240 research outputs found
Questions on the Structure of Perfect Matchings inspired by Quantum Physics
We state a number of related questions on the structure of perfect matchings.
Those questions are inspired by and directly connected to Quantum Physics. In
particular, they concern the constructability of general quantum states using
modern photonic technology. For that we introduce a new concept, denoted as
inherited vertex coloring. It is a vertex coloring for every perfect matching.
The colors are inherited from the color of the incident edge for each perfect
matching. First, we formulate the concepts and questions in pure
graph-theoretical language, and finally we explain the physical context of
every mathematical object that we use. Importantly, every progress towards
answering these questions can directly be translated into new understanding in
quantum physics.Comment: 10 pages, 4 figures, 6 questions (added suggestions from peer-review
Quantum Experiments and Graphs: Multiparty States as coherent superpositions of Perfect Matchings
We show a surprising link between experimental setups to realize
high-dimensional multipartite quantum states and Graph Theory. In these setups,
the paths of photons are identified such that the photon-source information is
never created. We find that each of these setups corresponds to an undirected
graph, and every undirected graph corresponds to an experimental setup. Every
term in the emerging quantum superposition corresponds to a perfect matching in
the graph. Calculating the final quantum state is in the complexity class
#P-complete, thus cannot be done efficiently. To strengthen the link further,
theorems from Graph Theory -- such as Hall's marriage problem -- are rephrased
in the language of pair creation in quantum experiments. We show explicitly how
this link allows to answer questions about quantum experiments (such as which
classes of entangled states can be created) with graph theoretical methods, and
potentially simulate properties of Graphs and Networks with quantum experiments
(such as critical exponents and phase transitions).Comment: 6+5 pages, 4+7 figure
Quantum Experiments and Graphs III: High-Dimensional and Multi-Particle Entanglement
Quantum entanglement plays an important role in quantum information
processes, such as quantum computation and quantum communication. Experiments
in laboratories are unquestionably crucial to increase our understanding of
quantum systems and inspire new insights into future applications. However,
there are no general recipes for the creation of arbitrary quantum states with
many particles entangled in high dimensions. Here, we exploit a recent
connection between quantum experiments and graph theory and answer this
question for a plethora of classes of entangled states. We find experimental
setups for Greenberger-Horne-Zeilinger states, W states, general Dicke states,
and asymmetrically high-dimensional multipartite entangled states. This result
sheds light on the producibility of arbitrary quantum states using photonic
technology with probabilistic pair sources and allows us to understand the
underlying technological and fundamental properties of entanglement.Comment: 7 pages, 7 figures; Appendix 3 pages, 5 figure
Gouy Phase Radial Mode Sorter for Light: Concepts and Experiments
We present an in principle lossless sorter for radial modes of light, using
accumulated Gouy phases. The experimental setups have been found by a computer
algorithm, and can be intuitively understood in a geometric way. Together with
the ability to sort angular-momentum modes, we now have access to the complete
2-dimensional transverse plane of light. The device can readily be used in
multiplexing classical information. On a quantum level, it is an analog of the
Stern-Gerlach experiment -- significant for the discussion of fundamental
concepts in quantum physics. As such, it can be applied in high-dimensional and
multi-photonic quantum experiments.Comment: main text: 7 pages, 5 figures. Supplementary Information: 5 pages, 4
figure
Phenomenology of complex structured light in turbulent air
The study of light propagation has been a cornerstone of progress in physics
and technology. Recently, advances in control and shaping of light have created
significant interest in the propagation of complex structures of light --
particularly under realistic terrestrial conditions. While theoretical
understanding of this research question has significantly grown over the last
two decades, outdoor-experiments with complex light structures are rare, and
comparisons with theory have been nearly lacking. Such situations show a
significant gap between theoretical models of atmospheric light behaviour and
current experimental effort. Here, in an attempt to reduce this gap, we
describe an interesting result of atmospheric models which are feasible for
empirical observation. We analyze in detail light propagation in different
spatial bases and present results of the theory that the influence of
atmospheric turbulence is basis-dependent. Concretely, light propagating as
eigenstate in one complete basis is stronger influenced by atmosphere than
light propagating in a different, complete basis. We obtain these results by
exploiting a family of the continuously adjustable, complete basis of spatial
modes -- the Ince-Gauss modes. Our concrete numerical results will hopefully
inspire experimental efforts and bring the theoretical and empirical study of
complex light patterns in realistic scenarios closer together.Comment: 9 pages and 5 figures; supplementary: 2 pages and 6 table
Quantum Experiments and Graphs II: Quantum Interference, Computation and State Generation
We present a conceptually new approach to describe state-of-the-art photonic
quantum experiments using Graph Theory. There, the quantum states are given by
the coherent superpositions of perfect matchings. The crucial observation is
that introducing complex weights in graphs naturally leads to quantum
interference. The new viewpoint immediately leads to many interesting results,
some of which we present here. Firstly, we identify a new and experimentally
completely unexplored multiphoton interference phenomenon. Secondly, we find
that computing the results of such experiments is #P-hard, which means it is a
classically intractable problem dealing with the computation of a matrix
function Permanent and its generalization Hafnian. Thirdly, we explain how a
recent no-go result applies generally to linear optical quantum experiments,
thus revealing important insights to quantum state generation with current
photonic technology. Fourthly, we show how to describe quantum protocols such
as entanglement swapping in a graphical way. The uncovered bridge between
quantum experiments and Graph Theory offers a novel perspective on a widely
used technology, and immediately raises many follow-up questions.Comment: 12+7 pages, 8+9 figure
Structural and biochemical insights into small RNA 3' end trimming by Arabidopsis SDN1.
A family of DEDDh 3'→5' exonucleases known as Small RNA Degrading Nucleases (SDNs) initiates the turnover of ARGONAUTE1 (AGO1)-bound microRNAs in Arabidopsis by trimming their 3' ends. Here, we report the crystal structure of Arabidopsis SDN1 (residues 2-300) in complex with a 9 nucleotide single-stranded RNA substrate, revealing that the DEDDh domain forms rigid interactions with the N-terminal domain and binds 4 nucleotides from the 3' end of the RNA via its catalytic pocket. Structural and biochemical results suggest that the SDN1 C-terminal domain adopts an RNA Recognition Motif (RRM) fold and is critical for substrate binding and enzymatic processivity of SDN1. In addition, SDN1 interacts with the AGO1 PAZ domain in an RNA-independent manner in vitro, enabling it to act on AGO1-bound microRNAs. These extensive structural and biochemical studies may shed light on a common 3' end trimming mechanism for 3'→5' exonucleases in the metabolism of small non-coding RNAs
Quantum Experiments and Hypergraphs: Multi-Photon Sources for Quantum Interference, Quantum Computation and Quantum Entanglement
We introduce the concept of hypergraphs to describe quantum optical
experiments with probabilistic multi-photon sources. Every hyperedge represents
a correlated photon source, and every vertex stands for an optical output path.
Such general graph description provides new insights for producing complex
high-dimensional multi-photon quantum entangled states, which go beyond
limitations imposed by pair creation via spontaneous parametric
down-conversion. Furthermore, properties of hypergraphs can be investigated
experimentally. For example, the NP-Complete problem of deciding whether a
hypergraph has a perfect matchin can be answered by experimentally detecting
multi-photon events in quantum experiments. By introducing complex weights in
hypergraphs, we show a general many-particle quantum interference and
manipulating entanglement in a pictorial way. Our work paves the path for the
development of multi-photon high-dimensional state generation and might inspire
new applications of quantum computations using hypergraph mappings.Comment: 14pages, 11figure
SGCRNN: A ChebNet-GRU fusion model for eeg emotion recognition
The paper proposes a deep learning model based on Chebyshev Network Gated Recurrent Units, which is called Spectral Graph Convolution Recurrent Neural Network, for multichannel electroencephalogram emotion recognition. First, in this paper, an adjacency matrix capturing the local relationships among electroencephalogram channels is established based on the cosine similarity of the spatial locations of electroencephalogram electrodes. The training efficiency is improved by utilizing the computational speed of the cosine distance. This advantage enables our method to have the potential for real-time emotion recognition, allowing for fast and accurate emotion classification in real-time application scenarios. Secondly, the spatial and temporal dependence of the Spectral Graph Convolution Recurrent Neural Network for capturing electroencephalogram sequences is established based on the characteristics of the Chebyshev network and Gated Recurrent Units to extract the spatial and temporal features of electroencephalogram sequences. The proposed model was tested on the publicly accessible dataset DEAP. Its average recognition accuracy is 88%, 89.5%, and 89.7% for valence, arousal, and dominance, respectively. The experiment results demonstrated that the Spectral Graph Convolution Recurrent Neural Network method performed better than current models for electroencephalogram emotion identification. This model has broad applicability and holds potential for use in real-time emotion recognition scenarios
Distracted driving behavior recognition based on improved MobileNetV2
In recent years, research on distracted driving behavior recognition has made significant progress, with an increasing number of researchers focusing on deep-learning-based algorithms. Aiming at the problems of the existing distracted driving recognition algorithm, such as its oversized model and difficulty in adapting to low computing environments, a lightweight network MobileNetV2, is chosen as the backbone network and improved to design a distracted driving behavior detection method that is both accurate and practical. The Ghost module is employed to replace point-by-point convolution to reduce the computation, the Leaky ReLU function helps mitigate the problem of dead neurons, as it prevents gradients from becoming zero for negative inputs. Finally, the channel pruning algorithm is used to further reduce the model parameters. The experiment results on the State Farm dataset show that the model’s test accuracy can reach 94.66%, and the number of parameters is only 0.23 M. The improved model has significantly fewer parameters than the baseline model, which demonstrates the effectiveness and applicability of the method
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