scholarly journals Classifying affine line bundles on a compact complex space

2019 ◽  
Vol 6 (1) ◽  
pp. 103-117
Author(s):  
Valentin Plechinger
Keyword(s):  
Line Bundle ◽  
Deformation Theory ◽  
Complex Space ◽  
Main Idea ◽  
Difficult Problem ◽  
Line Bundles ◽  
Compact Complex Space ◽  
Affine Line ◽  
Picard Functor

AbstractThe classification of affine line bundles on a compact complex space is a difficult problem. We study the affine analogue of the Picard functor and the representability problem for this functor. Let be a compact complex space with . We introduce the affine Picard functor which assigns to a complex space the set of families of linearly -framed affine line bundles on parameterized by . Our main result states that the functor is representable if and only if the map is constant. If this is the case, the space which represents this functor is a linear space over whose underlying set is , where is a Poincaré line bundle normalized at . The main idea idea of the proof is to compare the representability of to the representability of a functor considered by Bingener related to the deformation theory of -cohomology classes. Our arguments show in particular that, for = 1, the converse of Bingener’s representability criterion holds

scholarly journals MultiKOC: Multi-One-Class Classifier Based K-Means Clustering

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 134
Author(s):  
Loai Abdallah ◽  
Murad Badarna ◽  
Waleed Khalifa ◽  
Malik Yousef
Keyword(s):  
Clustering Algorithm ◽  
Main Idea ◽  
Molecular Classification ◽  
Positive Sample ◽  
Classification Problems ◽  
Multiple Cancer ◽  
Multiple Tumor ◽  
One Class Classifier ◽  
The Given

In the computational biology community there are many biological cases that are considered as multi-one-class classification problems. Examples include the classification of multiple tumor types, protein fold recognition and the molecular classification of multiple cancer types. In all of these cases the real world appropriately characterized negative cases or outliers are impractical to achieve and the positive cases might consist of different clusters, which in turn might lead to accuracy degradation. In this paper we present a novel algorithm named MultiKOC multi-one-class classifiers based K-means to deal with this problem. The main idea is to execute a clustering algorithm over the positive samples to capture the hidden subdata of the given positive data, and then building up a one-class classifier for every cluster member’s examples separately: in other word, train the OC classifier on each piece of subdata. For a given new sample, the generated classifiers are applied. If it is rejected by all of those classifiers, the given sample is considered as a negative sample, otherwise it is a positive sample. The results of MultiKOC are compared with the traditional one-class, multi-one-class, ensemble one-classes and two-class methods, yielding a significant improvement over the one-class and like the two-class performance.

scholarly journals Dopamine antagonists for the treatment of drug addiction: PF-4363467 and related compounds

2020 ◽  
Vol 11 (1) ◽  
pp. 84-90 ◽  
Author(s):  
Ana Martinez
Keyword(s):  
Drug Addiction ◽  
Main Idea ◽  
Electron Donors ◽  
Health Concern ◽  
Dopamine Antagonists ◽  
Donor Acceptor ◽  
Homo And Lumo ◽  
Related Compounds ◽  
Receptor Agonists And Antagonists

Drug addiction refers to an out-of-control and compulsive use of substances, which can reach epidemic magnitudes. It is a health concern throughout the world and has major economic impact. Dopamine receptor agonists and antagonists have been cited as molecular targets for the treatment of drug addiction. In this report, the main idea is to analyze the new D3R/D2R ligands that are proposed for the treatment of drug abuse, in terms of their electron donor/acceptor properties. Substances catalogued as agonists represent good electron donors, whereas antagonists represent good electron acceptors. HOMO and LUMO eigenvalues indicate that more energy is necessary to remove an electron from the antagonists, and likewise more energy is gained when antagonists accept an electron. The combination of two molecules (PF-592379 and PNU-177864) produces a new compound (PF-4363467) with properties that are intermediate. Irrespective of the characteristics of the receptor, the classification of ligands is important, in order to further understanding of the reaction mechanism of these compounds. This may help in the design of new molecules for the treatment of drug addiction.

scholarly journals UNARY FA-PRESENTABLE SEMIGROUPS

2012 ◽  
Vol 22 (04) ◽  
pp. 1250038 ◽  
Author(s):  
ALAN J. CAIN ◽  
NIK RUŠKUC ◽  
RICHARD M. THOMAS
Keyword(s):  
Difficult Problem ◽  
Decision Problems ◽  
Finite Model ◽  
Locally Finite ◽  
Letter Alphabet ◽  
Significant Interest ◽  
Automatic Presentations ◽  
The Relationship ◽  
Completely Simple

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has been the classification of those structures of some species that admit automatic presentations. Whilst some successes have been obtained, this appears to be a difficult problem in general. A restricted problem, also of significant interest, is to ask this question for unary automatic presentations: automatic presentations over a one-letter alphabet. This paper studies unary FA-presentable semigroups. We prove the following: Every unary FA-presentable structure admits an injective unary automatic presentation where the language of representatives consists of every word over a one-letter alphabet. Unary FA-presentable semigroups are locally finite, but non-finitely generated unary FA-presentable semigroups may be infinite. Every unary FA-presentable semigroup satisfies some Burnside identity. We describe the Green's relations in unary FA-presentable semigroups. We investigate the relationship between the class of unary FA-presentable semigroups and various semigroup constructions. A classification is given of the unary FA-presentable completely simple semigroups.

The strength for line bundles

2021 ◽  
Vol 127 (3) ◽  
Author(s):  
Edoardo Ballico ◽  
Emanuele Ventura
Keyword(s):  
Line Bundle ◽  
Algebraic Variety ◽  
Commutative Algebra ◽  
Upper Bounds ◽  
Line Bundles ◽  
Homogeneous Polynomials

We introduce the strength for sections of a line bundle on an algebraic variety. This generalizes the strength of homogeneous polynomials that has been recently introduced to resolve Stillman's conjecture, an important problem in commutative algebra. We establish the first properties of this notion and give some tool to obtain upper bounds on the strength in this framework. Moreover, we show some results on the usual strength such as the reducibility of the set of strength two homogeneous polynomials.

scholarly journals Pulse Waveform Classification Using Support Vector Machine with Gaussian Time Warp Edit Distance Kernel

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Danbing Jia ◽  
Dongyu Zhang ◽  
Naimin Li
Keyword(s):  
Quantitative Research ◽  
Edit Distance ◽  
Difficult Problem ◽  
Average Error ◽  
Support Vector ◽  
Pulse Waveform ◽  
Vector Machines ◽  
Processing Techniques ◽  
Gaussian Time

Advances in signal processing techniques have provided effective tools for quantitative research in traditional Chinese pulse diagnosis. However, because of the inevitable intraclass variations of pulse patterns, the automatic classification of pulse waveforms has remained a difficult problem. Utilizing the new elastic metric, that is, time wrap edit distance (TWED), this paper proposes to address the problem under the support vector machines (SVM) framework by using the Gaussian TWED kernel function. The proposed method, SVM with GTWED kernel (GTWED-SVM), is evaluated on a dataset including 2470 pulse waveforms of five distinct patterns. The experimental results show that the proposed method achieves a lower average error rate than current pulse waveform classification methods.

scholarly journals Transfer Learning with Convolutional Neural Networks for Diabetic Retinopathy Image Classification. A Review

2020 ◽  
Vol 10 (6) ◽  
pp. 2021 ◽  
Author(s):  
Ibrahem Kandel ◽  
Mauro Castelli
Keyword(s):  
Diabetic Retinopathy ◽  
Deep Learning ◽  
Transfer Learning ◽  
Main Idea ◽  
Diabetic Patients ◽  
Domain Transfer ◽  
Domain Transfer Learning ◽  
Enormous Number ◽  
Deep Learning Model

Diabetic retinopathy (DR) is a dangerous eye condition that affects diabetic patients. Without early detection, it can affect the retina and may eventually cause permanent blindness. The early diagnosis of DR is crucial for its treatment. However, the diagnosis of DR is a very difficult process that requires an experienced ophthalmologist. A breakthrough in the field of artificial intelligence called deep learning can help in giving the ophthalmologist a second opinion regarding the classification of the DR by using an autonomous classifier. To accurately train a deep learning model to classify DR, an enormous number of images is required, and this is an important limitation in the DR domain. Transfer learning is a technique that can help in overcoming the scarcity of images. The main idea that is exploited by transfer learning is that a deep learning architecture, previously trained on non-medical images, can be fine-tuned to suit the DR dataset. This paper reviews research papers that focus on DR classification by using transfer learning to present the best existing methods to address this problem. This review can help future researchers to find out existing transfer learning methods to address the DR classification task and to show their differences in terms of performance.

scholarly journals Projective surfaces with K-very ample line bundles of degree ≤ 4K + 4

1994 ◽  
Vol 136 ◽  
pp. 57-79 ◽  
Author(s):  
Edoardo Ballico ◽  
Andrew J. Sommese
Keyword(s):  
Line Bundle ◽  
Projective Space ◽  
Smooth Surface ◽  
Negative Integer ◽  
Line Bundles ◽  
Restriction Map ◽  
Projective Surface ◽  
Projective Surfaces

A line bundle, L, on a smooth, connected projective surface, S, is defined [7] to be k-very ample for a non-negative integer, k, if given any 0-dimensional sub-scheme with length , it follows that the restriction map is onto. L is 1-very ample (respectively 0-very ample) if and only if L is very ample (respectively spanned at all points by global sections). For a smooth surface, S, embedded in projective space by | L | where L is very ample, L being k-very ample is equivalent to there being no k-secant Pk−1 to S containing ≥ k + 1 points of S.

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