Explanatory Multi-Scale Adversarial Semantic Embedding Space Learning for Zero-Shot Recognition

The goal of zero-shot recognition is to classify classes it has never seen before, which needs to build a bridge between seen and unseen classes through semantic embedding space. Therefore, semantic embedding space learning plays an important role in zero-shot recognition. Among existing works, semantic embedding space is mainly taken by user-defined attribute vectors. However, the discriminative information included in the user-defined attribute vector is limited. In this paper, we propose to learn an extra latent attribute space automatically to produce a more generalized and discriminative semantic embedded space. To prevent the bias problem, both user-defined attribute vector and latent attribute space are optimized by adversarial learning with auto-encoders. We also propose to reconstruct semantic patterns produced by explanatory graphs, which can make semantic embedding space more sensitive to usefully semantic information and less sensitive to useless information. The proposed method is evaluated on the AwA2 and CUB dataset. These results show that our proposed method achieves superior performance.

EMBEDDING THEOREMS ON CAMPANATO-MORREY SPACES FOR VECTOR FIELDS OF HoRMANDER TYPE

This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from the known Poincare estimates. The main ingredients of the proofs rely on the fractional maximal functions. These results evidently have applications to the regularity of subelliptic PDE.

THE EMBEDDING THEORY OF NATIVE SPACES

In the theory of radial basis functions, mathematicians use linear combinations of the translates of the radial basis functions as interpolants. The set of these linear combinations is a normed vector space. This space can be completed and become a Hilbert space, called native space, which is of great importance in the last decade. The native space then contains some abstract elements which are not linear combinations of radial basis functions. The meaning of these abstract elements is not fully known. This paper presents some interpretations for the these elements. The native spaces are embedded into some well-known spaces. For example, the Sobolev-space is shown to be a native space. Since many differential equations have solutions in the Sobolev-space, we can therefore approximate the solutions by linear combinations of radial basis functions. Moreover, the famous question of the embedding of the native space into L2(Ω) is also solved by the author.

The Spatial Equivalence Between Wavelet Decomposition and Phase Space Embedding of EEG

Using both the wavelet decomposition and the phase space embedding, the phase trajectories of electroencephalogram (EEG) is described. It is illustrated based on the present work,that is,the wavelet decomposition of EEG is essentially a projection of EEG chaotic attractor onto the wavelet space opened by wavelet filter vectors, which is in correspondence with the phase space embedding of the same EEG. In other words, wavelet decomposition and phase space embedding are equivalent in methodology. Our experimental results show that in both the wavelet space and the embedded space the structure of phase trajectory of EEG is similar to each other. These results demonstrate that wavelet decomposition is effective on characterizing EEG time series.

Reversible Data Hiding Algorithm in Encrypted Images Based on Adaptive Median Edge Detection and Ciphertext-Policy Attribute-Based Encryption

With the rapid advancement of cloud computing technology,reversible data hiding algorithms in encrypted images(RDH-EI)have developed into an important field of study concentrated on safeguarding privacy in distributed cloud environments.However,existing algorithms often suffer from low embedding capacities and are inadequate for complex data access scenarios.To address these challenges,this paper proposes a novel reversible data hiding algorithm in encrypted images based on adaptive median edge detection(AMED)and ciphertext-policy attributebased encryption(CP-ABE).This proposed algorithm enhances the conventional median edge detection(MED)by incorporating dynamic variables to improve pixel prediction accuracy.The carrier image is subsequently reconstructed using the Huffman coding technique.Encrypted image generation is then achieved by encrypting the image based on system user attributes and data access rights,with the hierarchical embedding of the group’s secret data seamlessly integrated during the encryption process using the CP-ABE scheme.Ultimately,the encrypted image is transmitted to the data hider,enabling independent embedding of the secret data and resulting in the creation of the marked encrypted image.This approach allows only the receiver to extract the authorized group’s secret data,thereby enabling fine-grained,controlled access.Test results indicate that,in contrast to current algorithms,the method introduced here considerably improves the embedding rate while preserving lossless image recovery.Specifically,the average maximum embedding rates for the(3,4)-threshold and(6,6)-threshold schemes reach 5.7853 bits per pixel(bpp)and 7.7781 bpp,respectively,across the BOSSbase,BOW-2,and USD databases.Furthermore,the algorithm facilitates permission-granting and joint-decryption capabilities.Additionally,this paper conducts a comprehensive examination of the algorithm’s robustness using metrics such as image correlation,information entropy,and number of pixel change rate(NPCR),confirming its high level of security.Overall,the algorithm can be applied in a multi-user and multi-level cloud service environment to realize the secure storage of carrier images and secret data.

THE STATE SPACE RECONSTRUCTION TECHNOLOGY OF DIFFERENT KINDS OF CHAOTIC DATA OBTAINED FROM DYNAMICAL SYSTEM

Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different kinds of chaotic data obtained from dynamical system has also been discussed in detail.

THE EMBEDDED THEOREM FOR FAMILY OF QUASI METRIC SPACES IN MENGER SPACE AND ITS APPLICATION

In this paper the notion of embedding for family of quasi metric spaces in Menger spaces is introduced and its properties are investigated. A common fixed point theorem for sequence of continuous mappings in Menger spaces is proved. These mappings are assumed to satisfy some generalizations of the contraction condition. The proving technique herein seems to be new even for mappings in Menger spaces.

The Banach Space of Multiply Excited Atoms

We present, for the first time, a unified description of adiabatic collision channels and the Wannier channel in electron-atom scattering. We identify the Wannier channel as the solution of a recently presented partial differential equation of parabolic type. The kernel of that equation has been constructed near the ionization threshold. Its eigenstates are shown to be members of a Banach space. For the purpose of demonstration, this paper embeds one adiabatic channel into a Bannach space. The full set of an adiabatic spectrum will be embedded into the Wannier continuum of a Banach space in a forthcoming paper. This technique delivers amended non-adiabatic collision channnels with ebergy-dependent potentials. That dependence manifests itself as energy-dependent discontinuity at the threshold. The branch above threshold describes the double escape of electrons, whereas the branch below threshold replaces an infinity of strongly coupled adiabatic channels by one new channel. The present paper is restricted to two-electron atoms consisting only of s2 1S configurations. Our model shows new unexpected effects including an electron-electron attraction similar to a Cooper pair except that our electron pair couples only to one nucleus at rest rather than to a vibrating lattice. Our electron-electron attraction stems from a dynamic deformation of the potential surface.

Effect of Gaussian Noise Amplitude on Translation Error Estimated Using Double-Wayland Algorithm

The Wayland algorithm has been improved in order to evaluate the degree of visible determinism for dynamical systems that generate time series. The objective of this study is to show that the Double-Wayland algorithm can distinguish between time series generated by a deterministic process and those generated by a stochastic process. The authors conducted numerical analysis of the van der Pol equation and a stochastic differential equation as a deterministic process and a Ganssian stochastic process, respectively. In case of large S/N ratios, the noise term did not affect the translation error derived from time series data, but affected that from the temporal differences of time series. In case of larger noise amplitudes, the translation error from the differences was calculated to be approximately 1 using the Double-Wayland algorithm, and it did not vary in magnitude. Furthermore, the translation error derived from the differenced sequences was considered stable against noise. This novel algorithm was applied to the detection of anomalous signals in some fields of engineering, such as the analysis of railway systems and bio-signals.

PL Embeddings of PL Manifolds into Some Euclidean Spaces

The main result in this paper is the following:Theorem. Assume that W is a k-connected compact PL n-manifold with boundary, BdW is,（k-Ⅰ）-connect,k≥Ⅰ. （BdW is Ⅰ-connected for k=Ⅰ）, 0≤h≤2k, 2n-h>5 and there exists a normal block（n-h-Ⅰ）-bundle v over W. then（1） There is neat PL embedding W→D2n-hwhich normal block bundle is isomorphic to v（?） ε.（2） There is a PL embedding W→S2n-h-1which normal block bundle is isomorphic to v. Where ε denotes the trivial block l-boundle, D2n-h={x=(x1, x2,…, x2n-h∈R2n-h||xi|≤Ⅰ} and S2n-h-Ⅰ=BdD2n-h.

Normal Systems over ANR's, Rigid Embeddings and Nonseparable Absorbing Sets

Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-di- mensional absolute retracts. Michigan Math. J., 33, 291-313 （1986）] on strong Z-sets in ANR＇s and absorbing sets is generalized to nonseparable case. It is shown that if an ANR X is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and w（U） ---- w（X） （where ＂w＂is the topological weight） for each open nonempty subset U of X, then X itself i,~ homotopy dense embeddable in a Hilbert manifold. It is also demonstrated that whenever X is an AR, its weak product W（X, ＊） ---- {（xn）=l C X ： x~ = ＊ for almost all n} is homeomorphic to a pre-Hilbert space E with E EE. An intrinsic characterization of manifolds modelled on such pre-Hilbert spaces is given.