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Belief dynamics extraction
[article]
2019
arXiv
pre-print
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Animal behavior is not driven simply by its current observations, but is strongly influenced by internal states. Estimating the structure of these internal states is crucial for understanding the neural basis of behavior. In principle, internal states can be estimated by inverting behavior models, as in inverse model-based Reinforcement Learning. However, this requires careful parameterization and risks model-mismatch to the animal. Here we take a data-driven approach to infer latent states
arXiv:1902.00673v1
fatcat:di3rrhiqpjcjvggx5kdr5nhtg4
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... ctly from observations of behavior, using a partially observable switching semi-Markov process. This process has two elements critical for capturing animal behavior: it captures non-exponential distribution of times between observations, and transitions between latent states depend on the animal's actions, features that require more complex non-markovian models to represent. To demonstrate the utility of our approach, we apply it to the observations of a simulated optimal agent performing a foraging task, and find that latent dynamics extracted by the model has correspondences with the belief dynamics of the agent. Finally, we apply our model to identify latent states in the behaviors of monkey performing a foraging task, and find clusters of latent states that identify periods of time consistent with expectant waiting. This data-driven behavioral model will be valuable for inferring latent cognitive states, and thereby for measuring neural representations of those states.
Quantum Fourier Analysis
[article]
2020
arXiv
pre-print
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Quantum Fourier analysis is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum symmetry. We establish bounds on the quantum Fourier transform , as a map between suitably defined L^p spaces, leading to a new uncertainty principle for relative entropy. We cite several applications of the quantum Fourier analysis in subfactor theory, in category
arXiv:2002.03477v1
fatcat:3qkrkzz2yfdwbfonvjtazfp3ta
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... y, and in quantum information. We suggest a new topological inequality, and we outline several open problems.
Block maps and Fourier analysis
[article]
2017
arXiv
pre-print
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Zhengwei Liu would like to thank V. F. R. Jones for constant encouragement and T. Tao for helpful suggestions. Parts of the work was done during visits of Zhengwei Liu and ...
Zhengwei Liu was supported by a grant from Templeton Religion Trust and an AMS-Simons Travel Grant. Jinsong Wu was supported by NSFC (Grant no. ...
Jinsong Wu to
Preliminaries 2.1. Subfactors and the dual pair of C * -algebras. Jones classified the Jones index δ 2 of a subfactor in [10] . ...
arXiv:1706.03551v1
fatcat:3kpxj7qzjbbwzlqxr7eltjlnai
Non-commutative Rényi Entropic Uncertainty Principles
[article]
2019
arXiv
pre-print
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Part of the work was done during visits of Zhengwei Liu and Jinsong Wu to Hebei Normal University and of Jinsong Wu to Harvard University. ...
Zhengwei Liu was supported by Templeton religion trust under grant TRT 0159. Jinsong Wu was supported by NSFC (Grant no. 11771413) and partially by TRT 0159. ...
arXiv:1904.04292v1
fatcat:fzpmxly6d5frvi4ntqkgnxct5e
Antisymmetric characters and Fourier duality
[article]
2019
arXiv
pre-print
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Inspired by the quantum McKay correspondence, we consider the classical ADE Lie theory as a quantum theory over sl_2. We introduce anti-symmetric characters for representations of quantum groups and investigate the Fourier duality to study the spectral theory. In the ADE Lie theory, there is a correspondence between the eigenvalues of the Coxeter element and the eigenvalues of the adjacency matrix. We formalize related notions and prove such a correspondence for representations of Verlinde
arXiv:1805.04783v2
fatcat:kgbjfjrjqncuvcx5g2jfgucw4y
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... ras of quantum groups: this includes the quiver of any module category acted on by the representation category of any simple Lie algebra g at any level ℓ. This answers an old question posed by Victor Kac in 1994 and a recent comment by Terry Gannon.
Rational thoughts in neural codes
[article]
2019
bioRxiv
pre-print
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The transition probability Wu et al.
Supporting Information Appendix (SI September 11, 2019 | 11 . ...
Although some of these changes are driven directly by the sensory observations (colors), that only explains part of the belief updates: even 6 of 14 | Wu et al. ...
doi:10.1101/765867
fatcat:yxro2yve7zehle5hvemm6h4dtm
Young's inequality for locally compact quantum groups
[article]
2016
arXiv
pre-print
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Zhengwei Liu was supported by a grant from Templeton Religion Trust and an AMS-Simons Travel Grant. ...
Part of the work was done during multiple of visits of Jinsong Wu to Hebei Normal University and Jinsong Wu was supported by NSFC (Grant no. A010602). ...
Wu [9] proved Young's inequality for subfactors. In this paper, our goal is to generalize Young's inequality for locally compact quantum groups. We show that Main 1.1 (Theorem 3.4). ...
arXiv:1611.04630v1
fatcat:ys2hfmgndreedeuqql7yll6e5e
Quantum convolution inequalities on Frobenius von Neumann algebras
[article]
2022
arXiv
pre-print
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Jinsong Wu was supported by NSFC (Grant no. 12031004) and a grant from Beijing Institute of Mathematical Sciences and Applications.. ...
Zhengwei Liu was supported by NKPs (Grant no. 2020YFA0713000), by Tsinghua University (Grant no. 04200100122) and by Templeton Religion Trust (TRT 159). ...
arXiv:2204.04401v1
fatcat:amrtisgeyzhbxon52sjnkyq2qy
Laplacian Spectral Properties of Graphs from Random Local Samples
[article]
2013
arXiv
pre-print
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The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and the structure of 'local' subgraphs of the network. We call a subgraph local when it is induced by the set of nodes obtained from a breath-first search (BFS) of radius r around a node. In this paper, we propose techniques to estimate spectral properties of
arXiv:1310.4899v1
fatcat:q77jt2t7vfgwtgx65bpgwc6ryi
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... normalized Laplacian matrix from a random collection of induced local subgraphs. In particular, we provide an algorithm to estimate the spectral moments of the normalized Laplacian matrix (the power-sums of its eigenvalues). Moreover, we propose a technique, based on convex optimization, to compute upper and lower bounds on the spectral radius of the normalized Laplacian matrix from local subgraphs. We illustrate our results studying the normalized Laplacian spectrum of a large-scale online social network.
Store Location Selection via Mining Search Query Logs of Baidu Maps
[article]
2016
arXiv
pre-print
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Some * Haishan Wu is the corresponding author. (a) Detecting the spatial distribution of customer demand from query data from Baidu Maps. ...
arXiv:1606.03662v1
fatcat:wz7v3lkdbnaoxny244zxfiqhfq
MOESM1 of Measuring economic activity in China with mobile big data
2017
Figshare
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Supplementary Material for Measuring Economic Activity in China with Mobile Big Data. (pdf)
doi:10.6084/m9.figshare.c.3923437_d1.v1
fatcat:amzcddry7rb4bjn5ldopjw2mm4
Quantum smooth uncertainty principles for von Neumann bi-algebras
[article]
2021
arXiv
pre-print
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Zhengwei Liu was supported by NKPs (Grant no. 2020YFA0713000) and by Tsinghua University (Grant no. 100301004). Jinsong Wu was supported by NSFC (Grant no. 11771413 and 12031004). ...
arXiv:2107.09057v1
fatcat:sfpy5ex62rhi7nw6uprr356wnu
Modulation of viscoelastic fluid response to external body force
2019
Scientific Reports
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Author Contributions Meng Zhang and Wu Zhang initiated the idea, performed the calculations and theoretical analysis. Zhengwei Wu, Yinan Shen and Huayin Wu contributed on the theoretical analysis. ...
Meng Zhang and Wu Zhang contributed equally to this paper.
Additional Information Competing Interests: The authors declare no competing interests. ...
doi:10.1038/s41598-019-45612-2
pmid:31253813
pmcid:PMC6599053
fatcat:sdwzifup45h37j75bkenwwzudy
Ghost Cities Analysis Based on Positioning Data in China
[article]
2015
arXiv
pre-print
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Real estate projects are developed excessively in China in this decade. Many new housing districts are built, but they far exceed the actual demand in some cities. These cities with a high housing vacancy rate are called ghost cities. The real situation of vacant housing areas in China has not been studied in previous research. This study, using Baidu positioning data, presents the spatial distribution of the vacant housing areas in China and classifies cities with a large vacant housing area
arXiv:1510.08505v2
fatcat:2rf2robkvze3fglebijcphx6yi
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... cities or tourism sites. To the best of our knowledge, it is the first time that we detected and analyzed the ghost cities in China at such fine scale. To understand the human dynamic in ghost cities, we select one city and one tourism sites as cases to analyze the features of human dynamics. This study illustrates the capability of big data in sensing our cities objectively and comprehensively.
Steel Fibre Reinforced Concrete Meso-Scale Numerical Analysis
2020
Advances in Civil Engineering
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Wu, Y. J. Cui, and Z. W. Li performed the methodologies, supervised the study, and reviewed and edited the article. J. W. ...
Liang and Wu [30] modelled fibre and concrete separately and linked them with slide line contact to truly reflect the interfacial behaviour of fibre and mortar. ...
doi:10.1155/2020/2084646
fatcat:4jcw7n4u5jgrfbvxa33oskr62q
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