Investigation of Faddeev variant of embedding theory

Faddeev variant of embedding theory is an example of using the embedding approach for the description of gravity. In the original form of the embedding approach, the gravity is described by an embedding function of a four-dimensional surface representing our spacetime. In Faddeev variant, the independent variable is a non-square vielbein, which is a derivative of embedding function in embedding theory. We study the possibility of the existence of extra solutions in Faddeev variant, which makes this theory non-equivalent to GR. To separate the degrees of freedom corresponding to extra matter, we propose a formulation of this theory as GR with an additional contribution to the action. We analyze the equations of motion for a specific class of solutions corresponding to a weak gravitational field. We construct a simple exact solution corresponding to arbitrary matter and nontrivial torsion, which is an extra solution in Faddeev variant in the absence of real matter.

HEE and HSC for flavors: perturbative structure in open string geometries

Introduction of electric field in the D-brane worldvolume induces a horizon in the open string geometry perceived by the brane fluctuations. We study the holographic entanglement entropy (HEE) and subregion complexity (HSC) in these asymptotically AdS geometries in three, four and five dimensions aiming to capture these quantities in the flavor sector introduced by the D-branes. Both the strip and spherical subregions have been considered. We show that the Bekenstein-Hawking entropy associated with the open string horizon, which earlier failed to reproduce the thermal entropy in the boundary, now precisely matches with the entanglement entropy at high temperatures. We check the validity of embedding function theorem while computing the HEE and attempt to reproduce the first law of entanglement thermodynamics, at least at leading order. On the basis of obtained results, we also reflect upon consequences of applying Ryu-Takayanagi proposal on these non-Einstein geometries.

Stability analysis of an ensemble of simple harmonic oscillators

In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to variations of the parameters, viz. the mass, temperature and the frequency of oscillators. Here, we introduce the Hessian matrix of the partition function as the model embedding function from the space of parameters to the set of real numbers. In this framework, we classify the regions in the parameter space of the harmonic oscillator fluctuations where they yield a stable statistical configuration. The mechanism of stability follows from the notion of the fluctuation theory. In Secs. ?? and ??, we provide the nature of local and global correlations and stability regions where the system yields a stable or unstable statistical basis, or it undergoes into geometric phase transitions. Finally, in Sec. ??, the comparison of results is provided with reference to other existing research.

Predicting Alignment Distances via Continuous Sequence Matching

Sequence comparison is the basis of various applications in bioinformatics. Recently, the increase in the number and length of sequences has allowed us to extract more and more accurate information from the data. However, the premise of obtaining such information is that we can compare a large number of long sequences accurately and quickly. Neither the traditional dynamic programming-based algorithms nor the alignment-free algorithms proposed in recent years can satisfy both the requirements of accuracy and speed. Recently, in order to meet the requirements, researchers have proposed a data-dependent approach to learn sequence embeddings, but its capability is limited by the structure of its embedding function. In this paper, we propose a new embedding function specifically designed for biological sequences to map sequences into embedding vectors. Combined with the neural network structure, we can adjust this embedding function so that it can be used to quickly and reliably predict the alignment distance between sequences. We illustrated the effectiveness and efficiency of the proposed method on various types of amplicon sequences. More importantly, our experiment on full length 16S rRNA sequences shows that our approach would lead to a general model that can quickly and reliably predict the pairwise alignment distance of any pair of full-length 16S rRNA sequences with high accuracy. We believe such a model can greatly facilitate large scale sequence analysis.

Graph Few-Shot Learning via Knowledge Transfer

Towards the challenging problem of semi-supervised node classification, there have been extensive studies. As a frontier, Graph Neural Networks (GNNs) have aroused great interest recently, which update the representation of each node by aggregating information of its neighbors. However, most GNNs have shallow layers with a limited receptive field and may not achieve satisfactory performance especially when the number of labeled nodes is quite small. To address this challenge, we innovatively propose a graph few-shot learning (GFL) algorithm that incorporates prior knowledge learned from auxiliary graphs to improve classification accuracy on the target graph. Specifically, a transferable metric space characterized by a node embedding and a graph-specific prototype embedding function is shared between auxiliary graphs and the target, facilitating the transfer of structural knowledge. Extensive experiments and ablation studies on four real-world graph datasets demonstrate the effectiveness of our proposed model and the contribution of each component.

Diachronic Embedding for Temporal Knowledge Graph Completion

Knowledge graphs (KGs) typically contain temporal facts indicating relationships among entities at different times. Due to their incompleteness, several approaches have been proposed to infer new facts for a KG based on the existing ones–a problem known as KG completion. KG embedding approaches have proved effective for KG completion, however, they have been developed mostly for static KGs. Developing temporal KG embedding models is an increasingly important problem. In this paper, we build novel models for temporal KG completion through equipping static models with a diachronic entity embedding function which provides the characteristics of entities at any point in time. This is in contrast to the existing temporal KG embedding approaches where only static entity features are provided. The proposed embedding function is model-agnostic and can be potentially combined with any static model. We prove that combining it with SimplE, a recent model for static KG embedding, results in a fully expressive model for temporal KG completion. Our experiments indicate the superiority of our proposal compared to existing baselines.

Histogram Based Data Cryptographic Technique with High Level Security

Histogram shifting plays a major role in reversible data hiding technique. By this shifting method the distortion is reduced and the embedding capacity may be increased. This proposed work uses, shifting and embedding function. The pixel elements of the original image are divided into two disjoint groups. The first group is used to carry the secret data and the second group adds some additional information which ensures the reversibility of data. The parameter such as PSNR, embedding capacity and bit rate are used for comparisons of various images