相关论文: An Algorithmic Approach to Algebraic and Dynamical…
In this article, a spectral sequence analysis of a filtered Novikov complex $(\mathcal{N}_{\ast}(f),\Delta)$ over $\mathbb{Z}((t))$ is developed with the goal of obtaining results relating the algebraic and dynamical settings. Specifically,…
We develop the symplectic elimnation algorithm. This algorithm using simple row operations reduce a symplectic matrix to a diagonal matrix. This algorithm gives rise to a decomposition of an arbitrary matrix into a product of a symplectic…
At the intersection of Topological Data Analysis (TDA) and machine learning, the field of cellular signal processing has advanced rapidly in recent years. In this context, each signal on the cells of a complex is processed using the…
Reducing a chain complex (whilst preserving its homotopy-type) using algebraic Morse theory gives the same end-result as Gaussian elimination, but AMT does it only on certain rows/columns and with several pivots (in all matrices…
Modern datasets often exhibit high dimensionality, yet the data reside in low-dimensional manifolds that can reveal underlying geometric structures critical for data analysis. A prime example of such a dataset is a collection of cell cycle…
Synthetic aperture radar (SAR) tomography (TomoSAR) is an appealing tool for the extraction of height information of urban infrastructures. Due to the widespread applications of the MUSIC algorithm in source localization, it is a suitable…
Discrete Morse theory helps us compute the homology groups of simplicial complexes in an efficient manner. A "good" gradient vector field reduces the number of critical simplices, simplifying the homology calculations by reducing them to…
We propose an approach for multiple sequence alignment (MSA) derived from the dynamic time warping viewpoint and recent techniques of curve synchronization developed in the context of functional data analysis. Starting from pairwise…
End-to-End deep learning has shown promising results for speech enhancement tasks, such as noise suppression, dereverberation, and speech separation. However, most state-of-the-art methods for echo cancellation are either classical…
Simultaneous sparse approximation (SSA) seeks to represent a set of dependent signals using sparse vectors with identical supports. The SSA model has been used in various signal and image processing applications involving multiple…
We develop a behavioural theory of reflective sequential algorithms (RSAs), i.e. sequential algorithms that can modify their own behaviour. The theory comprises a set of language-independent postulates defining the class of RSAs, an…
This study introduces Skewed Fully Asynchronous Cellular Automata (SACA), a novel update scheme in cellular automata that updates the states of only two consecutive and adjacent cells, such as ci and ci+1, simultaneously at each time step.…
We proposed a probabilistic algorithm to solve the Multiple Sequence Alignment problem. The algorithm is a Simulated Annealing (SA) that exploits the representation of the Multiple Alignment between $D$ sequences as a directed polymer in…
Carbon isotope labeling method is a standard metabolic engineering tool for flux quantification in living cells. To cope with the high dimensionality of isotope labeling systems, diverse algorithms have been developed to reduce the number…
The Multiple Sequence Alignment (MSA) is a computational abstraction that represents a partial summary either of indel history, or of structural similarity. Taking the former view (indel history), it is possible to use formal automata…
Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and…
Aiming at overcoming practical issues of successive interference cancellation (SIC), this paper proposes a dual-polarized rate-splitting multiple access (RSMA) technique for a downlink massive multiple-input multiple-output (MIMO) network.…
A generalized downlink multi-antenna non-orthogonal multiple access (NOMA) transmission framework is proposed with the novel concept of cluster-free successive interference cancellation (SIC). In contrast to conventional NOMA approaches,…
The design of highly scalable multiple access schemes is a main challenge in the evolution towards future massive machine-type communications, where reliability and latency constraints must be ensured to a large number of uncoordinated…
Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some…