301 research outputs found
A Novel Model for DNA Sequence Similarity Analysis Based on Graph Theory
Determination of sequence similarity is one of the major steps in computational phylogenetic studies. As we know, during evolutionary history, not only DNA mutations for individual nucleotide but also subsequent rearrangements occurred. It has been one of major tasks of computational biologists to develop novel mathematical descriptors for similarity analysis such that various mutation phenomena information would be involved simultaneously. In this paper, different from traditional methods (eg, nucleotide frequency, geometric representations) as bases for construction of mathematical descriptors, we construct novel mathematical descriptors based on graph theory. In particular, for each DNA sequence, we will set up a weighted directed graph. The adjacency matrix of the directed graph will be used to induce a representative vector for DNA sequence. This new approach measures similarity based on both ordering and frequency of nucleotides so that much more information is involved. As an application, the method is tested on a set of 0.9-kb mtDNA sequences of twelve different primate species. All output phylogenetic trees with various distance estimations have the same topology, and are generally consistent with the reported results from early studies, which proves the new method\u27s efficiency; we also test the new method on a simulated data set, which shows our new method performs better than traditional global alignment method when subsequent rearrangements happen frequently during evolutionary history
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Flexible and Transparent High-Dielectric-Constant Polymer Films Based on Molecular Ferroelectric-Modified Poly(Vinyl Alcohol)
Tensor-network-assisted variational quantum algorithm
Near-term quantum devices generally suffer from shallow circuit depth and
hence limited expressivity due to noise and decoherence. To address this, we
propose tensor-network-assisted parametrized quantum circuits, which
concatenate a classical tensor-network operator with a quantum circuit to
effectively increase the circuit's expressivity without requiring a physically
deeper circuit. We present a framework for tensor-network-assisted variational
quantum algorithms that can solve quantum many-body problems using shallower
quantum circuits. We demonstrate the efficiency of this approach by considering
two examples of unitary matrix-product operators and unitary tree tensor
networks, showing that they can both be implemented efficiently. Through
numerical simulations, we show that the expressivity of these circuits is
greatly enhanced with the assistance of tensor networks. We apply our method to
two-dimensional Ising models and one-dimensional time-crystal Hamiltonian
models with up to 16 qubits and demonstrate that our approach consistently
outperforms conventional methods using shallow quantum circuits.Comment: 12 pages, 8 figures, 37 reference
Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems
The linearizability (or isochronicity) problem is one of the open problems for polynomial differential systems which is far to be solved in general. A progressive way
to find necessary conditions for linearizability is to compute period constants. In this
paper, we are interested in the linearizability problem of p : −q resonant degenerate
singular point for polynomial differential systems. Firstly, we transform degenerate
singular point into the origin via a homeomorphism. Moreover, we establish a new recursive algorithm to compute the so-called generalized period constants for the origin
of the transformed system. Finally, to illustrate the effectiveness of our algorithm, we
discuss the linearizability problems of 1 : −1 resonant degenerate singular point for a
septic system. We stress that similar results are hardly seen in published literatures
up till now. Our work is completely new and extends existing ones
Mutual Information Learned Regressor: an Information-theoretic Viewpoint of Training Regression Systems
As one of the central tasks in machine learning, regression finds lots of
applications in different fields. An existing common practice for solving
regression problems is the mean square error (MSE) minimization approach or its
regularized variants which require prior knowledge about the models. Recently,
Yi et al., proposed a mutual information based supervised learning framework
where they introduced a label entropy regularization which does not require any
prior knowledge. When applied to classification tasks and solved via a
stochastic gradient descent (SGD) optimization algorithm, their approach
achieved significant improvement over the commonly used cross entropy loss and
its variants. However, they did not provide a theoretical convergence analysis
of the SGD algorithm for the proposed formulation. Besides, applying the
framework to regression tasks is nontrivial due to the potentially infinite
support set of the label. In this paper, we investigate the regression under
the mutual information based supervised learning framework. We first argue that
the MSE minimization approach is equivalent to a conditional entropy learning
problem, and then propose a mutual information learning formulation for solving
regression problems by using a reparameterization technique. For the proposed
formulation, we give the convergence analysis of the SGD algorithm for solving
it in practice. Finally, we consider a multi-output regression data model where
we derive the generalization performance lower bound in terms of the mutual
information associated with the underlying data distribution. The result shows
that the high dimensionality can be a bless instead of a curse, which is
controlled by a threshold. We hope our work will serve as a good starting point
for further research on the mutual information based regression.Comment: 28 pages, 2 figures, presubmitted to AISTATS2023 for reviewin
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