Discrete Diffusion for Single-Cell Gene Expression Modeling

Achieving maximal coverage of service facilities has been of great interest to urban and regional planners. Examples include placing cellular towers, siting emergency response stations, and locating weather radars, among others. In some planning contexts, facilities could be sited almost anywhere in a region due to their small geographic footprints and demand is continuously distributed. This location problem has been represented as the continuous space maximal coverage problem (CSMCP). The CSMCP is widely acknowledged to be challenging to solve exactly. A broadly used solution approach for the CSMCP is to transform the problem into discrete maximal coverage models through continuous space discretization. A variety of discrete simplifications of CSMCP have been developed, attempting to address spatial representation issues that arise in the application of discrete models used as a continuous space approximation. However, the performance of applying these discrete coverage models to approximately solving the CSMCP has not been explicitly evaluated. It remains elusive as to which approach provides the best approximation for the CSMCP. This article therefore presents a comparative performance analysis of various discrete approximations for the CSMCP. Empirical results provide insights on how to achieve a balance between model representation detail and reasonable computation. Potential research directions are also suggested.

Cross-language plagiarism detection over continuous-space- and knowledge graph-based representations of language

Theoretical tools and insights from discrete mathematics, theoretical computer science, and topology now play essential roles our understanding of vital biomolecular processes. The related methods are now employed various fields of mathematical biology as instruments to zoom in on processes at a molecular level. This book contains expository chapters on how contemporary models from discrete mathematics domains such as algebra, combinatorics, and graph and knot theories can provide perspective on biomolecular problems ranging from data analysis, molecular and gene arrangements and structures, and knotted DNA embeddings via spatial graph models to the dynamics and kinetics of molecular interactions. The contributing authors are among the leading scientists this field and the book is a reference for researchers mathematics and theoretical computer science who are engaged with modeling molecular and biological phenomena using discrete methods. It may also serve as a guide and supplement for graduate courses mathematical biology or bioinformatics, introducing nontraditional aspects of mathematical biology.

In order to deal with the sequential decision problems with large or continuous state spaces, feature representation and function approximation have been a major research topic in reinforcement learning (RL). In this paper, a clustering-based graph Laplacian framework is presented for feature representation and value function approximation (VFA) in RL. By making use of clustering-based techniques, that is, K-means clustering or fuzzy C-means clustering, a graph Laplacian is constructed by subsampling in Markov decision processes (MDPs) with continuous state spaces. The basis functions for VFA can be automatically generated from spectral analysis of the graph Laplacian. The clustering-based graph Laplacian is integrated with a class of approximation policy iteration algorithms called representation policy iteration (RPI) for RL in MDPs with continuous state spaces. Simulation and experimental results show that, compared with previous RPI methods, the proposed approach needs fewer sample points to compute an efficient set of basis functions and the learning control performance can be improved for a variety of parameter settings.

In this paper, three stochastic mathematical models are developed for the spread of the coronavirus disease (COVID-19). These models take into account the known special characteristics of this disease such as the existence of infectious undetected cases and the different social and infectiousness conditions of infected people. In particular, they include a novel approach that considers the social structure, the fraction of detected cases over the real total infected cases, the influx of undetected infected people from outside the borders, as well as contact-tracing and quarantine period for travellers. Two of these models are discrete time-discrete state space models (one is simplified and the other is complete) while the third one is a continuous time-continuous state space stochastic integro-differential model obtained by a formal passing to the limit from the proposed simplified discrete model. From a numerical point of view, the particular case of Lebanon has been studied and its reported data have been used to estimate the complete discrete model parameters, which can be of interest in estimating the spread of COVID-19 in other countries. The obtained simulation results have shown a good agreement with the reported data. Moreover, a parameters' analysis is presented in order to better understand the role of some of the parameters. This may help policy makers in deciding on different social distancing measures.

Nonlinear Parity Equation Residual Generation for Fault Detection and Isolation

The submetric formalism for task representation

The logical foundations of urban economics are consistent

Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS

A deep learning approach for analyzing DNase-seq datasets is presented, which has promising potentials for unraveling biological underpinnings on transcription regulation mechanisms. Further understanding of these mechanisms can lead to important advances in life sciences in general and drug, biomarker discovery, and cancer research in particular. Motivated by recent remarkable advances in the field of deep learning, we developed a platform, Deep Semi-Supervised DNase-seq Analytics (DSSDA). Primarily empowered by deep generative Convolutional Networks (ConvNets), the most notable aspect is the capability of semi-supervised learning, which is highly beneficial for common biological settings often plagued with a less sufficient number of labeled data. In addition, we investigated a k-mer based continuous vector space representation, attempting further improvement on learning power with the consideration of the nature of biological sequences for features associated with locality-based relationships between neighboring nucleotides. DSSDA employs a modified Ladder Network for underlying generative model architecture, and its performance is demonstrated on the cell type classification task using sequences from large-scale DNase-seq experiments. We report the performance of DSSDA in both fully-supervised setting, in which DSSDA outperforms widely-known ConvNet models (94.6% classification accuracy), and semi-supervised setting for which, even with less than 10% of labeled data, DSSDA performs relatively comparable to other ConvNets using the full data set. Our results underscore, in order to deal with challenging genomic sequence datasets, the need of a better deep learning method to learn latent features and representation.

Generalizing the notion of continuous Hilbert space representations of compact topological groups we define unitary continuous corepresentations of C*-completions of compact quantum group Hopf algebras on arbitrary Hilbert spaces. It is proved that the unitary continuous corepresentations decompose in finite-dimensional irreducible corepresentations.

The hardware design space is high-dimensional and discrete. Systematic and efficient exploration of this space has been a significant challenge. Central to this problem is the intractable search complexity that grows exponentially with the design choices and the discrete nature of the search space. This work investigates the feasibility of learning a meaningful low-dimensional continuous representation for hardware designs to reduce such complexity and facilitate the search process. We devise a variational autoencoder (VAE)-based design space exploration framework called VAESA, to encode the hardware design space in a compact and continuous representation. We show that black-box and gradient-based design space exploration algorithms can be applied to the latent space, and design points optimized in the latent space can be reconstructed to high-performance realistic hardware designs. Our experiments show that performing the design space search on the latent space consistently leads to the optimal design point under a fixed number of samples. In addition, the latent space can improve the sample efficiency of the original algorithm by 6.8$\times$ and can discover hardware designs that are up to 5% more efficient than the optimal design searched directly in the high-dimensional input space.

Most of the continuous-time algorithms are implemented in the discrete domain. Therefore, it is of utmost importance to have a smooth transition between discrete and continuous time models for enhancing numerical conditioning. Delta-operator is known to provide such flexibility where a delta-operator based dynamic model converges to its continuous counterpart as the sampling time converges to zero. In this brief, delta-operator based novel reaching laws are established. Most importantly, the quasi sliding mode band (QSMB) is calculated via suitable stability analysis in the delta-operator framework. It is shown that when the sampling time converges to zero, the delta-operator based stability analysis provides a similar conclusion to that of continuous-domain analysis. Finally, the theoretical findings are corroborated by some simulation results.

It is very difficult to characterize, model and simulate the naturally fractured reservoirs (NFRs) due to the high static and dynamic heterogeneity, especially in the low matrix porosity and permeability reservoirs. The common used DFN modeling method is simple in upscale, with low accuracy. Therefore, this method has been challenged increasingly by reservoir engineers. In this study, we used an innovative EDFM (Embedded Discrete Fracture Modeling) method, which can combine the results of geological modeling with reservoir simulation, preserve the complexity of the DFN, and save the run time or steps compared with the conventional fluid flow simulation workflow. With EDFM method, any complex fracture planes can be modelled explicitly without discretization of the matrix domain into unstructured elements. EDFM method is high in computational efficiency, and it is feasible to conduct quick modelling of the fracture reservoirs with high-resolution with EDFM method.With EDFM method, NFRs modeling, calibration and simulation can be conducted. The workflow is as follows: Firstly, characterize the fracture parameters (including aperture, length, connectivity, and intensity) on the basis of the results of fine seismic interpretation, outcrop survey data, core data and borehole image, and build DFN models for individual well. The fractures are divided into two groups according to their size grades and their hydraulic influence on the fluid flow in the reservoir, namely the large-scale fractures and the small-scale diffuse fractures. The large-scale fractures can represent highly conductive corridors, while the small-scale diffuse fractures are lower in overall conductivity and connectivity; Secondly, calibrate DFN models by embedding the individual well reservoir model with EDFM, run well testing forward modeling to match with well testing data(K*h), and conduct reservoir simulation to optimize fracture parameters with the true production data; Thirdly, put the DFN properties of individual well into DFN model of the whole block. Finally, conduct numerical simulation of NFR. During this process, the EDFM method is used to simulate the large-scale fractures, and DPDK (Dual Porosity-Dual Permeability) method is used to simulate the influence of small-scale fractures on fluid flow, in order that both computational efficiency and accurate flow behavior can be improved.This workflow has been used successfully in a granite fractured oil reservoir. A whole block reservoir simulation has been conducted for history matching of 15 wells with EDFM method and DPDK method to test the workflow and understand the fracture system. More than 260 thousand small-scale fractures have been upscaled into DPDK model, and more than 13 thousand large-scale fractures have been embedded into the model. The result shows that the simulation result of oil production rate from 15 wells is matched very well with the actual data. The study result indicated that the new workflow with EDFM method can provide a practical solution for complex NFRs modeling and simulation.KeywordsNaturally fractured reservoirs (NFRs)Embedded discrete fracture modeling (EDFM)Reservoir simulation and calibrationDual porosity-dual permeability (DPDK)

Multi-agent multi-target search strategies can be utilized in complex scenarios such as post-disaster search and rescue by unmanned aerial vehicles. To solve the problem of fixed target and trajectory, the current multi-agent multi-target search strategies are mainly based on deep reinforcement learning (DRL). However, the training of agents by the DRL tend to be brittle due to their sensitivity to the training environment, which makes the strategies learned by the agents fall into local optima frequently, resulting in poor system robustness. Additionally, sparse rewards in DRL will lead to the problems such as difficulty in system convergence and low utilization efficiency of the sampled data. To address the problem that the robustness of the agents is weakened and the sparse rewards exist in the multi-objective search environment, we propose a MiniMax Multi-agent Deep Deterministic Policy Gradient based on the Parallel Hindsight Experience Replay (PHER-M3DDPG) algorithm, which adopts the framework of centralized training and decentralized execution in continuous action space. To enhance the system robustness, the PHER-M3DDPG algorithm employs a minimax learning architecture, which adaptively adjusts the learning strategy of agents by involving adversarial disturbances. In addition, to solve the sparse rewards problem, the PHER-M3DDPG algorithm adopts a parallel hindsight experience replay mechanism to increase the efficiency of data utilization by involving virtual learning targets and batch processing of the sampled data. Simulation results show that the PHER-M3DDPG algorithm outperforms the existing algorithms in terms of convergence speed and the task completion time in a multi-target search environment.