly by the measurement equipment. Our work represents an integrated optical circuit providing almost unity and loss-independent fidelity in the realization of arbitrary matrices, highlighting light’s credentials in resolving complex computations.
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