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Prediction and Prevention of Pandemics via Graphical Model Inference and Convexprogramming

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Research Square

Research Square 2021年

作者： Krechetov, Mikhail Sikaroudi, Amir Mohammad Esmaieeli Efrat, Alon Polishchuk, Valentin Chertkov, Michael Skolkovo Institute of Science and Technology Center for Energy Science and Technology Moscow121205 Russia University of Arizona Department of Computer Science TucsonAZ85721 United States University of Arizona Program in Applied Mathematics TucsonAZ85721 United States Linkoping Univeristy Communications and Transport Systems Norrkoping60174 Sweden University of Arizona Department of Mathematics TucsonAZ85721 United States

Hard-to-predict bursts of COVID-19 pandemic revealed significance of statistical modeling which would resolve spatio-temporal correlations over geographical areas, for example spread of the infection over a city with census tract granularity. In this manuscript, we provide algorithmic answers to the following two inter-related public health challenges of immense social impact which have not been adequately addressed (1) Inference Challenge: assuming that there are N census blocks (nodes) in the city, and given an initial infection at any set of nodes, e.g. any N of possible single node infections, any N(N−1)/2 of possible two node infections, etc, what is the probability for a subset of census blocks to become infected by the time the spread of the infection burst is stabilized? (2) Prevention Challenge: What is the minimal control action one can take to minimize the infected part of the stabilized state footprint? To answer the challenges, we build a Graphical Model of pandemic of the attractive Ising (pair-wise, binary) type, where each node represents a census track and each edge factor represents the strength of the pairwise interaction between a pair of nodes, e.g. representing the inter-node travel, road closure and related, and each local bias/field represents the community level of immunization, acceptance of the social distance and mask wearing practice, etc. Resolving the Inference Challenge requires finding the Maximum-A-Posteriory (MAP), i.e. most probable, state of the Ising Model constrained to the set of initially infected nodes. (An infected node is in the +1 state and a node which remained safe is in the −1 state.) We show that almost all attractive Ising Models on dense graphs result in either of the two possibilities (modes) for the MAP state: either all nodes which were not infected initially became infected, or all the initially uninfected nodes remain uninfected (susceptible). This bi-modal solution of the Inference Challenge allows us to re-st

关键词： Ising model

Prediction and Prevention of Pandemics via Graphical Model Inference and Convex programming

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arXiv 2021年

作者： Krechetov, Mikhail Sikaroudi, Amir Mohammad Esmaieeli Efrat, Alon Polishchuk, Valentin Chertkov, Michael Skolkovo Institute of Science and Technology Moscow121205 Russia University of Arizona Department of Computer Science TucsonAZ85721 United States University of Arizona Program in Applied Mathematics TucsonAZ85721 United States Linköping Univeristy Communications and Transport Systems Norrkoping60174 Sweden University of Arizona Department of Mathematics TucsonAZ85721 United States

Hard-to-predict bursts of COVID-19 pandemic revealed significance of statistical modeling which would resolve spatio-temporal correlations over geographical areas, for example spread of the infection over a city with census tract granularity. In this manuscript, we provide algorithmic answers to the following two inter-related public health challenges of immense social impact which have not been adequately addressed (1) Inference Challenge: assuming that there are N census blocks (nodes) in the city, and given an initial infection at any set of nodes, e.g. any N of possible single node infections, any N(N-1)=2 of possible two node infections, etc, what is the probability for a subset of census blocks to become infected by the time the spread of the infection burst is stabilized? (2) Prevention Challenge: What is the minimal control action one can take to minimize the infected part of the stabilized state footprint? To answer the challenges, we build a Graphical Model of pandemic of the attractive Ising (pair-wise, binary) type, where each node represents a census tract and each edge factor represents the strength of the pairwise interaction between a pair of nodes, e.g. representing the inter-node travel, road closure and related, and each local bias/field represents the community level of immunization, acceptance of the social distance and mask wearing practice, etc. Resolving the Inference Challenge requires finding the Maximum-A-Posteriory (MAP), i.e. most probable, state of the Ising Model constrained to the set of initially infected nodes. (An infected node is in the +1 state and a node which remained safe is in the-1 state.) We show that almost all attractive Ising Models on dense graphs result in either of the two possibilities (modes) for the MAP state: either all nodes which were not infected initially became infected, or all the initially uninfected nodes remain uninfected (susceptible). This bi-modal solution of the Inference Challenge allows us to re-sta

关键词： Ising model

Greybody factor for massive fermion emitted by a black hole in dRGT massive gravity theory

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arXiv 2021年

作者： Boonserm, P. Chen, C.H. Ngampitipan, T. Wongjun, Pitayuth Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Bangkok10330 Thailand The Institute for Fundamental Study Naresuan University Phitsanulok65000 Thailand Physics Program Faculty of Science Chandrakasem Rajabhat University Bangkok10900 Thailand Thailand Center of Excellence in Physics Ministry of Higher Education Science Research and Innovation Bangkok10400 Thailand

The greybody factor of the massive Dirac field around the black hole in the dRGT massive gravity theory is investigated using the rigorous bound and the WKB approximation methods. In both methods, the greybody factor significantly depends on the shape of the potential. If the potential is smaller, there is more probability for the Dirac field to transmit through the black hole, therefore, the greybody factor is higher. Moreover, there exists a critical mass of the Dirac field such that the greybody factor is maximum. By comparing the results from these two methods, we argue that it is useful to use the rigorous bound method for the low potential cases, while using the WKB approximation method for the high potential cases. Copyright © 2021, The Authors. All rights reserved.

关键词： Approximation theory

ReLSO: A Transformer-based Model for Latent Space Optimization and Generation of Proteins

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arXiv 2022年

作者： Castro, Egbert Godavarthi, Abhinav Rubinfien, Julian Givechian, Kevin Bhaskar, Dhananjay Krishnaswamy, Smita Computational Biology and Bioinformatics Program Yale University New HavenCT06511 United States Department of Applied Mathematics Yale University New HavenCT06511 United States Department of Genetics Yale University New HavenCT06511 United States Department of Computer Science Yale University New HavenCT06511 United States

The development of powerful natural language models have increased the ability to learn meaningful representations of protein sequences. In addition, advances in high-throughput mutagenesis, directed evolution, and next-generation sequencing have allowed for the accumulation of large amounts of labeled fitness data. Leveraging these two trends, we introduce Regularized Latent Space Optimization (ReLSO), a deep transformer-based autoencoder which features a highly structured latent space that is trained to jointly generate sequences as well as predict fitness. Through regularized prediction heads, ReLSO introduces a powerful protein sequence encoder and novel approach for efficient fitness landscape traversal. Using ReLSO, we explicitly model the sequence-function landscape of large labeled datasets and generate new molecules by optimizing within the latent space using gradient-based methods. We evaluate this approach on several publicly-available protein datasets, including variant sets of anti-ranibizumab and GFP. We observe a greater sequence optimization efficiency (increase in fitness per optimization step) by ReLSO compared to other approaches, where ReLSO more robustly generates high-fitness sequences. Furthermore, the attention-based relationships learned by the jointly-trained ReLSO models provides a potential avenue towards sequence-level fitness attribution information. © 2022, CC BY-NC-ND.

关键词： Proteins

The development of video analysis instrument to determine teacher's character

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AIP Conference Proceedings 2023年第1期2594卷

作者： Y. B. Gromang M. A. Rudhito D. Sudigyo T. Suparyanto B. Pardamean Department of Mathematics Education Universitas Sanata Dharma Paingan Maguwoharjo Depok Sleman Yogyakarta Indonesia 55282 Bioinformatics & Data Science Research Center Bina Nusantara University Jakarta Indonesia 11480 Computer Science Department BINUS Graduate Program - Master of Computer Science Bina Nusantara University Jakarta Indonesia 11480

This study aims to develop a valid and reliable video analysis instrument to determine teachers’ character in the opening lesson in terms of its utterances and produce video analysis on micro-teaching that will be used in training related to Artificial Intelligence (AI). The type of research used is research and development. The subject of this research is the micro-teaching video of class E students’ batch 2019, mathematics Education Study program at Sanata Dharma University. The product of this research is a video analysis instrument to find out the character of the prospective teachers, such as confidence, enthusiasm, and happiness in terms of voice utterances. This study uses the ADDIE research model. The results show that the video analysis instrument has a validity value of 4.80 which means it's very valid. Video analysis instrument to find out the enthusiastic character has a value of validity of 4.70, which means it's very valid. Then, the video analysis instrument to find out the character of happiness has a validity value of 4.60 which means it's very valid. The practicality of the developed video analysis instrument meets the required criteria with a practicality value of 4.31. Overall, the video analysis instrument developed belongs to an effective category.

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Solution of SEIRD mathematical model for the COVID-19 transmission using microsoft excel

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AIP Conference Proceedings 2023年第1期2594卷

作者： D. P. W. Putra M. A. Rudhito D. Sudigyo T. Suparyanto B. Pardamean Department of Mathematics Education Faculty of Teacher Training and Education Sanata Dharma University Yogyakarta Indonesia 55281 Bioinformatics & Data Science Research Center Bina Nusantara University Jakarta Indonesia 11480 Computer Science Department BINUS Graduate Program - Master of Computer Science Bina Nusantara University Jakarta Indonesia 11480

Mathematical modeling in the epidemiology study can be applied to describe the current transmission of viruses, one of which is compartments. However, this simulation model is rig...

Mathematical modeling in the epidemiology study can be applied to describe the current transmission of viruses, one of which is compartments. However, this simulation model is rigorous to understand, especially in interpreting the parameter values in influencing the solution. Therefore, it is necessary to present a coherent mathematical model solution. This study aims to determine the SEIRD model solution in the COVID-19 transmission using Microsoft Excel with three conditions (normal, new normal, and lockdown) to facilitate the interpretation of data. The SEIRD model used in this study considers natural population growth, namely natural births and deaths. Three stages to evaluate the model solution in this study are constructing a mathematical model, deciding the parameter intervals, and creating an applet in Microsoft Excel. The system of differential equations is converted into a system of difference equations to obtain numerical model solutions. The results showed that the differences in the infection rates for old normal, new normal, and lockdown conditions were 24%, 4%, and 3%, respectively.

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Applying Graph Theory and Mathematical-Computational Modelling to Study a Neurophysiological Circuit

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Open Journal of Modelling and Simulation 2021年第2期9卷 159-171页

作者： Camila de Andrade Kalil Maria Clícia Stelling de Castro Dilson Silva Célia Martins Cortez Postgraduate Program in Computational Sciences Rio de Janeiro State University Rio de Janeiro Brazil Department of Informatics and Computer Science Rio de Janeiro State University Rio de Janeiro Brazil Department of Applied Mathematics Rio de Janeiro State University Rio de Janeiro Brazil

The aim of the present study is to contribute to the knowledge about the functioning of the neuronal circuits. We built a mathematical-computational model using graph theory for a complex neurophysiological circuit consisting of a reverberating neuronal circuit and a parallel neuronal circuit, which could be coupled. Implementing our model in C++ and applying neurophysiological values found in the literature, we studied the discharge pattern of the reverberant circuit and the parallel circuit separately for the same input signal pattern, examining the influence of the refractory period and the synaptic delay on the respective output signal patterns. Then, the same study was performed for the complete circuit, in which the two circuits were coupled, and the parallel circuit could then influence the functioning of the reverberant. The results showed that the refractory period played an important role in forming the pattern of the output spectrum of a reverberating circuit. The inhibitory action of the parallel circuit was able to regulate the reverberation frequency, suggesting that parallel circuits may be involved in the control of reverberation circuits related to motive activities underlying precision tasks and perhaps underlying neural work processes and immediate memories.

关键词： Mathematical-Computational Modelling Neurophysiological Circuit Reverberating Circuit Parallel Circuit

Reconstruction of Fragmented Trajectories of Collective Motion using Hadamard Deep Autoencoders

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arXiv 2021年

作者： Gajamannage, Kelum Park, Yonggi Paffenroth, Randy Jayasumana, Anura P. Department of Mathematics and Statistics Texas A&M University–Corpus Christi Corpus ChristiTX78412 United States Department of Mathematical Sciences Department of Computer Science Data Science Program Worcester Polytechnic Institute WorcesterMA01609 United States Department of Electrical and Computer Engineering Colorado State University Fort CollinsCO80525 United States

Learning dynamics of collectively moving agents such as fish or humans is an active field in research. Due to natural phenomena such as occlusion and change of illumination, the multi-object methods tracking such dynamics might lose track of the agents where that might result fragmentation in the constructed trajectories. Here, we present an extended deep autoencoder (DA) that we train only on fully observed segments of the trajectories by defining its loss function as the Hadamard product of a binary indicator matrix with the absolute difference between the outputs and the labels. The trajectories of the agents practicing collective motion is low-rank due to mutual interactions and dependencies between the agents that we utilize as the underlying pattern that our Hadamard deep autoencoder (HDA) codes during its training. The performance of our HDA is compared with that of a low-rank matrix completion scheme in the context of fragmented trajectory reconstruction. © 2021, CC BY.

关键词： Learning systems

BPS2025 - Systematic embedding of biomechanics within dynamical graph grammars with application to actin networks in dendritic spine heads

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Biophysical Journal 2025年第3期124卷 206a-206a页

作者： Eric Mjolsness Matthew Hur Thomas M. Bartol Terrence J. Sejnowski Departments of Computer Science and Mathematics University of California Irvine Irvine CA USA Mathematical Computational and Systems Biology Program University of California Irvine Irvine CA USA Computational Neurobiology Laborartory Salk Institute for Biological Studies San Diego CA USA