SGBMN: Symplectic Group Bayesian Manifold Network for Few-shot Classification

2021 ◽  
Author(s):  
Jingyi Ding ◽  
Fanzhang Li
Keyword(s):  
Symplectic Group ◽  
Shot Classification

Actual issues of systematization of scientific knowledge on the conditions of shot in the forensic ballistics

2020 ◽  
Vol 2020 (3) ◽  
pp. 164-169
Author(s):  
Igor' Latyshov ◽  
Fedor Samuylenko
Keyword(s):  
Scientific Knowledge ◽  
Communication Systems ◽  
Production Method ◽  
Natural Phenomenon ◽  
Projectile Energy ◽  
Energy Characteristics ◽  
Shot Classification ◽  
Forensic Ballistics

In this research, there was considered a challenge of constructing a system of scientific knowledge of the shot conditions in judicial ballistics. It was observed that there are underlying factors that are intended to ensureits [scientific knowledge] consistency: identification of the list of shot conditions, which require consideration when solving expert-level research tasks on weapons, cartridges and traces of their action; determination of the communication systems in the course of objects’ interaction, which present the result of exposure to the conditions of the shot; classification of the shot conditions based on the grounds significant for solving scientific and practical problems. The article contains the characteristics of a constructive, functional factor (condition) of weapons and cartridges influence, environmental and fire factors, the structure of the target and its physical properties, situational and spatial factors, and projectile energy characteristics. Highlighted are the forms of connections formed in the course of objects’ interaction, proposed are the author’s classifications of forensically significant shooting conditions with them being divided on the basis of the following criteria: production from the object of interaction, production from a natural phenomenon, production method, results weapon operation and utilization, duration of exposure, type of structural connections between interaction objects, number of conditions that apply when firing and the forming traces.

scholarly journals Families of abelian surfaces with real multiplication over Hilbert modular surfaces

1982 ◽  
Vol 88 ◽  
pp. 17-53 ◽  
Author(s):  
G. van der Geer ◽  
K. Ueno
Keyword(s):  
Endomorphism Ring ◽  
Symplectic Group ◽  
Abelian Surface ◽  
Quadratic Relation ◽  
Holomorphic Map ◽  
Real Multiplication ◽  
Compact Complex Surfaces ◽  
Hilbert Modular Surfaces ◽  
Hilbert Modular ◽  
Abelian Functions

Around the beginning of this century G. Humbert ([9]) made a detailed study of the properties of compact complex surfaces which can be parametrized by singular abelian functions. A surface parametrized by singular abelian functions is the image under a holomorphic map of a singular abelian surface (i.e. an abelian surface whose endomorphism ring is larger than the ring of rational integers). Humbert showed that the periods of a singular abelian surface satisfy a quadratic relation with integral coefficients and he constructed an invariant D of such a relation with respect to the action of the integral symplectic group on the periods.

scholarly journals Meta Learning for Few-Shot One-Class Classification

AI ◽  
2021 ◽  
Vol 2 (2) ◽  
pp. 195-208
Author(s):  
Gabriel Dahia ◽  
Maurício Pamplona Segundo
Keyword(s):  
Feature Representation ◽  
Support Vector ◽  
Support Vector Data Description ◽  
Target Class ◽  
Feature Representations ◽  
Shot Classification ◽  
Training Stage ◽  
Comparable Performance ◽  
Meta Learning ◽  
One Class Classification

We propose a method that can perform one-class classification given only a small number of examples from the target class and none from the others. We formulate the learning of meaningful features for one-class classification as a meta-learning problem in which the meta-training stage repeatedly simulates one-class classification, using the classification loss of the chosen algorithm to learn a feature representation. To learn these representations, we require only multiclass data from similar tasks. We show how the Support Vector Data Description method can be used with our method, and also propose a simpler variant based on Prototypical Networks that obtains comparable performance, indicating that learning feature representations directly from data may be more important than which one-class algorithm we choose. We validate our approach by adapting few-shot classification datasets to the few-shot one-class classification scenario, obtaining similar results to the state-of-the-art of traditional one-class classification, and that improves upon that of one-class classification baselines employed in the few-shot setting.

scholarly journals Few-Shot Classification in Unseen Domains by Episodic Meta-Learning Across Visual Domains

2021 ◽  
Author(s):  
Yuan-Chia Cheng ◽  
Ci-Siang Lin ◽  
Fu-En Yang ◽  
Yu-Chiang Frank Wang
Keyword(s):  
Shot Classification ◽  
Meta Learning

-ADIC -FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS

2019 ◽  
Vol 19 (4) ◽  
pp. 1287-1347 ◽  
Author(s):  
Zheng Liu
Keyword(s):  
Eisenstein Series ◽  
Symplectic Group ◽  
Symplectic Groups ◽  
Simple Strategy ◽  
Doubling Method

We construct the $p$-adic standard $L$-functions for ordinary families of Hecke eigensystems of the symplectic group $\operatorname{Sp}(2n)_{/\mathbb{Q}}$ using the doubling method. We explain a clear and simple strategy of choosing the local sections for the Siegel Eisenstein series on the doubling group $\operatorname{Sp}(4n)_{/\mathbb{Q}}$, which guarantees the nonvanishing of local zeta integrals and allows us to $p$-adically interpolate the restrictions of the Siegel Eisenstein series to $\operatorname{Sp}(2n)_{/\mathbb{Q}}\times \operatorname{Sp}(2n)_{/\mathbb{Q}}$.

scholarly journals Regular and residual Eisenstein series and the automorphic cohomology of Sp(2,2)

2009 ◽  
Vol 146 (1) ◽  
pp. 21-57 ◽  
Author(s):  
Harald Grobner
Keyword(s):  
Algebraic Group ◽  
Eisenstein Series ◽  
Symplectic Group ◽  
Automorphic Forms ◽  
General Theorem ◽  
Simple Algebraic Group ◽  
Ramanujan Conjecture ◽  
Eisenstein Cohomology ◽  
Derivatives Of

AbstractLetGbe the simple algebraic group Sp(2,2), to be defined over ℚ. It is a non-quasi-split, ℚ-rank-two inner form of the split symplectic group Sp8of rank four. The cohomology of the space of automorphic forms onGhas a natural subspace, which is spanned by classes represented by residues and derivatives of cuspidal Eisenstein series. It is called Eisenstein cohomology. In this paper we give a detailed description of the Eisenstein cohomologyHqEis(G,E) ofGin the case of regular coefficientsE. It is spanned only by holomorphic Eisenstein series. For non-regular coefficientsEwe really have to detect the poles of our Eisenstein series. SinceGis not quasi-split, we are out of the scope of the so-called ‘Langlands–Shahidi method’ (cf. F. Shahidi,On certainL-functions, Amer. J. Math.103(1981), 297–355; F. Shahidi,On the Ramanujan conjecture and finiteness of poles for certainL-functions, Ann. of Math. (2)127(1988), 547–584). We apply recent results of Grbac in order to find the double poles of Eisenstein series attached to the minimal parabolicP0ofG. Having collected this information, we determine the square-integrable Eisenstein cohomology supported byP0with respect to arbitrary coefficients and prove a vanishing result. This will exemplify a general theorem we prove in this paper on the distribution of maximally residual Eisenstein cohomology classes.

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